Spin Transport In Rare-earth Magnetic Heterostructures By Aidan Thomas Hindmarch

Transcript

SPIN TRANSPORT IN RARE-EARTH MAGNETIC HETEROSTRUCTURES By Aidan Thomas Hindmarch SUBMITTED IN ACCORDANCE WITH THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF LEEDS DEPARTMENT OF PHYSICS AND ASTRONOMY LEEDS, WEST YORKSHIRE AUGUST 2003 The candidate confirms that the work submitted is his own and that appropriate credit has been given where reference has been made to the work of others. This copy has been supplied on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement. i List of Figures 1.1 Spin-polarised DOS for paramagnets, ferromagnets and half-metals. . 1.2 The effect of the Lorentz force on the classical trajectories of conduction 9 electrons between collisions, for a strong applied magnetic field. . . . 20 1.3 Spin-resolved Fermi surfaces in Fe. . . . . . . . . . . . . . . . . . . . 22 1.4 Typical MR for bulk and thin-film transition metal ferromagnets. . . 23 1.5 Angular dependence of the resistivity of a Co film at low temperature due to the AMR. The magnetisation and current are co-linear when θ = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 24 Current in Plane (CIP) and Current Perpendicular to the Plane (CPP) geometries for measuring GMR in magnetic multilayers. . . . . . . . . 25 1.7 Simple model of the giant magnetoresistance. 26 1.8 The sample structure used in calculations by Camley and Barna´s and . . . . . . . . . . . . . a fit to data from Binasch et. al. for an Fe/Cr multilayer . . . . . . . 28 Resistor network model of the GMR. . . . . . . . . . . . . . . . . . . 30 1.10 Calculations on a Co/Cu multilayer by Tsymbal and Pettifor. . . . . 32 1.9 1.11 Simulation of the effect of varying spin-polarisation within the modified BTK model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.1 Diagram showing the vacuum chamber and pumping system. . . . . . 45 2.2 Photograph of the sputtering system at Leeds. . . . . . . . . . . . . . 47 2.3 The sputtering process. . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.4 D.C. gas discharge sputtering. . . . . . . . . . . . . . . . . . . . . . . 49 2.5 The arrangement of magnets and sputtering target for magnetron sputtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 50 The metal contact masks used to define the shape of sputtered CIP samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.7 Crossed electrode structure used in tunnel junction samples. . . . . . 53 2.8 Luminous and dark regions of a D.C. glow discharge . . . . . . . . . . 55 2.9 The D.C. four-point probe technique used to measure CIP resistance. 57 2.10 The circuit for measuring I-V curves for tunnel junction samples. . . 64 2.11 The effect of changing the value of the standard resistor upon the measured dynamic conductance. . . . . . . . . . . . . . . . . . . . . . 65 2.12 Flow diagram of the A.C. feedback method used to measure G-V characteristics of MTJ and point contact junctions. . . . . . . . . . . . . 67 2.13 Schematic diagram of the Oxford Instruments Maglab VSM system. . 69 2.14 Plan view of the MOKE magnetometry system. . . . . . . . . . . . . 71 2.15 X-ray reflectivity from a single film of ruthenium deposited on Si, showing finite-size (Kiessig) fringes. . . . . . . . . . . . . . . . . . . . . . . 73 3.1 The RKKY range function. . . . . . . . . . . . . . . . . . . . . . . . 78 3.2 Spin-resolved density of states for Gd, showing the net spin-polarisation at the Fermi level. . . . . . . . . . . . . . . . . . . . . . . . . 82 3.3 Magnetoresistance and magnetisation of a Dy/Cu multilayer. . . . . . 85 3.4 Magnetisation and magnetoresistance for an MBE-grown Co/Cu/Co trilayer with and without Au doping on one of the Co layers. . . . . . 87 3.5 Magnetoresistance and magnetisation of a Gd/Cu multilayer. . . . . . 89 3.6 Magnetoresistance and magnetisation for a Nd/Cu multilayer. . . . . 90 3.7 Magnetoresistance of a Dy/Cu multilayer with the transport current applied at various angles to the magnetic field . . . . . . . . . . . . . 94 3.8 Magnetoresistance of a Dy/Cu/Co/Cu multilayer. . . . . . . . . . . . 96 3.9 Magnetoresistance of a Gd/Cu/Co/Cu multilayer. . . . . . . . . . . . 96 3.10 Magnetoresistance of a Nd/Cu/Co/Cu multilayer. . . . . . . . . . . . 97 3.11 Magnetoresistance and magnetisation for a Dy/Cu multilayer with the magnetic field applied perpendicular to the plane of the sample. . . . 99 3.12 Magnetoresistance and magnetisation for a Dy/Cu/Co/Cu multilayer with the magnetic field applied perpendicular to the sample plane. . . 100 3.13 Dependence of the magnetoresistance on the number of repeat units in ˚]/Cu[20˚ Dy[20A A] multilayers at 8.2K. . . . . . . . . . . . . . . . . . . 101 ii 3.14 Magnetoresistance of a Dy/Cu multilayer in each of the Dy magnetic phases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 3.15 Magnetoresistance of a Dy/Cu/Co/Cu multilayer in each of the Dy magnetic phases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 3.16 The form of the RKKY spin-density oscillation expected for light and heavy rare-earth ions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.17 Approximation to the RKKY spin-density oscillation by summing the single-ion polarisation function for various atomic separations. . . . . 107 4.1 Photograph and schematic diagram of the Mk. I CPP sample wheel. . 114 4.2 MTJ deposition system used at the IBM Almaden research center. . . 116 4.3 Photograph of the Mk. II CPP sample wheel mounted in the vacuum chamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.4 Diagram of the new contact mask system. . . . . . . . . . . . . . . . 118 4.5 Typical structure of a top spin-valve sample, as used to optimise the growth of thin aluminium films for tunnel junctions. . . . . . . . . . . 120 4.6 Hysteresis loops for spin-valve structures with Al spacer layers grown at different sputtering currents. . . . . . . . . . . . . . . . . . . . . . 122 4.7 Magnetic properties of samples with aluminium layers sputtered at 75mA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.8 MOKE loops for Co/Al/Py crossed-electrode structures with different aluminium thicknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.9 TMR vs. applied field for our first FeMn/Co/AlO/Py junction to show MR greater than 1% at 77K . . . . . . . . . . . . . . . . . . . . . . . 129 4.10 Junction resistance and TMR against glow discharge exposure time for junctions with a 10˚ A Al layer. . . . . . . . . . . . . . . . . . . . . . . 130 4.11 Room temperature TMR of 176% in a Co/AlO/Py junction due to geometrical enhancement. . . . . . . . . . . . . . . . . . . . . . . . . 131 4.12 Zero-bias resistance and TMR against nominal Al thickness for a 30s oxidation time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.13 TMR of Co/AlO/Py and FeMn/Co/AlO/Py MTJs, measured at room temperature and at 77K. . . . . . . . . . . . . . . . . . . . . . . . . . 136 4.14 TMR of a Co/AlO/Co/FeMn MTJ at room temperature and at 77K. iii 137 4.15 Zero-bias resistance as a function of barrier thickness for a set of samples exposed to the oxygen plasma for 30s, satisfying two of the three Rowell criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 ˚ barrier. The non-ohmic 4.16 I-V curve and fits for an MTJ with a 14.25A behaviour satisfies the remaining Rowell criterion. . . . . . . . . . . . 142 4.17 Zero-bias resistance at room temperature and 77K for a set of nominally identical Co/AlO/Co/FeMn MTJs, showing the degree of sampleto-sample consistency in our deposition. . . . . . . . . . . . . . . . . 143 4.18 TMR at room temperature and 77K for a set of nominally identical Co/AlO/Co/FeMn MTJs, again showing the degree of sample-tosample consistency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4.19 Conductance spectra for a Nb/Al/Cu Andreev point-contact at 4.2K. iv 146 v Acknowledgements First and foremost I would like to thank my supervisor, Prof. Bryan Hickey for his advice and encouragement both during the course of my Ph.D. studies and throughout my undergraduate degree. I am also grateful to Dr. Chris Marrows for the support and assistance he has given me over the past few years, and to Prof. Jim Morgan for all the knowledge he has passed on to me and the interest he has shown in my work – and I have read all of ‘electrons and phonons’, honest! I am grateful also to Dr. Norman Hughes and Dr. Rob Hicken at the University of Exeter both for the advice they have provided on MTJs and for their hospitality, and to Dr. Mark Blamire of Cambridge University for the many useful and interesting discussions whilst on sabbatical in Leeds. I would like to thank Mr. John Turton - without whom pretty much nothing in our labs would actually work - for all his technical assistance and for teaching me how to fix cryostats, and to Mr. Pete Harrison for the almost continuous flow of cryogens - even at 4pm on a friday. I would like to thank all of the staff of the mechanical workshop for the help which they have provided – particular thanks go to Mr. Brian Gibb and Mr. Paul Hector for their work on the CPP sample wheels and for putting up with my constant nagging. Many thanks also go to all of the staff of the electronics workshop for fixing all of the expensive electronic gizmos that I’ve managed to break. On a more personal note, I would like to ‘acknowledge’ everyone from the Condensed Matter group, both past and present, who have made the past few years a pleasant, enjoyable and fun experience. The list of people is far too long, so although no names are mentioned, no-one has been forgotten! Cheers also to everyone else who has kept me company in the Fenton after work on a friday... Last, but of course by no means least, I would like to thank my family for all the support that they have given to me. vi Abstract This thesis presents studies on two distinct types of sputtered thin-film magnetic heterostructure – the magnetic multilayer and magnetic tunnel junction (MTJ). New information on spin-transport effects in the rare-earth metals has been gained and a new facility for the deposition and characterisation of MTJs has been implemented. The magnetotransport properties of novel magnetic multilayers where some or all of the magnetic layers are comprised of rare-earth metals have been investigated. The giant magnetoresistance effect in magnetic multilayer samples has been utilised in order to probe the spin-dependent scattering of conduction electrons in rare-earth metals. This method allows the determination of the sign of the spin-polarisation of the electrons directly implicated in mediating the magnetic ordering interaction in these metals. The spin-polarisation is a direct consequence of the Ruderman-KittelKasuya-Yosida (RKKY) indirect interionic exchange coupling schema and has never before been unequivocally observed in pure rare-earth metals. These measurements on magnetic multilayers show a reversal in the sign of the conduction-band spinpolarisation in crossing from light to heavy rare-earth metals. This is predicted in the RKKY model as a consequence of the Russel-Saunders spin-orbit coupling, but again has never previously been experimentally observed. Equipment for the deposition and electrical characterisation of MTJ samples has been produced which will allow the future study of spin-dependent tunnelling in a variety of MTJ-based structures. Optimisations have been studied in order to consistently deposit high-quality MTJs with ultra-thin Al2 O3 barrier layers. Tunnelling magnetoresistance (TMR) values of up to 16.6% at room temperature, 24% at 77K and 24.5% at 4.2K have been obtained for junctions where both upper and lower electrodes are cobalt. These are presently the highest TMR values reported by any research group in the UK. vii Table of Contents List of Figures i Acknowledgements v Abstract vi Table of Contents ix Publications x Abbreviations xi Introduction 1 Theoretical aspects of magnetotransport phenomena 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Definitions of spin-polarisation . . . . . . . . . . . . . . 1.2.1 Resonant scattering and photoemission . . . . . 1.2.2 Metallic conduction . . . . . . . . . . . . . . . . 1.2.3 Quantum mechanical tunnelling . . . . . . . . . 1.2.4 Ballistic transport . . . . . . . . . . . . . . . . . 1.2.5 Andreev reflection . . . . . . . . . . . . . . . . 1.3 Lorentz magnetoresistance . . . . . . . . . . . . . . . . 1.3.1 Bulk materials . . . . . . . . . . . . . . . . . . 1.3.2 Thin films . . . . . . . . . . . . . . . . . . . . . 1.4 Anisotropic magnetoresistance . . . . . . . . . . . . . . 1.5 Giant magnetoresistance . . . . . . . . . . . . . . . . . 1.5.1 Simple picture of the GMR . . . . . . . . . . . 1.5.2 Semi-classical model . . . . . . . . . . . . . . . 1.5.3 Resistor network model . . . . . . . . . . . . . . 1.5.4 Quantum mechanical model . . . . . . . . . . . 1.5.5 Non-local model with band-structure effects . . 1.6 Tunnelling magnetoresistance . . . . . . . . . . . . . . 1.6.1 Julliere’s model . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 8 8 12 13 14 16 16 18 19 20 22 25 25 27 29 30 31 33 34 viii 1.7 1.8 1.9 1.6.2 Stationary-state models . . . . . . . . . . . . . . . 1.6.3 Band-structure effects in magnetic tunnel junctions Superconductor tunnelling . . . . . . . . . . . . . . . . . . Point-contact Andreev reflection . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental techniques 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Sample preparation . . . . . . . . . . . . . . . . . . . . . . 2.2.1 The high-vacuum system . . . . . . . . . . . . . . . 2.2.2 The sputtering process . . . . . . . . . . . . . . . . 2.2.3 D.C. magnetron sputtering . . . . . . . . . . . . . . 2.2.4 Deposition of CIP magnetic heterostructures . . . . 2.2.5 Deposition of tunnel junction structures . . . . . . 2.2.6 Tunnel barrier fabrication . . . . . . . . . . . . . . 2.3 Sample environment . . . . . . . . . . . . . . . . . . . . . 2.3.1 4 He cryogenics . . . . . . . . . . . . . . . . . . . . . 2.4 CIP resistance measurements . . . . . . . . . . . . . . . . 2.4.1 Four-probe D.C. resistance . . . . . . . . . . . . . . 2.4.2 The effect of the sense current . . . . . . . . . . . . 2.4.3 Resistivity, sheet resistance and magnetoresistance . 2.5 Transport measurements on junction structures . . . . . . 2.5.1 D.C. measurements . . . . . . . . . . . . . . . . . . 2.5.2 A.C. measurements . . . . . . . . . . . . . . . . . . 2.5.3 Magnetoresistance measurements . . . . . . . . . . 2.6 Magnetic measurements . . . . . . . . . . . . . . . . . . . 2.6.1 Vibrating sample magnetometry . . . . . . . . . . . 2.6.2 Magneto-optical Kerr effect magnetometry . . . . . 2.7 X-ray reflectivity . . . . . . . . . . . . . . . . . . . . . . . 2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 36 38 40 42 . . . . . . . . . . . . . . . . . . . . . . . 44 44 44 45 47 49 50 52 53 55 55 56 56 58 59 62 62 63 68 69 69 70 72 74 3 Probing the RKKY interaction in rare-earth metals with spin-dependent transport 75 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.2 The RKKY coupling interaction in the rare-earths . . . . . . . . . . . 76 3.2.1 The RKKY indirect exchange integral . . . . . . . . . . . . . 77 3.2.2 Limitations of the RKKY model . . . . . . . . . . . . . . . . . 80 3.2.3 Electronic structure calculations on the rare-earths . . . . . . 81 3.3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.5 Magnetotransport in rare-earth magnetic multilayers . . . . . . . . . 83 3.5.1 Dysprosium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.5.2 Gadolinium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 ix 3.5.3 Neodymium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.4 Magnetoresistance mechanisms in multilayers . . . . . . . . . 3.6 RE/Cu/Co/Cu multilayers . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Dysprosium and gadolinium . . . . . . . . . . . . . . . . . . . 3.6.2 Neodymium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Supporting evidence for the GMR mechanism . . . . . . . . . . . . . 3.7.1 Isotropic nature of the magnetoresistance . . . . . . . . . . . . 3.7.2 Dependence upon the number of repeat units . . . . . . . . . 3.8 Dependence of the magnetoresistance on the magnetic phase of the rare-earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9.1 The origin of the RKKY spin-polarisation in the rare-earths . 3.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Growth and characterisation of magnetic tunnel junctions 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Design and construction of the CPP sample wheel . . . . . . . . . 4.2.1 The Mk. I sample wheel . . . . . . . . . . . . . . . . . . . 4.2.2 The Mk. II sample wheel . . . . . . . . . . . . . . . . . . . 4.3 Optimisation of the growth conditions for thin aluminium layers . 4.3.1 Variation of film properties with deposition current . . . . 4.3.2 Deposition of thin aluminium layers . . . . . . . . . . . . . 4.3.3 Determination of the Al deposition rate . . . . . . . . . . . 4.4 Glow discharge oxidation of aluminium films . . . . . . . . . . . . 4.4.1 Oxygen gas pressure . . . . . . . . . . . . . . . . . . . . . 4.4.2 Exposure to the glow discharge . . . . . . . . . . . . . . . 4.4.3 Initial characterisation of junctions with thin AlO barriers 4.5 Geometrically enhanced TMR . . . . . . . . . . . . . . . . . . . . 4.5.1 Preventing geometrical enhancement effects . . . . . . . . 4.6 Characterisation of magnetic tunnel junctions . . . . . . . . . . . 4.7 Rowell criteria for tunnelling in normal-state junctions . . . . . . 4.7.1 Satisfying the Rowell criteria . . . . . . . . . . . . . . . . . 4.8 Sample to sample consistency . . . . . . . . . . . . . . . . . . . . 4.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10 Extensions to this work . . . . . . . . . . . . . . . . . . . . . . . . 4.10.1 Rare-earth electrode materials . . . . . . . . . . . . . . . . 4.10.2 Andreev point-contacts . . . . . . . . . . . . . . . . . . . . 4.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 92 95 95 97 98 98 100 102 104 105 109 111 111 112 113 115 119 119 122 125 126 126 128 128 132 133 134 138 140 141 144 145 145 145 147 5 Conclusion 149 5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 References 153 x Publications ‘Direct experimental evidence for the Ruderman-Kittel-Kasuya-Yosida interaction in the rare-earths’ A. T. Hindmarch and B. J. Hickey. Submitted to Physical Review Letters. ‘Characterisation of spin valves fabricated on opaque substrates by optical ferromagnetic resonance’ A. Barman, V. V. Kruglyak, R. J. Hicken, C. H. Marrows, M. Ali, A. T. Hindmarch and B. J. Hickey. Appl. Phys. Lett., 81, p1468, 2002. ‘Exchange bias in spin-engineered double superlattices’ P. Steadman, M. Ali, A. T. Hindmarch, C. H. Marrows, B. J. Hickey, S. Langridge, R. M. Dalgliesh and S. Foster. Phys. Rev. Lett., 89, 077201, 2002. ‘Mapping domain disorder in exchange-biased magnetic multilayers’ C. H. Marrows, S. Langridge, M. Ali, A. T. Hindmarch, D. T. Dekadjevi, S. Foster and B. J. Hickey. Phys. Rev. B, 66, 024437, 2002. ‘Vector magnetometry in spin-engineered double superlattices’ C. H. Marrows, M. Ali, A. T. Hindmarch, B. J. Hickey, S. Langridge, S. Foster and R. M. Dalgliesh, Highlight of ISIS Science, ISIS Annual Report, 2001. xi Abbreviations A.C.: Alternating Current AMR: Anisotropic Magnetoresistance BCS: Bardeen, Cooper, Schrieffer BDR: Brinkman, Dynes, Rowell BTK: Blonder, Tinkham, Klapwijk CIP: Current in Plane CPP: Current Perpendicular to the Plane D.C.: Direct Current DOS: Density of States DWBA: Distorted Wave Born Approximation GMR: Giant Magnetoresistance MOKE: Magneto-Optical Kerr Effect MR: Magnetoresistance MRAM: Magnetic Random Access Memory MTJ: Magnetic Tunnel Junction PCAR: Point-Contact Andreev Reflection PNR: Polarised Neutron Reflectometry Py: Permalloy – Ni80 Fe20 at. % RE: Rare-earth R.F.: Radio Frequency RKKY : Ruderman, Kittel, Kasuya, Yosida TM: Transition metal TMR: Tunnelling Magnetoresistance VSM: Vibrating Sample Magnetometry 1 Introduction Recent developments in high-vacuum thin-film deposition technology have lead to a paradigm shift in the field of high density magnetic data storage. Ultra-thin magnetic films and heterostructures show many interesting and exciting physical properties which are either not present or unobservable in bulk materials, for example the perpendicular magnetic anisotropy[1], exchange-bias in ferromagnet/antiferromagnet bilayer films[2], the oscillatory exchange coupling[3, 4] between ferromagnetic layers separated by a nanometer-scale non-ferromagnetic spacer layer and, following on from this, the giant magnetoresistance (GMR)[5, 6] and tunnelling magnetoresistance (TMR)[7, 8, 9, 10]. Application of these phenomena to technological gain have further pushed the limits of deposition technology. The work in this thesis concerns both the giant and tunnelling magnetoresistance phenomena, so these two topics are introduced in slightly more detail below. Giant magnetoresistance The giant magnetoresistance was discovered in 1988, more or less simultaneously, by two groups who were investigating the properties of the antiferromagnetically exchange coupled Fe/Cr system[5, 6]. In ferromagnet/non-magnetic multilayered structures such as these, the electrical resistance depends strongly on the relative orientation of the magnetisation of the two layers provided that the conduction electrons are able to cross the spacer layers with a low probability of scattering. When the magnetisation of the layers are aligned by the application of a saturating magnetic 2 field, the resistance of the structure is found to be lower than when the magnetisation of adjacent magnetic layers are aligned antiparallel. This change in resistance is related to the difference in the scattering rates for majority and minority conduction electrons in the ferromagnetic layers, with resistance changes of as much as 220% being reported in the literature in recent years[11]. Giant magnetoresistive structures such as magnetic multilayers and the so-called ‘spin-valve’[12] have found applications as magnetic field sensors in a host of devices such as hard-disc drives, anti-lock brake systems, remote current measurement, electronic compasses etc. since the discovery of the GMR[13]. Sensors such as these have, in many cases, all but taken over from those based upon the anisotropic magnetoresistance (AMR) which were employed until recently. The giant magnetoresistance is not only of interest from the point of view of device engineering but also for the wealth of new fundamental physics which it has opened up. GMR systems have been studied thoroughly in the past 15 years, with investigations on the effects of different multilayer composition[14], the relative importance of scattering at the layer interfaces in comparison to within the bulk of the layers[15], enhanced interlayer coupling due to the formation of quantum well states[16], and electron waveguide effects[17] to name but a few. Since the discovery of the GMR many other areas of fundamental research have expanded rapidly, mainly brought about by the new understanding of spin-dependent scattering in nanoscale magnetic heterostructures. Domain wall magnetoresistance[18], which was previously a mere sideline curiosity, has gained much more widespread attention along with the more recent field of ballistic magnetoresistance in magnetic nanoconstrictions[19]. The theoretical picture of these phenomena pose interesting fundamental questions regarding the ability of conduction electrons to track the spatially inhomogeneous local magnetic field within domain walls. 3 Magnetic Tunnel junctions Magnetic tunnel junctions consist, in the simplest case, of two ferromagnetic electrodes separated by a thin insulating barrier layer. In the classical approximation, the two electrodes act as separate systems and the perpendicular current flow across the junction is zero. When the insulating layer is an ultra-thin film - ∼10-100˚ A thick - electrons are able to quantum mechanically tunnel across the barrier layer, allowing a non-zero current to flow. It has been found that the tunnelling current is dependent upon the relative orientation of the magnetisation of the two electrodes – the conductance is higher for a parallel alignment compared to that for an antiparallel alignment due to the fact that the number of initial and final electronic states is limited by the spin sub-band with the lower tunnelling electron density of states at the Fermi level. The resultant change in resistance upon changing the relative orientation by the application of a magnetic field is called the tunnelling magnetoresistance. Fabrication of high quality MTJs is a complex task. Even though the TMR was first reported in 1975 [7], it was not until 1995 - some 20 years later - that significant room temperature TMR was routinely obtainable[10]. The main difficulties in fabricating MTJ structures is the insulating barrier layer itself. The technique most frequently utilised in both academia and industry consists of the deposition of an ultra-thin aluminium film, followed by oxidation to form Al2 O3 . It is obvious that the aluminium layer should be smooth and continuous in order to form a completely covering tunnel barrier. The oxidation step must also be precisely controlled in order both that the AlO barrier layer be defect-free and completely oxidised and that the underlying electrode is not oxidised. In order to achieve this, precise control over both the deposition and oxidation conditions are required. The vast majority of research work on MTJs is geared towards industrial applications, such as optimising the fabrication of thinner barriers in order to decrease 4 the resistance-area (RA) product and increase the TMR[20, 21], investigating different layer compositions to maximise the interfacial spin-polarisation and prevent interdiffusion during anneal stages[22, 23, 24] and reduction of the RA product of the junction by the use of novel barrier materials[25, 26]. Various methods of improving process control during oxidation have also been investigated[27, 28]. In terms of more fundamental research, the main questions remain obtaining a proper understanding of the bias- and temperature-dependence of the TMR[29] and of effects due to the band-structure and density of states of both the electrode materials and the tunnel barrier[30, 31]. Magnetic tunnel junctions provide the means to investigate a variety of spintransport phenomena such as, for example, the relaxation of an injected spin-polarised current in non-magnetic metals, or the effect on the TMR of inserting layers with widely varying electronic properties away from the electrode/barrier interface. The ability to switch the resistance of both spin-valves and MTJs between ‘low’ and ‘high’ resistance states by applying a magnetic field makes them promising contenders for a host of magnetoelectronics applications. It is found that the MTJ generally has a slightly higher sensitivity to small changes in magnetic field than spin-valve sensors and also has a lower power consumption due to its intrinsically higher resistance. The spin-valve structure, however, is less susceptible to thermally induced degradation. This makes it more suited to read-head applications where the head must withstand long periods of time at the operating temperature of such devices, typically >200o C at present. One of the main potential applications of MTJs is in magnetic random access memory (MRAM)[32]. Here the magnetoresistive state of the MTJ is used to store binary data which may be read back without affecting the magnetic state of the junction element. MRAM chips have the advantage that they only require power 5 during read/write operations, not just to ‘hold’ data. GMR-based MRAM has also been proposed. However these suffer from a reduced signal-per-element, the signal being inversely proportional to the number of memory elements. The quest for commercially viable MRAM products currently drives much of the research into MTJs. In order to compete with existing, established technologies e.g. Static RAM (SRAM) in terms of storage density and Dynamic RAM (DRAM) in terms of speed - MRAM devices require fabrication at . 1µm feature size and read times in the order of 1ns. An MTJ behaves not only as a resistor but also a capacitor, thus an MRAM element will have a characteristic time constant RC which governs the speed at which data may be accessed from the element. Faster read times necessitate the use of extremely thin barriers in order to minimise the resistance of the junction. For viable MRAM applications the MTJ element should have an RA product of .20kΩµm2 [33]. The magnetoresistive element must be capable of withstanding the high-temperature (∼500o C) anneal stage required for back-end integration with standard CMOS technology. Annealing MTJs at elevated temperatures (>300o C) results not only in degradation of the Al2 O3 tunnel barrier[34] but also of the composite electrode and exchange-biasing layers[22] – thus thermal stability of both spin-valve or MTJ device structures is critical for integration into technological applications. Aims of this thesis This thesis consist of a selection of experimental work describing spin-dependent transport effects in magnetic layered structures. The first aim is to study the giant magnetoresistance in novel magnetic multilayer samples where we use rare-earth (RE) metals as some or all of the magnetic layers. Our experiments aim to show that the albeit weak spin-polarisation of the conduction-band in the ferromagnetic phases of the rare-earths can produce a measurable GMR due to spin-dependent scattering of 6 conduction electrons in the rare-earth layers. Study of this spin-dependent scattering should allow us to gain new insight into the nature of the spin-polarisation of the conduction-band in the rare-earths. A second aim of the work in this thesis is to develop the facility for the deposition of magnetic tunnel junction samples in our sputtering system and the characterisation of their transport properties in our laboratory. This facility will eventually be used to investigate tunnelling phenomena in both technologically viable and academically interesting materials. The facility which we develop will also be used as a stepping stone to allow us to deposit a range of perpendicular transport structures with the aim towards ballistic spin-injection devices. We begin by outlining in chapter 1 the different manifestations of ‘spin-polarisation’ in magnetic materials and discuss the potential pitfalls in comparing spinpolarisations measured by different techniques. We discuss also the more important theoretical works on the different magnetotransport phenomena pertinent to the work in this thesis. Chapter 2 discusses the range of experimental techniques used for both the deposition and characterisation of our samples. Most of the experimental methods revolve around characterising the electron transport and magnetic properties of the samples, although structural characterisation is briefly discussed also. In chapter 3 we report an investigation on the GMR in magnetic multilayers where the magnetic layers are rare-earth metals. We show, firstly in the case of RE/Cu magnetic multilayers, that a definite GMR signal is exhibited by these multilayer samples. We then investigate multilayers where alternate rare-earth layers are replaced with cobalt. The correlation between the observed spin-polarisation of the conduction band and that naively anticipated due to the Ruderman-Kittel-Kasuya-Yosida (RKKY) indirect exchange interaction, which is thought to mediate the interionic 7 magnetic coupling within the rare-earth metals, is discussed. The development of equipment and procedures for the deposition of magnetic tunnel junction samples is discussed in chapter 4. Firstly we describe the equipment required in order to deposit the crossed-electrode MTJ structure and then look at the steps taken to optimise the deposition parameters in order to obtain samples exhibiting large tunnelling magnetoresistance. We show the results of initial measurements on samples with a variety of different electrode materials and briefly discuss other work related to our MTJ deposition studies. Finally, in chapter 5, we discuss the conclusions drawn from our results and elaborate on the variety of future continuations based around the work presented in this thesis. 8 Chapter 1 Theoretical aspects of magnetotransport phenomena 1.1 Introduction In this chapter we discuss some theoretical aspects of the effects of magnetism on the electron transport properties of materials. We shall begin by explaining what exactly is meant by ‘spin-polarised transport’ and how spin-polarisation can manifest itself differently depending upon the experimental technique used to probe it. We then go on to discuss the origin of the variety of different magnetoresistance effects, with particular emphasis on those which are most pertinent to the experimental work reported on in this thesis. 1.2 Definitions of spin-polarisation In recent years there has been huge interest in spin-polarised transport processes for applications in the fields of data storage[35] and so-called spin-electronics or ‘spintronics’[36]. It seems fitting to begin by describing the various different definitions that can be described as a ‘spin-polarisation’ and how different experimental techniques do not by any means measure the same manifestation of spin-polarisation. Any reasonable definition of what is meant by spin-polarisation should always reproduce two standard results – the cases of a paramagnet and of a half-metal; that is a metal which has a band gap at the Fermi energy in one spin channel. A paramagnet should have a spin-polarisation of zero in the absence of any outside influences, and in a half-metal the spin-polarisation must be ±100%, depending upon 9 Figure 1.1: Schematic diagram of the spin-polarised density of states for a) a paramagnet, b) a weak ferromagnet, c) a strong ferromagnet and half-metallic ferromagnets with d) positive and e) negative spin-polarisation. in which spin channel the band gap lies. A schematic diagram of the spin-polarised density of states for a paramagnet, weak and strong ferromagnets and half-metallic ferromagnets with positive and negative spin-polarisation is shown in figure 1.1. Half-metallic materials are obviously extremely desirable for any application where control of a spin-polarised current is required – the efficiency of such devices increases with the spin-polarisation of the magnetic electrodes, and it is, of course, impossible to do better than 100% polarisation. Before fabrication of devices based upon such materials can begin, the problem arises of showing conclusively that a material is a half-metal: the interesting properties of metals, insulators, superconductors and ferromagnets are all fairly simple to show, but proving the degree of spin-polarisation of an electric current is, however, non-trivial. There are many ways by which it is possible to define ‘spin-polarisation’. This can cause a great deal of confusion, as one person’s definition may be completely 10 incompatible with that of someone else. If one first considers simply the difference in population of the two electronic spin states one of course arrives at the definition of the volume magnetisation in an itinerant magnetic system MV = µB (n↑ − n↓ ) where the ↑ and ↓ represent the majority and minority spin channels respectively, µB is the Bohr magneton and n is the number density of electrons. This definition, however, does not always reproduce the required result of 100% polarisation in halfmetallic systems as is clear form figure 1.1e. To define polarisation in this fashion is suitable for some cases. However in terms of transport processes it is only the electrons at the Fermi level - or within thermal excitation thereof - which are able to respond to the application of an electric field. These are the only electrons with which we would generally concern ourselves when considering materials for spintronic device applications. A possible definition of (zero temperature) transport spin-polarisation which may be used is P = g↑ (EF ) − g↓ (EF ) g↑ (EF ) + g↓ (EF ) (1.1) where g (E) is the density of electronic states per unit energy per unit volume, which simply gives the asymmetry in the total spin-population at the Fermi level. If we consider for example the 3d transition metal series, the electronic levels at the Fermi level are comprised of a mixture of 4s, 4p and 3d states. The 3d band is obviously spin-split - this is, of course, the origin of ferromagnetism in these materials - however there is no spin-splitting of the 4sp density of states as any saving in exchange energy is unable to compensate for an increased kinetic energy for any spontaneous spinsplitting of these bands. Although the DOS of the 4sp band electrons shows no spin-splitting, the transport properties of these bands are spin-dependent due to hybridisation of these bands with the spin-split 3d band at the Fermi level, resulting in different resistivities for the spin-up and spin-down sub-bands. Thus in terms of transport processes, there is one effective spin-polarisation relating to the 4sp bands, another relating to the 3d band and yet another relating to the total density of states. When measuring a spin-polarisation then, it is of the utmost importance to know exactly what polarisation one is, in fact, really measuring. Is it the effective sp 11 polarisation, the d polarisation, or maybe some combination of the two? To further complicate matters there is the question of where the measured polarisation relates to spatially within the sample. Does the measurement represent the spin-polarisation within the bulk of the material, or is it a spin-polarisation specific to a surface or interface? One may also ask the question over what lengthscale the measured spinpolarisation is representative. These questions make comparison between spin-polarisations measured by different experimental techniques extremely difficult to make quantitatively, and even in some cases qualitatively. Again, the ferromagnetic transition metals (and their alloys) provide a good example of the ‘confusion’ surrounding spin-polarisation measurements. The density of states obtained from band-structure calculations or measured by photoemission type experiments show a large negative spin-polarisation at the Fermi level in cobalt and nickel, as may be seen from figure 1.1 c) and in almost any text on elementary solid state physics. The first measurement of the transport spin-polarisation of the transition metal ferromagnets by the superconductor tunnelling method found, however, a positive spin-polarisation of ∼30-40% [37]. It was found also that the spin-polarisation of the alloys of Fe, Co and Ni measured by this method roughly follows the SlaterPauling curve[38]. More recent measurements of the transport spin-polarisation of NiFe alloys using the point-contact Andreev reflection (PCAR) technique has shown that the spin-polarisation measured by this technique is independent of both the alloy composition and magnetisation[39]. We must consider how is it possible to reconcile these three apparently contradictory results. The answer is quite simply that the spin-polarisation probed by different techniques do not necessarily represent a measurement of exactly the same property of the material. In the remainder of this section we shall discuss a range of experimental methods by which a ‘spin-polarisation’ may be measured, and attempt to explain how the measured spin-polarisation relates in each case to the actual properties of the sample examined. In terms of spintronic device applications, of course, it is far more important to know the properties and behaviour of a material when it is incorporated into a device, rather than the intrinsic bulk properties of the isolated material. A material may well 12 be half-metallic in the bulk, but that by no means ensures that it will behave as such in e.g. a spin-valve or MTJ structure. 1.2.1 Resonant scattering and photoemission Spin-polarised photoemission or resonant x-ray scattering are two techniques which may be used in order to measure a spin-polarisation. X-ray resonant exchange scattering (XRES)[40] relies on the spin-polarised excitation and relaxation of core electrons to and from the Fermi level. By tuning the incident photon energy and polarisation, and analysing the polarisation of the scattered beam, it is possible to pick out particular resonance transitions. As transitions are excited to the Fermi level, the polarisation measured by this technique is similar to that defined by equation 1.1. However data analysis is somewhat complicated by the presence of energy-dependent absorption which must often be corrected for in order to measure a polarisation[41]. Such a technique is often also referred to as x-ray magnetic scattering (XRMS). This term, however, implies that the technique is sensitive to the magnetisation of the sample, which is not strictly true. In fact, due to the selection rules the polarisation sampled by this technique is - in the case of the LIII resonance in the rare-earth metals at least - the total spin asymmetry of the DOS at the Fermi level for electrons with both s and d character. As the 5d band is spin-split at the fermi level and the 6s band is not, the polarisation seen in an XRES measurement is best described by P = g5d↑ (EF ) − g5d↓ (EF ) g6s↑ (EF ) + g6s↓ (EF ) + g5d↑ (EF ) + g5d↓ (EF ) where the difference in the number of states at the Fermi level is due only to the splitting of the 5d band whereas the total number of states comprises both 5d and 6s levels. Spin-polarised photoemission measures an energy dependent polarisation by exciting the emission of electrons from conduction band states using sufficiently energetic photons. Detecting electrons emitted at a specific energy allows energy-dependent mapping of the density of states and the polarisation thereof. The polarisation measured at the Fermi energy by this technique is also that given by equation 1.1. Photoemission and resonant scattering techniques, however, generally do not have the sub-meV energy resolution required to precisely probe the electronic states at the 13 Fermi level. In the case of photoemission, the guide field used to maintain the polarisation of the ejected electrons may also have an unwanted effect upon the magnetic state of the sample. Although neither of these techniques are discussed further in this thesis, they are included here for the sake of completeness. 1.2.2 Metallic conduction Ideally the total spin-polarisation in the case of any transport process would be defined in terms not of the density of states directly, but instead in terms of a spin-resolved current density P = (J↑ − J↓ ) (J↑ + J↓ ) If we consider the case of metallic conduction again in a ferromagnetic transition metal we have three types of electron - s, p and d - at the Fermi level. If, for the moment, we ignore the strong hybridisation between bands in such materials, we may say that each band has its own (effective) spin-polarisation. Due to the relative width of the two types of band in energy - the d band typically spans ∼5eV in comparison to ∼15eV for an s or p band[42] - the d electrons may be considered, in a simple picture, as having a far higher effective mass and lower Fermi velocity. Each individual d electron then makes a smaller contribution to the current than does a ‘lighter’, more mobile, s or p electron. A large proportion of current is, however, still carried by the d band electrons simply due to the far greater population of these bands at the Fermi level. If we assume the spin-up and spin-down channels to be non-interacting, i.e. no spin-flip scattering, the current in each spin-channel may be written[43]  Jσ = e2 E g (EF ) vF2 σ τσ where e is the charge of the electron, E is the electric field and hg (EF ) vF2 i represents the total DOS averaged over the Fermi surface and weighted by the Fermi velocity for that band[44]. If we assume not only that the two spin-channels are non-interacting but also that both spins may be characterised by the same relaxation time, we may define the spin-polarisation by   2 2 hg (EF ) vF i↑ − hg (EF ) vF i↓  P = 2 2 hg (EF ) vF i↑ + hg (EF ) vF i↓ (1.2) 14 If however, the above assumptions are invalid, e.g. in the case of magnetic multilayers at finite temperatures where we have both spin-dependent and spin-flip scattering, the expressions for the spin-resolved currents become dependent upon both spin channels due to spin-mixing, and the relaxation times no longer cancel due to the spin-dependence of the scattering. The expression for the spin-polarisation in such a system - the analogue of equation 1.2 - then becomes extremely complex. Despite this complication, the essence of spin-polarised conduction in metals can be understood in terms of a weighting of the density of states for each band by the square of its respective Fermi velocity[45]. 1.2.3 Quantum mechanical tunnelling Transport by quantum mechanical tunnelling describes the transfer of single electrons between two metallic systems separated by an insulating potential barrier that, in classical physics, would have the effect of separating the two metals into discrete non-interacting systems. By the phenomenon of quantum mechanical barrier penetration[46] however, there is a finite probability that a particle on one side of the potential barrier may ‘tunnel’ through the barrier and appear on the other side. Two methods of performing calculations relating to such phenomena are generally employed, the first of these being the ‘stationary-state’ model which will be described further in section 1.6 and the second the ‘transfer Hamiltonian’ method which is more pertinent here. The transfer Hamiltonian method describes two metals separated by an insulating barrier using perturbation theory and was first applied to the problem of barrier tunnelling by Bardeen in 1961[47]. The conduction electron wavefunctions in the two metals are taken as those for individual separated systems and the effect of electrons tunnelling across the barrier is treated as a perturbation to the resulting energy levels. By this method it is possible to derive the matrix elements for electron transfer from one side of the tunnel barrier to the other, the resultant matrix being known as the transfer matrix, or T-matrix. The transfer Hamiltonian method makes the crucial and, unfortunately, incorrect - assumption that a detailed description of the tunnel barrier is unimportant. 15 The simple barrier penetration model predicts an exponentially decreasing dependence of the T-matrix elements on the barrier thickness. Due to this exponential decrease, the transfer probability is by far the highest for an electron to ‘disappear’ from one metal at the barrier interface, and ‘reappear’ in the other metal at the interface on the other side of the barrier. The probability obviously falls off for electrons ‘disappearing’ or ‘reappearing’ further from the interface. By this argument it may be seen that any probe of the density of states made by an electron tunnelling method is going to be strongly influenced by the local DOS in the region of the interface. In fact, the characteristic length-scale over which tunnelling measurements sample the DOS has been shown[48, 49] to be just ∼10˚ A, corresponding to typically 2-3 atomic planes. A further constraint on the DOS sampled by tunnelling experiments is the fact that the T-matrix elements for electrons with non-parabolic band character decay far more quickly within the tunnel barrier than those for electrons with free-electron-like band structure[50, 51, 52, 53]. Reduced transition probability for certain electron states has also been attributed to a reduction in coupling across the barrier due to the symmetry of conduction electron Bloch functions[30, 31]. The most frequently used expression – although not strictly correct for the reasons discussed above – for the spin-polarisation seen by tunnelling experiments is P = kF↑ − kF↓ kF↑ + kF↓ where the kFσ are in a direction where the component of k perpendicular to the electrode/barrier interface is comparable to |k|. Polarisation of the s and p-like electrons in the transition metals generally studied arises due to hybridisation with the d band electrons which are mainly responsible for the magnetic moment. This is thought to be the cause of the strong correlation observed between the measured tunnelling spin-polarisation and magnetisation[38] in the transition metals and their alloys. From the above discussion, spin-polarisation measured by quantum mechanical barrier tunnelling experiments shows a strong bias towards the polarisation of the sand p-character conduction electrons with quasimomentum perpendicular (or close to perpendicular) to the sample plane. The measured spin-polarisation is thought to 16 represent the local polarisation at the electrode/barrier interface with a decay length of about 10˚ A into the electrode. As the band structure in the vicinity of the interface may be very different from that in the bulk of the layers, the polarisation seen by tunnelling can be very different from that observed in other measurements, including those by other transport processes. 1.2.4 Ballistic transport Looking briefly now at the case of transport in the purely ballistic contact with ideal interface transmission, the current flowing ballistically across the junction is related to the projection of the Fermi surface onto the interface plane[45, 54]. The current density for each spin-channel is now given by[43] Jσ = e2 U hg (EF ) vF iσ where eU is the increase in energy of the electron due to the electric field across the contact. This results in a spin-polarisation given by the expression P = hg↑ (E) vF i − hg↓ (E) vF i hg↑ (E) vF i + hg↓ (E) vF i As the weighting of each state in this case is now simply by its respective Fermi velocity as opposed to its square, it is clear that the spin-polarisation seen in the simple ballistic transport limit is a somewhat different quantity to that measured by either metallic conduction or tunnelling. Due to the constraint of ideal interface transmission, i.e. no mismatch in the Fermi velocity across the interface, such a simple picture is not completely appropriate for a full description of the spin-polarisation observed in ballistic transport experiments such as the spin-valve transistor[55] or magnetic tunnel transistor[56, 57] – as in the case of metallic conduction, however, such an analysis is still useful to gain insight into the nature of spin-polarisation in such systems. 1.2.5 Andreev reflection When an electron is incident upon a normal metal/superconductor boundary, sub-gap electron transport is enabled by the Andreev reflection process[58]. This involves the 17 retro-reflection of electrons incident on the boundary as holes, and subsequent formation of a Cooper pair continuing in the forward direction. This effect gives a double contribution to the conductance since two electrons - a Cooper pair - continue into the superconductor for each electron which is Andreev reflected. In the 1-dimensional case, the conductance may be calculated within the Blonder, Tinkham and Klapwijk (BTK)[59] model which is discussed further in section 1.8. Andreev reflection in ferromagnet/superconductor junction structures is intrinsically sensitive to the spin-polarisation of the ferromagnet as the population of the two spin channels at the Fermi level are unequal. This causes a suppression of the Andreev conductance as not all electrons may join with another of opposite spin to form a Cooper pair and so contribute to the sub-gap conduction[60]. The exact nature of the spin-polarisation measured by Andreev reflection shows a strong dependence on both the interface ‘transparency’ and the lateral dimensions of the junction. Junction dimensions play an important role due to the nature of the transport processes taking place; for a junction with dimensions smaller than the electronic mean-free-path, electrons travel ballistically within the contact, whereas the diffusive contribution will be enhanced with increasing junction size. The influence of the interface transparency is enhanced due to the fact that Andreev reflection probability is proportional to the square of the transmission coefficient, as it involves transfer of two electrons across the boundary. In the BTK formalism, the interface is characterised by a δ-function potential of height V , in order to model the mismatch in Fermi velocity between the metallic and superconducting electrodes and any other scattering mechanisms taking place at the interface. The nature of the spin-polarisation probed may be related to a dimensionless ‘barrier strength’ parameter, Z. In the large Z limit the spin resolved current density, and hence the spin-polarisation is shown again to be that given by equation 1.2 [45], but in situations other than this limit the expression for the spin-resolved current density becomes analytically intractable. Nadgorny et. al. find that the polarisation measured by Andreev reflection for the Nix Fe1−x series of alloys is effectively independent of the alloy composition. This is in contrast with the spin-polarisation results by tunnelling[38], which is not totally 18 surprising as the two techniques measure a slightly different quantity. Nadgorny et. al. attempt to justify accompanying tunnelling results as corresponding to the Z → ∞ limit of conduction across a Fermi velocity mismatched junction. Due to the fact that these two techniques only sample the same spin-polarisation under very limited circumstances this may be seen to be somewhat distant from the truth. At this point we shall conclude the discussion on the nature of spin-polarisation in various experimental situations and shall, for the remainder of this chapter, discuss a selection of magnetotransport phenomena, emphasising the most important theoretical and experimental works in each area. 1.3 Lorentz magnetoresistance The Lorentz magnetoresistance (often also referred to as the ‘ordinary’ or ‘normal’ magnetoresistance) describes the change in resistivity of a metal when placed in a magnetic field; usually defined as the change in resistivity upon application of the field, normalised to the zero field resistivity thus ∆ρ ρ (B) − ρ0 = ρ0 ρ0 The effect of the magnetic field on the resistivity of metals has been used for magnetic field detection for well over a century, a popular material being the semi-metal bismuth, which shows an ∼18% increase in resistivity in the bulk, for a magnetic field of about 0.6T at room temperature[61]. The Lorentz magnetoresistance is generally measured in either transverse (magnetic field perpendicular to current) or longitudinal (magnetic field and current colinear) orientations. However we shall limit our discussion here to the longitudinal case for the sake of simplicity. The physical mechanism underlying the magnetoresistance is the same in both cases. The classical pictureof the cause of the magnetoresistance is the Lorentz force acting on the conduction electrons in a metal[62]. In the absence of a magnetic field, the resistivity of the metal may be expressed using the Drude equation ρ0 = m∗ ne2 τ 19 which is derived by assuming that the conduction electrons scatter catastrophically with a characteristic scattering rate τ −1 . Conduction electrons are assumed to follow straight line trajectories between collisions. Upon the application of a magnetic field, the Lorentz force causes the electrons to follow curved paths – the degree of curvature and hence the effect on the resistivity being dependent upon the strength of the magnetic field. It can be seen that a sufficiently strong magnetic field will wind the electronic trajectories into helical paths between collisions, as shown in figure 1.2, distorting the conduction process. Hence the effect of the normal magnetoresistance on the resistivity is strongly dependent upon the degree of scattering within the metal, the important property here being the product ωc τ where ωc = Bσ/nqτ is the cyclotron frequency. In order for a metal to show a significant magnetoresistance the conduction electrons should complete many ‘turns’ around their helical path between each scattering event – requiring a large cyclotron frequency and/or long relaxation time. For the case of Cu, for example, we would typically find σ ∼ 0.5 MScm−1 (corresponding to ρ ∼ 2µΩcm) and n ∼ 8 × 1028 m−3 – thus the quantity ωc τ ∼ 5 × 10−3 B which requires an extremely large magnetic field in order to show a significant magnetoresistance. The Lorentz MR may have completely different functional behaviour simply due to the dimensions of the sample. For this reason it is instructive to briefly discuss the cases of bulk and thin film magnetoresistance separately, as the main source of scattering in these two cases are very different. 1.3.1 Bulk materials In the case of a bulk material, collisions between conduction electrons and the crystal lattice are the main source of resistivity in the classical picture and the argument outlined above is entirely valid. In high quality single-crystals it is quite possible to achieve the situation where ωc τ  1 – this is not, however, a guarantee of large magnetoresistance. As the electrons follow helical trajectories in both real and kspace, their quasimomenta will sample several full loops of the Fermi surface between each collision. Thus the topology and local properties of the Fermi surface of the metal in question is of great importance in determining the magnetoresistive effect. 20 Figure 1.2: The effect of the Lorentz force on the classical trajectories of conduction electrons between collisions, for a strong applied magnetic field. This is the reason for the large magnetoresistance of bismuth as it is a compensated metal, having equal numbers of electrons and holes on the Fermi surface, which can help produce a large magnetoresistance[62]. Magnetoresistance in bulk materials is often discussed in terms of K¨ohler’s rule[63]. This states that in the case where it is possible to factor out the field dependence of the scattering rate, the magnetoresistance may be described by some functional relationship ∆ρ =F ρ0  B ρ0  where the functional dependence is generally different for longitudinal and transverse orientations. Free-electron metals are unable to show magnetoresistance in either transverse or longitudinal orientations, whereas in a two-band metal the relationship 2  RH B = [64]. between magnetoresistance and magnetic field may be shown to be ∆ρ ρ0 ρ0 Typically, Cu shows a magnetoresistance of ∼2% in a 24T field at room tempera- ture[65]. 1.3.2 Thin films In systems with either one or two lateral dimensions reduced to a situation where t < λ, scattering at the boundaries of the material will play a much more significant part in the resistivity than for bulk materials. The classical theory of resistance due to boundary scattering in thin films due to Fuchs and Sondheimer[66, 67] treats the 21 boundary scattering as entirely diffusive – electrons scatter randomly back into the film at the boundary, independent of their initial momentum. As the thickness of the sample decreases, the boundary scattering contribution to the resistivity dominates over the lattice scattering contribution and the resistivity rises. The effect of the normal magnetoresistance in such a system may be described in terms of a small diameter wire (or thin film). In this case we see that the application of a sufficiently large longitudinal magnetic field will cause all of the electrons to follow spiral trajectories along the wire (or film) without encountering the sample boundaries at all. The resistivity will then fall to zero at a critical magnetic field, in the absence of lattice scattering. If we now consider the occurrence of catastrophic scattering events also, it may be seen that the application of a magnetic field causes a smaller fraction of the electrons to scatter diffusively at the boundary, so the resistivity decreases. The general theory based upon the above argument was initially worked out by Chambers[68]. It is clear that in the Fuchs-Sondheimer regime the application of a magnetic field has a similar effect to increasing the dimensions of the sample in that the probability of boundary scattering is reduced. We would expect that in a sufficiently thin sample the application of a magnetic field produces a negative magnetoresistance; i.e. the resistivity falls with increasing magnetic field. Such a negative magnetoresistance was first observed experimentally in 1950 by MacDonald[69], who measured an MR of roughly −0.05% at 1T in a 20µm diameter sodium wire. MacDonald was also the first to explain this result in terms of the Lorentz force and boundary scattering. The Lorentz MR may be observed in magnetic multilayer samples, where the resistivity is seen to slowly decrease further if the magnetic field is increased beyond magnetic saturation[70]. The Lorentz magnetoresistance in both bulk and thin film metals is strongly dependent on the topology of the Fermi surface. So far we have not explicitly mentioned the magnetic properties of the material and discussed the cyclotron orbits described by the electrons in a purely classical fashion. If we consider for a moment a ferromagnetic metal with an asymmetry in the spin-population at the Fermi level, we can imagine that the Fermi surface for the two electron spin channels is by no means 22 Figure 1.3: a) Spin-up and b) spin-down Fermi surfaces in Fe [71]. the same - this is shown in figure 1.3 which shows the spin-up and spin-down Fermi surfaces in bcc Fe[71]. The two electron sub-currents will behave differently as the different spins encounter regions of Fermi surface with differing properties and it is likely that, as for all electron transport processes in ferromagnets, more of the current will be carried by one spin channel. Although the Lorentz magnetoresistance is a phenomenon which is not at all confined to ferromagnetic materials, in these metals the spin of the electron is important in defining the transport properties. 1.4 Anisotropic magnetoresistance The ferromagnetic anisotropy of resistivity - what has more recently come to be known as the anisotropic magnetoresistance (AMR) - was discovered by William Thompson (later Lord Kelvin) in 1857[72]. As it does not rely on the spin-polarisation of the conduction band it is not strictly speaking a spin-transport phenomenon per se; in fact many theoretical treatments explicitly assume no spin asymmetry in the conduction band[73]. Despite this fact the AMR is of great significance to much of the work reported on in chapter 3 of this thesis and so merits discussion here. The AMR manifests itself as a variation in the electrical resistance of a polycrystalline ferromagnet as a function of the angle between the vector magnetisation and current density. The magnitude of the AMR is defined by ρk − ρ⊥ ∆ρ = ρ ρ0 where ρk and ρ⊥ are the resistivities with the magnetisation and current parallel and perpendicular to one another respectively. ρ0 is the resistivity in the demagnetised 1.015 1.004 a) 1.010 1000Å Co b) 1.002 30Å Co 1.005 R/R(0) R/R(0) 23 1.000 1.000 0.998 0.995 Longitudinal Transverse 0.990 -10 0.996 -5 0 5 10 -6 -2 2 6 B (T) B (T) Figure 1.4: Typical MR for a) bulk and b) thin-film transition metal ferromagnets, after reference [76]. The low-field is due to the AMR whilst the behaviour at highfields is due to the Lorentz magnetoresistance. state, which may be given by ρ0 = 31 ρk + 32 ρ⊥ , assuming a bulk-like domain distribution. Figure 1.4 shows curves typical of the AMR in a bulk and thin-film transition metal ferromagnet in which case the ρk is usually (but not always) greater than the ρ⊥ . The AMR can reach up to ∼ 20% in some NiFe and NiCo alloys[74, 75], making it useful for technological applications. The fact that there is a difference in resistivity between the saturated and demagnetised states of a ferromagnetic metal was shown in 1932 by Englert[77], who noticed peaks in the resistivity at the coercive field of a Fe92 Ni8 alloy. Coercive peaks in the resistivity of cobalt may be observed in figure 1.4. The physical mechanism by which the AMR arises has been shown by Kondo[73] and Berger[78] to be the spin-orbit interaction. Both the magnitude and temperature dependence of the AMR in transition metals are well modelled by the spin-orbit scattering of 4s electrons by a small unquenched 3d orbital angular momentum. By setting the spin-orbit Hamiltonian as a perturbation to the energy of a free-electronlike metal and then solving the Boltzmann transport equation, Kondo derives an expression for the resistivity of the form  2 X ˆ εi εj ζi ζj ρ = ρ0 + ρ1 εˆ · ζ + ρ2 i>j where εˆ and ζˆ are unit vectors in the direction of the applied electric field and magnetisation, and the summation i > j is a summation over cyclic permutations of the 24 1.477 Resistance (Ω ) 1.475 1.473 1.471 1.469 0 0.5 1.0 1.5 2.0 θ /π (Rad) Figure 1.5: Angular dependence of the resistivity of a Co film at low temperature due to the AMR. The magnetisation and current are co-linear when θ = 0. ˆ orthogonal unit vectors ˆi, ˆj and k[73]. The term ρ0 is the normal resistivity due to phonon scattering, with the two following anisotropic terms being related to scattering by defects. The term ‘defects’ refers to anything which affects the lattice potential over the scale of the electronic mean-free-path; for example grain boundaries, crystal dislocations or impurities. Over this length scale the constituent atomic species of stoichiometric alloys may also appear as ‘defects’ to the conduction electrons, which may result in a greatly increased anisotropic scattering contribution. This goes some way to explaining the large values of the AMR in some binary alloys of transition metal ferromagnets. As the resistivity in materials such as these is generally quite large due to the high density of defect scattering centres, calculations are made in the relaxation time limit. This is the case where ωc τ  1, meaning that electrons scatter before completing a significant fraction of a cyclotron orbit and making detailed knowledge of the topology of the Fermi surface irrelevant[79]. The anisotropic scattering terms ρ1 and ρ2 result in a mean-free-path which has both cos2 θ and cos4 θ dependence and produce a resistivity which generally varies as cos2 θ, where θ is the angle between the magnetisation and current flow. The angular variation of resistivity for a polycrystalline Co film at low temperature is shown in figure 1.5 and shows good agreement with a cos2 θ dependence. More recent calculations involving the AMR do not treat the spin-orbit interaction explicitly, preferring to deal instead simply with an anisotropic mean-free-path[80] or conductivity tensor[74]. 25 CIP Contact Contact CPP Contact Contact Figure 1.6: Current in Plane (CIP) and Current Perpendicular to the Plane (CPP) geometries for measuring GMR in magnetic multilayers. In the rare-earth metals there is an additional anisotropic coulomb scattering mechanism due to the electric quadrupole moment of the 4f electrons. Kondo[73] has calculated the contribution to the resistivity due to this effect and shown it to be small in comparison to the spin-orbit term, except in the cases of thulium or ytterbium metals. 1.5 Giant magnetoresistance Since the discovery in 1988 that the resistance of Fe/Cr/Fe trilayers[6] and Fe/Cr superlattices[5] can be changed by as much as 100% by the application of a magnetic field, there has been a concerted and continued research interest in the field of socalled ‘Giant Magnetoresistance’ or GMR. In this section we shall discuss briefly a simple picture of the physical origins of the GMR, and then describe more fully some of the more important theoretical studies on the subject. 1.5.1 Simple picture of the GMR GMR may be measured in two distinct sample geometries; the current in the plane (CIP)or perpendicular to the plane (CPP) of the film. Figure 1.6 shows a schematic representation of the two geometries. Although the basic physical picture of GMR in these two systems is identical, it is often easier to describe using the CPP picture. The simplest possible picture of the physical origins of the GMR assumes two 26 Parallel Antiparallel ρ↑ ρ↑ ρ↓ ρ↓ Figure 1.7: Simple model of the giant magnetoresistance. non-interacting conduction channels corresponding to spin-up and spin-down electrons, where the spin is defined with reference to a global quantisation axis. We assume also that the conduction electrons pass through the spacer layers effectively without scattering (i.e. the mean-free-path in the spacer layer is much greater than the spacer thickness). In the ferromagnetic layers the scattering rate is assumed to be dependent upon the projection of the electron spin along the local magnetisation axis; i.e. electrons with e.g. spin antiparallel to the magnetisation scatter more frequently. In this case, the local resistivity for each layer in the parallel and antiparallel configurations will be as shown in shown in figure 1.7. For the parallel configuration it is easily seen that one spin channel has a higher resistance, but that the other channel effectively shunts the majority of the current, so the total resistance is low. For the antiparallel configuration, however, both spin channels have identical, intermediate resistance, so the total resistance is higher. This simply explains the origin of the GMR in terms of the spin-dependence of the resistivity in the ferromagnetic layers in a magnetic multilayer. The conjecture of Baibich et. al. that the GMR arises due to spin-dependent scattering of the conduction electrons is now accepted as the mechanism by which the 27 GMR arises, but there has long been debate as to exactly where this scattering occurs. Baibich et. al. thought that the scattering must occur at the interfaces between the magnetic and spacer layers. Many believe, however, that scattering by grown-in defects in the crystal lattice is far more important in determining the transport properties in thin-film structures, as it is in the bulk. The problem of conclusively proving the relative importance of one scattering mechanism over the other has been a goal of experimentalists since day one. However this problem is beyond the scope of this thesis and shall not be discussed further. 1.5.2 Semi-classical model The first theoretical calculation to attempt to fully model the GMR response of Fe/Cr spin-valve and multilayered structures was the model due to Camley and Barna´s[81]. Their semi-classical model involved solving the Boltzmann transport equation - in effect an extension of the Fuchs-Sondheimer theory to multiple layers. A diagram of the sample structure is shown in figure 1.8 - the dotted line at the centre of the spacer layer represents the point where the quantisation axis of the electron spin changes to a projection along the magnetisation in the nearest ferromagnetic layer. Reproducing the transport properties in the ferromagnetic layers relies on a spindependent relaxation time, and spin-dependent scattering was modelled using spindependent transmission coefficients between otherwise identical layers. The magnetic layers are assumed to behave as Stoner-Wohlfarth particles and the orientation of the layer magnetisation with applied field is found by minimising the sum of exchange, Zeeman and magnetocrystalline anisotropy energies. Figure 1.8 also shows the result of fitting Camley and Barna´s’ model to data from Binasch et. al.[6] with realistic anisotropy constants, mean-free-paths and scattering asymmetries. The fit is reasonable considering the simplicity of the model and numerous assumptions made. Models of the GMR based on Camley and Barna´s’ model have proved popular with experimentalists due to the ease of relating the required parameters to properties of real multilayer samples – the model basically describes the GMR in terms of the quality of the crystal structure of the layers (relaxation time) and the interfacial 28 FM NM A Ε -b B -a FM C D a b Figure 1.8: Diagram of the sample structure used in calculations by Camley and Barna´s, and a fit of the Camley and Barna´s model to data from Binasch et. al. for a Fe/Cr multilayer roughness (transmission coefficient). Due to this popularity, several extensions to this model have been developed. Spin-dependent scattering of conduction electrons within the bulk of the layers was ignored in the original model, but was later included by, e.g. Barna´s et. al.[82] and Dieny[83]. Another mechanism which was not initially included in the model is the effect of the anisotropic magnetoresistance. As the GMR observed by Binasch et. al. in their Fe/Cr multilayers was far greater than the AMR in such samples it was initially thought unimportant for approximate quantitative results. Several years later however, Rijks et. al.[80] extended the Camley and Barna´s model to include the AMR effect by including an anisotropic mean-free-path of the form ↑(↓) λ↑(↓) (θ) = λ0 1 − a↑(↓) cos2 θ − b↑(↓) cos4 θ
in the ferromagnetic layers in order to model the interplay between the AMR and GMR in Py/Cu/Py trilayer films. They found that although it is not strictly rigorous to assume the AMR and GMR to be additive quantities, to a very good approximation the total magnetoresistance of the system could be taken as a simple summation of the AMR and GMR over a wide range of thicknesses of both magnetic and spacer layers. 29 1.5.3 Resistor network model The resistor network model of the GMR proposed by Edwards et. al.[84] is an extension of the simple picture of the GMR discussed in section 1.5. The model attempts to predict the magnitude of the GMR - as opposed to the dependence upon magnetic field as in the Camley and Barna´s model - based purely upon knowledge of the bulk resistivity of the constituent layers. The resistor network model makes three assumptions: - The spin of the conduction electrons is conserved; i.e. there is no spin-flip or magnon scattering. - The interfaces between layers present no barrier to the conduction electrons, which are described within a free-electron framework. - The two spin channels are described by different mean-free-paths within the ferromagnetic layers. The resistor network model effectively models the GMR as arising solely due to a final-state spin-dependence of the lattice scattering of conduction electrons within the bulk of the magnetic layers. The spin-dependence is due to the Mott s-d scattering mechanism[85, 86, 87, 88] whereby the resistivity for each spin-channel is strongly enhanced by the presence of electronic d -levels for that spin at the Fermi energy. Spin-splitting of the d band in ferromagnets causes a difference in the number of d states at the Fermi level for each spin. Edwards et. al. derive, in the limit of the mean-free-path in each layer being far greater than the layer thickness, the expression where α = ρH M ρS and β = ρL M ρS (α − β)2 ∆R
= N R β+ 4 α+ M N M
(1.3) are the ratios of the majority and minority spin resistivity in the ferromagnet to that in the spacer layer and N and M are the thicknesses of the non-magnetic and magnetic layers respectively. In the limit of the mean-free-path being smaller that the layer thickness for each layer the GMR vanishes as electrons can no longer cross the spacer layer without scattering and the two arms of the resistor network become equivalent. 30 FM NM FM FM NM FM Spin ↑ Spin ↓ Spin ↑ R↑ R↑ R↑ R↓ R↓ R↓ R↓ R↑ Spin ↓ Figure 1.9: Resistor network model of the GMR. The resistor network model has been successful in predicting the magnitude of the GMR in both Fe/Cr and Co/Cu multilayer systems. However the values of α and β are often somewhat incompatible with what is expected from measurements on bulk materials. This is often attributed to differences in the band structure and local DOS between bulk materials and the thin layers which comprise the multilayer, and may be explained as evidence for an interfacial scattering contribution. 1.5.4 Quantum mechanical model The theoretical models discussed so far have been based upon purely classical ideas. In the semi-classical Fuchs-Sondheimer theory[66, 67] an electronic trajectory parallel to the plane of the film contributes the vast majority of the current flow due to its avoidance of the film boundaries. It can be seen that such a trajectory in fact requires absolute knowledge of both the electronic position and momentum in the z direction which is, of course, unacceptable in a rigorous quantum mechanical model. The quantum mechanical treatment of the conductivity of a single thin metal film by Te˘sanovi´c et. al.[89] uses a free-electron Greens function approach to model the conductivity of films where t  λ. The zero-point motion excludes trajectories confined to the x−y plane and models the resistivity with a Hamiltonian resulting in two contributions to the mean-free-path due to bulk impurity scattering and scattering from a random surface roughness profile. These two mean-free-path parameters result 31 in a crossover from ρ ∝ 1/t to ρ ∝ 1/t∼2 behaviour with decreasing film thickness t. Levy, Zhang and Fert[90, 91] extended the Te˘sanovi´c et. al. model to a layered structure and calculated the depth dependent conductivity profile σ (z) for a superlattice where the total thickness is far greater than the mean-free-path and for a spin-valve structure. Using this model, Levy et. al. have been able to successfully model the dependence of the GMR on both ferromagnetic and spacer layer thickness, and its dependence on the interfacial roughness, obtaining reasonable values for the resistivity of the multilayer. Field dependence of the resistivity has been modelled in a similar fashion to that used by Camley and Barna´s. 1.5.5 Non-local model with band-structure effects In recent years, the theoretical approach to modelling the GMR in magnetic multilayers has begun to include the electronic structure of the multilayer in a more holistic fashion. Tsymbal and Pettifor have performed calculations on multilayer[92, 93] and trilayer[94] systems using a model which describes the GMR as arising due to spin-independent scattering of electrons from grown-in defects into a realistic spinpolarised band-structure. The band structure of the sample structures is calculated within the tight-binding model. Previous work within the tight-binding framework has considered just a single band[95], whereas the Tsymbal and Pettifor model includes both s, p and d bands in the band-structure calculations. The use of a realistic band-structure describing the electronic properties of the system as a whole is a vast improvement on earlier models which either assume a homogenous free-electron-like band structure or treat the electronic properties of each layer individually with no outside influences. The use of defect scattering where the scattering potential is taken to be spinindependent - as opposed to the intrinsic spin-dependence usually assumed - is identical to the resistor network model of the GMR. In other words, the only spindependence in the scattering comes from Mott s-d scattering into a spin-split d band due to the spin-asymmetry in the density of final states. The conductivity of the structure in either CIP or CPP geometries is calculated from the Kubo-Greenwood formula and the GMR derived from separate calculations 32 Figure 1.10: Spin-resolved DOS, conductivity and GMR results for an infinitely repeating Co/Cu multilayer, from calculations by Tsymbal and Pettifor[92]. with alternate magnetic layers magnetised parallel and antiparallel. The degree of scattering, and hence the conductivity, is parameterised by the quantity γ which is the RMS displacement of the on-site energy levels, corresponding to the degree of disorder in the system. The value of γ is tuned to produce good agreement between the calculated conductivity and that of a real multilayer structure. Figure 1.10 shows model calculations by Tsymbal and Pettifor[92] on an infinitely repeating Co4 /Cu4 multilayer, where the subscripts are the number of atomic planes constituting each layer in the stack. The upper frame shows the majority and minority spin DOS for both parallel and antiparallel configurations. The lower frames show the parallel and antiparallel conductivities with spd hybridisation included, and the GMR as a function of Fermi-energy assuming a rigid band model in both CIP and 33 CPP geometries. The role of band-hybridisation between the s and p band electrons and the less mobile d band electrons is emphasised in this model. It is found that in the absence of spd hybridisation the conductivity in transition metals may be greatly overestimated, and values of the GMR are vastly inflated for calculations that do not include interband transitions. Within the Tsymbal and Pettifor model the GMR is vanishingly small for both Co/Cu and Fe/Cr systems[92] in the absence of spd hybridisation. The peak in the GMR observed in the case of Co/Cu for electron energies roughly 1eV above the Fermi level (figure 1.10) is in extremely good agreement with the value of ballistic magnetocurrent observed in a spin-valve transistor by Monsma et. al.[55]. However, the validity of this interpretation is somewhat questionable. The ability of the Tsymbal and Pettifor model to obtain realistic values of both GMR and resistivity for a variety of systems in both CIP and CPP geometries has been a much sought after goal in the theory of the GMR. The fact that this model manages to produce such good agreement with just one adjustable parameter is astounding. 1.6 Tunnelling magnetoresistance Tunnelling magnetoresistance (TMR) is the change in perpendicular resistance of a ferromagnet/insulator/ferromagnet (F/I/F) trilayer sandwich structure as a function of the alignment of the magnetisation of the ferromagnetic layers. The first reported change in tunnel junction conductance with magnetic field was reported by Julliere in 1975 [7], which claimed a fractional change in conductance of about 14% in an Fe/αGe/Co junction at 4.2K and zero junction bias. This large ‘magnetoconductance’ was in this case attributed to a so-called zero-bias anomaly caused by magnetic impurities in the insulating barrier. Several reports were made subsequently of the magnetic field dependence of the resistance in a magnetic tunnel junction, although the reported figures were of only a few percent change[8, 9, 96]. Interest in the subject was reignited in 1995 when Moodera et. al.[10] reported TMR values of 24% and 12% at 4.2K and 300K respectively in Co/AlO/Ni80 Fe20 junctions. Recent innovations have opened the door for magnetic tunnel junctions to be used as e.g. magnetic 34 random access memory (MRAM)[32] and as a replacement for spin-valve read-heads in high data density hard disc drives, making magnetic tunnel junctions an extremely important topic of research. 1.6.1 Julliere’s model In his paper of 1975, Julliere proposed an expression quantifying the maximum theoretical value of what is now known as the tunnelling magnetoresistance (TMR) as a function of the tunnelling spin-polarisation of the two ferromagnetic electrodes, P1 and P2 [7] where TMRV=0 = R↑↓ − R↑↑ 2P1 P2 = R↑↑ 1 − P1 P2 (1.4) The Julliere formula has proven to be a reasonable measure of the maximum TMR possible for a junction with electrodes of given polarisation. The Julliere model is a simple expression of the transfer Hamiltonian picture of tunnelling using spinindependent T-matrix elements, and as such is only valid for a very limited set of conditions. Firstly the model is only valid at low temperatures where spin-wave excitations are frozen out. Magnons act to decrease the polarisation of the electrodes by their very nature, and also increase the depolarisation of the tunnelling current by exciting inelastic spin-flip tunnelling processes. Secondly the model is only valid at zero-bias as the spin-polarisations P1 and P2 are those measured at the Fermi level of the electrodes by the superconductor tunnelling method. Thus the model only truly describes tunnelling from the Fermi level of one electrode to the Fermi level of the other. Thirdly, the Julliere model takes no account of interactions between the tunnelling electron and the band-structure of the tunnel barrier material. It has been shown recently[30, 31] that hybridisation of the electrode band-structure through the tunnel barrier can be of extreme importance in magnetic tunnel junctions. Despite these limitations, the Julliere model is to this day still regarded as a benchmark by which the quality of magnetic tunnel junctions is judged. 35 1.6.2 Stationary-state models The transfer Hamiltonian methods discussed in section 1.2.3 and above are only one of the methods of simply describing the quantum mechanical tunnelling phenomenon. In fact, almost all of the models that are extensively used today, e.g. those due to Simmons[97], Hartman[98], Brinkman, Dynes and Rowell (BDR)[99] and Slonczewski[100] are based upon the far simpler stationary state calculation within the Wentzel-Kramers-Brillouin (WKB) approximation often used in elementary quantum mechanics[101]. This technique describes the conduction electrons within each metallic electrode as standing waves and calculates the transmission and reflection coefficients at the barrier interfaces by simply matching the wavefunction and its derivative across each boundary for a given form of barrier potential. The Simmons model is that most often quoted in the literature for the determination of the barrier width and effective barrier height parameters in MTJ structures. Here the perpendicular current density is calculated as a function of junction bias, with the average barrier height φ and barrier width ∆s as fitting parameters. This model makes the standard assumption of the WKB approximation, and also assumes that tunnelling only takes place between electronic states at the Fermi level. Large bias voltages are excluded from the calculation. The simplest case of Simmons’ model[97] assumes absolute zero temperature and a symmetric tunnel barrier – in effect, the two electrode materials are identical. Simmons model was later extended to include a trapezoidal barrier[102] and finite temperature[103]. Popular variations on the Simmons model have been proposed by Hartman[98] who also calculated the tunnel current density as a function of junction bias, and by Brinkman, Dynes and Rowell[99] who calculated the tunnel conductance as a function of bias both within the WKB approximation and assuming abrupt interfaces. Recently Xiang et. al. have extended the BDR model of the tunnelling conductance to include a term representing the density of states in each electrode[104]. They have fitted their conductance data for symmetric Co/Al2 O3 /Co MTJs to this model for both magnetisation states and extracted the ‘density of states’ and ‘tunnelling electron spin-polarisation’ from their fits. Whether or not the multitude of fitting parameters obtained from this model are in any way physically meaningful shall not be discussed. 36 Seminal work based upon the stationary state method has been used to model the magnetoconductance of magnetic tunnel junctions by Slonczewski[100]. These calculations most importantly show the intrinsic effect of using half-metallic ferromagnets as the electrode materials in magnetic tunnel junctions. Slonczewskis ‘single band model’ predicts an infinite magnetoconductance for an MTJ where both electrodes are half-metals. His extended two-band free-electron model shows the expected dependence of the TMR on the angle θ between the magnetisation of the electrodes, but also predicts the possibility of inverse TMR for a pair of positively polarised electrodes simply due to the conditions imposed by the matching of electron wavefunctions at the junction interfaces. This model proved to be the first calculation where even a most vague description of the electronic properties of the insulating barrier layer (i.e. the position of the bottom of conduction band) was found to have a profound effect on the magnetotransport properties of the MTJ structure. Slonczewski’s model does suffer from several deficiencies which prevent its results from being strictly rigorous. Firstly the stationary state model relies upon the WKB approximation which is not really the case in a tunnel junction structure. Secondly these models use a constant effective electron mass which is not strictly valid within an insulator unless the tunnelling electron energy is very close to the top or bottom of the energy gap[29, 105]. 1.6.3 Band-structure effects in magnetic tunnel junctions Initial calculations on magnetic tunnel junctions featuring a realistically calculated band-structure concentrated on the Fe/ZnSe/Fe[106] epitaxial system. Although most magnetic tunnel junction structures studied experimentally at the time consisted of an amorphous alumina tunnel barrier, such systems are unsuited to first principles calculations due to the fact that the electronic k vector in the plane of the junction is not conserved because of the lack of translational symmetry of the structure within the amorphous barrier layer. Oleinik, Tsymbal and Pettifor[107] performed density functional theory calculations within the local spin-density approximation on Co/Al2 O3 superlattice structures. This model system aimed to give qualitative understanding of amorphous Al2 O3 systems by modelling crystalline Al2 O3 from first 37 principles. They modelled both Al and O2 terminated interfaces in order to see the effect of oxidation time on the electronic properties of a tunnel junction structure. Underoxidation, i.e. an Al terminated barrier, results in charge transfer from the Co underlayer producing a reduced Co magnetic moment of 1.15µB /atom. Oleinik et. al. also found the tunnelling spin-polarisation to be negative up to an Al2 O3 thickness of roughly 10˚ A, at which point the sign of the polarisation inverted. This was attributed to different decay rates of the evanescent waves corresponding to majority and minority states and again emphasises the fact that T-matrix elements cannot be taken to be either spin or band independent. In a second paper these authors considered an epitaxial Co/SrTiO3 /Co junction structure. A barrier with TiO2 termination is found to be most stable in this structure, which results in an induced magnetic moment of 0.25µB on the Ti sites, aligned antiparallel to the adjacent Co moment. This is thought to explain the negative tunnelling spin-polarisation observed in Co/SrTiO3 /La0.7 Sr0.3 MnO3 junctions[108, 109]. Due to the intractibility of amorphous barrier structures to first-principles calculations, the emphasis in modelling of magnetic tunnel junctions has shifted recently to consider epitaxial (100) oriented Fe/MgO/Fe and related junction structures. Calculations on this system have been performed within the tight-binding model by Mathon et. al.[30], and within the layer Korringa-Kohn-Rostocker (LKKR) method by Butler et. al.[31]. Both of these calculations show that one of the main factors governing the transmission of a particular state across the tunnel barrier is the symmetry of the electronic wavefunction both in the electrodes and within the tunnel barrier itself. Certain k states were found to have a decreased transmission probability due to the inability to couple to a similar state across the barrier. This emphasises the importance of ‘similar states’ on either side of the barrier, an argument which can be used to qualitatively explain the bias dependence of TMR as the ‘similarity’ between the states on either side of the barrier at the Fermi level changes with junction bias. These calculations both conclude that the conductance in the parallel magnetic configuration is dominated by majority-spin electrons with free-electron or sp-character as these states couple most strongly across the barrier and decay at a lower rate as evanescent 38 states. Mathon et. al. calculated an ‘optimistic’ TMR1 of ∼1200%, with the maximum occurring for a barrier thickness of about 10 atomic planes of MgO. Butler et. al. showed that the majority states dominate the conductance for all barrier thicknesses, and predicted a rise in TMR with increasing barrier thickness. 1.7 Superconductor tunnelling Long before the advent of magnetoresistance in MTJ structures there had been interest in tunnelling of electrons between ferromagnetic metals and superconductors[105]. In a series of pioneering experiments, Tedrow and Meservey[37] measured the tunnelling spin-polarisation of Fe, Ni, Co and Gd films by tunnelling across an Al2 O3 barrier into a superconducting Al film. The accurate determination of the spin-polarisation in ferromagnetic films relies on three key features: - The fact that close to the Fermi energy the quasiparticle DOS in the superconductor has sharply peaked features on an energy scale of ±1meV from EF , whereas on this energy scale the DOS of a normal metal is, to all intents and purposes, smooth and featureless. - The quasiparticle DOS may be Zeeman split by the application of a magnetic field. The energy of spin-down electronic levels will be raised by an energy µB B and the spin-up levels lowered by the same amount. For a sufficiently large magnetic field the spin-split peaks in the superconducting DOS may be resolved for both occupied and unoccupied states. - The spin-polarisation of the tunnelling current should be conserved both during the tunnelling process and within the superconductor. The ability to deposit high quality thin-films has helped forward this area of research in recent years. In order to determine the spin-polarisation to a high degree of accuracy it is necessary to separate the spin-up and spin-down peaks as far as 1 This is the difference in resistance between P and AP states, normalised to the resistance in the AP state as opposed to the P state. 39 possible – even at 3 He temperatures this requires the application of a magnetic field of several Tesla. In a sufficiently thin film, the situation may be achieved where the film thickness is less than the penetration depth of a magnetic field into the superconductor – the so-called ‘Clogston-Chandrasekhar’ limit[110, 111]. Due to the fact that the magnetic field is able to completely penetrate the film without destroying the superconductivity there is no basis for a critical field due to free-energy considerations. Superconductivity is eventually destroyed when the magnetic field becomes sufficiently strong to completely depolarise the Cooper pairs, the field required to do this being related to the normal state Pauli paramagnetic susceptibility. The tunnelling current may retain its spin-polarisation to a high degree provided that the tunnel barrier is of a sufficiently high-quality and the superconductor has sufficiently long relaxation times with respect to both spin-flip scattering and spinorbit depairing. In both of these respects Al proves to be the material of choice. Both the superconducting film and tunnel barrier may be formed by the depostion of an Al film and subsequent oxidation. Aluminium has the second lowest atomic mass of the metallic superconductors - the lightest being beryllium which has TC ∼0.03K [42] and so has a low cross-section for spin-orbit interactions. There are two primary methods by which the tunnelling spin-polarisation may be determined from the measured conductance. The simplest method, as used by Tedrow and Meservey, relates the tunnelling electron spin-polarisation to the relative heights of the DOS peaks measured from the differential conductance. This analysis yields a reasonable value for the spin-polarisation. However, values obtained by this method are generally reduced from the true value by ∼8% [112]. The reason for this is the fact that this method ignores the effect of spin-flip and spin-orbit depolarisation processes and also thermal broadening of the BCS peaks. The second method involves fitting the conductance spectra with a model by Bruno and Schwartz[113], where the conductance is calculated from the BCS Greens functions derived by Maki[114]. This model includes both spin-flip and spin-orbit depolarisation within the superconductor, and the zero-temperature DOS is easily convoluted with a temperature function to mimic thermal broadening. 40 A variation on the superconductor tunnelling method has been used to show the spin-filter effect on electrons tunnelling through antiferromagnetic EuSe tunnel barrier junctions[115]. Measuring the tunnel conductance as a function of magnetic field, the superconducting DOS is seen to shift linearly with increasing magnetic field, consistent with a close-to 100% spin-polarisation of the electrons tunnelling into the superconductor. This is a further example of the strong effects which may be observed due entirely to the insulating barrier material. 1.8 Point-contact Andreev reflection The phenomenon of Andreev reflection[58] at the interface between a superconductor and ferromagnet has recently found use in the measurement of the spin-polarisation of ferromagnetic metals[116, 117]. If we consider an electron-like quasiparticle with E > ∆ incident on a planar normal metal/superconductor interface at equilibrium, there are three possibilities which may occur at the interface. The quasiparticle may be simply reflected back from the interface, it may cross the interface and continue as a quasiparticle2 or it may be reflected back from the interface as a hole below the Fermi level, producing a Cooper-pair which continues in the superconducter as part of the condensate. This final possibility is commonly referred to as Andreev reflection and generally results in an increase in the normal metal/superconductor junction conductance for bias voltages less than the gap energy, where this is the only possible conduction mechanism. The probability of each of these occurrences may be calculated for the case of a one-dimensional point-contact from the Blonder, Tinkham and Klapwijk (BTK)[59] model which derives expressions for the four transmission and reflection coefficients by solving the Bogoliubov equations[118] at finite bias across an interface modelled as a delta-function barrier with dimensionless barrier strength Z. The Bogoliubov equations have ∆ (x) = 0 - where they reduce to the Schr¨odinger equation for an electron and hole - in the normal metal and ∆ (x) = ∆, the pair potential, in the superconductor. They are solved within a one-dimensional boundary condition implying ballistic 2 There are in fact two situations where this may occur, depending upon whether or not the transmitted quasiparticle momentum crosses the Fermi surface or not, leading to four transmission/reflection coefficients. 41 Normalised conductance 2.0 2.0 a) 1.5 1.5 1.0 1.0 0.5 0.5 0 0 -6 Normalised conductance 2.0 b) -3 0 3 6 -6 2.0 c) 1.5 1.5 1.0 1.0 0.5 0.5 0 -3 0 3 6 0 3 6 d) 0 -6 -3 0 Bias (mV) 3 6 -6 -3 Bias (mV) Figure 1.11: The simulated effect of varying spin-polarisation for a point-contact with Z = 0 and ∆ = 1meV at 4.2K calculated within the modified BTK model. Polarisation values are a) 0, b) 37%, c) 96% and d) 100%. transport within a point-contact with a width that is negligible in comparison to the mean-free-path. The BTK model gives an expression for the electric current of the form I∼ Z ∞ [f (E − eV ) − f (E)] [1 + A (E) − B (E)] dE −∞ where f is the Fermi-Dirac distribution function and A (E) and B (E) are the energy dependent amplitudes for Andreev and normal reflection respectively. The BTK model does not in itself give a value of spin-polarisation, rather giving the bias dependent transmission, reflection and Andreev reflection amplitudes for current flowing through the junction from an unpolarised normal metal. In order to determine the spin-polarisation a modified BTK model has been proposed by Soulen et. al.[116]. This models the total polarised current in a ferromagnet as comprising two distinct ‘types’ of electron; those which may be matched with another electron of opposite spin to form an unpolarised current, and those which cannot be matched, which form a polarised current. The conductance Gu due to the unpolarised current may be modelled within the BTK framework, whereas that for the polarised current, 42 Gp , has the Andreev reflection amplitude set identically to zero as there are no electrons of opposite spin with which to form a Cooper-pair. The total conductance is then simply given by G = (1 − P ) Gu + P Gp Figure 1.11 shows the variation of the calculated normalised conductance within the modified BTK model of PCAR. For an unpolarised electrode - frame a) - we see (roughly) a doubling of the conductance in the gap region due to Andreev reflection. As the spin-polarisation of the electrode increases the conductance within the energy gap decreases. Frames b) and c) show the conductance corresponding to the 37% and 96% polarisations anticipated in Ni and CrO2 [119] and frame d) that for a 100% polarised half-metal. Recently, discussion has reopened regarding the validity of the BTK formalism in describing the Andreev reflection process in ferromagnet/superconductor junctions. Mazin et. al.[43] have extended the BTK formulation to include a diffusive region between the superconducting contact and normal metal sample and by describing the reflected hole partially as an evanescent state. Xia et. al.[120] argue that the BTK barrier strength parameter should in-fact be spin-dependent and that the orbital character of the conduction electrons should be matched in some way across the junction. They show varying degrees of disagreement between first-principles calculation of the junction conductance and calculations within the BTK formalism for different normal metal electrodes (Cu, Ni and Co). The model which they propose does, however, claim a small negative spin-polarisation by fitting Andreev reflection data. 1.9 Summary In this chapter we have discussed various methods by which the transport properties of both homogeneous and heterogeneous structures may be modified according to their magnetic properties. We have shown the variety of guises which spin-polarisation may take, depending upon the details of the technique employed to probe it. For the transport processes discussed in the remainder of this thesis we may conclude the following: 43 - The spin-polarisation probed by most transport techniques is, to the first approximation, given by the DOS at the Fermi level, weighted by the square of the Fermi velocity for each state. - Point contact Andreev reflection, in the low interface transparency limit, is sensitive to this polarisation averaged over the Fermi surface. As the technique is only sensitive to the fact that there is a spin asymmetry, no information on the sign of the spin-polarisation may be obtained. - Tunnelling measurements sense the polarisation averaged over k-states where k is predominantly perpendicular to the barrier interface. The sign of the spin-polarisation may be found by reference to the Zeeman splitting of the quasiparticle DOS in superconductor junctions. - Giant magnetoresistance senses a complex variation on the Fermi surface average due to spin mixing and spin-dependent scattering, so cannot yield an absolute value for the spin-polarisation. The sign of the spin-polarisation in a given magnetic layer may be found only by reference to that in another layer. In conclusion, all of these techniques are sensitive to some form of ‘transport spin-polarisation’, but for each case it is not the same spin-polarisation that we shall measure. 44 Chapter 2 Experimental techniques 2.1 Introduction The results presented in this thesis are based on measurements made on two distinct types of magnetic heterostructure – magnetic multilayer samples with transport measurements performed in the current-in-plane (CIP) geometry and tunnel junction type structures where the current flows perpendicularly through a nanoscale insulating barrier layer. These samples are characterised primarily by transport and magnetic measurements, but we are also interested in the sample structure. The fabrication and characterisation of both types of sample require numerous experimental procedures which are detailed in this chapter. 2.2 Sample preparation At Leeds we are extremely fortunate to have apparatus not only for the magnetic, structural and transport characterisation of our samples, but also to have deposition facilities in order to fabricate the samples that we use ourselves. The group possesses both a custom built magnetron sputtering system (with another under construction at the time of writing) and a commercial molecular beam epitaxy (MBE) machine. All samples discussed in this thesis have been deposited in the sputtering system at Leeds, which is discussed below. 45 RGA head Meissner cold-trap Chamber lid with viewport Rubber seal Baseplate Roughing line and valve Mechanical pump Gate-valve Gate-valve control Cold head temperature sensor Cryopump Figure 2.1: Diagram showing the vacuum chamber and pumping system. 2.2.1 The high-vacuum system The vacuum system in which sputtered films are deposited consists of a stainless steel chamber lid with a Meissner cold-trap, viewport and rubber seal, which is mounted on a mechanical hoist. The chamber lid may be lifted from the baseplate, on which the magnetrons, shutter, sample wheel and pumping port are fixed. A diagram of the vacuum chamber and pumping system is presented in figure 2.1. The sputter deposition system was renovated by C. H. Marrows, and a further description of the system may be found in his Ph.D. thesis[121]. Initial pumpdown of the chamber is via a mechanical vane-type roughing pump to reduce the pressure from atmospheric pressure to the range of about 20-50mTorr. This typically takes between 10 and 20 minutes to accomplish. At this point the flow characteristics of the remaining gas switches from viscous flow, where the fluid dynamics are governed by intermolecular collisions, to the molecular flow regime[122] where the mean-free-path of the gas molecules is nominally larger than the dimensions of the vacuum chamber and collisions with the chamber walls dominate over those between molecules. The changeover between viscous and molecular flow may be quantified by the Knudsen number, defined as the ratio between the mean-free-path of the gas molecules and the characteristic dimension of the vacuum chamber NK = λ L 46 Residual gas Partial pressure, Partial pressure species no cold-trap (Torr) with cold-trap (Torr) H2 4 × 10−8 5 × 10−10 −8 He 6 × 10 2 × 10−9 H2 O 1 × 10−7 6 × 10−9 −8 N2 1 × 10 1 × 10−9 O2 1 × 10−9 1 × 10−10 CO2 1 × 10−8 1 × 10−10 Table 2.1: Typical partial pressures of residual gasses in the vacuum chamber before and after cooling the liquid nitrogen Meissner trap, as measured from the RGA. The changeover between flow regimes occurs when NK ∼ 1. At this point the pumping mechanism is changed from the mechanical vane pump to a cryopump. This pump operates by condensing gas molecules onto a 10K cold stage cooled by a closed-cycle 4 He refrigerator. This type of pump is extremely efficient at adsorbing most gasses remaining in the vacuum chamber, typically with the exceptions of H2 and He. After cryopumping the chamber for roughly 8 to 10 hours, the pressure is generally reduced to ∼10−7 Torr range. At this time the majority of residual gas is water vapour, which is removed prior to sample deposition using a liquid nitrogen cooled Meissner cold-trap. The base pressure after freezing out the residual water vapour is typically better that 2 × 10−8 Torr. Typical partial pressures of residual gasses before and after applying the liquid nitrogen cold-trap are presented in table 2.1. Pressures above 0.1mTorr are measured using an MKS Baratron capacitance pressure gauge and those below that using a Spectramass Dataquad quadrupole residual gas analyser (RGA). The typical times required for pumpdown and sample deposition means that it is possible to run the system on a 24 hour turnaround cycle, preparing a batch of samples each day, breaking vacuum and pumping out overnight. The vacuum chamber contains 6 planar magnetron sputtering guns which are suitable for both D.C. and R.F. sputtering as discussed in the following section. Above the magnetrons a stainless steel shutter plate is mounted onto a dual rotary motion feedthrough. This shutter allows multiple magnetron guns to remain lit simultaneously whilst depositing only one material on a single chosen substrate. Also mounted 47 Figure 2.2: Photograph showing the Leeds sputtering system with the chamber lid raised. The magnetron guns can be seen at the bottom of the picture and the shutter assembly and sample wheel above them. onto the rotary motion feedthrough is the copper sample mounting wheel. The large thermal mass of the sample wheel prevents excessive heating of the substrates during deposition. The sample wheel also ensures that the samples remain in electrical contact to earth. A photograph of the system with the chamber lid raised is shown in figure 2.2 – here the magnetron guns, shutter assembly and sample wheel are all visible. The motion of both the sample wheel and shutter, and the ignition of the magnetrons are computer controlled for reproducible sample growth. 2.2.2 The sputtering process Sputtering is a technique widely used in both research and industry for the controlled deposition of thin films1 . The sputtering process was discovered in 1852 by Grove[123] who was, at the time, investigating the properties of electrical discharges through low pressure gasses. He observed discolouration of the glass near the discharge electrode in his bell-jar vacuum system, similar to that which may be observed towards the ends of used fluorescent light tubes. Grove concluded that this discolouration was due to 1 The term ‘sputtering’ may also be used in reference to sputter cleaning or etching of surfaces, but we shall discuss only the process of sputter deposition. 48 Ar+ Sputtered atom θ Target Figure 2.3: A ‘cartoon’ of the sputtering process. Initial ion bombardment of the target surface excites collisions between atoms. The spread of these atomic collisions can cause atoms to be ejected from the target surface. The probability of ejection of an atom with angle θ varies approximately as P (θ) = cos θ. the removal of material from the discharge electrode and its subsequent adsorption onto the glass surface. The physical explanation of the sputtering mechanism essentially describes the ejection of the sputtered atom as resulting from a series of atomic collisions within the sputtering target, which are initiated by the impact of an impinging particle. The sputtering process by such a mechanism is shown in figure 2.3 which shows how, as the collision excitation is randomly distributed through the target, atoms may be ejected from the target surface. In order for such excitations to be initiated the incident particle should be massive enough to transfer sufficient momentum to the target, and sufficiently small as to transfer its momentum to a single surface atom[124]. For this purpose a ‘working gas’ is allowed into the vacuum chamber during sputtering and is ionised by collisions with electrons to create a plasma. Ions from the plasma are accelerated towards the target by applying an electric field, and these ions are used to excite the sputtering process. An inert gas is required for use as a working gas in order to prevent chemical reaction with the growing film and argon is generally used 49 Substrate (Anode) + D.C. - PSU Working gas inlet Target (Cathode) Figure 2.4: Schematic diagram of D.C. gas discharge sputtering. The sputtering target is the cathode of the discharge whilst the substrate and chamber walls are the anode. due to its ready availability in reasonably pure form. Figure 2.4 shows a schematic diagram of a simple gas discharge sputtering arrangement. The growth rates obtained from D.C. gas discharge sputtering are typically less than 1˚ As−1 , which can cause problems with film purity and growth morphology. Due to this difficulty, in most cases a magnetically enhanced plasma discharge is now used, known as magnetron sputtering. 2.2.3 D.C. magnetron sputtering Magnetron sputtering was first introduced in 1936 by Penning[125] and later developed by Penfold and Thornton[126] in the 1970’s. In this arrangement a set of permanent magnets are placed behind the sputtering target in such an arrangement as to create a magnetic field parallel to the target surface, as is represented in figure 2.5. This magnetic field is perpendicular to the electric field which is, in turn, normal to the target surface. This causes the Lorentz force to act on electrons in the vicinity of the target. The Lorentz force causes electrons to be trapped in an epicyclic path close to the target surface, acting to cause further ionisation of the working gas in the vicinity of the target by collisions. Thus the use of a magnetically assisted discharge allows the use of a lower working gas pressure by concentrating the plasma close to 50 Magnetic field Target Annular permanent magnet or magnet array S N N S S N Central permanent magnet Figure 2.5: The arrangement of magnets and sputtering target for magnetron sputtering, showing the magnetic field parallel to the target surface. The plasma is concentrated in the region close to the target by the magnetic field. the target surface, and increases the deposition rate by increasing the number of ions produced in the discharge plasma. The magnetron guns used in the system at Leeds feature an earthed shroud at a distance of roughly 0.5mm from the sputtering target in order to concentrate the discharge plasma close to the sputtering target. Of the six magnetron guns mounted in the vacuum chamber, four take targets of 2 inches diameter and are suitable for sputtering paramagnetic materials. The remaining two magnetron guns are of a smaller diameter for the deposition of materials which are ferromagnetic at room temperature. The use of smaller diameter guns is necessary as ferromagnetic targets cause the magnetron field to be distorted due to the target magnetisation. A smaller magnetron allows the field to be more concentrated and hence reduces this effect. The magnetron guns are water-cooled in order to dissipate heat caused by ion collisions. 2.2.4 Deposition of CIP magnetic heterostructures There are several important aspects which must be considered prior to depositing CIP multilayer samples, namely the choice of a suitable substrate material, ensuring that the substrates are properly cleaned in order to obtain a good vacuum and high sample quality, and masking the substrate in order that the shape of the sample is well defined to aide the calculation of resistivity and magnetisation. The material generally chosen for use as substrates in our sputtering system are 51 silicon (100) oriented wafers. These wafers may be easily cut to a suitable size and are reasonably robust and cheap. Silicon also has the benefit of forming a native amorphous oxide surface layer which is flat on approximately an atomic monolayer scale and has good adhesion properties over the range of metals and alloys deposited – this is obviously a good starting point when trying to deposit smooth, robust samples. Although many other materials may be used they are not generally as suitable; for example GaAs wafers are brittle and require far more careful handling due to their inherent toxicity, glass has a relatively rough surface, occasionally suffers from adhesion issues and is difficult to cut to size, and single crystal MgO or sapphire substrates have a greater surface roughness and are less cost-effective than Si for sputtering purposes. The Si wafers used in the sputtering system at Leeds are pdoped with boron and have a resistivity of the order of 1-10Ωcm. All CIP samples reported in this thesis are deposited onto such silicon (100) substrates. In order to ensure that a good vacuum is obtained it is necessary to carefully clean the Si substrates before mounting them in the vacuum chamber. The wafers are cut to size and numbered on the back using a diamond scribe. They are then thoroughly rinsed, roughly five times, in Acetone and then five times in Isopropyl alcohol. Acetone is used initially as it is an extremely good degreaser, ensuring that the substrate is clear of grease as well as dust etc.. Isopropyl alcohol is then used to rinse any traces of Acetone from the substrates – Isopropyl alcohol has a vapour pressure of 45.2 Torr whereas Acetone has a vapour pressure of 231 Torr[127]. The substrates are placed face down onto tissue paper to prevent contamination of the surface whilst drying. After inspection to ensure no degradation of the silicon oxide surface, dirt or ‘tide marks’ from the drying process, the substrates are mounted on holders with metal contact masks, one of which is depicted in figure 2.6. The masks are used to define the shape and size of the sample precisely. Several different sets of masks are available, but all CIP samples reported in this thesis are deposited through masks such as that shown, giving samples with a surface area of (20 + π)mm2 . The substrate holders are mounted onto the lower face of the Cu wheel which allows the substrates to be positioned over the required magnetron guns for deposition. The distance between 52 Figure 2.6: The metal contact masks used to define the shape of sputtered CIP samples. the target surfaces and the substrates is roughly 70mm, a distance which has been tuned to improve the thickness homogeneity of the growing film. For a working gas pressure of the order of 1mTorr, the mean-free-path of the sputtered atoms is roughly of the order of tens of millimeters, so a target-substrate distance of 70mm allows the sputtered atom flux to thermalise by collisions with working gas atoms and ions and creates a diffuse ‘effective’ sputtering source. Typical deposition conditions are: - Base pressure prior to deposition of better than 2 × 10−8 Torr with Meissner trap. - Argon working gas at a pressure of 2.5-3.0mTorr. - Ion current controlled sputtering at 50-100mA. - Sputtering power of 15-40W. - Deposition rates typically in the range 2-5˚ As−1 . These parameters have been used extensively and proven successful in the study of thin film heterostructures such as magnetic multilayers and spin-valves, as discussed in e.g. references [121, 128, 129]. 2.2.5 Deposition of tunnel junction structures For depositing crossed electrode tunnel junction structures - see figure 2.7 - the substrates are mounted onto a custom built CPP sample wheel which has several sets 53 Figure 2.7: Crossed electrode structure used in tunnel junction samples, showing the tunnel barrier and two electrode strips with contact pads. The two electrodes and barrier layer are each deposited through separate contact masks which are exchanged in-situ. of three metal contact masks to define the sample structure and which allows the contact masks to be changed in-situ without breaking vacuum. The CPP sample wheel is described in more detail in chapter 4. The substrates used are again cut from a silicon (100) wafer, this time into 8mm squares and cleaned as for the CIP samples discussed previously. The substrates are mounted into recessed holes on the sample holder plate of the CPP sample wheel and have glass slides mounted above them for support. The substrates and glass backing pieces are then held down with a sprung sample holder to ensure mechanical contact with the masks. Deposition of the electrode materials takes place with the mask and substrate plates in electrical contact with earth. However a bias may also be applied to the CPP sample wheel when required. 2.2.6 Tunnel barrier fabrication Thin insulating tunnel barriers are formed by the deposition of a thin metallic layer, followed by subsequent exposure to an oxygen D.C. glow-discharge in order to form an homogeneous insulating oxide layer. This technique for depositing an oxide film is chosen as metal on metal wetting is far superior to insulator on metal wetting. Thus the formation of thin, continuous tunnel barriers is more easily realisable by this method than by e.g. R.F. sputtering from an oxide sputtering target or reactive sputtering a metallic target in an O2 atmosphere. The glow-discharge electrode is an aluminium ring of roughly 55mm diameter and 54 8mm thickness, mounted ∼10mm below the shutter assembly and connected to a high voltage electrical feedthrough by a thick aluminium wire sheathed in ceramic beads. The electrode has been designed in order to maximise plasma intensity close to the sample position whilst minimising line-of-sight access to the sample for any atoms which may be sputtered from the electrode. The use of Al for the electrode also reduces the risk of contamination of the tunnel barrier by sputtered atoms during the oxidation process. The D.C. glow discharge Technically a ‘glow discharge’ is an electrical discharge through a gas, which glows due to emission of light from excited gas atoms. Many reports from the 1940’s onward have concerned themselves with the luminous properties of glow discharges, a summary being given in [122]. Figure 2.8 shows the various luminous and dark regions produced by a planar D.C. glow discharge. It has long been known that successful oxidation of a metal in an oxygen glow discharge requires the growing oxide sample to be maintained in the negative glow region of the D.C. glow discharge[130]. Varying the gas pressure or the electrode separation generally has the effect of changing the luminous features of the glow discharge. This fact probably goes a long way to explaining the wide range of oxidation geometries, pressures and times reported in the literature with regard to magnetic tunnel junctions. The glow discharge produced by the annular electrode employed in our sputtering system has far less well defined features than those produced in a planar discharge as represented in figure 2.8. The cathode glow and dark space regions may be seen immediately surrounding the discharge electrode whilst the anode glow and dark space are only observed when a large bias voltage is applied to the sample wheel. The negative glow and positive column regions are indistinguishable within this arrangement, necessitating a detailed study of the effects of oxygen gas pressure on the transport properties of the tunnel junction samples. The tunnel barrier material that has been investigated in this thesis is alumina. The deposition conditions for the initial aluminium film, as well as the oxygen pressure and oxidation power and time are discussed in chapter 4. 55 Cathode Glow Negative Glow Positive Column Anode Glow Cathode Aston Dark Space Anode Crooks (Cathode) Dark Space Faraday Dark Space Anode Dark Space Figure 2.8: The various luminous and dark regions of a D.C. glow discharge based upon the classification given by early researchers in the field. 2.3 Sample environment As the rare-earth metals used in many parts of this thesis have ordered magnetic phases that do not persist up to room-temperature it is necessary to perform the majority of our characterisation at low temperatures. The inspection of tunnelling behaviour in junction structures also requires the use of reduced temperature to verify the conduction mechanism. These measurements involve the use of several pieces of cryogenic apparatus which are described below. 2.3.1 4 He cryogenics Many of the transport measurements discussed in this thesis have been performed in a Thor Cryogenics 4 He gas-flow cryostat with a superconducting split-pair electromagnet producing a magnetic field of up to 4 Tesla. The samples are cooled by He gas which is allowed to enter into the sample space via a needle valve. The sample stick allows 2 multilayer samples to be mounted simultaneously, with the magnetic field applied either in the plane of the samples or perpendicular to it. With the field applied in the plane it is possible to rotate the sample stick in order to change the orientation between magnetic field and current flow in the sample. This cryostat has a base temperature of 8.20K. A 75Ω heater coil mounted on the sample stick enables 56 measurements at any temperature between base and room temperatures. The temperature is measured by means of a semiconductor diode thermometer also mounted on the sample stick, to an accuracy of ±0.01K. Measurements requiring a constant 4.2K temperature may be made in a 4 He immersion cryostat. This system allows low temperature measurements to be performed quickly on up to four CIP samples or one junction sample. The samples are immersed directly into a bath of liquid He which also contains a 5T solenoid electromagnet. The sample stick allows longitudinal, transverse or perpendicular field measurements to be carried out. However care must be taken not to insert the samples too quickly, subjecting them to rapid thermal shock which may cause damage. 2.4 CIP resistance measurements Transport measurements on our CIP samples use a standard D.C. four-point probe technique to accurately measure the resistance of the sample as a function of the applied magnetic field. Details of this technique along with the determination of the resistivity and magnetoresistance are described below. 2.4.1 Four-probe D.C. resistance The four-probe D.C. resistance technique[131] is used as it nullifies any contribution due to contact or lead resistances to the measurement; in the schematic diagram shown in figure 2.9 the two outer probes supply a known current from a Keithley 220 constant-current source – the current flowing in the sample is known to roughly one part in 106 and is independent of the lead and contact resistances. The two inner probes connect to a Keithley 181 or 182 nanovoltmeter which has an input impedance greater than 10GΩ and so should draw a negligible current – thus the contact and lead resistance of these probes has no effect on the measured voltage. The resistivity of the Si substrate material used for sputter deposition in Leeds is typically 1-10Ωcm. This is, in general, at least a factor of 103 greater than our sample resistivity, thus we expect to see no effects due to current shunting through the semiconductor substrates in our CIP samples even for very thin film samples measured at room temperature. The CIP samples that we measure should always show ohmic behavior and as both 57 I+ V+ V- I- Spring-loaded Gold contacts 2.5mm 2mm 10mm Figure 2.9: The D.C. four-point probe technique used to measure CIP resistance pseudo-non-destructively. The sample geometry for CIP sputtered samples grown at Leeds is also shown. The sample shape is formed by depositing through metal contact masks as described in section 2.2.4 and the shape produces a uniform current distribution in the region of the voltage probes. the current through, and voltage drop across, the sample are known, the resistance calculated is representative of the true sample resistance to a high degree of accuracy. In order to eliminate any spurious signal due to electrothermal EMFs caused by temperature gradients along the leads to samples mounted in cryostats, we reverse the current and take the average of the voltages measured with forward and reversed currents. Any electrothermal EMF vanishes thus Vmeasured = 1 2



1 VI+ + Vthermal − VI− + Vthermal = VI+ − VI− 2 All wires used for sample leads in cryogenic applications are made of similar materials in order to minimise any electrothermal EMFs that are generated. Cables are generally made as short as possible and wired as ‘twisted pairs’, and voltage measurements are typically performed over a timescale of 2-3 seconds in order to minimise and average out any electrical signal picked up from the A.C. mains and/or R.F. interference. 58 2.4.2 The effect of the sense current A further critical factor when making any current-biased transport measurement is the choice of exactly what magnitude of sense current to apply to the sample. For the CIP measurements presented in this thesis the sense current applied to the samples is typically ∼1mA. There are, of course, numerous factors affecting this choice; - The current should be sufficiently small so as not to cause any harm to the sample. Metallic CIP samples are fairly robust so this is not particularly an issue here, but this will be mentioned further with reference to tunnel junction structures in section 2.5. - The current applied to the sample should produce a sufficiently large voltage drop across the sample that it may be detected and measured above the noise level of the apparatus. A current of 1mA applied to a sample with a resistance of 2Ω results in a voltage drop of 2mV which is easily, and accurately, measurable. - Further to this the sense current should be chosen so as to be measurable with the digital voltmeter on as sensitive a range setting as possible. It is also desirable that the sample is measured on the same range setting in both low and high resistance states so that all resistance measurements are accurate to the same number of significant figures. In certain cases changing the voltage range setting may also affect baseline offset subtractions. - In order to maintain the sample temperature at a constant value throughout the measurement it is sensible to choose a sense current such that the Joule heating power, P = I 2 R, is not too large. This is necessary both at low temperatures where excessive heating may cause thermal instability and additional boil-off of cryogens, and at higher temperatures where the sample resistance is more strongly temperature dependent. Here in the case of a 1mA current applied to a 2Ω sample we have a Joule heating power of 2µW. Such a low level of power is unlikely to cause any excessive heating of the sample. - When making measurements on magnetic materials it is important to ensure that the magnetic state of the sample is not affected by the current flowing 59 through it. Obviously any current flow produces a magnetic field, and it is important to ensure that the field produced in the sample by the sense current is far lower than the coercive field of the magnetic layers involved. This problem mainly occurs in sub-micron scale structures used for device applications[14] and should not cause significant problems in our samples. Use of the experimental techniques described in this section and a modicum of care, we find it quite possible to measure D.C. resistances where the noise is at roughly the 0.001% level. 2.4.3 Resistivity, sheet resistance and magnetoresistance Electrical resistivity Electrical resistivity is the most fundamental measure of the transport properties of a given material. The resistance (R) is related to the sample dimensions and geometry in addition to the resistivity (ρ) by the relationship ρ = c.f. × A R l where A is the cross-sectional area of the sample with respect to the current flow, l is sample length and c.f. is a correction factor related to the shape of the sample. The sample geometry used in sputtered CIP samples at Leeds - as shown in figure 2.9 - has a cross-sectional area 2.0t×10−7 mm2 , where t is the total thickness of the film, measured in Angstrom units. The two voltage probes are separated by 2.5mm. As the sample width is far less than its length, the current flow is roughly uniform in the region of the voltage probes and, as is shown below, the geometrical correction factor is, to a good approximation, unity. The resistivity of the sample may now be obtained from the measured resistance as ρ= 2.0 t R = 0.8 t R 2.5 which may also be written (in more common units) as ρ = 0.008 t R µΩcm where t is measured in Angstroms and R measured in Ohms. 60 Sheet resistance Sheet resistance, R, is the resistance measured by the four-point probe technique, the measured sheet resistance being related to the ‘true’ sample resistance by R = c.f. × Vmeasured I where c.f. is again the geometrical correction factor. The sheet resistance is defined as the quotient of resistivity with sample thickness (or alternatively of the true sample resistance with ‘number of squares’, N = L/W ) R = ρ R = t N and is often used in relation to thin-films as it allows a simple and direct comparison to be drawn between samples with different shape and thickness. It is usually quoted in the somewhat bizarre units of Ω/ although some authors simply use Ω to further confuse matters. Geometrical correction factors The geometrical correction factor for deriving sample resistivity from the measured resistance are extensively tabulated in the literature. The correction factor takes into account the homogeneity of the current distribution through the sample in the region of the voltage probes, and the relation between the actual current flowing through that region of the sample to the current entering the sample. For a rectangular sample of length a, width d and voltage probe spacing s measured in the in-line four-point probe geometry, the correction factor may obtained from table 2.2 which is taken from reference [132]. We see that for a long, thin sample the geometrical factor approaches unity. Magnetoresistance The magnetoresistance values reported in this thesis are defined in one of three ways; - The difference in resistance from the saturated resistance, normalised to the saturated resistance (or resistance at the maximum applied magnetic field) R − RS ∆R = RS RS 61 d/s 1.0 1.25 1.5 1.75 2.0 2.5 3.0 4.0 5.0 7.5 10.0 15.0 20.0 40.0 ∞ a/d = 2 – – 1.4788 1.7196 1.9475 2.3532 2.7000 3.2246 3.5749 4.0361 4.2357 4.3947 4.4553 4.5129 4.5325 a/d = 3 0.998 1.2467 1.4893 1.7238 1.9475 2.3541 2.7005 3.2248 3.5750 4.0362 4.2357 4.3947 4.4553 4.5129 4.5325 a/d ≥ 4 0.9994 1.2248 1.4893 1.7238 1.9475 2.3541 2.7005 3.2248 3.5750 4.0362 4.2357 4.3947 4.4553 4.5129 4.5324 Table 2.2: Geometrical correction factors for a rectangular thin film sample. which is now the generally accepted definition for GMR (TMR) measurements, - The difference in saturated resistance as a function of angle, normalised to the zero-field resistance RS (θ) − RS (0) ∆RS (θ) = R0 R0 which is often used to describe the AMR effect, or - The difference in resistance from the zero-field resistance, normalised to the zero-field resistance R − R0 ∆R = R0 R0 which is the usual way of expressing the normal magnetoresistance and has been used in the literature to describe the GMR. This description is now no longer frequently used due to the fact that the zero-field resistance is dependent upon the magnetic history of the sample and as such is not generally reproducible. The first definition - that of the GMR - will be that used unless otherwise stated; however in certain cases analysis of the experimental results is somewhat clearer if an alternative definition of the MR is used. 62 It is exactly equivalent to define the magnetoresistance in terms of the resistivity of the sample rather than its (sheet) resistance, by replacing R with ρ: all geometrical factors simply cancel. In the case of experimental results however, this has the effect of introducing additional uncertainty into the resulting MR value as uncertainty in the measured thickness of the sample is included in the calculation. As this is generally more than an order of magnitude greater than the uncertainty in the resistance it makes no sense to calculate the magnetoresistance from the resistivity. All MR values reported in this thesis are derived from the four-point resistance rather than resistivity. 2.5 Transport measurements on junction structures Characterisation of the transport properties of our tunnel junction structures is somewhat more complicated than for CIP multilayer samples. The thin aluminium oxide tunnel barriers employed in these samples are extremely sensitive to electrostatic shock. Application of a sufficiently large voltage across the tunnel barrier may excite electromigration of oxygen and aluminium atomic species, creating metallic shortcircuits across the barrier. It is thus of utmost importance to ensure that the measurement apparatus is well grounded and that the samples are not subjected to voltage spikes or too large a bias voltage. It is imperative that electrostatic discharge equipment such as anti-static work surfaces and grounded wrist-straps be employed when handling tunnel junction samples. Characterisation of these samples may be performed at room temperature, at 77K by immersion in liquid nitrogen, or at 4.2K in our immersion cryostat. 2.5.1 D.C. measurements In general the initial measurement performed on tunnel junction samples is a currentvoltage (I-V) characterisation. I-V characterisation allows us to ascertain whether or not the junction behaves in an Ohmic fashion, a non-ohmic I-V characteristic constituting one of the Rowell criteria[133] for electron tunnelling. The I-V spectrum is measured by applying a bias voltage across the junction and measuring the current that flows. The bias voltage is supplied by the DAC output of a Stanford Research Systems SR830 lock-in amplifier and the bias across the sample 63 is measured using a Keithley 182 nanovoltmeter. The current is determined from the voltage measured across a standard resistor connected in series with the sample, using a Keithley 195 digital voltmeter. The only point in the measurement circuit which is connected to ground is the bias-low DAC output of the lock-in amplifier, all other parts of the circuit are floating in order to minimise the effect of ground-loops. The bias is applied such that the lower electrode of the junction is held at ground potential and the upper electrode biased relative to it. A diagram of the measurement apparatus is shown in figure 2.10. The magnitude of the standard resistor should be chosen to produce a sufficient signal to noise for a good measurement of the current, whilst at the same time keeping the circuit resistance far lower than the junction resistance. This is necessary in this case so as not to artificially limit the bias that may be applied to the sample. Choosing the correct standard resistor for the sample being measured allows measurement of the current, typically to better than 1 part in 105 . An approximation to the zero-bias resistance of the junction may be obtained by fitting a straight line through the data points close to V=0. The reason for applying a voltage to the sample as opposed to the current applied in CIP measurements is that the voltage across the junction is the critical factor in exciting dielectric breakdown of the barrier. If we were to drive a current directly, with no prior knowledge of the junction resistance, it could potentially create a sufficiently large voltage to damage the sample. 2.5.2 A.C. measurements Direct measurement of the conductance as a function of bias plays an important role in many techniques for the characterisation of both magnetic and non-magnetic tunnel junction structures, as well as point-contact junctions. The G-V spectrum may be generated by numerically differentiating the I-V data discussed above. However this method generally results in a worse signal to noise ratio and less sensitivity to localised features in the G-V curve. The so-called ‘zero-bias’ features in MTJ structures and conductance peaks due to the BCS DOS gap in superconductor junctions are not picked out as clearly in I-V data as in directly measured G-V data. A direct 64 V Standard resistor V Figure 2.10: The circuit for measuring I-V curves for tunnel junction samples. measurement of the dynamic conductance or resistance of tunnel junction samples can be performed using an A.C. lock-in technique. It is usually preferable – especially in the case of superconductor junctions – to measure the conductance as opposed to resistance, due to the fact that a value of zero conductance is more easily measurable directly than an infinite value of resistance! In order to measure the dynamic conductance, a small voltage modulation is superimposed upon the D.C. bias, thus the voltage applied to the sample at time t may be written V (t) = V0 + δV cos(ωt) It may be seen by employing a simple Taylor expansion that such a voltage will give rise to a tunnel current given by ∂I δV cos (ωt) + ∂V ∂I δV cos (ωt) + = I0 + ∂V I(t) = I0 +
∂2I δV 2 cos2 (ωt) + O δV 3 2 ∂V
1 ∂2I 2 3 δV cos (2ωt) + O δV 2 ∂V 2 Thus measuring the amplitude of the current at frequency ω gives a direct measure of the dynamic conductance harmonic, then gives troscopy (IETS). ∂2I ∂V 2 ∂I ∂V . Measurement at frequency 2ω, i.e. the second also, which is known as inelastic electron tunnelling spec- 65 1.8 Rs = 1Ω Rs = 10Ω Rs = 500Ω Rs = 2000Ω Normalised conductance 1.6 1.4 1.2 1.0 0.8 -0.2 -0.1 0 0.1 0.2 Bias (V) Figure 2.11: The effect of changing the value of the standard resistor upon the measured dynamic conductance. The resistance of the junction is 5720Ω and the values for the standard resistor are shown in the legend. Our initial experimental arrangement for A.C. characterisation consisted of an A.C. modulation voltage supplied by the oscillator output of the lock-in amplifier and fed into a summing amplifier[134] to be added to the D.C. bias. The conductance (or ∂G ) ∂V was measured by feeding the A.C. voltage across the standard resistor back into the lock-in amplifier. Other than this, the circuit was identical to that used for I-V characterisation. This method works well for very resistive junctions – if the sum of the lead resistance and standard current sense resistance is negligible in comparison to the junction resistance then the entire A.C. modulation voltage is, in effect, dropped across the sample. Thus the amplitude of the modulation across the sample is also held roughly constant and the conductance may be determined accurately. If, however, the constant voltage condition above is not satisfied, the portion of the modulation voltage dropped across the sample will vary with bias and the signal measured across the standard resistor is no longer a true representation of the sample conductance. Figure 2.11 shows dynamic conductance measured with a variety of current-sense resistors. It can be seen that as the standard resistance increases, the constant-voltage condition is no longer satisfied and the measured conductance deviates significantly from the true conductance. In order to maintain the amplitude of the modulation across the sample at a 66 constant value, a feedback circuit of some description must generally be utilised. The technique which we have chosen to employ is based upon that proposed by Hebard and Schumate[135] in 1974. In this arrangement, as shown in figure 2.12, a second lock-in amplifier is used to measure the amplitude of the modulation across the sample, connected in parallel with the DVM which measures the D.C. bias. The output of this lock-in amplifier is then subtracted from a D.C. signal corresponding to the required modulation amplitude, the combination of the two being amplified further. This signal is then fed into a multiplier along with the A.C. reference in order to provide an A.C. signal with the necessary amplitude to provide the correct modulation amplitude across the sample. The A.C. modulation is finally summed with the D.C. bias as before. The conductance is again measured as the amplitude of the A.C. voltage measured across a standard resistor in series with the sample – as the modulation across the sample is maintained at a constant value, the voltage measured across the standard resistor is always a true representation of the dynamic junction conductance. It is worth noting that only the A.C. modulation across the sample is subject to feedback. In other experimental arrangements, e.g. that proposed by Moody et. al.[136], both A.C. and D.C. signals are modified by the feedback circuitry, which may induce additional noise in the measured conductance. Often in the past a variety of bridge circuits have been used to measure dynamic conductance and ∂G , ∂V as the relative amplitudes of the first and second harmonic signals that are output from the bridge circuit vary as the bridge is set further from balance[105]. For a balanced conductance bridge, the ∂I ∂V signal is entirely suppressed, allowing simplification of the filter networks required to isolate the ∂G ∂V signal. A further feature of the Hebard-Schumate feedback circuit is that it may be simply integrated into a conductance bridge circuit. By simply changing the origin of the feedback signal, it is also possible to operate this circuit to measure the dynamic resistance. If the A.C. signal fed into the feedback lock-in amplifier is instead taken across the standard resistor rather than the junction, we now drive a constant amplitude A.C. current through the junction and may measure the dynamic resistance. For a current given by I (t) = I0 + δI cos (ωt) 67 Inverting sum Multiply (K) and invert KVREFA2(VOUT – VMOD)cos(
t) VB + KVREFA2(VMOD – VOUT)cos(
t) (-1) RLEAD VREFcos(
t) -VMOD -A2(VOUT – VMOD) Inverting sum with gain (-A2) Current flow -VB To computer RLEAD RLEAD DVM RJ VOUT Lock-in Amplifier (A1) RLEAD RSTANDARD V0+VJ(
)cos(
t) To computer Lock-in Amplifier VR cos(
t) Reference - 1V @ 5.725 kHz Figure 2.12: Flow diagram of the A.C. feedback method used to measure G-V characteristics of MTJ and point contact junctions. we find that the voltage signal V (t) = V0 +
∂V δI cos (ωt) + O δI 2 ∂I may be used to measure the dynamic junction resistance. Thus the Hebard-Schumate circuit employed is far more versatile than other feedback circuits. One factor which can drastically affect the signal to noise ratio of these experiments is the modulation frequency employed. It has been reported[137] that the signal to noise is improved by increasing the modulation frequency, which has been found to be the case in our measurements. The modulation frequency that has been settled upon is 5.725kHz as this is sufficiently high to give a good signal to noise whilst still allowing measurement of higher harmonics without exceeding the 102kHz/NHarm limit of the lock-in amplifier[138] for the required harmonics, or resulting in spurious signals due to lead capacitance effects. This frequency is not a harmonic of either the electric mains frequency or any nearby A.C. equipment. 68 2.5.3 Magnetoresistance measurements Magnetoresistance measurements on magnetic tunnel junction samples may be carried out in the following sets of apparatus, providing the capability of measuring at a range of temperatures: - Ambient temperature magnetoresistance in a 190 Oe air-core electromagnet, as described in references [128, 139]. - 77K magnetoresistance immersed in a liquid nitrogen dewar within an air-core solenoid which produces a magnetic field of 280 Oe. - 4.2K magnetoresistance in the 4 He immersion cryostat described previously. Magnetotransport measurements are carried out in one of two ways, either driving a constant D.C. current through the junction and measuring the voltage, as is the case for CIP samples, or by measuring the A.C. dynamic conductance directly at various bias voltages. The D.C. current-biased method is most useful for rapidly and precisely characterising the low-bias TMR properties of junctions. This method has an extremely good signal to noise ratio due to the use of a Keithley 220 current source and Keithley 181 nanovoltmeter. The lack of any other equipment reduces the length of cabling required and minimises pickup from external sources of noise, while minimising the potential for ground-loops. In this experimental arrangement the current-low output of the Keithley 220 is connected to chassis ground, this being the only point in the circuit which is directly earthed. The current is set – from prior knowledge of the I-V characteristics – to produce a voltage of just over 10mV across the sample in the low-resistance state. This allows all voltage measurements to be made without changing the voltmeter range, thus keeping the baseline offset intact. When measuring the resistance by this method the current cannot be reversed due to the non-ohmic nature of the I-V curve for a tunnel junction, which limits the applicability of this method to cases where electrothermal EMFs do not constitute a great problem. Measurement of the A.C. dynamic magnetoconductance allows the measurement of the variation of the TMR over a range of bias. This method has the added advantage of allowing direct measurement of the zero-bias magnetoconductance, which is a 69 Transducer Function generator Pickup Coils Lock-in amplifier Sample H Figure 2.13: Schematic diagram of the Oxford Instruments Maglab VSM system. The solenoid and pickup coils are contained within the helium reservoir and the sample is within a variable temperature insert. more direct probe of the electrode spin-polarisation via the Julliere formula (equation 1.4) than that at finite bias. The fact that this is an A.C. technique means that electrothermal EMFs are automatically removed, making this technique more suitable for measurement of TMR at cryogenic temperatures. 2.6 Magnetic measurements 2.6.1 Vibrating sample magnetometry Vibrating sample magnetometry (VSM)[140] has been used for magnetic characterisation of many of the samples discussed in this thesis. The system used is an Oxford Instruments Maglab VSM which allows measurements in the temperature range 1.5320K and magnetic fields of up to 9 Tesla. The principle of operation of VSM is based upon Faraday’s law, which was originally stated as ‘The law which governs the evolution of electricity by magneto-electric induction, is very simple, although rather difficult to express... When a piece of metal is passed either before a single pole, or between the opposite poles of a magnet, or near electro-magnetic poles, whether ferruginous or 70 not, electrical currents are produced across the metal transverse to the direction of motion.’ – Michael Faraday[141, 142] or, more commonly ‘When the magnetic flux through a circuit is changing, an electromotive force is induced in the circuit’[143]. The sample is mounted toward the end of a rigid carbon-fibre rod which is vibrated at a frequency of 55Hz by a transducer. A pair of pick-up coils are positioned close to the sample as shown in figure 2.13. Magnetisation of the sample - be it permanent or induced - causes a magnetic flux to pass through the coils, the quantity of which is proportional to the magnetic moment of the sample. The vibration of the sample causes the quantity of magnetic flux passing through the coils to change with time, thus inducing a time-varying voltage in the pick-up coils. By feeding this voltage into a lock-in amplifier we are able to extract the amplitude of the EMF induced at the driving frequency, which is proportional to the magnetic moment of the sample. The system is calibrated using a thin film of Ni of known dimensions and geometry similar to those of the samples to be measured. This is to ensure that the cross-section that the sample shows to the pick-up coils - and hence the magnetic flux profile - are similar for both the calibration sample and the samples to be measured; the field profile that the pick-up coils see is often referred to as the ‘filling factor’, which can affect the value measured for the magnetic moment. 2.6.2 Magneto-optical Kerr effect magnetometry Magneto-optical Kerr effect (MOKE) magnetometry[144] has been used to magnetically characterise thin transition metal samples at room temperature. The magneto-optical Kerr effect is a consequence of the spin-orbit interaction, the asymmetry between spin-up and spin-down electrons resulting in different ‘effective refractive indices’ for left-hand and right-hand circularly polarised light[145]. If the incident linearly polarised beam is thought of as a coherent superposition of both leftand right-handed circularly polarised beams, the net effect of the magnetisation in the sample will be to rotate (slightly) the plane of polarisation of the reflected beam, known as the Kerr rotation[146]. The MOKE magnetometry system at Leeds comprises a HeNe laser, a pair of 71 Figure 2.14: Plan view of the MOKE magnetometry system. polarising filters, a lens, a photodiode and an electromagnet. The system is set up on an optical bench as shown in figure 2.14. The polariser ensures that the laser beam incident at the sample is linearly polarised in the vertical direction (p-plane). A variation in the plane of polarisation of the reflected beam due to Kerr rotation is seen as a change in intensity after passing through the analyser. The Kerr rotation as a function of magnetic field is recorded as the output voltage of the photodiode, after passing through a broadband amplifier. A more detailed description of the experimental setup can be found in reference [147]. If the second polariser is set close to the extinction position, a change in the sample magnetisation produces a large change in intensity at the photodiode. In order for 72 the intensity to be roughly linear in the sample magnetisation, however, the analyser should be set away from extinction. The actual position at which the analyser is set is a compromise between these two ideals. The penetration of the laser beam into the sample is limited by the skin-depth of the metal film, typically being roughly 200˚ A at the characteristic HeNe wavelength. This limits the volume of sample which is actually measured, making the MOKE technique intrinsically insensitive to any background signal from e.g. the substrate – provided the film is of sufficient thickness. 2.7 X-ray reflectivity The x-ray system at Leeds is a Siemens two-circle diffractometer operating in the Bragg-Bretano geometry. The system uses an x-ray wavelength of 1.54˚ A, which is the characteristic wavelength of radiation originating from the Cu-Kα transition. The beam leaves the Cu target and passes through a collimating slit before reaching the sample. The diffracted beam then passes through a further collimating slit, a nickel filter and a Si bounce monochromator before the scintillation detector. The Ni filter acts to remove the majority of the Cu-Kβ portion of the diffracted beam and the monochromator to remove the bremsstrahlung background leaving just the Cu-Kα . All reflectivity spectra reported in this thesis are simple θ − 2θ scans. Here the detector is scanned through twice the angle as that of the sample, meaning that the angles that the incident and exit beams make with the sample surface remain equal at all times. From simple geometry it may be shown that Qz - the component of the scattering vector normal to the sample surface - is related to the diffraction angle and wavelength by Qz = 4π sin θ λ The scans are performed typically in the low-angle range with θ between roughly 1 and 10 degrees. This means that the scattering vector is of a comparable magnitude to the reciprocal space periodicities corresponding to the multilayer repeat unit and sample thickness. X-ray reflectivity has been used mainly for purposes of film thickness calibration 73 10 7 Intensity (arb. units) Data - 100s Ru @ 50mA DWBA simulation, 160Å 10 5 10 3 10 1 10 -1 1 2 3 4 5 2θ (degrees) Figure 2.15: X-ray reflectivity (blue curve) from a single film of ruthenium deposited on Si. The finite-size (Kiessig) fringes are due to interference between waves scattered from the air/film interface and the film/substrate interface. The film thickness may be accurately obtained by fitting the data within the DWBA (red curve). – the thickness of single thin films is measured as a means of calibrating the deposition rate for different materials. Figure 2.15 shows the reflectivity from a thin film of ruthenium. The modulation seen is due to interference between waves reflected from the top and bottom of the film and are known as Keissig fringes. This ‘finite size’ modulation has peaks in intensity at positions corresponding to constructive interference when p mλ = 2t sin2 θm − sin2 θc where t is the film thickness and θc is the critical angle for total external reflection. 2 The film thickness may be calculated from the slope of θm vs. m2 . However this leads to a large uncertainty in the film thickness if the θm are not close to θc . A more accurate method is to fit the measured reflectivity in order to obtain the film thickness. Analysis of our x-ray reflectivity data is carried out using commercial simulation software which calculates the specular reflectivity within the Distorted wave Born approximation (DWBA). 74 Reflectivity scans from multilayer samples are also used in order to verify the bilayer repeat distance of the multilayer stack[148]. The Bragg equation, nλ = 2d sin θ is used to calculate the multilayer repeat periodicity, where n is the order of the peak, λ is the x-ray wavelength and d is the real-space multilayer repeat distance. At the position where the Bragg condition is satisfied, i.e. n takes an integer value, constructive interference between waves reflected from each structural repeat takes place. 2.8 Summary In summary, we have described in this chapter the range of experimental procedures which are used for the preparation and characterisation - both electrical, magnetic and structural - of the samples discussed in this thesis. 75 Chapter 3 Probing the RKKY interaction in rare-earth metals with spin-dependent transport 3.1 Introduction In the field of magnetic multilayer research, the Ruderman-Kittel-Kasuya-Yosida (RKKY)[149, 150, 151] mechanism has become synonymous with the oscillatory indirect interlayer exchange coupling. This is the mechanism by which antiferromagnetic alignment of the magnetisation of adjacent magnetic layers within a multilayer stack may be acheived[5, 152]. A review on interlayer exchange coupling is given in [153]. However, as none of the magnetic multilayer samples discussed in this chapter make use of interlayer magnetic coupling this topic shall not be discussed further. Instead, we focus our attention on the theoretical explanation of the coupling interaction between ionic 4f magnetic moments in the rare-earth metals. Despite the huge volume of work that has been reported in the literature on this subject, the exact nature of the RKKY mechanism has never in fact been experimentally verified in a pure rare-earth metal system. All experimental work published to date concerns the coupling between local atomic moments, without concerning itself with the details of the effect on the conduction electrons which are thought to mediate the RKKY interaction. Despite this fact, the origin of magnetic order in the lanthanide metals via the RKKY indirect exchange interaction is now well accepted in the scientific community. Many previous investigations on the RKKY interaction have focussed on obtaining 76 the values of exchange integrals at - and coupling strengths between - various nuclear sites in magnetic alloy systems[154, 155, 156, 157] and metals[158]. Others have used photon correllation[159] and M¨ossbauer spectroscopy[160] to obtain the local field acting at the nuclear sites. More recently polarised neutron reflectrometry (PNR) has been used to observe twisted magnetic structures in thin Gd/Fe bilayer films[161]. In this chapter we present a study on magnetic multilayer samples where some or all of the magnetic layers are rare-earth metals. The RKKY picture of magnetic ordering in the rare-earths predicts an oscillatory spin-polarisation of the conduction-band at the Fermi level due to a spin-density wave caused by exchange coupling to a magnetic ion. The damped oscillatory nature of the spin-density wave results in a net spin-polarisation at the Fermi level[162]. GMR measurements on magnetic multilayer structures are sensitive to the transport spinpolarisation of the conduction-band at the Fermi level in the magnetic layers. It is possible also to determine the sign of the polarisation with respect to a magnetic reference layer[163, 164]. We begin this chapter by describing the RKKY picture of magnetic ordering in the rare-earths and its inherent limitations, before briefly discussing electronic structure calculations. We then show experimental evidence for the spin-polarisation of the conduction-band in the rare-earths and show how this result ties in with the RKKY picture of magnetic ordering. These results constitute the first direct experimental evidence for the spin-polarisation of the conduction-band due to the RKKY mechanism in pure rare-earth metals. 3.2 The RKKY coupling interaction in the rareearths The RKKY indirect exchange interaction was initially formulated as an explanation of the enhanced linewidths in nuclear magnetic resonance (NMR) studies of metallic silver, amongst other materials. The enhanced NMR linewidth is indicative of an increased coupling strength between nuclear moments over the expected magnetic dipolar coupling. Initial models due to Fr¨ohlich and Nabarro[165] and Zener[166] proposed a first order energy perturbation due to a single nuclear moment which causes 77 a uniform spin-polarisation of the free-electron gas in which they are embedded. Further nuclear moments then couple to this uniform spin-polarisation, resulting in an indirect exchange coupling. Ruderman and Kittel[149] proposed an indirect exchange interaction between nuclear spins mediated by the conduction electrons by a second order perturbation due to the introduction of a pair of nuclear moments into a free-electron gas. They derived an expression for the coupling between the two spins and show that an oscillatory spin-density wave is set up in the electron gas due to the perturbation applied to the conduction electron wavefunctions by introducing the first nuclear moment. In their model, the second nuclear moment couples to the spin-density wave and may align its moment either parallel or antiparallel to the first moment, depending on their relative separation. Kasuya was the first to point out the importance of the exchange interaction between localised moments and conduction electrons in the rare-earths[150]. He derived the effective exchange Hamiltonian between ions with L = 0, suitable for the case of e.g. Gd or transition metal ions, within a generalised Zener model and showed that both ferromagnetic and antiferromagnetic ground states could exist, noting also the similarity between this calculation and that of Ruderman and Kittel. Yosida[151] showed that the indirect exchange due to a second order perturbation to the wavefunctions, as introduced by Ruderman and Kittel, modifies the first order energy perturbation of Zener, Fr¨ohlich and Nabarro. The Ruderman-Kittel picture of an oscillatory polarisation of the electron gas is shown to actually include the uniform Fr¨ohlich-Nabarro/Zener polarisation as a limiting case, assuming the local moment-conduction electron exchange interaction to be short ranged. 3.2.1 The RKKY indirect exchange integral An extremely good review on the topic of electronic band-structure, the indirect exchange interaction and magnetic ordering in the rare-earths is given in [167]. Most of the theoretical work pertinent to discussion of the RKKY interaction is written in the language of second-quantisation. However, below we present a simplified account of the RKKY formalism. 78 0.04 0.03 P(r) 0.02 0.01 0 -0.01 0 5 10 15 kFr Figure 3.1: The RKKY range function, showing the oscillatory polarisation induced by an impurity spin as a function of distance from the impurity. The function diverges at r = 0 due to the delta-function form of the exchange integral. The RKKY model makes the following explicit assumptions in its derivation: - The perturbation to the electron gas is assumed due only to the first embedded magnetic impurity – further magnetic impurities act only as ‘test spins’ and have no further perturbing effect on the electron gas. - The susceptibility function of the electron gas - which describes its response to the magnetic perturbation - is taken to be that of the free-electron gas. - The perturbing potential is assumed to have delta function form – i.e. the interaction between the embedded moment and the electron gas is zero ranged, acting only at the site of the impurity atom. Within the RKKY model the real-space form of the historically named s-f exchange integral, a delta function potential located at the lattice site Ri , may be written A (r − Ri ) = A0 δ (r − Ri ) which yields the Hamiltonian pertaining to the RKKY exchange interaction[149] Hs−f = −A (r − Ri ) s · Si (3.1) 79 between the localised ionic spin Si and a conduction electron spin s. To first-order perturbation, assuming T = 0K, the polarisation arising due to a magnetic impurity located at Ri = 0 may be written as Z 9πZ 2 P (r) = φ (2kF · |r − r0 |) A (r0 ) dr0 2 2Ω EF (3.2) where Z is the atomic valency and Ω the atomic volume. The function φ (x) = sin x − x cos x x4 is the diminishing oscillatory ‘range function’ originally derived by Ruderman and Kittel and shown in figure 3.1, which falls off as approximately cos (kF · r) / (kF · r)3 at large distances. The RKKY oscillatory spin-density may be considered analogous to the Friedel charge-density oscillation which may be induced due to the electrostatic screening of a charged impurity in a metal[168]. In both cases the oscillation is due to the finite electron wavevector cutoff at the Fermi surface, which truncates the number of Fourier components contributing to the real-space charge- or spin-density at k = kF . The RKKY polarisation function is, in effect, derived from the susceptibility of the conduction electron gas. It is related to the Fourier transform of the susceptibility by P (r) = X A (q) χ (q) eiq·r q so we may write, using the reciprocal-space form of the RKKY exchange integral A (q) = A0 , the Fourier transform of the reciprocal-space susceptibility function of the free-electron gas as X q χ (q) eiq·r = 9πZ 2 φ (2kF · r) 2Ω2 EF This of course results in an identical polarisation function to that given by equation 3.2. We now consider the effect of adding a further magnetic impurity to the system. If a second localised moment is placed at a position Rj , the spin on this site Sj is assumed to couple to the spin-density wave produced by the initial impurity spin at 80 Ri , again by the s-f interaction. This gives the effective exchange interaction between the pair of localised moments in second order perturbation theory as Hi−j = −J (Ri − Rj ) Si · Sj where the general form of the effective exchange parameter is given by J (Ri − Rj ) = X A2 (q) χ (q) eiq·(Ri −Rj ) q Substituting the reciprocal space form of the RKKY exchange integral A (q) = A0 and the free-electron susceptibility function gives the expression Hi−j = − 9πZ 2 A20 (Si · Sj ) φ (2kF · |Ri − Rj |) 2Ω2 EF (3.3) which is the result originally derived by Ruderman and Kittel. 3.2.2 Limitations of the RKKY model Despite the insight of Kasuya, the application of the simple form of the RKKY interaction to the rare-earth metals is fraught with difficulties. The Fermi surfaces of the rare-earths are extremely complicated in comparison to the spherical Fermi surface assumed in the RKKY model. Most of the Lanthanides have conduction-bands comprised of two 5d electrons and a single 6s electron, making the application of the free-electron approximation somewhat dubious. Extension of the RKKY model by the evaluation of the range function for several slightly more complex Fermi surface geometries has been made by Roth et. al.[169]. A zero-ranged interaction potential is not expected to be a good approximation to the s-f exchange integral[170]. In the rare-earths the ionic ground-state generally has complicated symmetry – only in the case of Gd is the ground-state spherically symmetric. In all other cases the s-f coupling will have dependence not only upon distance, but also upon the relative orientation of the initial and final electronic momentum states. Yosida applied the Ruderman-Kittel model to the case of CuMn alloys[151], concluding that quantitative predictions rely heavily on the actual q dependence of the A (q). 81 The RKKY model effectively describes the magnetically ordered states of the rareearths in terms of a single localised moment setting up a spin-density wave in the conduction-band. Other ions then couple to this spin-density wave whilst causing no further perturbation to the local spin-density. De Gennes has attempted to model the N body RKKY interaction as a sum of N one-body RKKY interactions[171]. He calculated the spin-density at a given lattice site in terms of a summation of the polarisations due to magnetic ions located on the surrounding lattice sites. He derived an expression for the Weiss molecular field and hence TC in the mean-field approximation by this method. This expression - along with all other interionic exchange parameters - is related to the factor (gJ − 1)2 . As shall be discussed in section 3.9.1, this implies that any investigation into the coupling interaction between ionic moments can give no detail on the sign of the conduction-band spin-polarisation. 3.2.3 Electronic structure calculations on the rare-earths Until fairly recently, calculations on realistic systems were forced to employ conduction electron wavefunctions and energy band structures appropriate only to the paramagnetic phase. It has been shown that the paramagnetic DOS of the rare-earth metals does not vary by a great deal across the series[172]. Spin-polarised augmented plane-wave calculations on gadolinium have been performed by Harmon and Freeman[173], who determined the spin-resolved DOS of ferromagnetic Gd applying a rigid exchange splitting of the paramagnetic DOS. The shift was determined so as to obtain a good agreement between the calculated conductionband magnetic moment and the experimental value. The result of their calculation is shown in figure 3.2. This calculation shows a distinct spin-polarisation at the Fermi energy in the majority spin band. More recent calculations model the rare-earths - and the rare-earth/transition metal intermetallic compounds - using density functional theory within the local spindensity approximation[174, 175]. The band structure and DOS may be calculated by assuming the 4f electrons to be described by localised core wavefunctions and taking the number of 4f electrons and ionic magnetic moment consistent with Hunds rules. 82 Figure 3.2: Spin-resolved density of states for Gd as calculated by Harmon and Freeman[173]. The majority spin DOS is shown on the left and minority spin on the right. A small, but distinct, spin-polarisation in the majority spin at the Fermi level is apparent. The 4f -conduction electron exchange integrals are then determined self-consistently, and the conduction-band magnetic moment calculated again assuming a rigid shift of the paramagnetic DOS. Recent calculations, from the 1970s onwards, have concentrated purely on obtaining the band-structure, Fermi surface or density of states of the rare-earth metals. They make no attempt to calculate the form of the RKKY spin-density wave due to either one or many local magnetic moments. Despite the complications of applying the RKKY model to the rare-earth metals, it has long been accepted that this is the pertinent magnetic ordering interaction in the case of these materials. If the RKKY mechanism does mediate the magnetic order in the rare-earths, it should manifest itself - in the magnetically ordered phases - as a net spin-polarisation of the conduction-band at the Fermi level due to the anticipated damped oscillatory spin-density wave. As was mentioned earlier, GMR 83 measurements on magnetic multilayer samples allow us to probe the sign of the spindependent scattering in the magnetic layers, and hence determine the sign of the spin-polarisation at the Fermi level of the rare-earth in comparison to some reference material. 3.3 Experimental The multilayer samples reported in this chapter have been deposited by D.C. magnetron sputtering as discussed in chapter 2. Magnetotransport measurements are performed in the current-in-plane (CIP) geometry and are carried out by a standard four-probe D.C. technique in our 4 He gas-flow cryostat. Magnetisation measurements are made by VSM. All magnetic and transport measurements presented here were performed after cooling the sample in the absence of an applied field. Due to this preparation we expect the magnetic rare-earth layers to be initially in a randomdomain state at all temperatures below the corresponding TC (or TN ). Measurements made on samples that have been field cooled-produce identical results to those taken after zero-field-cooling. 3.4 Results The results presented below may be split into two sections; we firstly present a study on series of samples where all of the magnetic layers in the multilayer are a rare-earth metal and then show a similar investigation for samples where alternate rare-earth layers have been exchanged for cobalt. We show that we are able to rule out other possible MR mechanisms, with the exception of the GMR, and obtain information on the sign of the spin-polarisation in the rare-earths. 3.5 Magnetotransport in rare-earth magnetic multilayers Recent studies on rare-earth magnetic heterostructures carried out by the group in Leeds[128, 176, 177] have been concerned with the direct interlayer exchange coupling 84 between Dy and Co layers, and the effect on the GMR in Co spin-valve systems of hybridisation of Co and Dy densities of states across an interface. Simple analysis of these results may be hampered by the fact that Dy and Co form a series of stoichiometric compounds over a wide range of compositions[178]. Sputter deposition of rare-earth/transition metal bilayer systems, e.g. Gd/Cox Ni1−x multilayers, have shown deposition-order dependent interdiffusion[179] which further complicates matters. These studies have implicitly assumed the scattering to be dominated by the contribution from the cobalt layers, the rare-earths having little effect. Removal of the RE/Co interface from the structure allows the magnetotransport properties of the rare-earth layer alone to be unambiguously observed. 3.5.1 Dysprosium The system initially studied in this investigation was a series of magnetic multilayers with dysprosium magnetic layers, having a multilayer structure {Dy[20˚ A]/Cu[20˚ A]}N with Ta or Cu buffer and capping layers. The number of structural repeat units was initially made fairly large (N ≥ 60) in order to obtain as large a ‘GMR’ signal as possible[129]. Any magnetoresistance in such structures is expected to be extremely small. Dieny et. al. have reported GMR of ‘significantly less than 1%’ [14] in Gd/Ag/Py and Nd/Ag/Py spin-valve structures at 77K. This report led to the popular misconception that GMR cannot be seen from rare-earth metals. Measurement of the typical magnetotransport response of a Dy[20˚ A]/Cu[20˚ A]60 multilayer in the transverse orientation is shown in figure 3.3, along with the corresponding magnetisation loop. Concentrating firstly on the MR curve there are several distinct features: - Firstly it is clear that there is a magnetoresistance of some form or other present in this sample – the measured MR of -0.67% is far above the background noise level and is completely reproducible. Identical samples produced in separate vacuum cycles give the same MR to within experimental uncertainty. - Secondly it appears from the transport measurement that the sample does not reach complete magnetic saturation in the 4T magnetic field applied. 85 4.75 MR=0.67% Resistance (Ω ) 4.74 4.73 4.72 4.71 4.70 -4 -2 0 2 4 -4 -2 0 2 4 5.0 m (memu) 2.5 0 -2.5 -5.0 B (T) Figure 3.3: Magnetoresistance and magnetisation of a Dy[20˚ A]/Cu[20˚ A]60 multilayer in the transverse field orientation at 8.2K. - Finally, there is a distinct hysteresis observable in the magnetoresistance, typical of e.g. GMR multilayer samples without strong antiferromagnetic coupling. Analysis of the magnetisation loop shows that in fact we are close to reaching magnetic saturation in a 4T magnetic field, in apparent disagreement with the transport data. Although the loop appears at first glance to resemble a Langevin function indicative of paramagnetism as opposed to ferromagnetism - there is a non-vanishing hysteresis close to the origin. The solid line shown with the magnetisation curve in figure 3.3 is a Langevin function fitted to the data. The fit is not at all convincing. 86 The value of the magnetisation obtained from these curves is (3.0±0.1)×103 emu/cm3 , which is in very good agreement with that expected for bulk Dy[180]. Another interesting feature of the magnetisation loop is the reduced hysteresis in comparison with the transport measurements. Unfortunately, it is impossible to reconcile this difference as being simply due to the way in which magnetisation and transport measurements probe the magnetic state of the sample. Magnetisation measurements are generally performed in a geometry with a 1-D magnetic field and are sensitive only to the component of the magnetisation which is in the magnetic field direction. Transport measurements, on the other hand, are sensitive to scattering from the whole domain structure, not purely the component in the applied field direction. Unfortunately, this cannot explain the difference which we observe between transport and magnetisation data. Due to the large difference between the position of the peaks in the MR data and the coercive field from the magnetisation, one clearly cannot associate the magnetoresistance peaks with the coercive field of the magnetic layers as is the case in most GMR multilayers. This is, however, not completely surprising and does not rule out the GMR as the magnetoresistance mechanism. Other systems in which a GMR is observed with peaks uncorrelated to features in the measured magnetisation are films where the surface anisotropy term has been modified in some regions by adding a partial monolayer coverage of non-magnetic metal. In these systems, peaks in the magnetoresistance are predicted within a simple Stoner-Wohlfarth model which yields featureless magnetisation curves. A model consisting of two uncoupled magnetic domains with different anisotropies due to changes in the surface and/or volume anisotropy terms is used to fit the magnetisation data and calculate the GMR. The effective anisotropy K1 in each domain is given by the expression 1 KSurf K1 = KVol − µ0 MS2 + 2 t where KVol and KSurf are, respectively, the volume and surface anisotropy constants, MS is the saturation magnetisation and t is the film thickness. Figure 3.4 shows MR and magnetisation for a Co/Cu/Co trilayer film with and without a partial monolayer coverage of Au doped onto one of the Co layers[181]. 87 0.6 1.0 MR (%) 0.4 0.8 0.6 0.2 M/M s 0 -2 -1 0 1 2 -2 -1 0 1 2 0.6 0.4 MR (%) 0.4 0.2 0.2 With Au doping Without Au doping 0 0 0 0.5 1.0 1.5 B (T) B (T) Figure 3.4: Magnetisation and magnetoresistance for an MBE-grown Co/Cu/Co trilayer with and without Au doping on one of the Co layers, courtesy of [181]. The magnetic field is applied perpendicular to the film plane. The solid lines are fits to the magnetisation data and the calculated MR using the anisotropies extracted from this fit. The peak position moves as the anisotropy is changed and no features corresponding to these peaks are observed in the magnetisation data. The prominence of the peaks in the MR is enhanced as the GMR is so small – in e.g. a Co/Cu multilayer the GMR from adjacent antiparallel layers overwhelms the effect due to variations in the anisotropy. The peaks in that case are clearly associated with the coercivity of the layers as the antiparallel alignment contributes the dominant share of the MR. In our RE/Cu system, the MR is of a comparable magnitude to that observed from the GMR in a single Co film, in part because of the lack of good antiparallel alignment between the regions contributing to the MR and partly because of the poorer band-matching between Cu and the rare-earths in comparison to e.g. Cu and Co or Cr and Fe. In the case of RE/Cu multilayers, the peaks due to variations in the local anisotropy become apparent. We thus interpret the peaks in our MR data as arising due to variations in the 88 local anisotropy in different magnetic domains in the Dy layers. This may be brought about, for example, by the interface with the Cu spacer layer or local fluctuations in the film thickness modifying the surface or volume anisotropy terms. Alternatively, a random magnetocrystalline anisotropy may be present. The ‘GMR’ may then be brought about by spin-dependent scattering from domains within the Dy layers where the local magnetisations are non-collinear due to variations in the local magnetocrystalline anisotropy. This explains in part the small magnitude of the MR we observe. Large magnetoresistance has been reported in several Dy-containing systems previously. M¨ uller et. al. have reported negative MR of up to 25% in melt-spun DyCu alloy ribbons[182]. In this case the MR is attributed to a metamagnetic transition, and the magnitude related to the formation of the cubic CuAu structure DyCu5 compound[183]. Attempts to promote the formation of this compound by annealing our multilayer samples have proven unsuccessful. A sizeable magnetoresistance of ∼40% has been reported in epitaxial Dy/Sc superlattices[184]. The MR in this system is positive and is attributed to electron-channelling in the scandium layers. Attempts to reproduce these results elsewhere have also proven unsuccessful. 3.5.2 Gadolinium In order to show that the effect that we see in our Dy/Cu multilayer samples is not purely a consequence of layer composition we have replaced the magnetic dysprosium layers with gadolinium. This also allows us to compare our results with electronic structure calculations etc. as the Gd ion is more accessible to theorists. Typical MR and magnetisation curves for a Gd[20˚ A]/Cu[20˚ A] multilayer at 8.2K are shown in figure 3.5. We again see a negative MR of order 1%, and note that the position of the peaks is much reduced to roughly 500 Oe for these samples, as is shown in the inset of figure 3.5. This is due to the reduction in the strength of the anisotropy as the ground state of the Gd3+ ion has no orbital angular momentum component, hence the enhancement to the coercivity found in the other rare-earths due to the coupling between the orbital angular momentum of the ion and the crystal field is not present. The spherical symmetry of the Gd ionic ground state is one reason why Gd is more 89 1.0 10.98 R (Ω ) 0.8 10.97 10.96 0.6 MR (%) -4000 -2000 0 2000 4000 H (Oe) 0.4 0.2 0 -4 -2 -4 -2 0 2 4 0 2 4 0.004 m (emu) 0.002 0 -0.002 -0.004 µ H (T) 0 Figure 3.5: Magnetoresistance and magnetisation of a Gd[20]/Cu[20]40 multilayer in the transverse field orientation at 8.2K. The inset shows the peaks close to zero field in more detail. Note the change of units in the inset. accessible to theory than are the other rare-earth metals. The magnetisation loop this time shows a clear ferromagnetic component with a small coercivity. The measured coercivity, on the other hand, does still not agree well with the position of the peaks in the transport data. The saturation magnetisation is again in good agreement with that expected for bulk Gd. We observe a quasi-linear decrease in the sample resistance with increasing magnetic field up to the 4T field available to us. From the magnetisation data it is apparent that the sample should be magnetically saturated at this point. This effect could naively be ascribed to the Lorentz MR. However as was discussed in section 90 Resistance (Ω ) 22.69 22.67 22.65 22.63 -4 -2 0 2 4 0.00030 m (emu) 0.00015 5.0x10 -5 2.5x10 -5 -2.5x10 -5 m (emu) 0 -0.00015 0 -5 -5.0x10 -0.10 -0.05 0 0.05 0.10 B (T) -0.00030 -4 -2 0 2 4 B (T) Figure 3.6: Magnetoresistance and magnetisation for a Nd/Cu multilayer at 8.2K. The solid red line is a Langevin function fit through the magnetisation data. 1.3, the Lorentz MR in a pure sodium wire has been measured to be -0.05% in a 1T field[69] which is far smaller than that observed here. 3.5.3 Neodymium In the bulk, Nd has a complex antiferromagnetic structure with a N´eel temperature of roughly 20K[185]. It has recently been reported that in certain situations, the cubic sites in the dhcp Nd lattice may exhibit ferromagnetic ordering with a magnetic moment of roughly 1.5µB per cubic site, either under hydrostatic pressure[186] or 91 under epitaxial strain in Ce/Nd superlattice structures[187]. We find that our polycrystalline Nd/Cu multilayers exhibit ferromagnetic ordering within the Nd layers. At the time of writing, the mechanism behind the observed ferromagnetism of the Nd in our multilayers has not been thoroughly investigated, although it is likely to be related to the thin-film nature of our samples. It is possible that the Nd layers are either being forced to grow in an fcc crystal structure, or that the polycrystalline dhcp structure is strained by the adjacent Cu. Both of these may result in ferromagnetic ordering as opposed to the bulk antiferromagnetism. Finite size effects due to the layer thickness may also perturb the RKKY coupling interaction, resulting in different magnetic ordering. We have also observed ferromagnetically ordered Nd in sputtered Co/Nd/Co trilayer films measured by PNR[188]. In this case the magnetic moment is determined to be roughly 1µB per atom from fits to the neutron data. Figure 3.6 shows magnetoresistance and magnetisation for a Nd[20˚ A]/Cu[20˚ A] multilayer at 8.2K. Both the MR and magnetisation loops resemble those for Dy/Cu samples, with the peaks in the magnetoresistance again being uncorrelated with features in the magnetisation. From the magnetisation measurement we derive an atomic magnetic moment of (0.96±0.05)µB per atom. The solid red line on the magnetisation curve is a Langevin function fit through the data. The fit may again be seen to be far from convincing. Close to zero field the slope of the data is far steeper than the expected paramagnetic response. The approach to magnetic saturation at higher fields is less steep for the data than the Langevin function fit. There is also a nonvanishing hysteresis close to zero applied field which is shown in more detail in the inset. We observe a definite hysteretic magnetoresistance in our ferromagnetic Nd/Cu samples, similar to that seen in both Dy/Cu and Gd/Cu multilayers. These results are in contrast to the MR and magnetisation observed in granular GMR systems – such systems are superparamagnetic, thus the magnetisation is well described by a Langevin function, whilst the GMR in these systems lacks symmetric peaks about zero field[189]. 92 Assuming for a moment that the results we observe in all of our rare-earth magnetic multilayers are due to the GMR, we can say that there is a definite spindependence in the conduction electron scattering mechanism, implying a finite spinpolarisation of the conduction-band at the Fermi level in the rare-earths. Calculation within a simple model allows us to estimate the magnitude of the spin-polarisation. The scattering asymmetry in a ferromagnet may be defined by α= R↓ R↑ which may be related to the magnetoresistance by[190] (1 − α)2 ∆R = R 4α From this we may determine the magnitude of the spin-polarisation as |P | = α−1 − 1 α−1 + 1 yielding values of P ≈ 0.7% for dysprosium, P ≈ 1.0% for gadolinium and P ≈ 0.2% for neodymium. The value of the polarisation for gadolinium is comparable to that seen in figure 3.2. 3.5.4 Magnetoresistance mechanisms in multilayers To draw conclusions regarding the spin-polarisation of the conduction-band in terms of the GMR we need to show conclusively that the magnetotransport response that we observe is due to the GMR mechanism. Sceptics may say that there are several mechanisms other than the GMR which may contribute to the MR in our RE/Cu multilayers. We wish to show conclusively that no other magnetoresistance mechanism may account for the results on the transport properties of our RE/Cu multilayers, in order that they may be confidently attributed to the GMR mechanism. In order to eliminate other mechanisms by which the resistance may change with magnetic field we begin by discussing the possible causes of the magnetoresistance. Anisotropic magnetoresistance As discussed in section 1.4, the anisotropic magnetoresistance is the variation of the resistance of a ferromagnetic material with the relative orientation between the 93 applied magnetic field and current flow directions. Over the past decade or so, the group headed by Dahlberg at the University of Minnesota have performed extensive studies on the AMR in thin film systems such as single magnetic films, magnetic multilayers and spin-valves[191, 192]. They have shown that the AMR and GMR in spin-valve and magnetic multilayer samples may be separated by measuring the resistance as a function of the angle between current and magnetisation in a saturating magnetic field[193, 194], in agreement with the theoretical prediction of Rijks et. al.[80]. Thus by measuring the MR of our multilayers in both transverse, longitudinal and diagonal orientations, we are may compare the observed effects with the cos2 (θ) dependence of the resistance at saturation – or in this case the 4T field available to us. Figure 3.7 shows the MR of a Dy/Cu multilayer sample with the magnetic field applied at three different angles with respect to the current flow direction within the sample. Also shown is the angular dependence of the resistance in a 4T magnetic field. The exact agreement between the R (B = 4T) for the three orientations, and the R (θ = 0, π/4, π/2) in a 4T field is immediately apparent. The same correlation is observed in both Gd/Cu and Nd/Cu multilayer systems. In this way, we show that the AMR does not account for the magnetoresistance curves which we measure in our multilayers. The AMR gives the differences in resistance in a magnetic field of 4T as a function of the sample orientation, although it does not account for the overall shape of the magnetoresistance response. The AMR produces peaks or dips in the resistance. However these are caused due to randomisation of the domain structure within the material and thus always show up at the coercive field. Generally, in transition metals, the resistance at magnetic saturation is higher than at the coercive field (or zero field) for the longitudinal orientation and lower in the transverse orientation. In our samples, the resistance at saturation is always lower than that at zero field. Due to these facts, we are able to discount the AMR as being the mechanism causing the MR which we observe. Resistance (Ω ) 5.32 a) 5.32 MR = -0.55% b) 5.32 MR = -0.46% c) 5.32 MR = -0.38% 5.31 5.31 5.31 5.31 5.30 5.30 5.30 5.30 5.29 5.29 5.29 5.29 5.28 5.28 -4 -2 0 B (T) 2 4 5.28 -4 -2 0 B (T) 2 4 d) 5.28 -4 -2 0 B (T) 2 4 0 1 2 Angle θ / π (Rad) Figure 3.7: Magnetoresistance of a Dy/Cu multilayer with the transport current applied a) perpendicular, b) diagonal and c) parallel to the magnetic field. Frame d) shows the angular variation of resistance at a magnetic field of 4T. All measurements are taken at 8.2K. 94 95 Lorentz magnetoresistance The close-to-linear decrease in resistance with increasing field, most apparent for the case of Gd/Cu as seen in figure 3.5, may appear similar to that characteristic of the Lorentz MR in thin films. The magnitude - roughly 1% - is, however, far greater than would be expected due to the Lorentz MR in such a disordered system. Sputtered thin-film samples are notorious for their level of defect scattering centers. This may be seen from the residual resistance ratio (RRR), which in the case of these samples is of the order unity. As was discussed in section 1.3 the Lorentz MR is strongly dependent upon the purity and crystalline quality of the sample. It is generally several orders of magnitude smaller than that seen in our multilayers, even in particularly pure single crystals. The Lorentz MR is strongly material dependent, so varying the composition of the multilayer should produce a change in the negative magnetoresistance of the sample if this is the dominant MR mechanism. This is one of the reasons for replacing alternate rare-earth layers in the multilayer structure with another material – in this case cobalt. 3.6 RE/Cu/Co/Cu multilayers As is shown below, replacing alternate rare-earth layers with an equal thickness of cobalt immediately removes any doubt that the Lorentz MR is not responsible for the MR we observe. Further to this, we observe a distinct difference in the effect of Co addition between the heavy rare-earth metals Dy and Gd, and the light rare-earth metal Nd. These two sets of contrasting results are discussed below. 3.6.1 Dysprosium and gadolinium In the case of the heavy rare-earth metals Dy and Gd we observe a drastic, and quite distinct, change in the form of the MR when we replace alternate rare-earth layers with an equal thickness of Co. The general shape of the curve is inverted, resulting in a positive MR. This change in the sign of the MR immediately allows us to rule out the Lorentz MR as the mechanism which causes our results. Sharp peaks (or dips) 96 b) MR (%) a) c) 0 0 0 -0.1 -0.1 -0.1 -0.2 -0.2 -0.2 -0.3 -0.3 -4 -2 0 2 4 -0.3 -4 -2 0 B (T) 2 4 -4 -2 B (T) 0 2 4 B (T) MR (%) Figure 3.8: Magnetoresistance of a Dy/Cu/Co/Cu multilayer in a) longitudinal, b) diagonal and c) transverse orientations at 8.2K. 0 0 -0.1 -0.1 -0.2 -0.2 -0.3 -0.3 -0.4 -0.4 -4 -2 0 B (T) 2 4 -4 -2 0 2 4 B (T) Figure 3.9: Magnetoresistance of a Gd/Cu/Co/Cu multilayer in longitudinal and transverse orientations at 8.2K. in the MR appear close to zero applied magnetic field, which are associated with the AMR in the Co layers, as discussed in section 1.4. Figure 3.8 shows the MR response of Dy/Cu/Co/Cu multilayer in longitudinal, diagonal and transverse orientations at 8.2K. The resistance at a field of 4T is again consistent with the angular variation of resistance due to the AMR in the whole multilayer stack and the resistance at the coercive field of the Co layers is also consistent in each case as expected. A similar effect is seen in the case of Gd/Cu/Co/Cu multilayers. Again, the overall shape of the curve is inverted, with sharp peaks associated with the AMR in the Co layers. The high field resistance is consistent with the angular variation 97 MR (%) 0.4 0.4 a) 0.4 b) 0.3 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0 0 -4 -2 0 2 B (T) 4 c) 0 -4 -2 0 2 4 -4 -2 B (T) 0 2 4 B (T) Figure 3.10: Magnetoresistance of a Nd/Cu/Co/Cu multilayer in a) longitudinal, b) diagonal and c) transverse orientations at 8.2K. due to the AMR and the resistance of the coercive peaks of the Co layers are also consistent. The MR response of one of these samples in longitudinal and transverse orientations is shown in figure 3.9. The shape of the MR curve is very similar to that seen in figure 3.5 for a Gd/Cu multilayer; we observe a near-linear variation in resistance with increasing magnetic field up to 4T. In the Gd/Cu samples it was tempting to ascribe this to the Lorentz MR mechanism, however we now see that this linear response is somehow intrinsic to the Gd system. If this were due to the Lorentz MR, the slope of this section of the curve would not be inverted for our Gd/Cu/Co/Cu samples. 3.6.2 Neodymium We now investigate the effect of replacing alternate Nd layers again with an equal thickness of Co. This allows us to compare and contrast the magnetoresistance in a light rare-earth system with that in the heavy rare-earths. Figure 3.10 shows the magnetoresistance of a Nd/Cu/Co/Cu multilayer at 8.2K in longitudinal, diagonal and transverse orientations. We see that in this case the general shape of the MR is unchanged with respect to that seen for a Nd/Cu multilayer in figure 3.6. There is no inversion of the general shape of the MR – in this case it remains negative. We see sharp peaks which again correspond to the AMR in the Co layers. 98 If we tacitly assume that the GMR is the mechanism responsible for the MR we observe, we now have evidence for a reversal in the scattering spin-asymmetry in crossing from the light to heavy rare-earths. From this one would conclude that the sign of the spin-polarisation of the conduction-band at the Fermi level must be opposite in the heavy rare-earths (gadolinium and dysprosium) to in neodymium, and also cobalt. 3.7 Supporting evidence for the GMR mechanism In this section we describe several characteristic features of the GMR in magnetic multilayers and show that these features are present in our rare-earth magnetic multilayers. We concentrate on the Dy/Cu and Dy/Cu/Co/Cu systems for conciseness. 3.7.1 Isotropic nature of the magnetoresistance The GMR should be isotropic; the magnetic field may be applied in any direction in the plane, as seen previously, or perpendicular to the plane[164]. Both configurations should produce magnetoresistance with a similar form and magnitude. Here we supplement our previous in-plane data with measurements where the magnetic field is applied perpendicular to the sample plane. Note that the current still flows within the plane of the layers. Figure 3.11 shows MR and magnetisation for a Dy/Cu multilayer. There is again a clear negative MR of nearly -0.2%. The more rounded shape of the MR curve and increased peak separation appear to be representative of the harder axis for the out-of-plane magnetisation. From the magnetisation data, however, we again see that the sample is close to magnetic saturation in the 4T applied field. There is again a non-vanishing hysteresis close to zero field, similar to that seen in our in-plane magnetisation measurements. Comparison with the in-plane magnetisation data confirms that the out-of-plane magnetisation is a slightly harder axis, as would generally be expected in the thin-film geometry. Other than the shape anisotropy due to the sample geometry, the out-ofplane magnetisation confirms that there is a random magnetocrystalline anisotropy 99 0.20 MR (%) 0.15 0.10 0.05 0 -4 -2 0 2 4 -4 -2 0 2 4 m (arb. units) 0.004 0.002 0 -0.002 -0.004 B (T) Figure 3.11: Magnetoresistance and magnetisation for a Dy/Cu multilayer with the magnetic field applied perpendicular to the plane of the sample. present in these samples. Arbitrary units are used for the perpendicular magnetisation due to the sample geometry presenting a different ‘filling factor’ to the pickup coils in the VSM. Perpendicular magnetoresistance and magnetisation for a Dy/Cu/Co/Cu multilayer are shown in figure 3.12. The magnetoresistance is again clearly inverted in comparison to figure 3.11, confirming the isotropic nature of the magnetoresistance. Sharp peaks due to the reversal of the cobalt layer are again observed. However these cannot be related to the coercivity as the cobalt is magnetised out-of-plane, which is a hard-axis. These peaks most likely represent the point at which there is the 100 0 MR (%) -0.05 -0.10 -0.15 -0.20 -4 -2 0 2 4 -4 -2 0 2 4 m (arb. units) 0.004 0.002 0 -0.002 -0.004 B (T) Figure 3.12: Magnetoresistance and magnetisation for a Dy/Cu/Co/Cu multilayer with the magnetic field applied perpendicular to the sample plane. largest ‘magnetic disorder’ between adjacent magnetic layers, this being the closest approximation to the antiparallel magnetic state of single-domain layers. This data clearly shows that our RE/Cu and RE/Cu/Co/Cu multilayer samples do exhibit the magnetoresistance isotropy which is a characteristic of the GMR. 3.7.2 Dependence upon the number of repeat units The GMR exhibits a characteristic scaling behaviour[129]. This has been reported in many GMR systems, e.g. Co/Cu or Co/Ru multilayers[195], where the GMR is shown to depend on the number of bilayer repeat units in the multilayer stack. The room 101 0.6 MR (%) 0.4 0.2 0 0 40 80 120 # of bilayer repeats Figure 3.13: Dependence of the magnetoresistance on the number of repeat units in Dy[20˚ A]/Cu[20˚ A] multilayers at 8.2K. The solid line is a guide to the eye. temperature GMR in Co/Cu increases rapidly from ∼10% for 2 bilayer repeats up to roughly 75% for about 50 repeat units. After this the GMR saturates, remaining constant as the number of repeat units is increased. Freitas et. al. have previously shown a GMR-like signal of roughly 0.1% in antiferromagnetically coupled Gd/Y multilayers. In this case the magnetoresistance was found to be independent of the number of structural repeat units in the multilayer, the MR being attributed to scattering at the Y/Gd interfaces. Figure 3.13 shows the dependence of the magnetoresistance on the number of bilayer repeat units, N , in the Dy/Cu multilayer system. It is clear that the MR is strongly dependent upon the number of repeat units, up to a saturating value where it becomes roughly independent of N . The magnetoresistance observed in our rare-earth multilayers do show the features which are characteristic of the GMR. This gives further confidence in our conclusion that we are observing effects due to the GMR in our rare-earth multilayers. 102 Resistance (Ω ) 5.31 a) b) 5.31 5.31 5.30 5.30 5.30 5.29 5.29 5.29 5.28 5.28 5.28 -4 -2 0 2 4 -4 B (T) -2 0 B (T) 2 4 c) -4 -2 0 2 4 B (T) Figure 3.14: Magnetoresistance of a Dy/Cu multilayer at a) 8.2K, b) 100K and c) 200K in transverse (red) and longitudinal (blue) orientations. 3.8 Dependence of the magnetoresistance on the magnetic phase of the rare-earth In the rare-earth metals the magnetically ordered phases do not persist to room temperature, allowing us to easily study the transport properties of both ordered and disordered magnetic states. In order to effectively investigate the dependence of the magnetoresistance on the magnetic phase of the rare-earth metal, it is most instructive to examine the dysprosium system. Dy has two magnetic phase transitions which are located nicely in our range of measurement temperatures. At temperatures below about 89K Dy is ferromagnetic with an easy axis in the basal plane of the hcp crystal structure. The transition at 89K is to a helical antiferromagnetic phase, again with the moments lying in the basal plane. The turn-angle between moments in adjacent planes is temperature dependent, ranging from 26.5o just above the Curie temperature to 43.2o just below the N´eel point. The transition between the helical-AF and paramagnetic phases occurs at roughly 176K[185]. An interesting point to note is that there is a slight variation in the measured transition temperature depending upon the technique used to measure it, e.g. resistivity measurements, magnetisation measurements or neutron diffraction. Figure 3.14 shows the MR of a Dy/Cu multilayer at temperatures corresponding to each of the magnetic phases of the dysprosium layers. At 8.2K the Dy layers are in the ferromagnetic phase, at 100K they are in the helical-AF phase, and the 103 Resistance (Ω ) 2.250 2.300 a) 2.245 2.295 2.375 2.240 2.290 2.370 2.235 2.285 2.365 2.230 2.280 -4 0.0050 m (emu) 2.380 b) -2 0 2 4 2.360 -4 0.0050 d) -2 0 2 4 -4 0.0050 e) 0.0025 0.0025 0.0025 0 0 0 -0.0025 -0.0025 -0.0025 -0.0050 -0.0050 -4 -2 0 B (T) 2 4 c) -2 0 2 4 0 2 4 f) -0.0050 -4 -2 0 2 4 -4 B (T) -2 B (T) Figure 3.15: Magnetoresistance and magnetisation of a Dy/Cu/Co/Cu multilayer at a) 8.2K, b) 100K and c) 200K in transverse (red) and longitudinal (blue) orientations. The lower frames show the respective hysteresis loops at the same temperatures. The extent of the vertical scale on the MR data is the same in each case to aid comparison. layers are paramagnetic at 200K. The ‘large’ magnetoresistance is observed only in the ferromagnetic phase. In both the helical-AF and paramagnetic phases, we observe no magnetoresistance. MR and magnetisation measurements at the same temperatures are shown for a Dy/Cu/Co/Cu multilayer in figure 3.15. The sharp peaks due to AMR in the Co layers are present at all temperatures, whereas the positive background is only present at low temperatures when the Dy layers are ferromagnetic. We see a definite magnetic signal from the Dy layers only in the ferromagnetic phase. The same is also true of both Gd and Nd samples. Thus we may conclude that in the case of both RE/Cu and RE/Cu/Co/Cu multilayers, the MR which we observe is only apparent in the ferromagnetically ordered phase of the rare-earth layers. 104 3.9 Discussion We now discuss the preceding experimental results with a view to ascertaining that the GMR mechanism is responsible for the magnetoresistance which we observe. The anisotropic magnetoresistance mechanism cannot explain our data entirely. By performing measurements in a variety of orientations we are able to separate out the relative contributions from the AMR and GMR. The variation in saturated resistance with angle is consistent with the AMR in all of our multilayer samples. However, the dependence of the resistance upon the applied field is, in general, not explainable as due to the AMR. The Lorentz magnetoresistance is unable to explain the change in sign of the MR upon exchanging alternate Dy or Gd layers for an equal thickness of Co. If anything, the longer mean-free-path in Co should enhance the boundary scattering contribution and thus produce a greater negative magnetoresistance. The sign inversion that we see can only be explained due to spin-dependent scattering. We also note that the dependence of MR upon the number of repeat units is consistent with that observed in other GMR systems. As neither of the two magnetoresistance mechanisms discussed above are able to explain our results, we are left only with the GMR mechanism with which to explain our data. Further support for this is added by the N dependence of the MR and the isotropic nature of the MR. Whilst neither are necessarily compelling evidence in themselves, both are supportive of the claim that the magnetoresistance that we observe in our multilayers is due to the GMR mechanism. The temperature dependence of the magnetoresistance may be explained, assuming the GMR mechanism, as due to changes in the net spin-polarisation of the conduction-band at the Fermi level. The reason why the MR is only present in the ferromagnetic phase is that this is the only magnetic phase where there is a net spinpolarisation of the conduction-band in the rare-earth layers. Thus the ferromagnetic phase does produce a spin-dependence in the scattering, whereas the antiferromagnetic and paramagnetic phases do not. The crucial question now remains – why does the sign of the GMR change in the cases where we replace alternate dysprosium and gadolinium layers with cobalt, 105 but not in the case where we replace neodymium? The only plausible explanation for the inversion of the GMR is that the asymmetry in the spin-dependent scattering in dysprosium and gadolinium is the opposite way around to that in cobalt. On the other hand, the lack of a sign inversion in neodymium samples implies that the scattering asymmetry in neodymium is the same way round as in cobalt, and hence opposite to that in gadolinium and dysprosium. The implication of this is that the spin-polarisation of the conduction-band at the Fermi level is the opposite way around in dysprosium and gadolinium than in cobalt - i.e. in the majority spin - whereas in neodymium it is the same way around – i.e. in the minority spin. We show now how the spin-polarisation of the conduction-band in the rare-earths arises due to the RKKY magnetic ordering interaction, and how the sign of the spinpolarisation may be determined simply from the Russel-Saunders spin-orbit coupling. 3.9.1 The origin of the RKKY spin-polarisation in the rareearths Calculation of the true form of the RKKY spin-density wave due to the N ion perturbation, consistent with the collapse into a co-operative magnetic ground state, is by no means a trivial task. In light of this, we look to an intuitive extrapolation from the single-ion case to explain the conduction electron spin-polarisation. Any exchange interaction between two particles – e.g. that in equation 3.3 – must be related to their respective spin. In the case of the rare-earth metals, however, neither the ionic spin S nor angular momentum L fulfill the requirements to be ‘good’ quantum numbers. The spin-orbit angular momentum of the ion may be defined uniquely only by J, with the result that the only unique definition of the ionic spin is then the projection of S onto J. The value of this projection may be shown to be SJ = (gJ − 1) J (3.4) by eliminating L between the expressions L+2S = gJ J and J = L+S, where gJ is the Land´e splitting factor. This is equivalent to the Russel-Saunders coupling J = −λL·S which determines the relative orientations of J, L and S. In the heavy rare-earths (gadolinium to lutetium) the factor (gJ − 1) is positive 106 0.04 Light rare-earths Heavy rare-earths P(r) (arb. units) 0.02 µi 0 -0.02 -0.04 0 5 10 15 k Fr Figure 3.16: The form of the RKKY spin-density oscillation expected for light and heavy rare-earth ions. and the Russel-Saunders parameter λ is negative, with the result that J, L and S are parallel to one another. On the other hand, in the light rare-earths (lanthanum to europium), (gJ − 1) is now negative and λ is positive. We now have the situation where J and L are parallel, with S antiparallel. As the ionic magnetic moment is related to J by µ = gJ µ B J we see that in the light (heavy) rare-earths the ionic spin on any lattice site is antiparallel (parallel) to the local moment on that site. It may be see from equation 3.1 that the lowest energy state for the s-f exchange integral occurs for the situation when the conduction electron spin s and the local moments spin Si are parallel to one another. In this case the exchange Hamiltonian takes a negative value, resulting in an attraction of electrons with like-spin toward the ion. We may now determine the form of the RKKY spin-density oscillation in the light and heavy rare-earths. In the light rare-earths, conduction electrons from the minority spin channel will be attracted to the ion as Si is antiparallel to Ji , and hence also to the local moment µi . This results in an RKKY spin-density wave as shown by the blue curve in figure 3.16. For a heavy rare-earth, however, conduction electrons from the majority spin channel will be attracted most strongly as Si is now P(r) 107 0.04 0.04 0.04 0.03 0.03 0.03 0.02 0.02 0.02 0.01 0.01 0.01 0 -0.01 0 a) 0 -0.01 10 20 30 2kFr 0 b) 0 -0.01 6 12 18 c) 0 5 2kFr 10 15 2kFr Figure 3.17: Approximation to the RKKY spin-density oscillation by summing the single-ion polarisation function for various atomic separations. parallel to µi resulting in an inversion of the spin-density wave, as shown by the red curve in figure 3.16. For any oscillatory polarisation such as that associated with the RKKY interaction, the net spin-polarisation of the conduction-band[162] is given by Z PNet = P (r) dr From the form of the P (r) for light and heavy rare-earths shown in 3.16, it is instantly obvious that the sign of the net spin-polarisation should be different for light and heavy rare-earths. In the case of a light rare-earth, we expect to find PNet < 0, whereas we should find PNet > 0 for a heavy rare-earth. At this point, we must again stress that the argument for a net spin-polarisation thus far is based upon the single-ion RKKY perturbation to the conduction electron gas. A qualitative extension to multi-ion systems follows simply from the single-ion free-electron case, similar to that presented by de Gennes[171], by simply summing the single-ion spin-density waves. If we consider two rare-earth ions separated by a sufficient distance as to be non-interacting, the spin-polarisation resulting by their ferromagnetic alignment is trivially the sum of that due to each ion. If we now allow the two ions to approach one another, we eventually arrive at the situation depicted for a heavy rare-earth in figure 3.17a. Here the spin-density waves due to each ion have just begun to mix, 108 resulting in an indirect exchange coupling between the two ions. The spin-polarisation due to the spin-density waves produced by summing the two contributions is little different from that obtained for two isolated ions. As we allow the ions to further approach one another, we see that the form of the resultant spin-density oscillation changes significantly – figures 3.17b and c. Although the form of the spindensity oscillation is no longer a good approximation to the true two-body solution due to the stronger interaction between the two spin-density waves, we may still gain further qualitative understanding. In both figures 3.17b and c, the net spinpolarisation between the lattice sites is negative. This negative spin-polarisation is, however, obviously extremely small in comparison with the large positive spin-polarisation close to the lattice sites. Even if we abandon the free-electron approximation, it is extremely unlikely that the spin-polarisation induced between the lattice sites will be anywhere near sufficient to negate that induced close to the local moments. We may thus conclude that the sign of the net spin-polarisation in a ferromagnetic rareearth may be simply deduced from the Russel-Saunders coupling which determines the alignment between the ionic spin S and the total spin-orbit angular momentum J. The RKKY spin-density waves shown in figure 3.16 are comprised of electrons on the Fermi surface, as these are the only electrons which are able to ‘respond’ to the perturbation Hamiltonian. Below the ordering temperature, the magnetic ground state must then have a finite spin-polarisation of the conduction-band electrons at the Fermi level. In the antiferromagnetic phases of the rare-earths, the spin-polarisation of the conduction-band vanishes. The reason for this is that in order to produce no net magnetic moment the individual local moments cancel exactly. In this case the spinpolarisation due to each of these moments must also cancel one another. This ties in with the results of our MR measurements – we only observe a GMR when the rare-earth layers are ferromagnetically ordered. It should be noted that the only way to determine the sign of the polarisation is by performing transport measurements as reported in this chapter. Neutron diffraction is sensitive to the total magnetic moment associated with each lattice site. As 109 the magnetic moment due to entire conduction-band is only ∼10% of the total moment, and electrons at the Fermi level make up only a minuscule fraction of this, the magnetic moment due to the RKKY polarisation is completely swamped by the ionic moments. Neither neutron nor x-ray measurements are able to determine the sign of the polarisation. As the measured quantity in both cases is the intensity, all phase information - which would in principle allow the sign of the polarisation to be determined - is lost. Other measurement techniques are only able to determine e.g. the strength of the exchange interaction between localised moments. However as these results are related to the factor (gJ − 1)2 , it is impossible to extract the sign of the spin-polarisation of the conduction-band from these measurements. In addition to this, most measurements on bulk samples require complex theoretical models in order to obtain a value for the coupling strength. Our measurements on magnetic multilayers thus represent the only method of unambiguously determining the sign of the conduction-band spin-polarisation. 3.10 Conclusion From the experimental work presented in this chapter we conclude the following: We have shown compelling evidence for the GMR effect in rare-earth magnetic multilayers where the rare-earth layers are either dysprosium, gadolinium or ferromagnetically ordered neodymium. The GMR is only present when the rare-earth layers are in the ferromagnetic phase. We have shown that we are able to separate out the contribution due to the AMR, and also that the Lorentz MR does not account for the MR which we see. We thus conclude that we are observing GMR in our samples. Exchanging alternate rare-earth layers in the multilayer structure for an equal thickness of cobalt has the effect of inverting the GMR when the rare-earth metal is one of the heavy rare-earths dysprosium and gadolinium, but not when it is the light rare-earth neodymium. The GMR mechanism can only show an inverted magnetoresistance when the scattering spin-asymmetry in alternate layers is opposite, i.e. in one layer the minority carriers scatter more strongly than the minority carriers, whereas the opposite is true in the next magnetic layer. We thus conclude that the 110 scattering asymmetry - and hence the spin-polarisation of the conduction-band at the Fermi level - is opposite in dysprosium and gadolinium to that in cobalt, and that the spin-polarisation in neodymium is in the same sense as in cobalt. The conduction electrons probed by GMR measurements are exactly those which are responsible for carrying the RKKY indirect exchange interaction. Thus the spinpolarisation which we see in our GMR measurements may be correlated precisely with what is theoretically anticipated due to the magnetic ordering interaction in the rare-earths. The sign of the spin-polarisation in both the light and heavy rare-earths is shown to agree with that expected due to a short-ranged exchange interaction between the conduction electrons and a rare-earth ion following the Russel-Saunders spin-orbit coupling scheme. The temperature dependence of the GMR is again in excellent agreement with this picture. GMR is only observed when the rare-earth metal layers are in the ferromagnetic phase. In either antiferromagnetic or paramagnetic phases of the rareearth there is no net spin-polarisation of the conduction-band in the RKKY model, and in these cases no GMR is observed in our multilayers. We finally conclude that the work presented in this chapter provides the first direct experimental evidence for the net spin-polarisation of the conduction-band in the rareearth metals due to the RKKY damped oscillatory spin-density wave and thus for the RKKY picture of a conduction-band mediated interionic exchange coupling in the rare-earth metals. We have used recently developed physical principles in order to investigate a longstanding question regarding the RKKY mechanism. Although the RKKY theory is now accepted in the scientific community, this work presents the first experimental evidence that this picture is correct in actuality. 111 Chapter 4 Growth and characterisation of magnetic tunnel junctions 4.1 Introduction This chapter describes an investigation of spin-polarised tunnelling in high quality magnetic tunnel junction (MTJ) samples. Tunnel junctions may eventually be incorporated into a variety of complex device structures including, for example, ballistic spin-injection devices for spintronic applications. Since the advent of large-magnetoresistance MTJ devices in 1995 [10], the MTJ has gained technological importance for data-storage applications, the most promising being non-volatile magnetic random access memory (MRAM)[32], and also as a replacement for GMR technology as the read-head in high data-density hard disc drives[33]. There is much interest also in the wealth of fundamental physics which underlies the tunnelling magnetoresistance (TMR) mechanism. There are two routes by which research groups have entered the field of MTJ research. The first, and probably most widely chosen, is to form a collaboration with a group or company which have a proven track record in MTJ deposition e.g. MIT, IBM, Motorola, etc.. The second, more difficult option, is to develop an in-house capability to deposit MTJ structures. We have opted for the second option as this allows us a much greater level of flexibility to explore fundamental aspects of the science of MTJs, without the need to ‘appease’ industrial collaborators. The deposition of good quality magnetic tunnel junction structures is usually 112 undertaken using one of two techniques. The crossed electrode structure and insulating barrier layer may be defined either using metal shadow or contact masks during growth, or post-deposition using some form of lithographic patterning. The contact mask approach was chosen as this method allows systematic study and rapid prototyping of different junction structures in a similar way to our studies on CIP samples. It would also be possible to deposit CPP multilayer structures using the same deposition system, further increasing the flexibility of this tool. Previous attempts to deposit MTJs in our sputtering system at Leeds were unable to deposit the entire structure in-situ. The deposition chamber vacuum had to be broken in order to change the contact masks used to define the structure, which causes unwanted exposure of the sample to the atmosphere, generally resulting in a less consistent tunnel barrier and reduced sample quality. To circumvent this problem a new sample wheel was built which enables the sample structure to be built up through a series of contact masks which may be changed in-situ without the need to break vacuum. This sample wheel is used for the deposition of both tunnel junction and CPP magnetic multilayer structures in our sputtering system. In this chapter we shall firstly describe the CPP sample wheel and the process of its design and construction. We then discuss the processes of optimising the various stages of deposition required for the fabrication of tunnel junction structures and the results obtained from initial characterisation of spin-valve-like magnetic tunnel junctions. 4.2 Design and construction of the CPP sample wheel The first, crucial step in the development of a deposition procedure for MTJ structures is, of course, the design and fabrication of a device to enable the exchange of contact masks to define the sample structure in-situ. Two different sample wheels incorporating such a device - have been build and tested. This work was undertaken in conjunction with L. A. Michez, and much of the work discussed in this section is also described in her Ph.D. thesis[196]. 113 4.2.1 The Mk. I sample wheel At the outset of this project, a new sample wheel with the facility to change contact masks had been designed, and was undergoing construction in our mechanical workshop. This sample wheel held up to 16 samples, each of which had an array of 3 metal contact masks to define the crossed electrode structure, resulting in a total of 48 individual contact masks. A photograph of the sample wheel and a schematic diagram are shown in figure 4.1, showing the upper sample plate with substrate holders, the middle contact mask plate with sprung, floating contact mask carriers, and the lower plate which locks the contact masks into position and frees them when the three actuators are powered up, separating the three plates. Powering the actuator solenoids results in the lower plate separating from the sample plate, allowing the contact mask holders to fall free of the substrates. The contact mask plate is then able to rotate freely, under control of a stepper motor, beneath the sample plate until the required set of masks are aligned with their respective sample holders. Removing power from the solenoids allows the lower plate to spring closed to the sample plate, in turn pushing the masks into contact with the substrates. Unfortunately, this contact masking system had several flaws. Firstly, we were unable to achieve a consistent contact between the masks and substrates, resulting in poor electrode profiles – the electrode profile should be rectangular, and of a consistent width in order to compare junction resistances from sample to sample. Attempts were made to correct for this problem by changing the solenoids for stepping linear actuators in order to ensure the proper closure of the lower plate against the sample plate. Problems with closing the lower plate arose due to the sheer number of springs holding different parts in contact with one another – each of the 16 contact masks had four springs which all needed to be compressed fully to ensure correct closure. The profile of the contact mask carriers was also modified in order to ensure mechanical contact between the faces of the masks and the substrate. Despite these attempts to rectify the situation, Dektak profile measurements showed good, rectangular profiles in only a few isolated instances. Another problem was the fact that the substrates were effectively located at the 114 Substrate holder Substrate Contact masks Contact mask plate Springs Contact mask carriers Lower plate Figure 4.1: Photograph and schematic diagram of the Mk. I CPP sample wheel. The bottom plate has been removed in the photograph to expose the contact masks. 115 top of a long cylindrical ‘chimney’, which resulted in a huge decrease in both the growth rate of films deposited through the mask system, and also in the rate of plasma oxidation of tunnel barriers. Deposition of samples took such a period of time as to render systematic study within a single batch of samples impossible. The weight of the Mk. I sample wheel, as it was machined from solid stainless steel, also presented several problems which had not been previously considered. The large mass caused extra stress to be placed upon the rotary motion mechanism, resulting in frequent failure of the flexible couplings used to transmit drive from the stepper motors to the sample wheel. Also, the excessive weight meant that several users were simply unable to lift the sample wheel into the vacuum chamber! Eventually it was decided that continued modification of this system was not a good use of the available time and the system was abandoned as a dead loss. At this point we began the design and construction of its replacement. 4.2.2 The Mk. II sample wheel Working on the modifications required to the Mk. I CPP sample wheel taught us several important lessons for the design of the Mk. II version. First and foremost it was decided that a simpler design with less moving parts would benefit substantially firstly in the time required for fabrication, but also by greatly reducing the weight of the sample wheel. It was decided that a design featuring a single set of three contact masks - as opposed to the three masks per substrate as used previously - would allow us to hold the substrate and mask in contact simply by gravity as opposed to any mechanical means. The initial design was loosely based upon that employed by Parkin at the IBM Almaden research center for the deposition of MTJ structures, a diagram of which is shown in figure 4.2 [197]. In our new design, the wheel is in two parts – the samples being mounted on a separate, floating plate which is ‘picked up’ on the lower plate which holds the contact masks. The lower plate may be raised and lowered by three stepping linear actuators which join it to the hub, mounted onto the rotary motion feedthrough. A PTFE spacer allows the sample wheel to be floated electrically with respect to ground. Figure 4.3 shows a photograph of the Mk. II CPP sample wheel mounted 116 Figure 4.2: MTJ deposition system employed at the IBM Almaden research center, courtesy of [197] in the sputtering system. Whilst changing between different masks and samples, the contact mask plate is lowered so that the the substrate plate rests on the shutter assembly on three adjustable legs. The contact mask plate is free to move beneath the sample plate, allowing any of the three contact masks to be aligned with any of the 18 sample positions. Both the sample and contact mask plates are made from 2.5mm thick aluminium plate, thus vastly reducing the overall mass of the wheel. The contact masks are made from stainless steel and are in the shape of small ‘top-hats’ which are pressed into holes in the lower plate. The substrates sit in recesses in the top plate, with glass backing pieces to provide support. They are held in place by sprung holders which press the substrate against the contact mask. A diagram of the contact mask assembly is shown in figure 4.4. Around the inner perimeter of the sample plate are 117 Figure 4.3: Photograph of the Mk. II CPP sample wheel mounted in the vacuum chamber. The mask is in the open position to show the three contact masks below the substrate wheel. 18 bevelled posts, which mate up with a series of bevelled holes on the lower plate when the two plates approach one another. These ensure that the contact mask is correctly aligned beneath the substrate before contact occurs. As there is only a single set of contact masks - and hence only a single substrate in contact with the masks at any one time - there is no longer any need for the large number of springs etc. which prevented the previous design from contacting properly for all samples. Due to the ease of contact in this system it is possible for the substrate to be held firmly against the contact mask simply through the weight of the sample plate pushing down on it via the sprung sample mount. During initial testing of the Mk. II sample wheel, one minor teething problem was discovered. It was found that the lower plate could often catch on the shutter assembly causing lateral stress to be applied to the linear actuator shafts, potentially damaging the motors. This was found to be due to warping of the metal shutter plate and so a new, more robust shutter plate was made from 3mm thick stainless steel. This does not warp so easily. In addition, three inserts were made in order to provide lateral support to the linear actuator shafts. 118 Sprung sample mount Si substrate and glass backing piece Sample plate with recess for unused masks Contact masks in ‘tophat’ carriers Figure 4.4: Diagram of the new contact mask system, showing how the mask contacts the substrate when the lower plate is raised to meet the sample plate. The initial set of contact masks had an electrode track width of 200µm. The slot was made by spark-eroding through the top of the ‘top-hat’ mask assembly, which is 400µm thick – the slots are thus twice as deep as they are wide. It was found that, due to the aspect ratio that the slot presents to the sputtered atom flux, the deposition rate through these masks was again vastly reduced in comparison to our CIP masks. The reduced deposition rate through these masks results in long deposition times and poor film morphology with an increased surface roughness. In order to combat this, further sets of contact masks were made where the slot widths are 500µm and 1mm. In both of these cases the slots are now wider than they are deep, resulting in a greatly increased deposition rate and improved film quality. We now have a fully functional contact masking system which allows us to deposit crossed electrode structures with a choice of electrode widths, without the need to break vacuum to change contact masks. At this point we shall begin to describe the process of developing the techniques required to deposit magnetic tunnel junction structures using this mask system. 119 4.3 Optimisation of the growth conditions for thin aluminium layers Initial attempts to deposit working MTJ structures using typical deposition parameters for our sputtering system proved unsuccessful. It was shown that a highly resistive tunnel barrier could be formed. However, the success rate for tunnel barrier formation was low and the samples failed to show any magnetoresistance at any temperature. These problems were mainly attributed to problems with the deposition of the ultra-thin aluminium layer from which the tunnel barrier is formed. One related problem was the choice of substrate material. Initially we chose to use Corning glass for the substrate as it is a good electrical insulator. We later determined, however, that the surface roughness of the glass microscope slides that we were using was far greater than anticipated – an RMS roughness of ∼70˚ A was measured for a thin Co film sputtered onto a typical glass substrate. When trying to deposit a continuous layer with a thickness of ∼10˚ A it is obvious that a close-to-atomically smooth substrate is a necessary prerequisite. To circumvent the problem of substrate roughness we decided to switch to using Si (100) substrates as used for our CIP samples. This does cause another problem however, as the resistivity of the Si substrate material is of the order 1-10Ωcm at room temperature. Thus for the case of highly resistive tunnel barriers (R0 & 200Ω) we find that some proportion of the current is shunted through the substrate, making room-temperature characterisation of these junctions difficult. Measurement at reduced temperature has the effect of freezing out the dopant charge carrier levels in the substrate and allows better measurement of the intrinsic transport properties of the MTJ. 4.3.1 Variation of film properties with deposition current In order to optimise the growth of the continuous, thin (10-20˚ A) aluminium layers necessary for the formation of good tunnel barriers, we have investigated the magnetic properties of a range of different sample structures. Our initial study was on the effects of the sputtering current during the aluminium deposition, in order to find the optimum deposition rate to grow a smooth, thin, continuous layer. This was done using samples with the so-called ‘top spin-valve’ structure, with a metallic Al spacer 120 Figure 4.5: Typical structure of a top spin-valve sample, as used to optimise the growth of thin aluminium films for tunnel junctions. layer. The structure of the samples is as shown in figure 4.5. In this study the buffer layer was an ∼300˚ A Cu film, both ferromagnetic layers were Co, the antiferromagnetic pinning layer was IrMn and the capping layer was Ta. The samples were deposited onto Si (100) substrates through standard CIP contact masks. Initially we investigate the effect of the sputtering conditions on the pinhole and N´eel orange-peel coupling between the ferromagnetic layers. By looking at the variation in the magnetic switching behaviour of the free ferromagnetic layer in the spinvalve structure we are able to gain information on the interlayer coupling through the spacer layer and hence on the film continuity and/or roughness[198, 199]. Although it is quite possible to extract quantitative values for the interlayer coupling strengths, we are not presently concerned with this. The magnitude of the exchange-bias field can be related to the crystalline quality of the sample, in particular the strength of the fcc (111) texture[200, 201]. This can be indicative of the morphology of the spacer layer in top spin-valves as, should the texture be unable to propagate through the sample structure due to a badly formed spacer layer, the exchange-bias field will be reduced. The effect of increasing the sputtering current is to change the thermalisation kinetics of the sputtered atom flux. Increasing the sputtering current - and hence power - can slightly increase the kinetic energy of atoms incident upon the substrate. 121 This increase in incidence energy enhances the ability of adatoms to diffuse about the surface upon adsorbtion, which in turn increases the probability of the adatom locating an energetically favourable position on the surface net, so reducing both the pinhole density and surface roughness. Should the energy of the incident atoms be too high, however, the atom will strike the surface of the growing film with sufficient energy to cause localised structural rearrangement or to dislodge other adatoms. This may adversely affect the morphology of the growing film, and enhance the surface roughness. For the initial investigation the sputtering current during growth of the Al spacer layer was varied between 10 and 100mA whilst keeping the sample structure and remaining sputtering parameters constant. The thickness of the spacer layer is maintained at a nominal value of approximately 30˚ A by varying the deposition time. Figure 4.6 shows hysteresis loops, recorded by MOKE magnetometry, for a range of sputtering currents. In the case of the sample with a spacer layer grown at 10mA it can clearly be seen that the two magnetic layers are coupled ferromagnetically and are both exchangebiased. This is a strong indication of incomplete continuity of the spacer layer. The sample grown at 25mA shows a definite offset in the switching of the free ferromagnetic layer. This is indicative of either a moderate pinhole density or of a rough surface resulting in strong N´eel coupling. The sample grown at a sputtering current of 70mA shows a vanishingly small offset in the switching of the ferromagnetic layer and the expected exchange-bias behaviour of the pinned layer. The samples grown at still higher sputtering currents show similar exchange-bias behaviour coupled with a slight increase in the free layer coercivity. This may be attributed to degradation of the surface of the free ferromagnetic layer caused by bombardment with excessively energetic Al atoms. From this initial study of the magnetic behaviour of spin-valves with an Al spacer layer it was concluded that the optimum sputtering current for deposition of smooth, pinhole-free Al layers in our sputtering system is roughly 75mA. This is the sputter current which will be used henceforth for the deposition of the aluminium barrier layer in our tunnel junction structures. 122 M/M S 1.0 1.0 a) 0.5 0.5 0 0 -0.5 -0.5 -1.0 -600 -400 -200 M/MS 1.0 0 200 400 600 -1.0 -600 -400 -200 1.0 c) 0.5 0.5 0 0 -0.5 -0.5 -1.0 -600 -400 -200 0 200 400 600 b) 0 200 400 600 0 200 400 600 d) -1.0 -600 -400 -200 H (Oe) H (Oe) Figure 4.6: Hysteresis loops for spin-valve structures as described in the text, where the sputtering current during deposition of the aluminium spacer layer was; a) 10, b) 25, c) 70 and d) 90mA. 4.3.2 Deposition of thin aluminium layers In order to achieve high TMR values in our tunnel junctions we require as thin an insulating barrier layer as possible. As the thickness of the barrier layer increases by around 50% upon oxidation[202], the initial metallic Al layer must also be as thin as possible whilst remaining continuous and free of pinholes. We now report on a study to investigate the magnetic behaviour of spin-valves where the thickness of the Al spacer layer was varied whilst keeping the sputtering current constant at the now standard 75mA. The hysteresis loops obtained are qualitatively similar to those shown in figure 4.6, the coupling between the layers decreasing and exchange-bias field increasing, in this case as a function of deposition time. The results from this study of the exchange-bias field (Hex ), coercivity of the pinned layer (Hcp ), free layer offset field (Hoffset ) and free layer coercivity (Hcf ) are 123 400 240 a) 180 Hcp Hex 300 200 100 0 120 60 0 2 4 6 0 8 0 80 120 c) 2 4 6 8 2 4 6 8 d) 60 Hcf 90 Hoffset b) 60 40 20 30 0 0 0 2 4 6 8 Depositon time (s) 0 Depositon time (s) Figure 4.7: a) Exchange bias field, b) pinned layer coercivity, c) free layer offset field and d) free layer coercivity against deposition time for samples deposited through CIP masks at an aluminium sputtering current of 75mA. shown in figure 4.7. Once a sufficient thickness has been reached that the two ferromagnetic layers are effectively decoupled (t∼3.0s), the exchange-bias field continues to increase with deposition time, indicating a gradual increase in the quality of fcc (111) texture within the sample, until it saturates at just below 400 Oe. The pinned layer coercivity increases rapidly and then levels of at its saturated value, the free layer offset field falls off roughly exponentially[198] and the free layer coercivity falls monotonically to roughly its bulk value. Having learned how to deposit a thin, continuous Al layer through our CIP sample masks, we must now also investigate the growth using our CPP sample wheel. The growth morphology is likely to be somewhat different as the deposition rates are slightly reduced, relating to the aspect ratio of the contact mask and mask carriers. For this study, a different sample structure was chosen. The deposition was as 124 similar as possible to a real MTJ structure, using 3 contact masks to define the lower electrode, Al spacer layer and top electrode respectively. The lower electrode was ∼200˚ A Co and the upper electrode ∼200˚ A Py, these thicknesses being chosen so as to to allow MOKE to again be used to probe the magnetic behaviour of the entire stack. The deposition field was applied in a direction parallel to the lower electrode and the contact masks used define electrodes with 0.5mm wide tracks. For this study, no exchange-bias layer was used. As discussed previously, the exchangebias properties give us information on the quality of fcc (111) texture propagating upwards through the sample stack. The active region of an MTJ type sample is in this case only ∼ 500 × 500µm2 , which is only a small fraction of the total electrode area. The exchange-bias properties are more strongly related to the electrode area as a whole rather than just the active junction area and so yield no useful information. Also, in a real MTJ structure the tunnel barrier is amorphous. Thus there should be no propagation of fcc (111) texture through the tunnel barrier. Deposition of a realistic MTJ-like structure gives a far better test of our ability to deposit a sufficiently high-quality thin Al layer – not only must the Al cover the upper surface of the lower electrode, it must cover the sides of the electrode also. This is one reason why sputtering is the deposition technique of choice for MTJ growth, as side-coverage by sputter deposition is generally far superior to that by evaporation methods. Hysteresis loops for samples with spacer layers deposited for 3.5, 4.5, 5.5 and 8.0s are shown in figure 4.8. We observe good separation of the switching of the two electrodes down to an Al deposition time of roughly 4.5-5.0s. For samples with Al layers deposited for 3.5s or less, the magnetic switching of the two layers is less distinct, possibly due to pinhole formation, but more likely due to magnetostatic coupling from the interfacial roughness or electrode geometry. At this point we have demonstrated the ability to deposit a reasonably thin aluminium layer and achieve independent magnetic switching of the two electrodes not only for samples deposited using the CIP sample wheel and masks, but also for samples with an MTJ-like structure deposited through our new CPP contact mask system. 125 M/MS 3.5s Al deposition 4.5s Al deposition 1.0 1.0 0.5 0.5 0 0 -0.5 -0.5 -1.0 -30 -20 -10 0 10 20 30 -1.0 -30 -20 M/MS 5.5s Al deposition 1.0 0.5 0.5 0 0 -0.5 -0.5 -20 -10 0 H (Oe) 10 0 10 20 30 20 30 8.0s Al deposition 1.0 -1.0 -30 -10 20 30 -1.0 -30 -20 -10 0 10 H (Oe) Figure 4.8: Hysteresis loops recorded by MOKE for Co/Al/Py crossed electrode structures with Al spacer layers deposited for 3.5, 4.5, 5.5 and 8.0s. 4.3.3 Determination of the Al deposition rate Discussion on the Al film has thus far focussed only on the deposition time, rather than the actual film thickness. We know that the deposition rates for most metals in our sputtering system are typically in the region of 3-5˚ As−1 , which for the purposes of optimisation has not caused any difficulty thus far, and gives a ballpark figure for our tunnel barrier thickness of 10-25˚ A. However, we now require quantitative knowledge of the actual thicknesses of the Al precursor layer. This may be obtained from x-ray reflectivity measurements. Using x-ray reflectivity it is simple to obtain information on the layer thickness, as discussed in section 2.7. On the down side, the x-ray scattering cross-section of aluminium is extremely small, meaning that it is not easy to characterise a sample containing purely Al using a laboratory x-ray source. This problem may be avoided 126 by depositing multilayer structures which allow thickness information to be gained from the Bragg peak positions. Firstly, a tantalum calibration film was deposited through the circular tunnel barrier mask. This calibration film was deposited for 50 s, and the total thickness determined to be (171±7) ˚ A, giving a Ta deposition rate of (3.4±0.1) ˚ As−1 . Note that this is not the same deposition rate as that for Ta deposited through the electrode masks. Next, a multilayer sample with structure Ta[10.0s]/{Al[2.0s]/Ta[5.0s]}×10 was deposited, again through the circular tunnel barrier mask. Ta has a large scattering cross-section for x-rays, resulting in a strong contrast between the effective refractive indices of alternate layers within the structure. As the deposition rate of Ta is now known, the positions of the multilayer Bragg peaks may be used to determine the thickness of the Al and its deposition rate. Each Al layer was deposited in the exact same fashion as the layer would be deposited as part of the MTJ stack, making this measured deposition rate truly representative of the Al barrier layer deposition rate. We find an Al layer thickness of (7.6±0.2)˚ A and hence a growth rate of (3.8±0.1)˚ As−1 . 4.4 Glow discharge oxidation of aluminium films The two important stages in the optimisation of the plasma oxidation conditions concern the pressure of the oxygen gas in the vacuum chamber - from which the plasma is formed - and the length of time required to plasma oxidise an Al film of a given thickness. In this section we shall discuss the steps taken to optimise the conditions used to form the alumina tunnel barrier by the glow discharge oxidation of thin aluminium films, deposited as previously outlined. 4.4.1 Oxygen gas pressure The first step to forming a reproducible plasma oxidised alumina tunnel barrier is to find the correct background pressure of oxygen gas to form the glow discharge plasma. As discussed in chapter 2, it is of vital importance that the growing oxide film be held in the negative glow region of the glow discharge in order to provide sufficient superthermal oxygen ions to assist the oxidation process. Variation of the oxygen 127 pressure affects the extent of the negative glow region of the discharge. Thus the background oxygen pressure must be tuned for the particular deposition system in question in order to provide oxygen ions to the growing oxide film. An oxygen pressure of 50mTorr was used previously by Miles and Smith[130] in their initial reports on plasma oxidised alumina. The group of Moodera at MIT, who pioneered the use of plasma oxidised alumina in MTJs, use an oxygen pressure of 75mTorr[10, 203] and an oxygen pressure of 100mTorr is used in the sputtering system at the University of Exeter[204]. Thus the ballpark figure would seem to be in the range of several tens to hundreds of mTorr. Visual inspection of the glow discharge through the vacuum chamber viewport allows an estimation of the optimum oxygen gas pressure. By applying a bias to the discharge electrode and then slowly introducing oxygen gas into the evacuated chamber, the variation of the spatial extent of the discharge with pressure is observed. For oxygen pressures below about 35-40mTorr the glow region does not reach out from the electrode to the sample position, resulting in an extremely low oxidation rate. In the range 50-150mTorr, the yellow glow - characteristic of an oxygen discharge is bright, and extends to the position of the growing sample. The luminosity at the sample position appears to decrease slightly with increasing oxygen pressure. Above 200mTorr the glow region no longer extends to the sample position, again resulting in a much reduced oxidation rate. From this initial inspection, it seems that a background oxygen pressure in the range 50-100mTorr should provide optimum conditions for glow discharge oxidation. For lower oxygen pressures in this range, it is found that the plasma discharge power is less strongly dependent upon the pressure – thus minor variations in oxygen pressure do not have such a strong effect on the oxidation process. Initial attempts to form tunnel barriers in a 50mTorr oxygen atmosphere proved successful, thus 50mTorr is taken to be the standard oxidation pressure for magnetic tunnel junctions deposited in our sputtering system. The power drawn by the plasma discharge at this pressure is typically in the range 80-110W with the discharge electrode biased at a voltage of -1250V with respect to ground. 128 4.4.2 Exposure to the glow discharge The final step in the optimisation process for the formation of thin alumina tunnel barriers for use in MTJs is to find the optimum length of time for which the aluminium film should be exposed to the glow discharge. This step in the fabrication process is crucial to obtaining a high TMR from magnetic tunnel junctions as both under- and over-oxidation lead to a rapid decrease in TMR. As the initial and final electronic states which take part in the tunnelling process are thought to be located close to the electrode/barrier interfaces the local properties of the interface are of extreme importance in determining the TMR characteristics of the junction. Under-oxidation can result in metallic aluminium remaining at the interface between the lower electrode and tunnel barrier, resulting in a reduction in the spin-polarisation and hence in the TMR. Alternatively, under-oxidation can produce a uniform sub-stoichiometric AlO film which may contain a high level of defect states, resulting in multi-step tunnelling and a loss of spin-coherence of the tunnel current. Over-oxidation, on the other hand, causes changes in both the electronic and magnetic structure of the lower electrode – oxides of Fe, Co and Ni behave very differently to the elemental metals. This may result in increased barrier thicknesses and paramagnetic or antiferromagnetic interfacial layers, both of which conspire to reduce the TMR of the junction. 4.4.3 Initial characterisation of junctions with thin AlO barriers For our initial study on oxidised full tunnel junction structures, we elected to deposit a series of samples with increasing Al spacer thickness. Two samples with each layer thickness were deposited and only one of the two was exposed to the glow discharge plasma. This allows a comparitive study of both the electrical and magnetic properties of the junctions before and after oxidation. The electrodes were composed of Ta[30˚ A]/Py[25˚ A]/FeMn[120˚ A]/Co[80˚ A] for the lower electrode and Py[200˚ A]/Ta[30˚ A] for the upper electrode, these thicknesses being chosen so as to produce a suitably well exchange-biased bottom electrode whilst still allowing the MOKE system to probe the important magnetic layers of the sample. The thickness of the Al layer prior to oxidation was varied between 8 and 17˚ A. The 129 4 TMR (%) 3 2 1 0 -300 -150 0 150 300 H (Oe) Figure 4.9: TMR vs. applied field for our first FeMn/Co/AlO/Py junction to show MR greater than 1% at 77K . oxidised samples were exposed to the glow discharge for 180s, which it turns out, generally results in some degree of overoxidation. From the initial transport characterisation of the oxidised junctions we saw a sensible increase in junction resistance with increasing barrier thickness, giving confidence that we are observing electron tunnelling. We also observed spin-valve-like magnetoresistance of between 0.5% and 3% at 77K. Figure 4.9 shows the TMR curve of our first sample to show an MR greater than 1%. None of the unoxidised samples showed any evidence of either electron tunnelling or magnetoresistance. Room temperature hysteresis loops were recorded for each pair of samples. The oxidation process seems to result in a slight reduction in the offset field of the Py free layer, indicative of a decrease in the magnetostatic coupling. This may be due either to the increase in barrier thickness upon oxidising, or to changes in the morphology of the upper surface of the alumina layer after exposure to the oxygen plasma. Further unoxidised samples were grown in a separate vacuum cycle, without any exposure to background oxygen gas during growth. The hysteresis loops for these samples are similar to those for the unoxidised samples grown alongside the tunnel junctions. This shows that the short exposure to background oxygen during the plasma oxidation of 130 10 R 0 (Ω ) 10 10 10 10 10 5 4 77 K 293 K 3 2 1 0 20 40 60 80 100 120 40 60 80 100 120 20 TMR (%) 15 10 5 0 20 Oxidation time (s) Figure 4.10: Junction resistance and TMR against glow discharge exposure time for junctions with a 10˚ A Al layer. other samples has no significant effect on the bulk oxidation state of a given Al layer. The results of this initial experiment show that our Al films are continuous down to a thickness of ∼8˚ A and shows that the interlayer coupling observed by MOKE is due to magnetostatic coupling rather than pinhole formation. We can be confident in our ability to deposit extremely thin aluminium layers for use as tunnel barriers. At this point it was decided that we should concentrate our efforts on optimising the oxidation conditions for junctions with as thin a barrier layer as possible. Low resistance tunnel junction samples with thin tunnel barriers generally show larger TMR than do junctions with more resistive barriers[199]. This is one reason for the recent resurgence in interest in natural (non-plasma assisted) oxidation, which results in a less resistive tunnel barrier. Also, a low junction resistance allows a relatively large sense current to be driven through the junction, significantly enhancing the signal-to-noise ratio of D.C. TMR measurements. 131 200 TMR (%) 150 100 50 0 -300 -150 0 150 300 H (Oe) Figure 4.11: Room temperature TMR of 176% in a Co/AlO/Py junction due to geometrical enhancement. For junctions with the above electrode structure, we have investigated the effect of oxidation time on both the zero-bias resistance and magnetoresistance. For samples oxidised for more than 30s we observe an increase in resistance and decrease in TMR with increasing oxidation time when the Al precursor layer is either 8 or 10˚ A thick. Figure 4.10 shows resistance and magnetoresistance against oxidation time for a set of junctions with 10˚ A Al precursor layers. This trend with oxidation time is typically indicative of overoxidation of the junction, as the formation of CoO causes an increase in the effective barrier thickness whilst causing a reduction in TMR[203]. Below tox ' 30 s, on the other hand, there is a rapid drop in junction resistance – in some cases the measured resistance even becomes negative. These junctions generally show a larger magnetoresistance than those with longer oxidation times, although the rapid increase in TMR is somewhat surprising. Figure 4.11 shows the room temperature magnetoresistance for an FeMn/Co/AlO/Py junction with a tunnel barrier formed by plasma oxidising an 8˚ A aluminium layer for 30s. The measured four-point resistance is 0.2Ω which is slightly lower than the 1.5Ω expected from a Simmons model calculation with an effective barrier thickness ∆s = 12˚ A and average barrier height φ = 1.75eV, a fairly typical value from the literature – and perhaps somewhat pessimistic. The Julliere formula (equation 1.4) gives the maximum possible TMR for a 132 Co/AlO/Py MTJ as 31.8% at zero bias and absolute zero temperature, using the values PCo = 42% and PPy = 45% [205]. Thus the 176% TMR measured at room temperature must be an artifact of some type. 4.5 Geometrically enhanced TMR The small and negative measured resistances and unrealistically large TMR values discussed above have been reported on in the early literature regarding magnetic tunnel junctions, the phenomenon being known as ‘geometrical enhancement’[206]. This effect occurs when the resistance of the lead electrodes within the junction area becomes comparable with the magnitude of the tunnel junction resistance, resulting in an inhomogeneous current distribution across the junction area. As the junction resistance decreases, the electrical current tends to follow the path of least resistance, which typically results in a high current density in the corner of the junction where the current leads intersect. This generally produces a reduced potential at the sides where the voltage leads meet the junction, due to the significant voltage drop across the junction area. Thus the derived four-point resistance may have a greatly reduced magnitude, in some cases even becoming negative. As both R↑↑ and R↑↓ are reduced by a similar amount, the derived TMR ratio is artificially enhanced. Geometrical reduction of the TMR has also been reported in large-area junctions[207]. However this effect has not been observed in our samples. Van de Veerdonk et. al. derive the position dependent tunnel current density and lines of equipotential within the junction area, using finite element calculations, in terms of a single parameter given by the ratio of the RA product of the tunnel barrier and the typical sheet resistance of the electrodes[203, 208]. This results in a so-called ‘typical length scale’ for the current distribution within the junction area ρj R,b(t) 2 = ltyp where the condition ltyp < l, w with l and w being the track widths of the two electrodes, results in an inhomogeneous current distribution and hence geometrically enhanced TMR. For a tunnel junction where both electrodes have the same track 133 width, the condition for geometrical enhancement reduces to Rj = R (4.1) thus the TMR is liable to geometrical enhancement when the sheet resistance of the electrode becomes comparable to the junction resistance. For the initial junctions used for this study i.e. with electrode structures of Ta/Py/FeMn/Co and Py/Ta, the typical values of the electrode sheet resistances are (25±1)Ω/ and (12±1)Ω/ for the pinned and free electrodes respectively. This requires a junction resistance of ∼100-125Ω at the very least[209] in order to avoid geometrical enhancement effects. This is obviously incompatible with the oxidation of an 8˚ A aluminium film with junction area 500×500µm2 from the previous Simmons model calculation. Turning back to figure 4.11, the 176% TMR shown by this junction is certainly indicative of geometrical enhancement. As the TMR for this sample is enhanced, the measured resistance must also be reduced by geometrical effects and must thus be somewhat greater than the 0.2Ω measured. This indicates that the optimum oxidation time for an 8˚ A Al layer is somewhat less than 30s. We are, however, unable to measure the true properties of such a junction due to geometrical enhancement. 4.5.1 Preventing geometrical enhancement effects There are three possible ways of circumventing the problem of geometrical enhancement of the TMR in magnetic tunnel junctions. These are: - Reducing the sheet resistance of the electrodes by adding conduction layers of a highly conducting metal such as Cu or Al, whilst leaving the tunnel resistance unchanged. - Reducing the track width of the electrode. Reduction of the track width by a factor α will increase the electrodes sheet-resistance by the same factor, but increase the tunnel resistance by a factor α2 . - Increasing the tunnel resistance whilst leaving the electrode sheet resistance unchanged. 134 Initially we have attempted to reduce the electrode sheet resistance by adding aluminium conduction layers to each electrode. The new electrode structures are Ta[30˚ A]/Al[200˚ A]/Py[25˚ A]/FeMn[120˚ A]/Co[80˚ A] and Py[200˚ A]/Al[200˚ A]/Ta[30˚ A]. Formation of the tunnel barrier seems to be unaffected by the increased thickness of the lower electrode – the Al conduction layer appears to produce no significant enhancement of the surface roughness or any problems regarding side-coverage of the electrode. The exchange-bias properties of the pinned lower electrode also seem to be unaffected. These new electrode stacks typically have sheet resistances of (4±1)Ω/ for both free and pinned electrodes. Unfortunately this is still roughly an order of magnitude more resistive than the anticipated tunnel barrier resistance for a junction formed from an 8˚ A Al layer with the present electrode track width of 0.5mm. Using these electrodes we have been able to measure samples with oxidation times slightly lower than for the previous electrode stack configuration. However geometrical enhancement effects are still observed. As most of the current shunts through the Al conduction layer at present, doubling the thickness of the Al conduction layers runs the risk of enhancing the surface roughness or causing problems with side-coverage, whilst only decreasing the electrode sheet resistance by a factor of ∼2. Thus we would ideally like to deposit electrodes with a narrower track width. The masks with a 200µm track that we have at present give low growth rates through the electrode slot, resulting in a much enhanced surface roughness. We are currently in the process of fabricating further contact masks with both a reduced track width and suitable aspect ratio. Using these masks we should be able to remove the effect of geometrical enhancement whilst not affecting the deposition rates or film morphology. These masks are, however, presently unavailable to us and so the only course of action is to increase the tunnel barrier resistance. 4.6 Characterisation of magnetic tunnel junctions An oxidation time of ∼30s seems to be reasonable for the formation of thin tunnel barriers from the previously presented data. We should be able to slowly increase the thickness of the Al layer whilst holding the oxidation time at 30s, and eventually 135 77 K 293 K R 0 (Ω ) 100 10 9 10 11 12 13 14 9 10 11 12 13 14 20 TMR (%) 15 10 5 0 Nominal Aluminium thickness (Å) Figure 4.12: Zero-bias resistance and TMR against nominal Al thickness for a 30s oxidation time. Note the logarithmic scale in the upper figure. we will find the optimum Al thickness for this oxidation time. That thickness should be slightly greater than 10˚ A, and due to the exponential dependence of junction resistance on barrier thickness[97], should result in a suitably resistive junction to avoid geometrical enhancement effects. The optimum barrier thickness should show up as a maximum in the TMR due to lack of defects, electrode oxidation or remaining Al metal at the interface. Figure 4.12 shows the TMR as a function of the nominal Al thickness at both room temperature and 77K for a set of FeMn/Co/AlO/Py MTJs. A maximum TMR of 17.5% is observed in these samples at an Al thickness of 10.6˚ A, although there is some scatter in the data. The room-temperature resistance of this sample is 27Ω, which is suitably resistive to avoid geometrical artifacts if the sheet resistance of the electrode is ∼4Ω. Several sets of samples with different electrode configurations have have been investigated so far. In all cases it has been found that the optimum oxidation time is close to 30s for a nominally 10.6˚ A thick TMR (%) 136 20 20 15 15 10 10 5 5 TMR (%) 0 -150 -50 50 150 0 -300 20 20 15 15 10 10 5 5 0 -150 -50 50 150 0 -300 H (Oe) -150 0 150 300 -150 0 150 300 H (Oe) Figure 4.13: TMR of Ta/Al/Co/AlO/Py/Al/Ta (left frames) and Ta/Al/Py/FeMn/Co/AlO/Py/Al/Ta (right frames) MTJs, measured at room temperature (upper frames) and at 77K (lower frames). Note the lower TMR due to the lack of a good antiparallel magnetic state in the non-exchange-biased sample. Al layer. Interestingly, both the zero-bias resistance and TMR characteristics of the junctions appear to show some dependence upon the material configuration of the electrodes. Non-exchange-biased Ta/Al/Co/AlO/Py/Al/Ta junctions show a larger zero-bias resistance than exchange-biased junctions with the structure Ta/Al/Py/FeMn/Co /AlO/Py/Al/Ta. On the other hand, the exchange-biased samples show a slightly larger TMR at all temperatures. One likely explanation for this is that the Py/FeMn pinning bilayer below the Co lower electrode acts to enhance the surface roughness of the lower electrode, increasing the occurrence of tunnelling ‘hotspots’ slightly. The lower TMR in the Co/AlO/Py junctions can be explained by the fact that we do not have such a well defined antiparallel magnetic configuration as in the samples with a Py/FeMn pinning bilayer, as is shown in figure 4.13. TMR (%) 137 25 25 20 20 15 15 10 10 5 5 0 -300 -150 0 150 300 0 -300 -150 H (Oe) 0 150 300 H (Oe) Figure 4.14: TMR of a Co/AlO/Co/FeMn MTJ at room temperature and at 77K. Another interesting result has been found when both magnetic electrodes are comprised of Co. The junction structure Ta/Al/Co/AlO/Co/FeMn/Al/Ta has a comparable zero-bias resistance to the Ta/Al/Co/AlO/Py/Al/Ta junctions discussed above, indicating that the increased junction resistance is related to the structure of the lower electrode. We observe a significantly larger TMR in these Co/AlO/Co/FeMn junctions than in our FeMn/Co/Al/Py samples. This is in no way related to the magnetic alignment of the samples as both structures show good exchange-bias properties. This increased TMR seems somewhat surprising given that Co is accepted to have a slightly lower tunneling spin-polarisation than Py – 42% as opposed to 45%[205]. The mechanism by which this increase in the TMR occurs is most probably to do with the oxidation state of the upper electrode/tunnel barrier interface. Table 4.1 shows the enthalpy of formation for oxides of some of the materials used in our MTJs. The most stable oxide is that of aluminium – the oxide which we intend to form by our glow discharge process. Fe3 O4 is clearly the next most stable compound, with CoO having a much lower enthalpy of formation. Thus it is quite likely that Fe atoms impinging on the surface of an already oxidised tunnel barrier may react chemically with oxygen atoms at the surface, forming an iron-oxide interface layer. Cobalt, on the other hand, would be far less likely to react chemically with the surface oxygen. This mechanism may explain why we observe a larger TMR in MTJs where both electrodes are Co than when the upper electrode is Py. The TMR values which we report above are in good agreement with those reported 138 Oxide compound Enthalpy of formation ∆f H 0 (kJ/mol) Al2 O3 -1675.7 CoO -237.9 Fe2 O3 -824.2 Fe3 O4 -1118.4 Ni2 O3 -489.5 Table 4.1: Formation enthalpies of the stoichiometric oxides which may form in our tunnel junction structures, after reference [127] in the literature in recent years. Kyung et. al.[210] observe a room temperature TMR of 15% in Co/AlO/Co junctions where the AlO thickness is 13˚ A, whilst Kuiper et. al.[202] observe typically 14-18% . Hughes et. al.[204, 211] measure 23.2% TMR at 2K and 14.9% at room temperature in Co/Al/Py junctions. Van de Veerdonk et. al.[203] measure ∼22% at 10K and ∼12% at room temperature in the same system. We measure 16.6% at room temperature, 24% at 77K and 24.5% at 4.2K in Co/AlO/Co MTJs and 12% at room temperature, 19.5% at 77K and 23% at 4.2K in the Co/AlO/Py MTJ system. We have developed the ability to deposit good quality tunnel barriers formed by the plasma oxidation of an aluminium film. It is, however, important to convince ourselves that tunnelling is the transport mechanism taking place in our junction structures. This may be determined by investigating whether or not our samples fulfill the so-called Rowell criteria. 4.7 Rowell criteria for tunnelling in normal-state junctions Tunnelling in superconductor/insulator/superconductor (SIS) and superconductor/ insulator/normal metal (SIN) junctions has long been used to probe the physical mechanisms behind the phenomenon of superconductivity. In order to verify that quantum mechanical tunnelling is the dominant transport mechanism in these structures, a set of criteria known as the Rowell criteria have been formulated[133]. In 139 tunnel junction structures where neither of the electrodes consist of a superconducting material, only three of the Rowell criteria for tunnelling remain valid. These three remaining criteria are: - Exponential dependence of the junction resistance upon the barrier thickness. - Non-ohmic current-voltage (I-V) characteristics or conductance-voltage (∂I/∂V V) characteristics which are well modelled by a rectangular or trapezoidal barrier model. - Weak non-metallic temperature dependence of the junction resistance. There has recently been heated debate in the literature as to whether or not the three remaining Rowell criteria are suitable to uniquely identify tunnelling behaviour in magnetic tunnel junctions. The first of these Rowell criteria - regarding the variation of junction resistance with thickness - has been attacked on the grounds that the expected exponential trend may allegedly be mimicked by a pinholed tunnel barrier. Rabson et. al.[212] describe the formation of an incomplete tunnel barrier using a lattice model and allow only classical conduction through the ‘pinholes’ between the two electrodes. They show that a pinhole density which is distributed according to Poisson statistics will produce an exponential dependence of the perpendicular resistance upon the nominal barrier thickness, and that the characteristic scaling length in the cases of both tunnelling and pinhole conduction is of the order of 1 monolayer thickness. Thus conduction through a pinholed barrier may be seen as indistinguishable from tunnelling across a complete barrier. The validity of the second Rowell criterion - non-ohmic I-V behaviour - has also been placed in doubt by the same group. ˚ Akerman et. al.[213] have shown that ‘tunnel barriers’ which have definite pinholes may also exhibit non-linear I-V characteristics which yield quite reasonable results when fitted with e.g. the Simmons[97], Hartman[98] or BDR[99] barrier tunnelling models. This shows that non-linear I-V behaviour may also not be seen as a definitive characteristic of the tunnelling mechanism. To date, only the third of the remaining Rowell criteria for normal state structures - nonmetallic temperature dependence of the junction resistance - has escaped 140 criticism with regard to its validity. Thus we now have only one criterion by which to uniquely classify a potential tunnel junction. 4.7.1 Satisfying the Rowell criteria Despite the recent misgivings regarding the Rowell criteria, we can show that our MTJs satisfy all three criteria, giving us confidence that tunnelling is the dominant transport mechanism. Figure 4.15 shows the room temperature and 77K zero-bias resistances against nominal Al2 O3 thickness for a set of samples where the deposition time of the Al precursor layer has been varied, whilst keeping the plasma exposure time constant. The Al2 O3 thickness has been calculated assuming that the Al film increases in thickness by 50% upon oxidation. Although the constant oxidation time results in a range of oxidation states from over- to under-oxidised with increasing Al deposition time, the total barrier thickness has been shown to remain roughly constant over such a range[202]. If we assume that the average barrier height does not vary significantly over the range of oxidation states, we may take this data as evidence for the exponential dependence of the junction resistance upon the barrier thickness. Although this is not a definitive test that tunnelling is the only active conduction mechanism in these samples, we have satisfied the first of the Rowell criteria. Examining the data in figure 4.15 further we see that the zero-bias resistance measured at 77K is, in each sample, consistently higher than the resistance as measured at room temperature. Although the data consist of only two points per sample, a non-metallic temperature dependence is clearly evident. Thus in this one set of measurements we have clearly satisfied two of the three Rowell criteria for tunnelling. We now turn to the current-voltage data for the individual samples, taking the sample with nominal Al2 O3 thickness of 14.25˚ A as a typical case. Figure 4.16 shows the I-V curve for this sample, measured at 77K in order to remove any spurious substrate signal. A clear non-ohmic behaviour is observed, which results in the following fitting parameters. Fitting with the Simmons model results in an average barrier height of (1.96 ± 0.02)eV and barrier thickness of (13.5 ± 0.1)˚ A, whilst the Hartman model gives barrier heights of (1.82 ± 0.02)eV and (2.06 ± 0.02)eV, with a 141 1000 77K 293K R 0 (Ω ) 100 10 1 12 14 16 18 Nominal Al2O3 thickness (Å) Figure 4.15: Zero-bias resistance as a function of barrier thickness for a set of samples exposed to the oxygen plasma for 30s. The exponential dependence on thickness satisfies one of the three Rowell criteria, a second being satisfied by the increase in resistance upon cooling from room temperature to 77K. barrier thickness of (13.6 ± 0.1)˚ A. The fitted barrier heights are in extremely good agreement with those reported in the literature, whilst the fitted barrier thickness is surprisingly close to the nominal barrier thickness. A likely explanation for this is that either we have a very low surface roughness on both sides of the tunnel barrier, or that the roughness is strongly conformal. This would result in few thinner ‘hot-spots’ and a closer agreement between the effective barrier thickness for tunnelling and the nominally deposited barrier width, or that measured by x-ray reflectivity. 4.8 Sample to sample consistency Although we have previously observed a strong degree of consistency between both the zero-bias resistance and TMR measured for nominally identical samples grown in separate vacuum cycles, it is necessary also to test the absolute consistency of nominally identical samples grown in the same vacuum cycle. Without performing this control experiment, it would be impossible to draw sensible conclusions regarding the systematic variation of some aspect of the junction growth. For this study we have grown a set of samples with a junction structure Ta[30˚ A]/Al[200˚ A]/Co[80˚ A]/Al[10.6˚ A]+O2 142 0.02 Simmons Hartman Current (A) 0.01 0 -0.01 -0.02 -0.4 -0.2 0 0.2 0.4 Bias (V) Figure 4.16: Current-voltage characteristics of a Co/AlO/Py MTJ with a nominally 14.25˚ A thick Al2 O3 barrier. Fits with the Simmons and Hartman barrier tunnelling models are shown. The apparent non-ohmic behaviour satisfies the remaining Rowell criterion. /Co[120˚ A]/FeMn[120˚ A]/Al[200˚ A]/Ta[30˚ A]. The oxidation is identical in each case, with the oxidation time being 30s. Figure 4.17 shows the zero-bias resistance at both room temperature and 77K for a set of samples with the above structure. It is immediately apparent that the zero-bias junction resistance shows a good degree of consistency from sample to sample. We obtain mean values for the junction resistance of (27±7)Ω at 77K and (21±5)Ω at room temperature. Despite the relatively large uncertainty in junction resistance, the spread is indicative of a good degree of control over both the deposition of the aluminium film, and both its roughness and that of the electrode beneath it. The relatively small magnitude of the spread in resistance is obvious in comparison with that in figure 4.15, which shows the exponential dependence of the resistance on tunnel barrier thickness. Figure 4.18 shows the TMR at both room temperature and at 77K, for the same set of nominally identical samples. We again see a strong degree of sample-to-sample consistency. The mean value of the TMR is (23±1)% at 77K and (15±2)% at room temperature. The variation in the TMR - especially at 77K - shows the good consistency in the tunnel barrier oxidation conditions, both with respect to the oxidation 143 100 R 0 (Ω ) 77 K 293 K 10 1 1 2 3 4 5 6 Sample number Figure 4.17: Zero-bias resistance at room temperature and 77K for a set of nominally identical Co/AlO/Co/FeMn MTJs, showing the degree of sample-to-sample consistency in our deposition. 30 77 K 293 K TMR (%) 20 10 0 1 2 3 4 5 6 Sample number Figure 4.18: TMR at room temperature and 77K for a set of nominally identical Co/AlO/Co/FeMn MTJs, again showing the degree of sample-to-sample consistency. 144 state of the electrode/barrier interface and the formation of defect states within the barrier. If either the interface is oxidised, or the barrier has numerous imperfections, then they are at least consistent from one sample to the next. The slightly larger variations in zero-bias resistance and TMR at room temperature may be in part attributed to substrate shunting effects. These data show that we are able to deposit MTJs with a sufficiently good degree of sample-to-sample consistency to be able to draw sensible conclusions based upon the variation of the TMR as a function of some systematically varied parameter. The reproducibility of control samples is, of course, the holy grail for any scientist wishing to perform systematic studies. 4.9 Summary We have successfully deposited magnetic tunnel junction samples with a variety of different electrode compositions. A summary of the magnetoresistive properties of junctions with different electrode structures are presented in the table below. Temperature Bottom electrode Top electrode TMR (K) material material (% ) 293 Co Py 12 Co Co 16.6 Co Py 19.5 Co Co 24 Co Py 231 Co Co 24.5 77 4.2 1 This sample did not have an exchange-bias layer and did not show a good antiparallel state. Thus the actual TMR would be greater than the 23% measured. 145 4.10 Extensions to this work Related to our MTJ study there are several areas of work which, although not presently at a sufficient level of completeness for inclusion in this thesis, merit some discussion here. 4.10.1 Rare-earth electrode materials We are presently in the process of investigating MTJs where one of the electrodes is a rare-earth metal. It was initially hoped that this study could be used to compare and contrast the GMR and TMR in RE/TM magnetic heterostructures. Unfortunately, rare-earths are somewhat more difficult to incorporate into an MTJ structure than was initially envisaged. We are presently working on MTJs where one electrode is comprised of a Dy/Co bilayer, with the Co film at the interface with the tunnel barrier. The idea is to investigate the dependence of the TMR on the Co layer thickness, in a similar fashion to that in [49, 177]. Deposition of these structures is hampered by the fact that the rare-earth oxides have large enthalpies of formation. The enthalpy of formation for e.g. Dy2 O3 is -1863.1 kJ/mol, in comparison to -1675.7 kJ/mol for Al2 O3 [127]. Thus dysprosium tends to form oxides when deposited under, upon, or even close to the tunnel barrier. In order to counteract this we are looking towards modifying our MTJ sample wheel to allow deposition of layers at cryogenic temperatures by incorporating a liquid nitrogen cooling system. This should prevent the formation of Dy oxides, resulting in consistent junctions with good tunnel barriers. 4.10.2 Andreev point-contacts Point contact Andreev reflection (PCAR) allows measurement of the spin-polarisation of ferromagnetic materials by the process of Andreev reflection at a ferromagnet superconductor interface. The usual experimental geometry for PCAR measurements is to have a superconducting wire, etched to form a sharp tip, which is brought into contact with a film or foil of the material under investigation by means of a micrometer screw. Recently, Andreev reflection has been used to probe the continuity of Al2 O3 films for use as barrier layers in magnetic tunnel junctions[213]. In this paper ˚ Akerman 146 Conductance (arb. units) 1.62x10 1.61x10 1.60x10 1.59x10 -4 -4 -4 -4 -3 -2 -1 0 1 2 3 Bias (mV) Figure 4.19: Conductance spectra for a Nb/Al/Cu Andreev point-contact at 4.2K. The reduced sub-gap conductance is due to thermal broadening. et. al. used Nb/Al2 O3 /Co junctions, and measured the conductance vs. bias both above and below TC of the Nb for different deposition and oxidation conditions of the Al film. Samples with a completely oxidised, continuous Al2 O3 barrier show a BCS quasiparticle DOS when measured below TC . In the case of junctions which have incomplete Al2 O3 barriers, the conductance-voltage spectra are indicative of Andreev reflection. Analysis of the conductance within the modified BTK formalism[59, 116, 117] allows the spin-polarisation of the ferromagnetic electrode to be measured. We have developed a technique for reliably forming superconducting point contacts, based upon the techniques discussed above for depositing MTJs. Our technique is subtly different to that reported by ˚ Akerman et. al. as their method relies upon forming a discontinuous Al2 O3 film, thus creating Nb/FM contacts. We deposit a thick, continuous insulating layer, and then deliberately short-circuit the junction to form Al/FM contacts where the Al becomes superconducting by proximity to the Nb lower electrode. This technique allows for more reproducible point-contact formation. 147 Unfortunately, due to time restrictions, we have not yet been able to obtain quantitative results from point-contact experiments. At present all our cryogenic measurements on MTJ and point-contact samples are performed at 4.2K. At this temperature the thermal broadening of the conductance spectra is of a comparable magnitude to the induced pair-potential in the Al point-contact. This means that the measured sub-gap Andreev conductance is much reduced even in the case of a paramagnet such as Cu. Figure 4.19 shows the measured conductance spectrum for a Nb/Al/Cu point-contact junction at 4.2K. The increase in conductance about zero bias is due to Andreev reflection at the Al/Cu interface. However the measured enhancement of the sub-gap conductance is far less than the anticipated 100%, predominantly due to thermal broadening. Experiments such as this would be far better performed at lower temperatures. In order to facilitate this we are in the process of recommissioning a 3 He cryostat system, which will allow us to obtain quantitative results on a range of magnetic systems including the rare-earth metals. 4.11 Conclusion The work presented in this chapter describes the steps taken in order to develop a facility for the deposition of high-quality magnetic tunnel junction samples in our sputtering system at Leeds. Beginning from scratch we have developed a contact masking system capable of depositing up to 18 samples per vacuum cycle, whilst being able to change between contact masks without the need to break vacuum. We have developed the processes for both electrode and tunnel barrier deposition. We are able to deposit continuous aluminium films with thicknesses down to (at least) 8˚ A whilst remaining pinhole free. A plasma oxidation technique has been implemented, allowing consistent and reproducible tunnel barrier formation from aluminium layers of various thicknesses. Exchange-bias may be used to control the relative orientations of the electrode magnetisation with applied field, allowing us to achieve good antiparallel alignment over a wide range of magnetic field. No postdeposition annealing is required in order to set the exchange-bias direction. Using the contact masks currently available to us we are able to consistently deposit magnetic tunnel junctions with a 10.6˚ A aluminium precursor layer, having 148 a junction RA product typically of ∼5MΩµm2 . The ‘hit-rate’ of successful tunnel junctions is presently at the 75-80% level and improving. The magnetoresistance that we observe in our junctions is in reasonably good agreement with those presented in the literature in recent years. In conclusion, we are now able to deposit magnetic tunnel junction samples with the levels of quality, consistency and reproducibility required to present systematic studies on the fundamental physics of spin-polarised tunnelling phenomena. 149 Chapter 5 Conclusion The aim of this thesis has been the investigation of spin-polarised transport mechanisms in thin-film magnetic structures, many of which contain magnetic lanthanide metals. The giant magnetoresistance mechanism has firstly been investigated, with the main focus being on the heavy rare-earth metal dysprosium. Gadolinium has been discussed mainly due to its to accessibility to theory and neodymium has been used to draw comparisons with the light rare-earths. Secondly, the facility for the deposition and characterisation of magnetic tunnel junctions has been realised. The ability to deposit very good quality samples has been shown and we are now beginning to investigate samples where rare-earth metals are included in the sample structure. 5.1 Conclusion Spin-polarised conduction in the rare-earths has been investigated using polycrystalline rare-earth/copper magnetic multilayers. When the rare-earth layers are in ferromagnetically ordered phases a GMR of ∼-1% is observed. No GMR is observed when the rare-earth layers are in either antiferromagnetic or paramagnetic phases, indicating that the GMR is related to the net spin-polarisation of the conductionband which is present only in the ferromagnetic phase. We have deconvoluted the contribution of the anisotropic magnetoresistance from our results in order to prove that the magnetoresistance is definitely due to the GMR. Upon exchanging alternate rare-earth layers in the multilayer stack for an equal thickness of cobalt, an inversion 150 of the GMR is clearly observed when the rare-earth metal is dysprosium or gadolinium and is not seen when it is neodymium. This may be related to the sign of the conduction electron spin-polarisation of the rare-earth metal at the Fermi level. The inversion of the GMR in dysprosium and gadolinium shows that the polarisation in these metals is opposite to that in cobalt, whereas that in neodymium is not. The spin-polarisation of the transport current in cobalt is well known to be biased toward the minority spin channel. Thus we find that the spin-polarisation in neodymium is also in the minority spin, whereas in gadolinium and dysprosium it is in the majority spin channel. This result has been related to the spin-polarisation which is naively expected from the simple free-electron RKKY interionic coupling mechanism assumed to mediate the magnetic ordering interaction in the rare-earths. The sign of the expected polarisation agrees with that determined from our GMR measurements. This result constitutes the first direct experimental evidence of the RKKY conduction electron spin-polarisation in pure rare-earth metals. We have developed the facility for both the deposition and characterisation of magnetic tunnel junction samples in our laboratory. An in-situ contact mask changing system has been designed and built, allowing a variety of crossed electrode structures, i.e. magnetic tunnel junctions, CPP magnetic multilayers and Andreev point-contacts, to be deposited in our sputtering system without the need to expose the samples to atmosphere at any point during growth. The ability to form good quality tunnel barriers has been shown, with optimisation of both the aluminium deposition parameters and oxidation conditions having been explored. Our MTJ samples have been shown to satisfy the three Rowell criteria for non-superconducting tunnel junctions, which gives as strong an indication as is possible that quantum mechanical electron tunnelling is the dominant transport mechanism in our samples. Large TMR values have been exhibited in our magnetic tunnel junctions. In the FeMn/Co/AlO/Py system initially studied, TMR values of 12% at room temperature, 19.5% at 77K and 23% at 4.2K have been observed. Strangely, larger still TMR values are found in the Co/AlO/Co/FeMn system. Here we measure 16.6% at room 151 temperature, 24% at 77K and 24.5% at 4.2K. This is somewhat surprising considering that the tunnelling electron spin-polarisation of cobalt is generally accepted to be slightly lower than that of permalloy. This result may be attributed to oxidation of the permalloy electrode during the initial stages of growth. The TMR values measured in our junctions are in reasonably good agreement with those reported in the literature over recent years. Our peak TMR values are, at the time of writing, the highest reported by any research group in the U.K. for MTJs using conventional transition metal electrode materials. 5.2 Future work Almost all of the work reported on in this thesis is ongoing. Although the study of GMR in the rare-earths has reached a suitable point of conclusion with regard to the RKKY mechanism, there are still many interesting questions which remain unanswered. At present we do not know whether or not the crystal structure of the samples plays an important role in the magnetic properties. Studies using different spacer layer materials or fully epitaxial samples may yield interesting results. It is also not fully clear what the mechanism is by which we find ferromagnetism in our neodymium/copper multilayers. Whether it is related to the crystal structure or whether some kind of size effect is responsible is presently unknown. We intend to investigate the role of the interplay between the crystal structural and magnetic ordering more fully in sputtered neodymium/copper multilayers. The development work on the deposition of magnetic tunnel junction structures continues apace. The work in this thesis provides a strong foothold from which to continue developing the deposition parameters in order to improve the spin-coherence of the tunnelling current in our junctions. The work on MTJs presented in this thesis represents just the tip of the iceberg in terms of the physics which may be studied using magnetic tunnel junctions. Most work in this field is highly focussed on device applications with little ‘blue skies’ work on other, perhaps less commercially viable, materials. Studies on rare-earth/transition metal composite electrode structures - as 152 discussed briefly at the end of chapter 4 - in both MTJ and superconductor tunnelling structures will allow precise measurement of the tunnelling spin-polarisation in such hybrid structures. Double barrier junctions also present a novel method for injecting and analysing spin-polarised currents into, and from, a variety of non-magnetic materials. This will allow us to test ideas on how an electron loses spin-coherence over macroscopic distances. We intend for a Ph.D. student to continue this area of research. The MTJ may also be incorporated into more complex device structures such as the magnetic tunnel transistor (MTT), in effect a solid-state implementation of the ballistic electron emission microscopy (BEEM) technique. Such a structure allows the injection of a highly spin-polarised current into a semiconductor with control over the degree of spin-polarisation, obviously a highly sought after property for spintronics applications. We have recently received EPSRC funding to work on the development of such devices, based upon the techniques for depositing MTJs developed in this thesis and will have a Ph.D. student to work on this project also. The ability to measure Andreev reflection in superconducting point contacts opens the door for a wide variety of future work in this new and exciting area. Measurements reported on in the literature thus far have concentrated upon the search for half-metallicity in candidate materials. However, measurement of the spin-polarisation arising in heterostructures has not been discussed thus far. 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