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Contents
1    Introductory Magnetism ......................................................    1
1.1       Fundamental Concepts and Definitions ...............................    1
1.1.1    Basic Electrostatics.............................................    2
1.1.2    Basic Magnetostatics ...........................................    3
1.1.3    Demagnetization in Uniformly Magnetized Bodies ..........    4
1.1.4    Domains in Partially Magnetized Bodies .....................    6
1.2       Induced Magnetism.....................................................    8
1.2.1    Diamagnetism and Paramagnetism ............................    8
1.2.2    Temperature Dependence of Susceptibility ...................  11
1.3       Spontaneous Magnetism ...............................................  15
1.3.1    Classical Ferromagnetism and Antiferromagnetism ..........  15
1.3.2    Solutions of the Brillouin¨CWeiss Equation ...................  16
1.3.3    Quantum Origins of the Molecular Field .....................  19
1.3.4    The Ising Approximation ......................................  24
1.4       Gyromagnetism .........................................................  25
1.4.1    Larmor Precession and Resonance ............................  26
1.4.2    Phenomenological Relaxation Theory ........................  27
1.4.3    Complex Susceptibility Theory................................  29
1.4.4    Resonance Line Shapes ........................................  33
Appendix 1A    Spin¨CLattice Contribution to Linewidth .....................  34
References.......................................................................  35
2    Magnetic Ions in Oxides ......................................................  37
2.1       The Transition Metals ..................................................  37
2.1.1    The Periodic Table .............................................  38
2.1.2    Iron Group 3d
n Ions ...........................................  40
2.1.3    Rare Earth 4f
n Ions............................................  42
2.1.4    4d
n and 5d
n Ions ..............................................  42
2.2       Oxygen Coordinations .................................................  43
2.2.1    Crystal Systems and Point Groups ............................  44
2.2.2    Cubic Symmetry ...............................................  45
2.2.3    Lower Symmetries .............................................  47
2.3       Crystal Electric Fields ..................................................  48
2.3.1    Angular Momentum States ....................................  49
ixx Contents
2.3.2    Crystal Field Hamiltonian .....................................  50
2.3.3    Hierarchy of Perturbations .....................................  54
2.3.4    Weak-Field Solutions ..........................................  55
2.3.5    Group Theory and Lower Symmetry ..........................  64
2.3.6    Strong Field Solutions and Term Diagrams ...................  68
2.3.7    Rare-Earth Ion Solutions.......................................  71
2.4       Orbital Energy Stabilization ...........................................  73
2.4.1    One-Electron Model ...........................................  73
2.4.2    High- and Low-Spin States ....................................  75
2.4.3    Orbit¨CLattice Stabilization (Jahn¨CTeller Effects) .............  79
2.4.4    Spin¨COrbit¨CLattice Stabilization ..............................  82
2.5       Covalent Stabilization ..................................................  88
2.5.1    Molecular-Orbital Theory......................................  89
2.5.2    Determinant Method ...........................................  91
2.5.3     and  Bonds and the Molecular Orbital Diagram ..........  95
2.5.4    Valence Bond Method..........................................  99
Appendix 2A    Homonuclear Molecule Ion...................................102
Appendix 2B    Valence-Bond Diatomic Molecule ...........................103
References.......................................................................105
3    Magnetic Exchange in Oxides ................................................107
3.1       Interionic Magnetic Exchange .........................................108
3.1.1    Molecular-Orbital Exchange Approximation .................109
3.1.2    Valence-Bond Solutions .......................................113
3.1.3    Spin Alignment in Oxides .....................................119
3.1.4    Ferromagnetism by Spin Transfer .............................121
3.1.5    Goodenough¨CKanamori Rules. ................................125
3.2       Antiferromagnetism ....................................................129
3.2.1    Superexchange and Molecular Fields .........................129
3.2.2    Molecular Field Theory of Antiferromagnetism ..............131
3.2.3    Antiferromagnetic Spin Configurations .......................135
3.3       Antiferromagnetic Oxides..............................................139
3.3.1    One-Metal Oxides ..............................................139
3.3.2    ABO 3 and A 2 BO 4 Perovskites ...............................140
3.3.3    The Mixed-Valence Manganite Anomaly .....................143
Appendix 3A    Analysis of M 2 CO 2  Exchange Interactions ................146
Appendix 3B    Curie Temperature Model for (La,Ca) MnO 3 ................147
References.......................................................................149
4    Ferrimagnetism ................................................................151
4.1       Ferrimagnetic Order ....................................................151
4.1.1    Generic Ferrimagnetic Systems ...............................152
4.1.2    Molecular Field Theory of Ferrimagnetism...................153
4.1.3    Magnetic Frustration and Spin Canting .......................157Contents xi
4.2       Theory of Superexchange Dilution ....................................161
4.2.1    Superexchange Energy Stabilization ..........................161
4.2.2    Molecular Field Coefficients...................................164
4.2.3    Solution for Yttrium Iron Garnet ..............................165
4.3       Ferrimagnetic Oxides...................................................168
4.3.1    Spinel Ferrites AOEB 2 O 4 ......................................169
4.3.2    Garnet Ferrites f c 3 g OEa 2 .d 3 /O 12 .............................175
4.3.3    Rare-Earth Garnet Ferrites .....................................180
4.3.4    Rare-Earth Canting Effect .....................................184
4.3.5    Hexagonal Ferrites .............................................190
4.3.6    Orthoferrites ....................................................193
Appendix 4A    Molecular Field Analysis of LiZnTi Ferrite .................193
Appendix 4B    High-Magnetization Limits ...................................195
Appendix 4C    Brillouin Functions in Exchange Energy Format ............196
References.......................................................................197
5    Anisotropy and Magnetoelastic Properties .................................201
5.1       Quantum Paramagnetism of Single Ions ..............................202
5.1.1    Theory of Anisotropic g Factors ...............................202
5.1.2    Conventional Perturbation Solutions ..........................205
5.1.3    The Spin Hamiltonian for 3d n Ions ...........................209
5.1.4    The Crystal-Field Hamiltonian for 4f
n  Ions..................210
5.2       Anisotropy of Single Ions ..............................................212
5.2.1    3d
1 and 3d
6
D-State Triplet ..................................213
5.2.2    3d
4 and 3d
9 D-State Doublet (J¨CT Effect) ...................217
5.2.3    3d
2 and 3d
7 F-State Triplet ...................................219
5.2.4    3d
3 and 3d
8 F-State Singlet ...................................220
5.2.5    3d 5 S-State Singlet .............................................222
5.2.6    4f
n Ion Anisotropy ............................................226
5.3       Magnetocrystalline Anisotropy and Magnetostriction ................228
5.3.1    Phenomenological Anisotropy Theory ........................229
5.3.2    Phenomenological Magnetostriction Theory .................231
5.3.3    Dipolar Pair Model of Magnetic Anisotropy..................234
5.3.4    Single-Ion Model of Ferrimagnetic Anisotropy ..............236
5.3.5    Cooperative Single-Ion Effects: Anisotropy ..................241
5.3.6    Cooperative Single-Ion Effects: Magnetostriction ............246
5.4       Magnetization Process and Hysteresis.................................250
5.4.1    Initial Permeability and Coercivity ............................251
5.4.2    Anisotropy Field and Remanence Ratio.......................254
5.4.3    Approach to Saturation ........................................256
5.4.4    Demagnetization and Permanent Magnets ....................258
Appendix 5A    Four-Level Degenerate Perturbation Solution
for d
1 ....................................................................261xii Contents
Appendix 5B    T 2g Solution for d
1 in an Exchange Field....................263
Appendix 5C    Orbital States of d
5 in a Cubic Field .........................265
Appendix 5D    Angular Dependence of Cubic Anisotropy Fields ...........267
References.......................................................................269
6    Electromagnetic Properties ...................................................273
6.1       Magnetic Relaxation ...................................................274
6.1.1    Nonresonant Longitudinal Relaxation ........................274
6.1.2    Quantum Mechanisms of Spin¨CLattice Relaxation ...........278
6.1.3    Perturbation Theories of Spin¨CPhonon Interaction ...........286
6.2       Gyromagnetic Resonance and Relaxation .............................287
6.2.1    Paramagnetic Resonance.......................................288
6.2.2    Ferromagnetic Resonance .....................................292
6.2.3    Uniform Precession Damping .................................295
6.2.4    Inhomogeneous Resonance Line Broadening.................297
6.2.5    Fast-Relaxing Ion Effects ......................................300
6.2.6    The Exchange Isolation Effect.................................306
6.3       Exchange-Coupled Modes (Spin Waves) ..............................307
6.3.1    Uniform Precession Decoherence (Degenerate
Spin Waves) ....................................................307
6.3.2    Instability Threshold (Classical Approximation) .............311
6.3.3    Instability Threshold (Nonlinear Spin Waves) . ...............315
6.3.4    Magnetostatic Modes ..........................................317
6.4       Permeability and Propagation ..........................................318
6.4.1    Low-Frequency Longitudinal Permeability ...................318
6.4.2    High-Frequency Transverse Limits............................322
6.4.3    Snoek¡¯s Law Considerations ...................................324
6.4.4    Circular Polarization and Nonreciprocal Properties ..........327
6.4.5    Linear Polarization and Faraday Rotation.....................332
Appendix 6A    Transverse Permeability Tensor ..............................333
Appendix 6B    Classical Instability Threshold ...............................336
Appendix 6C    Domain Wall Susceptibility Equation ........................338
References.......................................................................340
7    Magneto-Optical Properties ..................................................343
7.1       Infrared Exchange Resonance .........................................344
7.1.1    Classical Precession Model ....................................344
7.1.2    Quantum Spin Transition Model ..............................346
7.1.3    Experimental Exchange Spectra ...............................351
7.2       Combined Permeability and Permittivity ..............................352
7.2.1    The ["]  [] Tensor Solutions ..................................352
7.2.2    Propagation Parameters and Faraday Rotation ...............353
7.3       Magneto-Optical Spectra ...............................................355
7.3.1    Electric-Dipole Transitions ....................................355
7.3.2    Yttrium Iron Garnet Spectra (Paramagnetic) .................360Contents xiii
7.3.3    Iron Garnets with Bismuth Ions (Diamagnetic)...............366
7.3.4    Fe
3 C¨CBi
3 C Hybrid Excited States ...........................371
7.3.5    Intersublattice Transitions and the S D 0Rule.............376
Appendix 7A    Magnetic Circular Birefringence and Dichroism ............381
References.......................................................................382
8    Spin Transport Properties ....................................................385
8.1       Polarons and Charge Transfer..........................................386
8.1.1    Transfer Among Equivalent Energy Sites (Small Polarons) .388
8.1.2    Transfer to Higher Energy Sites (Large Polarons) ............389
8.1.3    Transfer by Covalent Tunneling ...............................392
8.1.4    The Holstein Polaron Theory ..................................394
8.2       Metallic Oxides with Polarized Spins .................................396
8.2.1    Simple Oxides ..................................................397
8.2.2    Complex Oxides ................................................397
8.2.3    Classical Resistivity¨CTemperature Model.....................400
8.3       Magnetoresistance in Oxides (CMR) ..................................401
8.3.1    Manganese-Ion Exchange Interactions ........................402
8.3.2    Magnetoresistivity-Temperature Model .......................405
8.3.3    Dilute Magnetic Oxides ........................................410
8.4       Superconductivity in Oxides ...........................................413
8.4.1    Classical Foundations ..........................................413
8.4.2    Zero-Spin Polarons and Magnetic Frustration ................419
8.4.3    Large-Polaron Superconductivity .............................423
8.4.4    Normal Resistivity and Critical Temperature .................426
8.4.5    Layered Cuprate Superconductors ............................430
8.5       Supercurrents and Magnetic Fields ....................................439
8.5.1    Supercurrent Formation ........................................439
8.5.2    Condensation Energy ..........................................442
8.5.3    London Penetration Depth .....................................443
8.5.4    Critical Magnetic Field ........................................445
8.5.5    Critical Current Density........................................447
8.5.6    Coherence Length ..............................................450
8.5.7    Type-II Superconductors .......................................452
Appendix 8A    Magnetic Levitation ...........................................455
References.......................................................................456
Index .................................................................................461

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