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-Weiss 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-Lattice 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 3dn Ions ............................. 40
2.1.3 Rare Earth 4ƒn Ions ............................. 42
2.1.4 4dn and 5dn 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
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-Lattice Stabilization (Jahn-Teller
Effects) ........................................ 79
2.4.4 Spin-Orbit-Lattice Stabilization ................ 82
2.5 Covalent Stabilization ................................. 88
2.5.1 Molecular-Orbital Theory ........................ 89
2.5.2 Determinant Method .............................. 91
2.5.3 σ and π 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-Kanamori 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 ABO3 and A2BO4 Perovskites ...................... 140
3.3.3 The Mixed-Valence Manganite Anomaly ............ 143
Appendix 3А Analysis of M2+O2- Exchange Interactions ........ 146
Appendix 3B Curie Temperature Model for (La,Ca)MnO3 ........ 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 .......... 157
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 А[В2]О4 ........................ 169
4.3.2 Garnet Ferrites {c3}[α2](d3)O12 ................. 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 3dn Ions .............. 209
5.1.4 The Crystal-Field Hamiltonian for 4ƒn Ions ..... 210
5.2 Anisotropy of Single Ions ............................. 212
5.2.1 3d1 and 3d6 D-State Triplet .................... 213
5.2.2 3d4 and 3d9 D-State Doublet (J-T Effect) ....... 217
5.2.3 3d2 and 3d7 F-State Triplet .................... 219
5.2.4 3d3 and 3d8 F-State Singlet .................... 220
5.2.5 3d5 S-State Singlet ............................ 222
5.2.6 4ƒn 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 d1 ......................................... 261
Appendix 5B T2g Solution for d1 in an Exchange Field ....... 263
Appendix 5C Orbital States of d1 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-Lattice
Relaxation ..................................... 278
6.1.3 Perturbation Theories of Spin-Phonon
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 [ε]•[μ] 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) ..... 360
7.3.3 Iron Garnets with Bismuth Ions (Diamagnetic) ... 366
7.3.4 Fe3+-Bi3+ Hybrid Excited States ................ 371
7.3.5 Intersublattice Transitions and the ΔS =
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-Temperature 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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