Magnetic Oxides (eBook)

Preface 6
Contents 8
1 Introductory Magnetism 13
1.1 Fundamental Concepts and Definitions 13
1.1.1 Basic Electrostatics 14
1.1.2 Basic Magnetostatics 15
1.1.3 Demagnetization in Uniformly Magnetized Bodies 16
1.1.4 Domains in Partially Magnetized Bodies 18
1.2 Induced Magnetism 20
1.2.1 Diamagnetism and Paramagnetism 20
1.2.2 Temperature Dependence of Susceptibility 23
1.3 Spontaneous Magnetism 27
1.3.1 Classical Ferromagnetism and Antiferromagnetism 27
1.3.2 Solutions of the Brillouin–Weiss Equation 28
1.3.3 Quantum Origins of the Molecular Field 31
1.3.4 The Ising Approximation 36
1.4 Gyromagnetism 37
1.4.1 Larmor Precession and Resonance 38
1.4.2 Phenomenological Relaxation Theory 39
1.4.3 Complex Susceptibility Theory 41
1.4.4 Resonance Line Shapes 45
Appendix 1A Spin–Lattice Contribution to Linewidth 46
Appendix 1A Spin–Lattice Contribution to Linewidth 45
2 Magnetic Ions in Oxides 48
2.1 The Transition Metals 48
2.1.1 The Periodic Table 49
2.1.2 Iron Group 3dn Ions 51
2.1.3 Rare Earth 4fn Ions 53
2.1.4 4dn and 5dn Ions 53
2.2 Oxygen Coordinations 54
2.2.1 Crystal Systems and Point Groups 55
2.2.2 Cubic Symmetry 56
2.2.3 Lower Symmetries 58
2.3 Crystal Electric Fields 59
2.3.1 Angular Momentum States 60
2.3.2 Crystal Field Hamiltonian 61
2.3.3 Hierarchy of Perturbations 65
2.3.4 Weak-Field Solutions 66
2.3.5 Group Theory and Lower Symmetry 75
2.3.6 Strong Field Solutions and Term Diagrams 79
2.3.7 Rare-Earth Ion Solutions 82
2.4 Orbital Energy Stabilization 84
2.4.1 One-Electron Model 84
2.4.2 High- and Low-Spin States 86
2.4.3 Orbit–Lattice Stabilization (Jahn–Teller Effects) 90
2.4.4 Spin–Orbit–Lattice Stabilization 93
2.5 Covalent Stabilization 99
2.5.1 Molecular-Orbital Theory 100
2.5.2 Determinant Method 102
2.5.3 and Bonds and the Molecular Orbital Diagram 106
2.5.4 Valence Bond Method 110
Appendix 2A Homonuclear Molecule Ion 113
Appendix 2A Homonuclear Molecule Ion 112
Appendix 2B Valence-Bond Diatomic Molecule 114
3 Magnetic Exchange in Oxides 118
3.1 Interionic Magnetic Exchange 119
3.1.1 Molecular-Orbital Exchange Approximation 120
3.1.2 Valence-Bond Solutions 124
3.1.3 Spin Alignment in Oxides 130
3.1.4 Ferromagnetism by Spin Transfer 132
3.1.5 Goodenough–Kanamori Rules 136
3.2 Antiferromagnetism 140
3.2.1 Superexchange and Molecular Fields 140
3.2.2 Molecular Field Theory of Antiferromagnetism 142
3.2.3 Antiferromagnetic Spin Configurations 146
3.3 Antiferromagnetic Oxides 150
3.3.1 One-Metal Oxides 150
3.3.2 ABO3 and A2BO4 Perovskites 151
3.3.3 The Mixed-Valence Manganite Anomaly 154
Appendix 3A Analysis of M2+O2- Exchange Interactions 113
Appendix 3A Analysis of M2+O2- Exchange Interactions 156
Appendix 3B Curie Temperature Model for (La,Ca) MnO3 114
References 159
4 Ferrimagnetism 162
4.1 Ferrimagnetic Order 162
4.1.1 Generic Ferrimagnetic Systems 163
4.1.2 Molecular Field Theory of Ferrimagnetism 164
4.1.3 Magnetic Frustration and Spin Canting 168
4.2 Theory of Superexchange Dilution 172
4.2.1 Superexchange Energy Stabilization 172
4.2.2 Molecular Field Coefficients 175
4.2.3 Solution for Yttrium Iron Garnet 176
4.3 Ferrimagnetic Oxides 179
4.3.1 Spinel Ferrites A[B2]O4 180
4.3.2 Garnet Ferrites {c3}[a2](d3)O12 186
4.3.3 Rare-Earth Garnet Ferrites 191
4.3.4 Rare-Earth Canting Effect 195
4.3.5 Hexagonal Ferrites 201
4.3.6 Orthoferrites 204
Appendix 4A Molecular Field Analysis of LiZnTi Ferrite 113
Appendix 4A Molecular Field Analysis of LiZnTi Ferrite 205
Appendix 4B High-Magnetization Limits 114
Appendix 4C Brillouin Functions in Exchange Energy Format 207
Appendix 4C Brillouin Functions in Exchange Energy Format 207
5 Anisotropy and Magnetoelastic Properties 211
5.1 Quantum Paramagnetism of Single Ions 212
5.1.1 Theory of Anisotropic g Factors 212
5.1.2 Conventional Perturbation Solutions 215
5.1.3 The Spin Hamiltonian for 3dn Ions 219
5.1.4 The Crystal-Field Hamiltonian for 4fn Ions 220
5.2 Anisotropy of Single Ions 222
5.2.1 3d1 and 3d6 D-State Triplet 223
5.2.2 3d4 and 3d9 D-State Doublet (J–T Effect) 227
5.2.3 3d2 and 3d7 F-State Triplet 229
5.2.4 3d3 and 3d8 F-State Singlet 230
5.2.5 3d5 S-State Singlet 232
5.2.6 4fn Ion Anisotropy 236
5.3 Magnetocrystalline Anisotropy and Magnetostriction 238
5.3.1 Phenomenological Anisotropy Theory 239
5.3.2 Phenomenological Magnetostriction Theory 241
5.3.3 Dipolar Pair Model of Magnetic Anisotropy 244
5.3.4 Single-Ion Model of Ferrimagnetic Anisotropy 246
5.3.5 Cooperative Single-Ion Effects: Anisotropy 251
5.3.6 Cooperative Single-Ion Effects: Magnetostriction 256
5.4 Magnetization Process and Hysteresis 260
5.4.1 Initial Permeability and Coercivity 261
5.4.2 Anisotropy Field and Remanence Ratio 264
5.4.3 Approach to Saturation 266
5.4.4 Demagnetization and Permanent Magnets 268
Appendix 5A Four-Level Degenerate Perturbation Solution for d1 113
Appendix 5A Four-Level Degenerate Perturbation Solution for d1 270
Appendix 5B T2g Solution for d1 in an Exchange Field 114
Appendix 5B T2g Solution for d1 in an Exchange Field 273
Appendix 5C Orbital States of d5 in a Cubic Field 207
Appendix 5D Angular Dependence of Cubic Anisotropy Fields 277
References 279
6 Electromagnetic Properties 282
6.1 Magnetic Relaxation 283
6.1.1 Nonresonant Longitudinal Relaxation 283
6.1.2 Quantum Mechanisms of Spin–Lattice Relaxation 287
6.1.3 Perturbation Theories of Spin–Phonon Interaction 295
6.2 Gyromagnetic Resonance and Relaxation 296
6.2.1 Paramagnetic Resonance 297
6.2.2 Ferromagnetic Resonance 301
6.2.3 Uniform Precession Damping 304
6.2.4 Inhomogeneous Resonance Line Broadening 306
6.2.5 Fast-Relaxing Ion Effects 309
6.2.6 The Exchange Isolation Effect 315
6.3 Exchange-Coupled Modes (Spin Waves) 316
6.3.1 Uniform Precession Decoherence (Degenerate Spin Waves) 316
6.3.2 Instability Threshold (Classical Approximation) 320
6.3.3 Instability Threshold (Nonlinear Spin Waves) 324
6.3.4 Magnetostatic Modes 326
6.4 Permeability and Propagation 327
6.4.1 Low-Frequency Longitudinal Permeability 327
6.4.2 High-Frequency Transverse Limits 331
6.4.3 Snoek's Law Considerations 333
6.4.4 Circular Polarization and Nonreciprocal Properties 336
6.4.5 Linear Polarization and Faraday Rotation 341
Appendix 6A Transverse Permeability Tensor 113
Appendix 6B Classical Instability Threshold 114
Appendix 6B Classical Instability Threshold 345
Appendix 6C Domain Wall Susceptibility Equation 207
References 348
7 Magneto-Optical Properties 352
7.1 Infrared Exchange Resonance 353
7.1.1 Classical Precession Model 353
7.1.2 Quantum Spin Transition Model 355
7.1.3 Experimental Exchange Spectra 360
7.2 Combined Permeability and Permittivity 361
7.2.1 The [] [] Tensor Solutions 361
7.2.2 Propagation Parameters and Faraday Rotation 362
7.3 Magneto-Optical Spectra 364
7.3.1 Electric-Dipole Transitions 364
7.3.2 Yttrium Iron Garnet Spectra (Paramagnetic) 369
7.3.3 Iron Garnets with Bismuth Ions (Diamagnetic) 375
7.3.4 Fe3+–Bi3+ Hybrid Excited States 380
7.3.5 Intersublattice Transitions and the S=0 Rule 385
Appendix 7A Magnetic Circular Birefringence and Dichroism 113
Appendix 7A Magnetic Circular Birefringence and Dichroism 389
References 391
8 Spin Transport Properties 394
8.1 Polarons and Charge Transfer 395
8.1.1 Transfer Among Equivalent Energy Sites (Small Polarons) 397
8.1.2 Transfer to Higher Energy Sites (Large Polarons) 398
8.1.3 Transfer by Covalent Tunneling 401
8.1.4 The Holstein Polaron Theory 403
8.2 Metallic Oxides with Polarized Spins 405
8.2.1 Simple Oxides 406
8.2.2 Complex Oxides 406
8.2.3 Classical Resistivity–Temperature Model 409
8.3 Magnetoresistance in Oxides (CMR) 410
8.3.1 Manganese-Ion Exchange Interactions 411
8.3.2 Magnetoresistivity-Temperature Model 414
8.3.3 Dilute Magnetic Oxides 419
8.4 Superconductivity in Oxides 422
8.4.1 Classical Foundations 422
8.4.1.1 The London Equations 422
8.4.1.2 The Macroscopic Molecule 425
8.4.1.3 Nonlocal Considerations 426
8.4.1.4 Carrier Statistics 427
8.4.2 Zero-Spin Polarons and Magnetic Frustration 428
8.4.3 Large-Polaron Superconductivity 432
8.4.4 Normal Resistivity and Critical Temperature 435
8.4.5 Layered Cuprate Superconductors 439
8.5 Supercurrents and Magnetic Fields 448
8.5.1 Supercurrent Formation 448
8.5.2 Condensation Energy 451
8.5.3 London Penetration Depth 452
8.5.4 Critical Magnetic Field 454
8.5.5 Critical Current Density 456
8.5.6 Coherence Length 459
8.5.7 Type-II Superconductors 461
Appendix 8A Magnetic Levitation 113
Appendix 8A Magnetic Levitation 464
References 465
Index 469