1. The Magnetic Susceptibility ................................. 1
1.1. The Magnetic Moment ................................... 2
1.2. The Magnetization ..................................... 7
1.3. The Generalized Susceptibility ....................... 12
1.3.1. The Kramers-Kronig Relations ................. 14
1.3.2. The Fluctuation-Dissipation Theorem .......... 15
1.3.3. Onsager Relation ............................. 20
1.4. Second Quantization .................................. 21
1.4.1. Example: The Degenerate-Electron Gas ......... 26
1.4.2. Example: The Zeeman Interaction .............. 29
2. The Magnetic Hamiltonian ................................... 33
2.1. The Dirac Equation ................................... 33
2.2. Sources of Fields .................................... 35
2.2.1. Uniform External Field ....................... 35
2.2.2. The Electric Quadrupole Field ................ 36
2.2.3. The Magnetic Dipole (Hyperfine) Field ........ 41
2.2.4. Other Electrons on the Same Ion .............. 43
2.2.5. Crystalline Electric Fields .................. 44
2.2.6. Dipole-Dipole Interaction .................... 50
2.2.7. Direct Exchange .............................. 51
2.2.8. Superexchange ................................ 58
2.2.9. Molecular Magnets ............................ 62
2.2.10. Double Exchange .............................. 65
2.2.11. Exchange on a Surface ........................ 66
2.3. The Spin Hamiltonian ................................. 67
2.3.1. Transition-Metal Ions ........................ 67
2.3.2. Rare-Earth Ions .............................. 75
2.3.3. Semiconductors ............................... 77
3. The Static Susceptibility of Noninteracting Systems ........ 85
3.1. Localized Moments .................................... 85
3.1.1. Diamagnetism ................................. 88
3.1.2. Paramagnetism of Transition-Metal Ions ....... 89
3.1.3. Paramagnetism of Rare-Earth Ions ............. 91
3.2. Metals ............................................... 94
3.2.1. Landau Diamagnetism .......................... 94
3.2.2. The de Haas-van Alphen Effect ................ 98
3.2.3. Quantized Hall Conductance .................. 102
3.2.4. Pauli Paramagnetism ......................... 106
3.3. Measurement of the Susceptibility ................... 112
3.4. Local Moments in Metals ............................. 115
3.4.1. Virtual Bound States ........................ 116
3.4.2. Anderson's Theory of Moment Formation ....... 119
3.4.3. The Kondo Effect ............................ 124
4. The Static Susceptibility of Interacting Systems: Local
Moments ................................................... 133
4.1. High Temperatures ................................... 135
4.2. Low Temperatures .................................... 146
4.3. Temperatures Near Tc ................................ 149
4.4. Landau Theory of Second-Order Transitions ........... 153
4.5. Critical Phenomena .................................. 154
4.5.1 Order in 2D .................................. 155
4.6. Stoner-Wohlfarth Model .............................. 159
4.7. Dynamic Coercivity .................................. 162
4.8. Magnetic Viscosity .................................. 165
5. The Static Susceptibility of Interacting Systems:
Metals .................................................... 169
5.1. Fermi Liquid Theory ................................. 169
5.2. Heavy Fermion Systems ............................... 176
5.3. Itinerant Magnetism ................................. 177
5.3.1. The Stoner Model ............................ 177
5.3.2. The Hubbard Model ........................... 187
6. The Dynamic Susceptibility of Weakly Interacting
Systems: Local Moments .................................... 193
6.1. Equation of Motion .................................. 193
6.2. The Bloch Equations ................................. 197
6.3. Resonance Line Shape ................................ 202
6.3.1. The Method of Moments ....................... 202
6.3.2. The Relaxation-Function Method .............. 206
6.3.3. Spin Diffusion .............................. 210
6.4. Spin Echoes ......................................... 211
6.4.1. Measurement of T1 ........................... 211
6.4.2. Calculation of T1 ........................... 213
7. The Dynamic Susceptibility of Weakly Interacting
Systems: Metals ........................................... 219
7.1. Paramagnons ......................................... 221
7.2. Fermi Liquid Theory ................................. 223
7.3. Conduction-Electron Spin Resonance .................. 228
7.4. Spin Waves .......................................... 230
7.5. Local Moments in Metals ............................. 231
7.6. Faraday Effect ...................................... 235
8. The Dynamic Susceptibility of Strongly Interacting
Systems ................................................... 237
8.1. Broken Symmetry ..................................... 237
8.2. Insulators .......................................... 238
8.2.1. Spin-Wave Theory ............................ 240
8.2.2. Coherent Magnon State ....................... 248
8.2.3. Magnetostatic Modes ......................... 249
8.2.4. Solitons..................................... 250
8.2.5. Thermal Magnon Effects ...................... 253
8.2.6. Nonlinear Processes ......................... 255
8.2.7. Chaos ....................................... 259
8.2.8. Optical Processes ........................... 262
8.3. High Temperatures ................................... 266
8.4. Micromagnetics ...................................... 269
8.4.1. Magnetic Force Microscope ................... 270
8.4.2. Phenomenological Damping .................... 273
8.5. Metals .............................................. 274
9. Thin Film Systems ......................................... 281
9.1. Interfaces .......................................... 281
9.1.1. Exchange Bias ............................... 281
9.1.2. Biquadratic Exchange ........................ 284
9.2. Trilayers ........................................... 285
9.2.1. The RKKY Ineraction ......................... 286
9.2.2. Quantum Well Model .......................... 289
9.2.3. Giant Magnetoresistance (GMR) ............... 292
9.2.4. Tunneling ................................... 300
9.2.5. Spin Transfer ............................... 306
9.2.6. Spin Hall Effect ............................ 310
10. Neutron Scattering ........................................ 315
10.1. Neutron Scattering Cross Section .................... 315
10.2. Nuclear Scattering .................................. 317
10.2.1. Bragg Scattering ............................ 318
10.2.2. Scattering of Phonons ....................... 320
10.3. Magnetic Scattering ................................. 324
10.3.1. Bragg Scattering ........................... 328
10.3.2. Spin Dynamics .............................. 333
10.4. Example: Manganese Oxides ........................... 337
10.5. Example: Quantum Phase Transitions .................. 341
References .................................................... 345
Index ......................................................... 355
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