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Chapter 1．History of Magnetism1

1.1．Physics and Metaphysics3

1.2．Gilbert and Descartes6

1.3．Rise of Modern Science12

1.4．Electrodynamics16

1.5．The Electron23

1.6．The Demise of Classical Physics26

1.7．Quantum Theory31

1.8．Modern Foundations35

1.9．Magnetic Bubbles39

1.10．Ultimate Thin Films44

1.11．Dilute Magnetic Alloys47

1.12．New Directions49

Chapter 2．Currents or Spins?53

2.1．Charge Currents or Spins?53

2.2．The Magnetic Dipole56

2.3．The Magnetic Dipole-Dipole Interactions57

2.4．The Exchange Interactions63

2.5．Metals and Their Alloys65

2.6．Superconductivity68

2.7．The Need to Study Spin Angular Momentum69

Chapter 3．Quantum Theory of Angular Momentum70

3.1．Kinetic Angular Momentum70

3.2．Spherical Harmonics74

3.3．Reason for Integer l and m78

3.4．Matrices of Angular Momentum80

3.5．Pauli Spin Matrices82

3.6．Compounding Angular Momentum83

3.7．Equations of Motion of Interacting Angular Momenta87

3.8．Coupled Boson Representation87

3.9．Rotations90

3.10．More on Compound Angular Momentum92

3.11．Other Representations95

3.12．Spins Ohe-Half:Special Tricks96

3.13．Spins One98

3.14．Quadratic Forms100

3.15．Projection Operators101

Chapter 4．Magnetism and the Many-Body Problem104

4.1．Hamiltonian Physics and Degeneracy104

4.2．The Pauli Principle107

4.3．The Two-Fermion Problem111

4.4．Electrons in One Dimension:A Theorem113

4.5．The Wronskian116

4.6．States of Three Electrons118

4.7．Eigenfunctions of Total S2 and Sz120

4.8．Hund's Rules125

4.9．p3 Configuration127

4.10．p2 and p4 Configurations133

4.11．Second Quantization139

4.12．Double Exchange143

4.13．Superexchange146

4.14．Jellium149

4.15．Hubbard Model:An Introduction154

4.16．Nagaoka's Ferromagnetism163

4.17．One Dimension:Exact Solutions167

4.18．Ferrimagnetism168

4.19．Spin-Dependent Tunneling172

Chapter 5．From Magnons to Solitons:Spin Dynamics175

5.1．Spin Waves as Harmonic Oscillators176

5.2．One-Magnon Eigenstates in Ferromagnets185

5.3．Two-Magnon States and Eigenstates in Ferromagnets186

5.4．Bound States in One Dimension195

5.5．Bound States in Two and Three Dimensions196

5.6．Antiferromagnetic Magnons:The One-Dimensional XY Model200

5.7．Bethe's Solution of One-Dimensional Heisenberg Antiferromagnet206

5.8．Linearized Antiferromagnetic Magnons215

5.9．Ferrimagnetism224

5.10．Some Rigorous Notions in Antiferro-and Ferri-Magnetism226

5.11．Vortices228

5.12．Solitons and Bloch Domain Walls:Introductory Material231

5.13．Solitary Wave Solution235

5.14．More on Magnetic Domains241

5.15．Time-Dependent Phenomena242

5.16．Majumdar-Ghosh Model and"Quantum Frustration"247

5.17．Integer Spins250

5.18．The AKLT Spin One Chain254

5.19．Defective Antiferromagnets255

Chapter 6．Magnetism in Metals257

6.1．Bloch and Wannier States259

6.2．Tight-Binding260

6.3．Weak Magnetic Properties267

6.4．Exchange in Solids:Construction of a Model Hamiltonian273

6.5．Perturbation-Theoretic Derivation of Heisenberg Hamiltonian281

6.6．Heisenberg Hamiltonian in Metals284

6.7．Ordered Magnetic Metals:Deriving the Ground State287

6.8．Kondo Effect296

6.9．Spin Glasses304

6.10．Magnetism without Localized Spins:Preliminaries310

6.11．Degenerate Bands and Intra-Atomic Exchange Forces314

6.12．Magnons in Metals320

6.13．Marginal Magnetism of Impurities327

6.14．Correlations and Equivalence to s-d Model337

6.15．Periodic Anderson Model342

Chapter 7．Statistical Thermodynamics344

7.1．Spins in a Magnetic Field344

7.2．The Partition Function349

7.3．The Concept of the Molecular Field354

7.4．Discontinuity in Specific Heat358

7.5．Magnetic Susceptibility and Spontaneous Magnetization361

7.6．Adiabatic Demagnetization365

7.7．Antiferromagnetism366

7.8．Short-Ranged versus Long-Ranged Interactions369

7.9．Fermions,Bosons,and all that375

Fermions375

Bosons375

Gaussian376

Legendre Transformations377

7.10．Gaussian and Spherical Models378

Gaussian Model379

Spherical Model382

Watson's Integrals Generalized387

7.11．Magnetic Susceptibility in Gaussian and Spherical Models389

7.12．Spherical Antiferromagnet392

7.13．Spherical Model Spin Glass395

Magnetic Properties of Spin Glass399

7.14．Thermodynamics of Magnons407

7.15．Magnetism in Two Dimensions414

7.16．The XY Model:1D418

7.17．The XY Model:2D426

7.18．Transfer Matrix of Plane Rotator Model433

Chapter 8．The Ising Model438

8.1．High Temperature Expansions441

8.2．Graph Theory445

8.3．Low Temperature Expansions and the Duality Relations448

8.4．Peierls' Proof of Long Range Order452

8.5．1D Ising Model in Longitudinal Fields454

8.6．1D Ising Model in Transverse Fields462

8.7．Concerning Quadratic Forms of Fermion Operators474

8.8．Two-Dimensional Ising Model:The Transfer Matrix478

8.9．Solution of Two-Dimensional Ising Model in Zero Field485

8.10．Spontaneous Magnetization and Magnetic Susceptibility494

8.11．Zeros of the Partition Function502

8.12．Miscellania,Including 2D Antiferromagnets507

8.13．The Three-Dimensional Ising Model517

8.14．Ising Gauge Glass526

8.15．Frustration528

Chapter 9．Miscellaneous Advanced Topics533

9.1．Critical Phenomena533

9.2．Green Functions Formalism536

9.3．Nonlinear Responses and Chaos539

9.4．Kondo Phenomenon:The s-d Model Redux539

9.5．Scaling,Renormalization and Information Theory547

Bibliography549

Index561