Prologue
Chapter 1. History of Magnetism
1.1. Physics and Metaphysics
1.2. Gilbert and Descartes
1.3. Rise of Modern Science
1.4. Electrodynamics
1.5. The Electron
1.6. The Demise of Classical Physics
1.7. Quantum Theoiy
1.8. Modern Foundations
1.9. Magnetic Bubbles
1.10. Ultimate Thin Films
1.11. Dilute Magnetic Alloys
1.12. New Directions
Chapter 2. Currents or Spins?
2.1. Charge Currents or Spins?
2.2. The Magnetic Dipole
2.3. The Magnetic Dipole-Dipole Interactions
2.4. The Exchange Interactions
2.5. Metals and Their Alloys
2.6. Superconductivity
2.7. The Need to Study Spin Angular Momentum
Chapter 3. Quantum Theory of Angular Momentum
3.1. Kinetic Angular Momentum
3.2. Spherical Harmonics
3.3. Reason for Integer l and m
3.4. Matrices cf Angular Momentum
3.5. Pauli Spin Matrices
3.6. Compounding Angular Momentum
3.7. Equations of Motion of Interacting Angular Momenta
3.8. Coupled Bosch Representation
3.9. Rotations
3.10. More on Compound Angular Momentum
3.11. Other Representations
3.12. Spins One-Half: Special Tricks
3.13. Spins One
3.14. Quadratic Forms
3.15. Projection Operators
Chapter 4. Magnetism and the Many-Body Problem
4.1. Hamiltonian Physics and Degeneracy
4.2. The Pauli Principle
4.3. The Two-Fermion Problem
4.4. Electrons in One Dimension: A Theorem
4.5. The Wronskian
4.6. States cf Three Electrons
4.7. Eigenfunctions cf Total S2 and Sz
4.8. Hund's Rules
4.9. p3 Configuration
4.10. p2 and p4 Configurations
4.11. Second Quantization
4.12. Double Exchange
4.13. Superexchange
4.14. Jellium
4.15. Hubbard Model: An Introduction
4.16. Nagaoka's Ferromagnetism
4.17. One Dimension: Exact Solutions
4.18. Ferrimagnetism
4.19. Spin-Dependent Tunneling
Chapter 5. From Magnons to Solitons: Spin Dynamics
5.1. Spin Waves as Harmonic Oscillators
5.2. One-Magnon Eigenstates in Ferromagnets
5.3. Two-Magnon States and Eigenstates in Ferromagnets
5.4. Bound States in One Dimension
5.5. Bound States in Two and Three Dimensions
5.6. Antiferromagnetic Magnons: The One-Dimensional XY Model
5.7. Bethe's Solution of One-Dimensional Heisenberg Antiferromagnet
5.8. Linearized Antiferromagnetic Magnons
5.9. Ferrimagnetism
5.10. Some Rigorous Notions in Antiferro- and Ferri-Magnetism
5.11. Vortices
5.12. Solitons and Bloch Domain Walls: Introductory Material
5.13. Solitary Wave Solution
5.14. More on Magnetic Domains
5.15. Time-Dependent Phenomena
5.16. Majumdar-Ghosh Model and "Quantum Frustration"
5.17. Integer Spins
5.18. The AKLT Spin One Chain
5.19. Defective Antiferromagnets
Chapter 6. Magnetism in Metals
6.1. Bloch and Wannier States
6.2. Tight-Binding
6.3. Weak Magnetic Properties
6.4. Exchange in Solids: Construction of a Model Hamiltonian
6.5. Perturbation-Theoretic Derivation of Heisenberg Hamiltonian
6.6. Heisenberg Hamiltonian in Metals
6.7. Ordered Magnetic Metals: Deriving the Ground State
6.8. Kondo Effect
6.9. Spin Glasses
6.10. Magnetism without Localized Spins: Preliminaries
6.11. Degenerate Bands and Intra-Atomic Exchange Forces
6.12. Magnons in Metals
6.13. Marginal Magnetism of Impurities
6.14. Correlations and Equivalence to s-d Model
6.15. Periodic Anderson Model
Chapter 7. Statistical Thermodynamics
7.1. Spins in a Magnetic Field
7.2. The Partition Function
7.3. The Concept of the Molecular Field
7.4. Discontinuity in Specific Heat
7.5. Magnetic Susceptibility and Spontaneous Magnetization
7.6. Adiabatic Demagnetization
7.7. Anti ferromagnetism
7.8. Short-Ranged versus Long-Ranged Interactions
7.9. Fermions, Bosons, and all that
Fermions
nosons
Gaussian
Legendre Transformations
7.10. Gaussian and Spherical Models
Gaussian Model
Spherical Model
Watson's Integrals Generalized
7.11. Magnetic Susceptibility in Gaussian and Spherical Models
7.12. Spherical Antiferromagnet
7.13. Spherical Model Spin Glass
Magnetic Properties of Spin Glass
7.14. Thermodynamics of Magnons
7.15. Magnetism in Two Dimensions
7.16. The XY Model: 1D
7.17. The XY Model: 2D
7.18. Transfer Matrix of Plane Rotator Model
Chapter 8. The Ising Model
8.1. High Temperature Expansions
8.2. Graph Theory
8.3. Low Temperature Expansions and the Duality Relations
8.4. Peierls' Proof of Long Range Order
8.5. 1D Ising Model in Longitudinal Fields
8.6. 1D Ising Model in Transverse Fields
8.7. ConcerningQuadratic Forms of Fermion Operators
8.8. Two-Dimensional Ising Model: The Transfer Matrix
8.9. Solution of Two-Dimensional Ising Model in Zero Field
8.10. Spontaneous Magnetization and Magnetic Susceptibility
8.11. Zeros of the Partition Function
8.12. Miscellania, Including 2D Antiferromagnets
8.13. The Three-Dimensional Ising Model
8.14. Ising Gauge Glass
8.15. Frustration
Chapter 9. Miscellaneous Advanced Topics
9.1. Critical Phenomena
9.2. Green Functions Formalism
9.3. Nonlinear Responses and Chaos
9.4. Kondo Phenomenon: The s-d Model Redux
9.5. Scaling, Renormalization and Information Theory
Bibliography
Index
