| |
| |
| |
| Basic Facts | |
| |
| |
| |
| Macroscopic Maxwell Equations | |
| |
| |
| |
| Magnetic Moment and Magnetization | |
| |
| |
| |
| Susceptibility | |
| |
| |
| |
| Classification of Magnetic Materials | |
| |
| |
| |
| Diamagnetism | |
| |
| |
| |
| Paramagnetism | |
| |
| |
| |
| Collective Magnetism | |
| |
| |
| |
| Elements of Thermodynamics | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Atomic Magnetism | |
| |
| |
| |
| Hund's Rules | |
| |
| |
| |
| Russell-Saunders (Z.S-) Coupling | |
| |
| |
| |
| Hund's Rules for LS Coupling | |
| |
| |
| |
| Dtirac Equation | |
| |
| |
| |
| Electron Spin | |
| |
| |
| |
| Spin-Orbit Coupling | |
| |
| |
| |
| Wigner-Eckart Theorem | |
| |
| |
| |
| Rotation | |
| |
| |
| |
| Rotation Operator | |
| |
| |
| |
| Angular Momentum | |
| |
| |
| |
| Rotation Matrices | |
| |
| |
| |
| Tensor Operators | |
| |
| |
| |
| Wigner-Eckart Theorem | |
| |
| |
| |
| Examples of Application | |
| |
| |
| |
| Electron in an External Magnetic Field | |
| |
| |
| |
| Nuclear Quadrupole Field | |
| |
| |
| |
| Hyperfine Field | |
| |
| |
| |
| Magnetic Hamiltonian of the Atomic Electron | |
| |
| |
| |
| Many-Electron Systems | |
| |
| |
| |
| Coulomb Interaction | |
| |
| |
| |
| Spin-Orbit Coupling | |
| |
| |
| |
| Further Couplings | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Diamagnetism | |
| |
| |
| |
| Bohr-van Leeuwen Theorem | |
| |
| |
| |
| Larmor Diamagnetism (Insulators) | |
| |
| |
| |
| The Sommerfeld Model of a Metal | |
| |
| |
| |
| Properties of the Model | |
| |
| |
| |
| Sommerfeld Expansion | |
| |
| |
| |
| Landau Diamagnetism (Metals) | |
| |
| |
| |
| Free Electrons in Magnetic Field (Landau Levels) | |
| |
| |
| |
| Grand Canonical Potential of the Conduction Electrons | |
| |
| |
| |
| Susceptibility of the Conduction Electrons | |
| |
| |
| |
| The de Haas-Van Alphen Effect | |
| |
| |
| |
| Oscillations in the Magnetic Susceptibility | |
| |
| |
| |
| Electron Orbits in Magnetic Field | |
| |
| |
| |
| Physical Origin of the Oscillations | |
| |
| |
| |
| Onsager Argument | |
| |
| |
| |
| Problems | |
| |
| |
| References | |
| |
| |
| |
| Paramagnetism | |
| |
| |
| |
| Pauli Spin Paramagnetism | |
| |
| |
| |
| "Primitive" Theory of the Pauli Spin Paramagnetism | |
| |
| |
| |
| Temperature Corrections | |
| |
| |
| |
| Exchange Corrections | |
| |
| |
| |
| Paramagnetism of the Localized Electrons | |
| |
| |
| |
| Weak Spin-Orbit Interaction | |
| |
| |
| |
| Strong Spin-Orbit Coupling | |
| |
| |
| |
| Van Vleck Paramagnetism | |
| |
| |
| |
| Problems | |
| |
| |
| References | |
| |
| |
| |
| Exchange Interaction | |
| |
| |
| |
| Phenomenological Theories | |
| |
| |
| |
| The Exchange Field | |
| |
| |
| |
| Weiss Ferromagnet | |
| |
| |
| |
| Direct Exchange Interaction | |
| |
| |
| |
| Pauli's Principle | |
| |
| |
| |
| The Heitler-London Method | |
| |
| |
| |
| Dirac's Vector Model | |
| |
| |
| |
| Indirect Exchange Interaction | |
| |
| |
| |
| Rudermann-Kittel-Kasuya-Yosida (RKKY) Interaction | |
| |
| |
| |
| Superexchange | |
| |
| |
| |
| Double Exchange | |
| |
| |
| |
| Problems | |
| |
| |
| References | |
| |
| |
| |
| Ising Model | |
| |
| |
| |
| The Model | |
| |
| |
| |
| The One Dimensional Ising Model | |
| |
| |
| |
| Spontaneous Magnetization | |
| |
| |
| |
| One Dimensional Ising Model in External Field | |
| |
| |
| |
| The Phase Transition of Two-Dimensional Ising Model | |
| |
| |
| |
| The Method of Proof | |
| |
| |
| |
| Finite Ising Lattice with Special Boundary Conditions | |
| |
| |
| |
| Probabilities | |
| |
| |
| |
| Realization Possibilities for the Polygons | |
| |
| |
| |
| Magnetization of the Finite Lattice | |
| |
| |
| |
| Thermodynamic Limit | |
| |
| |
| |
| The Free Energy of the Two-Dimensional Ising Model | |
| |
| |
| |
| High-Temperature Expansion | |
| |
| |
| |
| Spin Products as Graphs | |
| |
| |
| |
| Loops | |
| |
| |
| |
| Directed Paths | |
| |
| |
| |
| Matrix M1 | |
| |
| |
| |
| Free Energy per Spin | |
| |
| |
| |
| Curie Temperature Tc | |
| |
| |
| |
| Specific Heat | |
| |
| |
| |
| Spontaneous Magnetization | |
| |
| |
| |
| Problems | |
| |
| |
| References | |
| |
| |
| |
| Heisenberg Model | |
| |
| |
| |
| Model Hamiltonian | |
| |
| |
| |
| Spin Operators | |
| |
| |
| |
| Model Extensions | |
| |
| |
| |
| Exact Statements | |
| |
| |
| |
| Mermin-Wagner Theorem | |
| |
| |
| |
| One-lylagnon States of a Ferromagnet | |
| |
| |
| |
| Molecular Fields Approximations | |
| |
| |
| |
| Ferrorqagnet | |
| |
| |
| |
| Antiferromagnet | |
| |
| |
| |
| Ferrimagnet | |
| |
| |
| |
| Spin Waves | |
| |
| |
| |
| Linear Spin Wave Theory for the Isotropic Ferromagnet | |
| |
| |
| |
| "Renormalized" Spin Waves | |
| |
| |
| |
| Harmonic Approximation for Antiferromagnets | |
| |
| |
| |
| Harmonic Approximation for a Ferromagnet with Dipolar Interaction | |
| |
| |
| |
| Thermodynamics of S = 1 /2 Ferromagnet | |
| |
| |
| |
| Tyablikov Decoupling | |
| |
| |
| |
| Spontaneous Magnetization | |
| |
| |
| |
| Thermodynamic Potentials | |
| |
| |
| |
| Thermodynamics of S > 1/2 Ferromagnets | |
| |
| |
| |
| Green's Functions | |
| |
| |
| |
| Spontaneous Magnetization | |
| |
| |
| |
| The Callen Method | |
| |
| |
| |
| Problems | |
| |
| |
| References | |
| |
| |
| |
| Hubbard Model | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Model for Band Magnets | |
| |
| |
| |
| Solid as a Many-Body System | |
| |
| |
| |
| Electrons in Narrow Energy Bands | |
| |
| |
| |
| Hubbard Model | |
| |
| |
| |
| Stoner Model | |
| |
| |
| |
| Stoner Ansatz (Ferromagnet) | |
| |
| |
| |
| Stoner Excitations | |
| |
| |
| |
| Magnetic Phase Transition | |
| |
| |
| |
| Static Susceptibility | |
| |
| |
| |
| Exact Statements and General Properties | |
| |
| |
| |
| Mermin-Wagner Theorem | |
| |
| |
| |
| The Infinitely Narrow Band | |
| |
| |
| |
| The Two-Site Model | |
| |
| |
| |
| The Exactly Half-Filled Band | |
| |
| |
| |
| Strong-Coupling Regime | |
| |
| |
| |
| Spectral Moments | |
| |
| |
| |
| High-Energy Expansions | |
| |
| |
| |
| Weak-Coupling Regime | |
| |
| |
| |
| Infinite Dimensions | |
| |
| |
| |
| Effective "impurity"-Problem | |
| |
| |
| |
| Magnetism and Electronic Correlations | |
| |
| |
| |
| Hubbard-I Approximation | |
| |
| |
| |
| Interpolation Method | |
| |
| |
| |
| Correlation Effects and Ferromagnetism | |
| |
| |
| |
| Criterion for Ferromagnetism | |
| |
| |
| |
| Static Susceptibility and Ferromagnetism | |
| |
| |
| |
| Spin-Dependent Band Shift | |
| |
| |
| |
| Quasiparticle Damping | |
| |
| |
| |
| Dynamical Mean Field Theory | |
| |
| |
| |
| Modified Perturbation Theory | |
| |
| |
| |
| Curie Temperature, Magnetization and Static Susceptibility | |
| |
| |
| |
| Problems | |
| |
| |
| References | |
| |
| |
| |
| Second Quantization | |
| |
| |
| |
| Identical Particles | |
| |
| |
| |
| Continuous Fock Representation | |
| |
| |
| |
| Symmetrized Many-Particle States | |
| |
| |
| |
| Construction Operators | |
| |
| |
| |
| Many-Body Operators | |
| |
| |
| |
| Discrete Fock Representation (Occupation Number Representation) | |
| |
| |
| |
| Symmetrized Many-Particle States | |
| |
| |
| |
| Construction Operators | |
| |
| |
| |
| Examples | |
| |
| |
| |
| Bloch Electrons | |
| |
| |
| |
| Wannier Electrons | |
| |
| |
| |
| Density Operator | |
| |
| |
| |
| Coulomb Interaction | |
| |
| |
| |
| Problems | |
| |
| |
| |
| The Method of Green's Functions | |
| |
| |
| |
| Linear Response Theory | |
| |
| |
| |
| Kubo Formula | |
| |
| |
| |
| Magnetic Susceptibility | |
| |
| |
| |
| Dielectric Function | |
| |
| |
| |
| Spectroscopies and Spectral Densities | |
| |
| |
| |
| Double-Time Green's Functions | |
| |
| |
| |
| Definitions and Equations of Motion | |
| |
| |
| |
| Spectral Representations | |
| |
| |
| |
| Spectral Theorem | |
| |
| |
| |
| Spectral Moments | |
| |
| |
| |
| Kramer's-Kronig Relations | |
| |
| |
| |
| Simple Applications | |
| |
| |
| |
| The Quasiparticle Concept | |
| |
| |
| |
| Interacting Electrons | |
| |
| |
| |
| Electronic Self-energy | |
| |
| |
| |
| Quasiparticles | |
| |
| |
| |
| Quasiparticle Density of States | |
| |
| |
| |
| Thermodynamics | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Solutions to Problems | |
| |
| |
| Index | |