Contents Basic Facts Atomic Magnetism

Transcription

1 Contents 1 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 (LS-)Coupling Hund s Rules for LS Coupling DiracEquation ElectronSpin Spin OrbitCoupling Wigner Eckart Theorem Rotation RotationOperator Angular Momentum RotationMatrices TensorOperators Wigner Eckart Theorem ExamplesofApplication Electron in an External Magnetic Field Nuclear Quadrupole Field Hyperfine Field Magnetic Hamiltonian of the Atomic Electron Many-ElectronSystems CoulombInteraction ix

2 x Contents Spin OrbitCoupling FurtherCouplings 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 TemperatureCorrections Exchange Corrections Paramagnetism of the Localized Electrons WeakSpin OrbitInteraction StrongSpin OrbitCoupling Van Vleck Paramagnetism Problems References Exchange Interaction Phenomenological Theories The Exchange Field Weiss Ferromagnet Direct Exchange Interaction Pauli sprinciple The Heitler London Method Dirac s Vector Model Indirect Exchange Interaction Rudermann Kittel Kasuya Yosida (RKKY) Interaction Superexchange

3 Contents xi 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 TheMethodofProof 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 DirectedPaths Matrix M FreeEnergyperSpin Curie Temperature T c Specific Heat Spontaneous Magnetization Problems References Heisenberg Model Model Hamiltonian SpinOperators Model Extensions Exact Statements Mermin Wagner Theorem One-Magnon States of a Ferromagnet Molecular Field Approximations Ferromagnet Antiferromagnet Ferrimagnet SpinWaves Linear Spin Wave Theory for the Isotropic Ferromagnet Renormalized Spin Waves Harmonic Approximation for Antiferromagnets Harmonic Approximation for a Ferromagnet with Dipolar Interaction

4 xii Contents 7.5 Thermodynamics of S = 1/2 Ferromagnet Tyablikov Decoupling Spontaneous Magnetization Thermodynamic Potentials Thermodynamics of S 1/2 Ferromagnets Green s Functions Spontaneous Magnetization TheCallenMethod Problems References Hubbard Model Introduction Model for Band Magnets SolidasaMany-BodySystem 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 TheInfinitelyNarrowBand The Two-Site Model The Exactly Half-Filled Band Strong-Coupling Regime Spectral Moments High-Energy Expansions Weak-Coupling Regime InfiniteDimensions Effective impurity -Problem Magnetism and Electronic Correlations Hubbard-I Approximation InterpolationMethod Correlation Effects and Ferromagnetism Criterion for Ferromagnetism Static Susceptibility and Ferromagnetism Spin-Dependent Band Shift QuasiparticleDamping Dynamical Mean Field Theory Modified Perturbation Theory

5 Contents xiii Curie Temperature, Magnetization and Static Susceptibility Problems References A Second Quantization A.1 IdenticalParticles A.2 Continuous Fock Representation A.2.1 SymmetrizedMany-ParticleStates A.2.2 ConstructionOperators A.2.3 Many-BodyOperators A.3 Discrete Fock Representation (Occupation Number Representation) A.3.1 SymmetrizedMany-ParticleStates A.3.2 ConstructionOperators A.4 Examples A.4.1 BlochElectrons A.4.2 Wannier Electrons A.4.3 DensityOperator A.4.4 CoulombInteraction A.5 Problems B The Method of Green s Functions B.1 Linear Response Theory B.1.1 KuboFormula B.1.2 Magnetic Susceptibility B.1.3 Dielectric Function B.2 Spectroscopies and Spectral Densities B.3 Double-Time Green s Functions B.3.1 DefinitionsandEquationsofMotion B.3.2 Spectral Representations B.3.3 Spectral Theorem B.3.4 Spectral Moments B.3.5 Kramer s KronigRelations B.3.6 SimpleApplications B.4 The Quasiparticle Concept B.4.1 InteractingElectrons B.4.2 Electronic Self-energy B.4.3 Quasiparticles B.4.4 QuasiparticleDensityofStates B.4.5 Thermodynamics B.5 Problems C Solutions to Problems Index...743

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