Linked e-resources
Details
Table of Contents
Intro; Preface; Contents; List of Symbols; 1 Introduction; References; 2 Basics of Metallic Magnetism; 2.1 Magnetic Susceptibility: Macroscopic Approach; 2.1.1 Generalized Magnetic Susceptibility; 2.1.2 Symmetry Relations; 2.1.3 Dispersion Relations; 2.2 Magnetic Susceptibility: Microscopic Approach; 2.2.1 Magnetization and Spin; 2.2.2 Linear Response Theory; 2.2.3 Fluctuation-Dissipation Theorem; References; 3 Many-Electron Problem; 3.1 One-Electron States; 3.2 Many-Electron States; 3.3 Second Quantization; 3.3.1 General Theory; 3.3.2 Specific Operators; Charge Density
Spin Density: Wannier RepresentationSpin Density: Bloch Representation; Single-Site Spin; Hamiltonian; 3.4 Noninteracting Electrons; References; 4 Mean-Field Theory; 4.1 The Hubbard Model; 4.2 Stoner Mean-Field Theory; 4.2.1 Hartree-Fock Approximation; 4.2.2 Magnetization: The T2 Law; 4.2.3 Uniform Static Susceptibility; 4.3 Band Calculations in Metals; References; 5 Random-Phase Approximation; 5.1 Magnetic Susceptibilities; 5.1.1 Longitudinal Susceptibility; 5.1.2 Transverse Susceptibility; 5.2 Magnetic Excitations; 5.2.1 Spin-Density Waves; 5.2.2 Magnetization: The T3/2 Law
5.2.3 Stoner Spin-Flip ExcitationsReferences; 6 Green Functions at Finite Temperatures; 6.1 Fermion-Type Green Functions; 6.1.1 Real-Time Green Function; General Properties; Equation of Motion; Spectral Function; 6.1.2 Temperature Green Function; Relation with Charge and Spin Density; Relation with the Real-Time Green Function; 6.2 Boson-Type Green Functions; 6.2.1 Dynamic Susceptibility; Longitudinal Susceptibility; Transverse Susceptibility; 6.2.2 Thermodynamic Susceptibility; Relation with the Spin Correlator; Relation with the Dynamic Susceptibility; Noninteracting Electrons
Summation RuleMeasurement and Calculation Methods; References; 7 Spin Fluctuation Theory in the Ising Model; 7.1 Spins in the Fluctuating Field; 7.2 Approximations of the Free Energy; 7.2.1 Quadratic Part of the Free Energy; 7.2.2 Higher-Order Terms of the Free Energy; 7.3 Local Fluctuating Field; 7.4 Magnetic Phase Diagrams; References; 8 Functional Integral Method; 8.1 Multiband Hubbard Hamiltonian; 8.1.1 Intraatomic Interaction and Hund's Rule; 8.1.2 Atomic Charge and Spin Density; 8.2 Functional Integral over Fluctuating Fields; 8.2.1 Thermodynamic ``Time'' Dependence
8.2.2 Electrons in the Fluctuating Field8.2.3 Charge Fluctuations; 8.3 Exact Relations; 8.3.1 Field-Dependent Thermodynamic Potential; 8.3.2 Mean Spin and Spin-Density Correlator; References; 9 Gaussian Approximation; 9.1 Motivation; 9.2 Saddle-Point Approximation; 9.3 Free Energy Minimum Principle; 9.4 Optimal Gaussian Approximation; 9.4.1 General Formulation; 9.4.2 Ferromagnetic State; 9.4.3 Self-Energy Equation; References; 10 Single-Site Gaussian Approximation; 10.1 Coherent Potential Equation; 10.2 Single-Site Gaussian Fluctuating Field; 10.3 Mean Single-Site Green Function
Spin Density: Wannier RepresentationSpin Density: Bloch Representation; Single-Site Spin; Hamiltonian; 3.4 Noninteracting Electrons; References; 4 Mean-Field Theory; 4.1 The Hubbard Model; 4.2 Stoner Mean-Field Theory; 4.2.1 Hartree-Fock Approximation; 4.2.2 Magnetization: The T2 Law; 4.2.3 Uniform Static Susceptibility; 4.3 Band Calculations in Metals; References; 5 Random-Phase Approximation; 5.1 Magnetic Susceptibilities; 5.1.1 Longitudinal Susceptibility; 5.1.2 Transverse Susceptibility; 5.2 Magnetic Excitations; 5.2.1 Spin-Density Waves; 5.2.2 Magnetization: The T3/2 Law
5.2.3 Stoner Spin-Flip ExcitationsReferences; 6 Green Functions at Finite Temperatures; 6.1 Fermion-Type Green Functions; 6.1.1 Real-Time Green Function; General Properties; Equation of Motion; Spectral Function; 6.1.2 Temperature Green Function; Relation with Charge and Spin Density; Relation with the Real-Time Green Function; 6.2 Boson-Type Green Functions; 6.2.1 Dynamic Susceptibility; Longitudinal Susceptibility; Transverse Susceptibility; 6.2.2 Thermodynamic Susceptibility; Relation with the Spin Correlator; Relation with the Dynamic Susceptibility; Noninteracting Electrons
Summation RuleMeasurement and Calculation Methods; References; 7 Spin Fluctuation Theory in the Ising Model; 7.1 Spins in the Fluctuating Field; 7.2 Approximations of the Free Energy; 7.2.1 Quadratic Part of the Free Energy; 7.2.2 Higher-Order Terms of the Free Energy; 7.3 Local Fluctuating Field; 7.4 Magnetic Phase Diagrams; References; 8 Functional Integral Method; 8.1 Multiband Hubbard Hamiltonian; 8.1.1 Intraatomic Interaction and Hund's Rule; 8.1.2 Atomic Charge and Spin Density; 8.2 Functional Integral over Fluctuating Fields; 8.2.1 Thermodynamic ``Time'' Dependence
8.2.2 Electrons in the Fluctuating Field8.2.3 Charge Fluctuations; 8.3 Exact Relations; 8.3.1 Field-Dependent Thermodynamic Potential; 8.3.2 Mean Spin and Spin-Density Correlator; References; 9 Gaussian Approximation; 9.1 Motivation; 9.2 Saddle-Point Approximation; 9.3 Free Energy Minimum Principle; 9.4 Optimal Gaussian Approximation; 9.4.1 General Formulation; 9.4.2 Ferromagnetic State; 9.4.3 Self-Energy Equation; References; 10 Single-Site Gaussian Approximation; 10.1 Coherent Potential Equation; 10.2 Single-Site Gaussian Fluctuating Field; 10.3 Mean Single-Site Green Function