Spin fluctuations in itinerant electron magnetism

1. Introduction. - 1.1 Local Magnetic Moment and the Weiss Theory of Ferromagnetism. - 1.2 Magnetic Moments of Atoms. - 1.3 Heisenberg Localized Electron Model. - 1.4 Itinerant Electron Model. - 1.5 Localized vs Itinerant Electron Models. - 1.6 Random-Phase Approximation Theory of Spin Fluctuations in Itinerant Electron Magnets. - 1.7 Local Moments in Metals. - 1.8 Self-Consistent Renormalization Theory of Spin Fluctuations and Weakly Ferro- and Antiferromagnetic Metals. - 1.9 Unified Picture of Magnetism. - 1.10 Organization of the Book. - 2. Mean-Field Theory of Itinerant Electron Magnetism. - 2.1 Model Hamiltonians. - 2.2 Ferromagnetism. - 2.3 Antiferromagnetism. - 2.4 Spin-Density Waves. - 2.5 Stability of Various Spin Orderings. - 3. Dynamical Mean-Field Theory of Spin Fluctuations. - 3.1 Stoner Excitations and Spin Waves in Ferromagnetic Metals. - 3.2 General Spin Fluctuations and Dynamical Susceptibilities. - 3.3 Critical Spin Fluctuations. - 3.4 Antiferromagnets. - 3.5 Limitations of the Hartree-Fock-RPA Theory. - 4. Self-Consistent Renormalization (SCR) Theory of Spin Fluctuations. - 4.1 Expressions for the Free Energy of an Interacting Electron System. - 4.2 Paramagnon Theories. - 4.3 SCR Theory of Ferromagnetic Metals. - 4.3.1 Curie Temperature and Magnetic Susceptibility Above TC. - 4.3.2 Analytical Explanation of the New CW Law. - 4.3.3 Magnetization Below TC. - 4.3.4 Rotationally Invariant Treatment. - 4.4 Phenomenological Mode-Mode Coupling Theory. - 4.5 SCR Theory of Antiferro- and Helimagnetic Metals. - 4.6 Physical Origin of the New Curie-Weiss Susceptibility. - 4.6.1 Temperature Variation of the Mean-Square Local Amplitude of Spin Fluctuation. - 4.6.2 Spatial Spin Correlation. - 4.7 Coexistence of and Phase Transitions Between Ferro- and Antiferromagnetism. - 4.8 Quantitative Aspects of the SCR Theory for Weak Itinerant Ferromagnets. - 5. Physical Properties of Weakly and Nearly Ferro- and Antiferromagnetic Metals. - 5.1 Properties of Spin Fluctuations. - 5.2 Thermal Expansion. - 5.3 Specific Heat. - 5.4 Nuclear Spin Relaxation. - 5.4.1 Weakly and Nearly Ferromagnetic Metals. - 5.4.2 Weakly and Nearly Antiferromagnetic Metals. - 5.5 Electrical and Thermal Resistivities and Magnetoresistance. - 5.5.1 Weakly and Nearly Ferromagnetic Metals. - 5.5.2 Antiferromagnets. - 5.6 Coupling Between Spin and Charge Density Fluctuations. - 6. Local Magnetic Moments. - 6.1 Local Moments in Insulator Magnets. - 6.2 Metal-Insulator (Mott) Transition. - 6.3 s-d or s-f Exchange Model. - 6.4 Local Moment Formation in Metals. - 6.4.1 Virtual Bound State. - 6.4.2 The Anderson Model. - 6.4.3 The Wolff-Clogston Tight-Binding Model. - 6.5 Physical Properties of a Single Local Moment in Metals. - 6.6 Interaction Between a Pair of Local Moments in Metals. - 6.7 Local Moment Description of Magnetic Transition Metals. - 7. A Unified Theory and Its General Consequences. - 7.1 General Considerations Toward a Unified Theory. - 7.2 A Phenomenological Description of the Unified Theory. - 7.3 General Mechanism for the Curie-Weiss Susceptibility. - 7.3.1 A Mean Mode-Mode Coupling Theory of Magnetic Susceptibility. - 7.3.2 General Expressions for the Curie Temperature and Susceptibility. - 7.3.3 Spin Correlations and Magnetic Susceptibility. - 7.4 Possibility for Systematic Analyses of Experimental Results. - 7.5 Temperature Variation of the Local Amplitude of Spin Fluctuation. - 7.5.1 General Remarks. - 7.5.2 Temperature-Induced Local Moments. - 7.6 Limitations of the Adiabatic Approximation. - 8. Functional Integral Theory. - 8.1 Basic Formalism. - 8.2 Local Moment in Metals. - 8.3 Band Magnetism - A General Formalism. - 8.4 Methods of Calculating the Free Energy Functional. - 8.4.1 A Closed-Form Expression for ? [? , ? ]. - 8.4.2 Long-Wavelength Approximations. - 8.5 A Unified Description of Magnetism in Narrow-Band Systems. - 8.6 Approximation Methods of Evaluating the Functional Integrals. - 8.6.1 Unified Theory. - 8.6.2 Molecular Field (Single-Site) Approximation. - 8.6.3 Choice of Forms for the Interaction Hamiltonian. - 8.7 Results of Numerical Calculations. - 8.7.1 Ferromagnetic Transition Metals ? -Fe, Co, Ni. - 8.7.2 Antiferromagnetic Transition Metals. - 8.7.3 FeSi, Nearly Ferromagnetic Semiconductor. - 8.7.4 Temperature-Induced Local Moments in CoS2, CoSe2. - 8.7.5 Magnetovolume Effects. - 8.8 Supplementary Discussions on Various Approaches and Physical Pictures. - 8.8.1 The Hartree-Fock Theory for Excited States with Spatially Varying Spin Density. - 8.8.2 Local Band Theory. - 8.8.3 Persistence of Exchange Splitting of the Band Above TC. - 9. Spin Fluctuations in d-Electron Systems. - 9.1 Spin Fluctuations and Neutron-Scattering Measurements. - 9.2 Local Moment Systems. - 9.2.1 Heusler Alloys. - 9.2.2 EuO. - 9.3 Substances Close to the Local Moment Limit. - 9.3.1 MnPt3, FePd3. - 9.3.2 FePt3. - 9.4 Substances Close to the Weakly Ferro- and Antiferromagnetic Limits. - 9.4.1 MnSi. - 9.4.2 Cr. - 9.5 Substances in the Intermediate Regime: q-Space Description. - 9.5.1 Fe3Pt. - 9.5.2 CeFe2. - 9.5.3 ? -Mn, ? -(FeMn), ? -Fe. - 9.5.4 ? -Mn. - 9.6 Ferromagnetic Transition Metals Fe, Co, and Ni. - 9.7 Some Systematic Trends in Paramagnetic Scattering. - 10. Toward a Unified Theory of Dynamical Spin Fluctuations. - 10.1 General Considerations. - 10.2 Green's Function Theory of Dynamical Susceptibilities. - 10.3 Effect of Electron Lifetime on RPA-SCR Spin Fluctuations. - 11. Concluding Remarks. - References.