Spin Fluctuations in Itinerant Electron Magnetism, Softcover reprint of the original 1st ed. 1985 Coll. Springer Series in Solid-State Sciences, Vol. 56

Ferromagnetism of metallic systems, especially those including transition metals, has been a controversial subject of modern science for a long time. This controversy sterns from the apparent dual character of the d-electrons responsible for magnetism in transition metals, i.e., they are itinerant elec­ trons described by band theory in their ground state, while at finite tem­ peratures they show various properties that have long been attributed to a system consisting of local magnetic moments. The most familiar example of these properties is the Curie-Weiss law of magnetic susceptibility obeyed by almost all ferromagnets above their Curie temperatures. At first the problem seemed to be centered around whether the d-elec­ trons themselves are localized or itinerant. This question was settled in the 1950s and early 1960s by various experimental investigations, in particular by observations of d-electron Fermi surfaces in ferromagnetic transition metals. These observations are generally consistent with the results of band calculations. Theoretical investigations since then have concentrated on explaining this dual character of d-electron systems, taking account of the effects of electron-electron correlations in the itinerant electron model. The problem in physical terms is to study the spin density fluctuati·ons, which are ne­ glected in the mean-field or one-electron theory, and their influence on the physical properties.

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.