Recent progress in the theory of itinerant electron magnetism

Itinerant-electron ferromagnetism at finite temperatures is discussed by using the functional-integral method with two fields within the static and saddle-point approximations combined with the single-site approximation; a single atom of a pure metal is regarded as an impurity embedded in the host which is treated by a kind of the alloy-analogy approximation. The amplitude of the local magnetic moment is shown to have a weak temperature dependence and to remain finite even in the paramagnetic state, where the spin susceptibility obeys an approximate Curie-Weiss law. Numerical calculations are made with the use of a simplified model for the density of states of bcc transition metals. Calculated results are discussed with reference to experimental data of iron.

Single-Site Functional-Integral Approach to Itinerant-Electron Ferromagnetism

The spin fluctuation theory of itinerant-electron magnetism is developed by using the static functional integral method combined with the single-site alloy analogy approximation. The theory is shown to provide an interpolating description of itinerant electron magnetism yielding good results in some important limits; in the weak interaction limit or T =0 K it reduces to the Hartree-Fock theory, and in the strong coupling limit for the half-filled band it reproduces the results of the molecular-field theory. With the use of the half-filled Bell shape band the temperature dependences of the average moment, the local moment, the susceptibility and the specific heat are calculated numerically for various values of the electron-electron interaction.

Single-Siet Spin Fluctuation Theory of Itinerant-Electron Systems with Narrow Bands

Using a multiple-scattering approach and the local-density and rigid-spin approximations, the exchange interactions are calculated for Fe, Ni, and Co, and the spin-wave spectrum obtained. The interactions contributing to the spin-wave spectrum are found to be rather long-ranged. The exchange parameters are calculated as a function of band filling, and predict transition to antiferromagnetic behavior for electron-deficient alloys of bcc Fe and fcc Co.

First-principles exchange interactions in Fe, Ni, and Co

Publisher Summary This chapter discusses rare earth compounds. The number of stable binary intermetallic compounds in which one of the components is a rare earth element is of the order of a thousand. Combination with elements of much smaller metallic radii then encompasses a much larger number of possible atomic arrangements of sufficiently high space filling than would be the case for two components of almost equal size. A meaningful study of the physical properties of intermetallic compounds can only be made on single phase materials. Only a fraction of the compounds is in single phase condition after the melting together of the components. The chapter explains the compounds with non-magnetic elements and compounds with d-transition metals. It also explains ternary compounds or hydrides.

Chapter 4 Rare earth compounds

The high-temperature properties of itinerant magnetic systems are examined by using the coherent-potential approximation We assume a local moment on each atom so that at elevated temperatures there is a number of reversed spins The coherent potential is solved, and from that the moment on each atom is determined self-consistently It is found that when the condition for ferromagnetic ordering is satisfied, the local moments persist even above the critical temperature Conversely, if local moments do not exist at high temperatures, the system can at most condense into a spin-density-wave state Furthermore, spin-flip scatterings of the conduction electrons from the local moments give rise to additional correlation not treated in the coherent-potential approximation This correlation energy is an important part of the coupling energy of the local moments The relations between our work and the theories of Friedel, Hubbard, and others are discussed

Quasispin model of itinerant magnetism: High-temperature theory

The problem of spin waves in itinerant ferromagnets and antiferromagnets is discussed from the band-theory point of view. In the ground state, the energy bands are spin split and there is a spin-density cloud around each ion site. When a spin wave is excited, we postulate that the spin cloud of each ion precesses as a rigid unit, i.e., a quasispin. This gives rise to a modulation of the effective exchange potential, and the difference between the modulated potential and the ground-state exchange potential has the form of the $s\ensuremath{-}d$ interaction. Here the $s$ part includes all the conduction electrons and the $d$ part arises from the precession of the quasispins. The magnon energy, electron band splitting, and the magnon-magnon interaction are discussed. In every case the agreement between the result and the experiment is as good as or better than the existing theories.

S. H. Liu

Papers

Quasispin model of itinerant magnetism: High-temperature theory

Quasispin model of itinerant magnetism