A Modern Model Description of Magnetism

TL;DR

This paper reviews the development of theoretical models of magnetism, focusing on many-electron approaches, their interrelations, and applications to strongly correlated systems like half-metallic ferromagnets and Kondo lattices.

Contribution

It provides a comprehensive comparison of fundamental many-electron models and discusses their relevance to modern strongly correlated magnetic materials.

Findings

Analysis of the interrelation between Heisenberg, Hubbard, and Anderson models.

Discussion of atomic representation of X-operators in magnetism.

Application of models to half-metallic ferromagnets and Kondo lattices.

Abstract

A comparison is given of the fundamental works of S. V. Vonsovsky on the many-electron polar and s-d(f) exchange models with the subsequent development of the theory of magnetism of transition and rare earth metals and their compounds. Special attention is given to the derivation of different many-electron models (by Heisenberg, Hubbard, Anderson) and to the interrelation between them. Among the problems considered in this review, of most importance are the many-electron approaches used in the description of systems of d and f electrons, the atomic representation of X-operators, and the problem of strong itinerant magnetism and formation of local moments. The application of these concepts to highly correlated systems, in particular, to the half-metallic ferromagnets and the Kondo lattices is discussed.