A Contemporary Model Description of Magnetism

TL;DR

This paper reviews and develops models of magnetism in transition and rare-earth metals, focusing on many-electron interactions, model derivations, and their applications to strongly correlated systems like half-metallic ferromagnets and Kondo lattices.

Contribution

It provides a comprehensive derivation of key many-electron models and explores their internal relationships and applications to complex magnetic systems.

Findings

Derivation of Heisenberg, Hubbard, Anderson, and t-J models

Analysis of strong itinerant magnetism and local moments

Application to half-metallic ferromagnets and Kondo lattices

Abstract

A treatment of many-electron polar and $s-d(f)$ exchange models is carried out in connection with the development of the theory of magnetism of transition and rare-earth metals, as well as their compounds. Particular emphasis is placed on the derivation of the many-electron Heisenberg, Hubbard, Anderson and $t-J$ models, as well as the internal relationship between them. Among the topics discussed are many-electron approaches in describing systems of $d$- and $f$-electrons, atomic representation of Hubbard's $X$-operators, slave-particle representations, the problem of strong itinerant magnetism and the formation of local moments, the role of non-quasiparticle (incoherent states). The application of these concepts to strongly correlated systems, in particular, to half-metallic ferromagnets and Kondo lattices, is discussed. A comparison is performed with modern field-theoretical and topological approaches.