Itinerant Electron Magnets: Curie Temperature and Susceptibility in Density-Functional Theory

Abstract

Groundstate properties of solids are astonishingly well described by the local density functional approximation (LDA) [1]. This is also true of metallic magnets for which the situation was recently described by this author [2]. Excited-state properties of magnets (and other systems), however, are still a great challenge and it was believed until recently that the band-picture, based in the LDA, fails entirely in describing magnetism at elevated temperatures. We emphasize here that this is not so, attempting first to expose the reason why it was thought that the band-picture fails. Since historically the underlying physical picture was developed by Stoner and Wohlfarth, we begin with a discussion of their theory using, however, an approach that reveals the essential assumptions. This is Mermin’s [3] finite-temperature density functional theory. Two points emerge: one is the essential noncollinearity of the magnetic moments at finite temperatures, the other is the form of the exchange-correlation contribution to the thermodynamic potential. We know how to deal with noncollinear order in the LDA and we explain how we might use this knowledge to advance the issue. Exchange and correlation at finite temperatures are, however, at the present state not well understood. This statement not only applies to density functional theory but also to many-body treatments addressed at this workshop.

We will show in particular that the theory of magnons in the band-LDA- picture at low temperatures is in good shape. At high temperatures we opt for a theory involving spin fluctuations and argue that, although broad features of the magnetic phase transition are described satisfactorily, many details await further improvements.