Density-functional theory of magnetic instabilities in metals

Abstract

A density-functional formulation of magnetic states in metals is set up in which, initially, a spin-dependent external potential is switched on to the metal. The usual Hartree-Fock treatment of strong short-range correlations in an s-band is shown to follow very simply from the theory. Building up this Hartree-Fock theory for the lattice by switching on the interactions one site at a time suggests an approximate way of incorporating correlation effects into the density-functional theory. This is consistent with the philosophy that electron correlation effects are best treated via a picture in which the electron density, and, in magnetic metals, the spin density distributions are thought of as localized round atomic sites. In keeping with this philosophy, a new general magnetic instability condition for the lattice is proposed, which is essentially that for the one-site model and involves the density of states through the band, and not simply at the Fermi level, as with the Hartree-Fock condition. The properties of the Green function associated with this new instability condition are considered. While it is not possible, within the present framework, to resolve completely some ambiguity in higher-order terms of the Green function, nevertheless it is possible to set up a Green function which includes the band and the atomic limits correctly, has required symmetry properties, and exactly conserves states in the band. The density of states in this model does not show simple exchange in the magnetic metal but corresponds to deformation of the magnetic sub-bands by the electron interactions. It seems possible still that the inclusion of the long-range Coulomb correlations may, even in the non-magnetic case, after the basic character of the bands from that of a “cell” model.