Theory of Localized Magnetic States in Metals

Abstract

The problem of determining the conditions for the occurrence of localized moments in dilute alloys on the basis of Anderson's model is re-examined. From a coupled set of Green's-function equations an approximate solution is found which includes the electron correlation in the impurity levels and which passes over to the exact solution in the limiting case of an isolated impurity. The Hartree-Fock theory is obtained only if the Coulomb repulsion $U$ is relatively small. When $U$ is large the correlation effects are important, and magnetic states are found only if the energy shift caused by the impurity-band electron scattering satisfies certain fairly restrictive conditions. Possible modifications when the degeneracy of the impurity levels, the intra-atomic exchange interactions, and the electron interactions in the host metal are taken into account are qualitatively discussed.