An exactly soluble model for the combined direct and indirect exchange interaction between two magnetic moments in an electron gas

Abstract

An exactly soluble model is presented for the case of two localized magnetic moments with spin S = 1 2 , which are directly coupled by the Heisenberg interaction of strength G and indirectly by the s-f or s-d interaction of strength J via the conduction electrons. This Zener model displays important differences among the four existing cases corresponding with the possible signs of G and J, e.g., both magnetic moments are only correlated in an antiferromagnetic way in case the direct interaction is antiferromagnetic. It appears that the most interesting case viz. a ferromagnetic s-f interaction and an antiferromagnetic Heisenberg interaction displays a very unexpected feature, namely the correlation function describing the relative direction of both magnetic moments in the ground state exhibits a discontinuity as a function of J/G when the spin clouds, which are built up by the electron gas around the moments, overlap.