Localized Moments in Metals

A simple model is used to study the occurrence of localized magnetic moments in dilute alloys. The phenomenon is treated as a scattering problem in which conduction electrons scatter from impurity potentials. Under appropriate circumstances the scattering amplitude may show a resonance---corresponding to a virtual level of the impurity. It is shown that if such a level is sufficiently sharp and lies close enough to the Fermi level, the impurity atom will develop an exchange potential that polarizes neighboring electrons. The potentials for spin-up and spin-down electrons are determined by a pair of coupled equations, whose solutions are discussed in a number of interesting cases.