Many-Body Theory of Localized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>States in Metals. II. Pair of Impurities

Abstract

A previous rotationally invariant perturbation treatment of localized $d$ states is extended to the case of neighboring sites interacting via direct $d\ensuremath{-}d$ exchange and indirect $s\ensuremath{-}d$ scattering. It is found that the parallel alignment of two localized moments is never the ground state of the pair. For certain values of the unperturbed $d$-state energy (depending upon the exchange interactions) only one of the sites will be occupied by a $d$ electron so the pair can have a net moment. If the conditions are such that both sites are occupied by $d$ electrons, these electrons must be aligned antiparallel so there is only a small net moment due to scattering to and from the band states.