Green's-Function Theory of an Induced-Moment System Containing Impurities. II. Vacancy Impurities

Abstract

The bulk susceptibility of an induced-moment system containing substitutional vacancy impurities is studied in the low-impurity-concentration limit, utilizing a Green's-function method in the random-phase approximation. It is found that the variation of the inverse susceptibility with the impurity concentration is strongly temperature dependent, in contrast to the temperature-independent result predicted by the simple molecular-field theory in which the exchange interaction is merely scaled by the factor $1-c$. At low temperatures the deviation can be up to 35% for a simple cubic lattice. A further investigation shows that a refined molecular-field theory taking account of the nonuniform distribution of the magnetization in the impure crystal recovers most of the features predicted by the Green's-function theory. However, no molecular-field theory can account for the behavior of systems of small energy gap, or systems of low ordering temperature. In these systems the contribution of the collective excitations greatly alters the results at low temperatures not only quantitatively but also qualitatively.