Abstract

In the present work the effective spin Hamiltonian in ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{xA}}$ (A=Te,Se,S) is obtained as a result of an indirect exchange between Mn atoms via band electrons and holes. The effective Hamiltonian and the exchange integrals are calculated for nonzero temperature using the finite-temperature Green-function approach. As a result, the effective Hamiltonian is expressed in a form of a rapidly convergent series. The first term of that series corresponds to the zero-temperature result, while other terms represent temperature corrections to it. A criterion of the validity of the zero-temperature Green-function approach in a finite temperature is proposed. \textcopyright{} 1996 The American Physical Society.

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