Conduction-Electron-Spin-Impurity-Electron-Spin Correlation Function Using thet-Matrix Formalism for the Exchange Interaction

Abstract

The conduction-electron-spin-impurity-electron-spin correlation function $〈{\mathrm{S}}^{\mathrm{el}}\mathrm{}\left(r\right)\mathrm{}·{\mathrm{S}}^{\mathrm{imp}}〉$ in a dilute magnetic alloy arising from the contact exchange interaction is computed using the $t$-matrix method. Non-perturbational as well as perturbational expressions are formulated. The nonperturbational expression for the correlation function can only be expressed in terms of certain integrals involving the $t$ matrix. A general expression for the computation of the perturbation terms in powers of the exchange coupling parameter $J$ has been found. Under specific approximations, a second-order expression along with the Ruderman-Kittel-Kasuya-Yosida term is found to be in agreement with the direct perturbational results.