Singlet-Triplet Formulation for Dilute Magnetic Alloys. I.s−dExchange Model

Abstract

Singlet-triplet pair (STP) Green functions are formulated and studied for the $s-d$ exchange model of dilute magnetic alloys having a single magnetic impurity. Special poles of these STP Green functions (on the unphysical sheet) represent quasibound pair states commonly assumed responsible for the anomalous low-temperature properties of these systems. The STP Green functions are evaluated by an approximate decoupling procedure along with additional approximations for the single-particle averages. For a ferromagnetic interaction, the triplet states show no pole except at zero temperature. A singlet-triplet pole is found for finite temperature for an antiferromagnetic interaction, no pure singlet pole being found except for $T=0\mathrm{}$. These results follow from evaluation of the poles which involves conditions on both the real and the imaginary parts of the frequency; the more common but incorrect evaluation on the real frequency axis leads to quite different conclusions.