Local moment and ferromagnetic state formation in dilute,degenerate d-electron alloys: Ferromagnetic versus antiferromagnetic interactions

In this note the Kim 1] non-degenerate Anderson model (NDAM) of random dilute alloys treatment of local moment and ferromagnetic state formation is generalized to the ten-fold degenerate Anderson model (TDAM) of Siegel and Kemeny 2], Siegel 3,4] and Moriya 12]. We first determine how an impurity state is modified by neighboring impurities. For a simple binary alloy the local electron state at each impurity site depends upon the local distribution of other impurities. Second we derive a TDAM general relationship for the occurrence of a local moment on one impurity and the ferromagnetic ordering of the total impurity spins. Lastly we derive the impurity-impurity TDAM magnetic interaction; for the direct transfer interaction the impurity-impurity magnetic interaction can be ferromagnetic or antiferromagnetic depending upon the fractional occupation of impurity states. At each stage we compare our results with those of Kim's NDAM treatment.