Magnetic exchange in disordered metals.

Abstract

We consider the indirect exchange between magnetic moments placed in a metallic environment that is weakly disordered due to the presence of randomly distributed nonmagnetic impurities. We find that the even moments of the isotropic exchange interactions are long-ranged, falling off as a power law in the spin separation distance just as in the pure metal. Depending on the experimental quantity of interest, the effective coupling between spins is given by either the first or the second moment of the distribution of exchange couplings in the system. The effect of spin-orbit scattering on the interaction between local moments is considered. In the case of isotropic spin-orbit scattering in both bulk materials and thin films, the isotropic exchange interactions are exponentially suppressed at large distances. In strictly two dimensions, however, there are long-range anisotropic spin-exchange couplings that have power-law fall-off with the square of the distance. In this case the interaction becomes effectively Ising at large distances. The distribution of couplings is seen to be broad, reflecting the sensitivity of the interactions to changes in the impurity configuration. Correlations of the couplings between sites are also found to have power-law fall-off with distance; however, these are higher order in the perturbation expansion. The relevance to experiments is discussed.