Anisotropic exchange

The origin and physical nature anisotropic exchange interactions is investigated. Emphasis is on nonrelativistic exchange anisotropies, as encountered, for example, in intermetallics with layered crystal structures. The summation of site-resolved exchange interactions is analyzed, and it is shown that Ruderman–Kittel-type long-range exchange yield converging exchange-stiffness expressions down to atomic length scales. In general, the resulting exchange stiffness is anisotropic, even if the interaction is mediated by an isotropic free electron gas. The determination of the mean-field Curie temperature from pair-exchange interactions requires the diagonalization of an interaction matrix, as opposed to simple site averaging