Ruderman-Kittel-Kasuya-Yosida interactions between spin distributions of arbitrary shape

The net Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between well-separated spin distributions can be mapped onto a RKKY interaction between two point-like effective moments. The effective moments, which a strongly oscillating dependence on the size, shape, and orientation of the spin distribution, are discussed for a variety of microscopic and macroscopic configurations. Particular emphasis is on the relation between RKKY interactions and band-structure Heisenberg exchange constants in itinerant magnets and on two-ion anisotropy contributions to the magnetocrystalline anisotropy of rare-earth ions. (C) 2000 American Institute of Physics. [S0021-8979(00)50608-2].