RKKY interactions between nanomagnets of arbitrary shape

The RKKY interaction between well-separated magnetic particles in a nonmagn etic metallic matrix is calculated. It turns out that the net interaction c an be mapped onto an RKKY interaction between two point-like effective mome nts. The effective moments exhibit a strongly oscillating dependence on the particle's size, shape; and orientation, but their magnitudes are governed by scaling laws. As a rule, magnetostatic interactions tend to suppress th e RKKY effect in particles larger than about 1 nm. Surface roughness leaves the effective-moment picture unaltered but tends to yield a moderate reduc tion of the effective moments. The results are discussed in the context of magnetic recording, spin-glass magnetism, and cluster physics.