Origin of fourfold anisotropy in square lattices of circular ferromagnetic dots

We discuss the fourfold anisotropy of the in-plane ferromagnetic resonance field H-r, found in a square lattice of circular Permalloy dots when the interdot distance a becomes comparable to the dot diameter d. The minimum H-r along the lattice < 11 > axes and the maximum along the < 10 > axes differ by similar to 50 Oe at a/d=1.1. This anisotropy, not expected in uniformly magnetized dots, is explained by a mechanism of nonuniform magnetization m(r) in a dot in response to dipolar forces in the patterned magnetic structure under strong enough applied field. It is well described by an iterative solution of a continuous variational procedure.