Origin of fourfold anisotropy in square lattices of circular ferromagnetic dots

Abstract

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 $\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}$ at $a∕d=1.1$. This anisotropy, not expected in uniformly magnetized dots, is explained by a mechanism of nonuniform magnetization $\mathbf{m}(\mathbf{r})$ 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.