Origin of four-fold anisotropy in square lattices of circular   ferromagnetic dots
  We discuss the four-fold anisotropy of in-plane ferromagnetic resonance (FMR) field $H_r$, found in a square lattice of circular Permalloy dots when the interdot distance $a$ gets comparable to the dot diameter $d$. The minimum $H_r$, along the lattice $<11>$ axes, and the maximum, along the $<10>$ axes, differ by $\sim$ 50 Oe at $a/d$ = 1.1. This anisotropy, not expected in uniformly magnetized dots, is explained by a non-uniform magnetization $\bm(\br)$ in a dot in response to dipolar forces in the patterned magnetic structure. It is well described by an iterative solution of a continuous variational procedure. 
G.N. Kakazei, Yu.G. Pogorelov, M. D. Costa, T. Mewes, P.E. Wigen, P.C.   Hammel, V.O. Golub, T.Okuno, and V. Novosad