Magnetostatic interactions on a square lattice

The metastable zero field magnetic states of elongated Permalloy islands on square lattices of different geometries are investigated by means of magnetic force microscopy and numerical calculations. Keeping the island shape L/w=10 fixed while varying the interparticle distances a, it is demonstrated that the relative frequencies of observed magnetic configuration at remanence strongly depend on the packing density of an array and the magnetic history (i.e., in which direction the array has been saturated before measurement). From 16 possible arrangements, only two are experimentally observed. For small L/a, a mixture of configurations, i.e., a spin ice, is found in agreement with previous studies, while for large L/a, an onion state unexpectedly prevails independent of the direction of the previously applied field. The results are discussed within the framework of potential theory and general stray field interaction. The relative frequencies of metastable states as well as the absence of the true ground state are in good agreement with theory.