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Dipole coupling induced magnetic ordering in an ensemble of nanostructured islands

The magnetic ordering due to the long range dipole coupling in an ensemble of magnetic islands is investigated. If the islands are large enough and closely separated, the average dipole energy per island can explain the magnitude of the observed ordering temperature of such an ensemble. The energetical degeneracy with respect to a continuous in-plane rotation of the magnetic moments in a periodic ensemble of islands is lifted in presence of an island size dispersion and an irregular island array. Many different (metastable) magnetic states are obtained, reminiscent of a spin-glass behavior. We obtain that the average magnetic binding energy per island due to the dipole coupling increases with increasing positional disorder. The island ensembles exhibit non-collinear magnetic structures, resulting in non-saturated ensemble magnetizations. The calculations are performed with a classical spin model for ensembles of islands in unit cells with periodic boundary conditions. The point dipole sums are augmented by an island areal correction.