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We develop an analytical approach for studying the FMR frequency shift due todipolar interactions and surface effects in two-dimensional arrays ofnanomagnets with (effective) uniaxial anisotropy along the magnetic field. Forthis we build a general formalism on the basis of perturbation theory thatapplies to dilute assemblies but which goes beyond the point-dipoleapproximation as it takes account of the size and shape of the nano-elements,in addition to their separation and spatial arrangement. The contribution tothe frequency shift due to the shape and size of the nano-elements has beenobtained in terms of their aspect ratio, their separation and the latticegeometry. We have also varied the size of the array itself and compared theresults with a semi-analytical model and reached an agreement that improves asthe size of the array increases. We find that the red-shift of theferromagnetic resonance due to dipolar interactions decreases for smallerarrays. Surface effects may induce either a blue-shift or a red-shift of theFMR frequency, depending on the crystal and magnetic properties of thenano-elements themselves. In particular, some configurations of thenano-elements assemblies may lead to a full compensation between surfaceeffects and dipole interactions.

Ferromagnetic resonance of a two-dimensional array of nanomagnets: Effects of surface anisotropy and dipolar interactions