Ferromagnetic resonance of a two-dimensional array of nanomagnets: Effects of surface anisotropy and dipolar interactions
Abstract
We develop an analytical approach for studying the ferromagnetic resonance (FMR) frequency shift due to dipolar interactions and surface effects in two-dimensional arrays of nanomagnets with (effective) uniaxial anisotropy along the magnetic field. For this we build a general formalism on the basis of perturbation theory that applies to dilute assemblies but which goes beyond the point-dipole approximation as it takes account of the size and shape of the nanoelements, in addition to their separation and spatial arrangement. The contribution to the frequency shift due to the shape and size of the nanoelements has been obtained in terms of their aspect ratio, their separation, and the lattice geometry. We have also varied the size of the array itself and compared the results with a semianalytical model and reached an agreement that improves as the size of the array increases. We find that the red-shift of the ferromagnetic resonance due to dipolar interactions decreases for smaller arrays. Surface effects may induce either a blue-shift or a red-shift of the FMR frequency, depending on the crystal and magnetic properties of the nanoelements themselves. In particular, some configurations of the nanoelements' assemblies may lead to a full compensation between surface effects and dipole interactions.