Spin excitation frequencies in magnetostatically coupled arrays of vortex state circular Permalloy dots

Broadband ferromagnetic resonance in square arrays of Permalloy circular dots with different interdot separations was measured in the vortex ground state. The detected spin excitations show a complicated dependence of their frequencies on the interdot coupling strength. A considerable influence of the interdot separation on the gyrotropic vortex frequency and splitting of the azimuthal spin wave frequencies was detected. The gyrotropic frequency and the first azimuthal doublet frequency splitting depend nonmonotonously on the interdot spacing, whereas the dependence of the second doublet frequency splitting on this parameter is monotonous. The observed effects are explained by the influence of both the dipolar and quadrupolar contributions to the dynamic magnetostatic interactions.