Fine structure of excitation spectra of magnetic vortex dot clusters

Low-frequency gyrotropic dynamics (100 MHz range) in clusters of interacting magnetic vortex state dots are considered. The clusters consist of 3 or 4 laterally placed cylindrical ferromagnetic dots on a dielectric substrate in the form of equilateral triangles or squares. The interdot dynamical magnetostatic interactions are considered in the form of explicit multipole decompositions on the inverse dot center-to-center distance. The eigenfrequencies of collective magnetic vortex oscillations are calculated analytically and compared with the results of recent experiments conducted on clusters of permalloy dots.