Large frequency nonreciprocity of azimuthal spin-wave modes in submicron vortex state disks

Vortex states in thin film disks host spin-wave modes that are geometrically quantized according to their radial and azimuthal indices. Previous studies have shown that hybridization between these modes and the vortex core results in a sizable frequency nonreciprocity between low-order clockwise and counterclockwise propagating azimuthal modes. Here, we present a computational study of these spin-wave modes in submicron disks in which the spatial extension of the vortex core becomes comparable to the wavelength of certain modes. In such cases, we find that the frequency nonreciprocity can be large even for higher-order radial and azimuthal indices, reaching several GHz and comparable to the mode frequencies themselves.