Effects of the competition between the exchange and dipolar interactions in the spin-wave spectrum of two-dimensional circularly magnetized nanodots

We use a microscopic theory taking into account the dipolar and nearest-neighbour exchange interactions for exploring spin-wave excitations in two-dimensional magnetic dots in the vortex state. Normal modes of different profiles are observed: azimuthal and radial modes, as well as fundamental (quasiuniform) and highly localized modes. We examine the dependence of the frequencies and profiles of these modes on the dipolar-to-exchange interaction ratio and the size of the dot. Special attention is paid to some particular modes, including the lowest mode in the spectrum and the evolution of its profile, and the fundamental mode, the frequency of which proves almost independent of the dipolar-to-exchange interaction ratio. We also provide a selective overview of the experimental, analytical and numerical results from the literature, where different profiles of the lowest mode are reported. We attribute this diversity to the competition between the dipolar and exchange interactions. Finally, we study the hybridization of the modes, show the multi-mode hybridization and explain the selection rules.