Spin-wave excitation modes in thick vortex-state circular ferromagnetic nanodots

We study both experimentally and using micromagnetic simulations how the spin excitation spectra of the vortex-state circular dots made of soft magnetic material change with the dot thickness t in the range t = 20-80 nm. It is found that in addition to higher-order gyrotropic modes which are nonuniform along the dot thickness and were observed earlier, azimuthal spin-wave modes having curled structure at the dot top and bottom faces appear in the spectrum when increasing the dot thickness. For the dot thickness t > 50 nm these "curled" modes become the lowest ones in the spin-wave excitation spectrum. It is also shown that all spin-wave modes with azimuthal index m = +/- 1 are hybridized with the vortex gyrotropic modes. However, while "common" azimuthal (0, +/- 1) modes are hybridized with the main gyrotropic G(0) mode and reveal large frequency splitting of their doublet, the curled modes can be hybridized with higher-order gyrotropic modes and the doublet frequency splitting vanishes with the dot thickness increase.