Micromagnetic simulations of vortex-state excitations in soft magnetic nanostructures

The dynamic susceptibility spectra of Permalloy nanodots, supporting a vortex-type magnetic configuration, are studied within the frequency range $0.2\char21{}20\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$ as a function of dot thickness $(10\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\ensuremath{\leqslant}{L}_{z}\ensuremath{\leqslant}80\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ by means of three-dimensional dynamic micromagnetic simulations. In addition to the low-frequency vortex translation mode (gyrotropic motion of the vortex core), a second vortex core mode is revealed at a higher frequency for thicker nanodots (in-plane pumping field). This mode whose resonance frequency decreases rapidly with increasing dot thickness originates from the nonuniform vortex structure along the dot normal axis. Higher frequency modes are also observed for both in-plane and perpendicular pumping field orientations and correspond mostly to spin excitations localized outside the vortex core. The possible detection of the two vortex core modes within an individual nanodot using resonance experiments is discussed on the basis of the dispersion relation frequency versus perpendicular static magnetic field.

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