Spin-wave modes in a thin submicron cobalt square with a closure domain structure are obtained by using a micromagnetic equation of motion approach. In addition to modes with amplitude over the whole sample, some low-frequency modes, localized at the center, corners, and diagonals of the square, are also found. In analogy with the modes found in a circular vortex, the nonlocalized modes can be broadly classified into radial-like and azimuthal-like modes, and their frequencies can be understood qualitatively in terms of the dispersion relation of spin-wave modes of an unconfined film. Other modes that can be interpreted as the combination of radial and azimuthal modes are also observed.
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Yan et al. (2006) studied this question.
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