We found, by micromagnetic numerical and analytical calculations, that the clockwise (CW) and counterclockwise (CCW) circular-rotational motions of a magnetic vortex core in a soft magnetic circular nanodot are the elementary eigenmodes existing in the gyrotropic motion with respect to the corresponding CW and CCW circular-rotational-field eigenbasis. The oppositely rotating eigenmodes show a giant asymmetric resonance behavior, i.e., for the up-core orientation the CCW eigenmode shows a strong resonance at the field frequency equal to the vortex eigenfrequency, but the other CW eigenmode shows nonresonance. This asymmetric resonace effect is reversed by changing the vortex polarization. The orbital radius amplitudes and phases of the two circular eigenmodes vary with the polarization and chirality of the given vortex state as well as the field frequency. The overall linear-regime steady-state vortex gyrotropic motions driven by arbitrary polarized oscillating in-plane magnetic field in the linear regime can be perfectly understood according to the superposition of the two circular eigenmodes.
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