  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. Any steady-state vortex
gyrotropic motions driven by a linearly polarized oscillating in-plane magnetic
field in the linear regime can be perfectly understood according to the
superposition of the two circular eigenmodes, which show asymmetric resonance
characteristics reflecting the vortex polarization. The relative magnitudes in
the amplitude and phase between the CCW and CW eigenmodes determine the
elongation and orientation of the orbital trajectories of the vortex core
motions, respectively, which trajectories vary with the polarization and
chirality of the given vortex as well as the field frequency across the
resonance frequency.
