The authors found that there exist two different rotational eigenmodes of oppositely rotating sense in spin-polarized current-driven vortex gyrotropic motions in soft magnetic elliptical nanodots. Simple mathematical expressions were analytically calculated by adopting vortex-core (VC)-rotation-sense- dependent dynamic susceptibility tensors based on the linearized Thiele equation [Phys. Rev. Lett. 30, 230 (1973)]. The numerical calculations of those analytical expressions were confirmed by micromagnetic simulations, revealing that linear-regime steady-state VC motions driven by any polarized oscillating currents can be interpreted simply by the superposition of the clockwise and counterclockwise rotational eigenmodes. The shape of the orbital trajectories of the two eigenmodes is determined only by the lateral dimension of elliptical dots. Additionally, the orbital radii and phases of the two eigenmodes' VC motions were found to markedly vary with the frequency of applied currents, particularly across the vortex eigenfrequency and according to the vortex polarization, which results in overall VC motions driven by any polarized oscillating currents.
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