Understanding eigenfrequency shifts observed in vortex gyrotropic motions in a magnetic nanodot driven by spin-polarized out-of-plane dc current

We observed sizable eigenfrequency shifts in spin-polarized dc-current-driven vortex gyrotropic motions in a soft magnetic nanodot, and clarified the underlying physics through micromagnetic numerical calculations. It was found that the vortex eigenfrequency is changed to higher (lower) values with increasing Oersted field (OH) strength associated with the out-of-plane dc current for the vortex chirality parallel (antiparallel) to the rotation sense of the OH circumferential in-plane orientation. The eigenfrequency shift was found to be linearly proportional to the current density j(0) in the linear regime as in Delta nu(D)similar or equal to +/-eta j(0)/parallel to G parallel to, where G is the gyrovector constant and eta is a positive constant, e.g., 1.9x10(-8) erg/A for a model Permalloy dot of 300 nm diameter and 20 nm thickness. This behavior originates from the sizable contribution of the OH to the effective potential energy of a displaced vortex core in the gyrotropic motion. The present results reveal that nu(D), an intrinsic dynamic characteristic of a given nanodot vortex state, is controllable by changes in both the density and direction of spin-polarized out-of-plane dc currents.