Harmonic oscillator model for current- and field-driven magnetic vortices

In experiments, the distinction between spin-torque and Oersted-field-driven magnetization dynamics is still an open problem. Here, the gyroscopic motion of current- and field-driven magnetic vortices in small thin-film elements is investigated by analytical calculations and by numerical simulations. It is found that for small harmonic excitations, the vortex core performs an elliptical rotation around its equilibrium position. The global phase of the rotation and the ratio between the semiaxes are determined by the frequency and the amplitude of the Oersted field and the spin torque.