Nonlinear gyrotropic vortex dynamics in ferromagnetic dots

The quasistationary and transient (nanosecond) regimes of nonlinear vortex dynamics in a soft magnetic dot driven by an oscillating external field are studied. We derive a nonlinear dynamical system of equations for the vortex core position and phase, assuming that the main source of nonlinearity comes from the magnetostatic energy. In the stationary regime, we demonstrate the occurrence of a fold-over bifurcation and calculate analytically the resonant nonlinear vortex frequencies as a function of the amplitude and frequency of the applied driving field. In the transient regime, we show that the vortex core dynamics are described by an oscillating trajectory radius. The resulting dynamics contain multiple frequencies with amplitude decaying in time. Finally, we evaluate the ranges of the system parameters leading to a vortex core instability (core polarization reversal).