Double resonance response in nonlinear magnetic vortex dynamics

We present experimental evidences for the dynamical bifurcation behavior of ac-driven magnetic vortex core gyration in a ferromagnetic disk. The dynamical bifurcation, i.e., appearance and disappearance of two stable dynamical states in the vortex gyration, occurring as the amplitude of the driving Oersted field increases to B_Oe>BOecr, manifests itself in a double resonance response in the dependence of homodyne the dc-voltage signal on the frequency ω of the applied microwave current. We find that the frequency range δω between the two resonance features strongly increases with the excitation power. Our analysis based on the model of a low dissipative nonlinear oscillator subject to a resonant alternating force is in good agreement with the experimental results. This allows us to determine quantitatively key parameters of magnetic vortex dynamics, i.e., the critical value of the driving Oersted field BOecr for nonlinear dynamics to occur, the resonant frequency, and the quality factor as well as damping of the magnetic vortex gyration.