Parametric excitation of magnetic vortex gyrations in spin-torque nano-oscillators

We experimentally demonstrate that large amplitude magnetic vortex gyrations can be parametrically excited by the injection of radio-frequency (rf) current at twice the natural frequency of the gyrotropic vortex-core motion. The mechanism of excitation is based on the parallel pumping of vortex motion by the rf orthoradial field generated by the injected current. Theoretical analysis shows that experimental results can be interpreted as the manifestation of parametric amplification when the rf current is small, and of parametric instability when the rf current is above a certain threshold. By taking into account the energy nonlinearities, we succeed to describe the amplitude saturation of vortex oscillations as well as the coexistence of stable regimes.