Parallel pumping of magnetic vortex gyrations in spin-torque nano-oscillators

We experimentally demonstrate that large magnetic vortex oscillations can be parametrically excited in a magnetic tunnel junction by the injection of radio-frequency (rf) currents 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 rf current is small, and of parametric instability when 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.