  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.
