  We investigate experimentally the synchronization of a vortex based spin
transfer oscillator to an external rf current whose frequency is at multiple
integers, as well as half integer, of the oscillator frequency. Through a
theoretical study of the locking process, we highlight both the crucial role of
the symmetries of the spin torques acting on the magnetic vortex and the
nonlinear properties of the oscillator on the phase locking process. Through
the achievement of a perfect injection locking state, we report a record phase
noise reduction down to -90dBc/Hz at 1 kHz offset frequency. The phase noise of
these nanoscale oscillators is demonstrating as being low and controllable
which is of significant importance for real applications using spin transfer
devices.
