  The self-synchronization of spin torque oscillators is investigated
experimentally by re-injecting its radiofrequency (rf) current after a certain
delay time. We demonstrate that the emission power and the spectral linewidth
are improved for optimal delay times. Moreover by varying the phase difference
between the emitted power and the re-injected one, we find a clear oscillatory
dependence with a 2\pi\ periodicity of the frequency of the oscillator as well
as its power and linewidth. Such periodical behavior within the self-injection
regime is well described by the general model of nonlinear auto-oscillators
including not only a delayed rf current but also all spin torque forces
responsible for the self-synchronization. Our results reveal new approaches for
controlling the non-autonomous dynamics of spin torque oscillators, a key issue
for rf spintronics applications as well as for the development of
neuro-inspired spin-torque oscillators based devices.
