Self-Injection Locking of a Vortex Spin Torque Oscillator by Delayed Feedback

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 integrated power and spectral linewidth are improved for optimal delays. Moreover by varying the phase difference between the emitted power and the re-injected one, we find a clear oscillatory dependence on the phase difference with a 2π 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.