Fractional locking of spin-torque oscillator by injected ac current

Fractional synchronization is one of the most interesting collective behaviors in coupled or driving-response oscillators system, very important for both a deep understanding of a particular oscillator and for its applications. We numerically investigate the fractional synchronization of a spin-torque oscillator by injected ac current. Multiple p:q locking regions are found, which display some sophisticated overlaps. The system can be analyzed as a perturbed heteroclinic cycle rather than a phase oscillator. Both the modulations on the output frequency and power are mainly due to the modulation by the external signals on the distance between the dynamical orbit and the saddle point in phase space. By using this dynamical picture, we can well understand all the numerical results, including the variation of the locking region with the amplitude |J_a| or frequency f of the injected signal, the influence by noise, and the difference among the output powers of coexisting locking attractors. These understandings are significant for both potential applications in electronic communications and a deep investigation into this novel device.