We study magnetization dynamics in spin-transfer devices subject to DC and microwave injected currents. When the frequency of the injected current is sufficiently close to the self-oscillation frequency of the device, phase-locking occurs. This phenomenon is theoretically studied by using Landau-Lifshitz equation with Slonczewski spin-torque term. By exploiting separation of time scales and using averaging technique, we derive equations which are applicable to the study of phase-locking for arbitrary large magnetization motion. The stability diagram in the (detuning, ac current)-plane is determined and it is shown that phase locking is hysteretic at sufficiently large ac currents.
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Serpico et al. (2009) studied this question.