Micromagnetic analysis of injection locking in spin-transfer nano-oscillators

The injection-locking mechanism of a spin-transfer nano-oscillator is studied for a system which is traversed by a spin-polarized electric current with both dc and ac components. The uniform mode theory is used to predict the control parameters for the synchronization between the magnetization self-oscillation and the external microwave current. It is found that micromagnetic simulations at zero temperature are in very good agreement with the theory, showing that magnetization dynamics is practically uniform in space. Then, the effect of temperature on synchronized regimes is analyzed. The locking band as well as the hysteretic character of the oscillation response are determined as function of the control parameters. Computations of the power spectral densities (PSD) of injection-locked and unlocked oscillations reveal that synchronized oscillations are quite stable with respect to thermal fluctuations. Secondary peaks in the PSD of injection-locked oscillations are reported and theoretically explained