Injection Locking and Phase Control of Spin Transfer Nano-oscillators

We have directly measured phase locking of spin transfer oscillators to an injected ac current. The oscillators lock to signals up to several hundred megahertz away from their natural oscillation frequencies, depending on the relative strength of the input. As the dc current varies over the locking range, time-domain measurements show that the phase of the spin transfer oscillations varies over a range of approximately $\pm 90°$ relative to the input. This is in good agreement with general theoretical analysis of injection locking of nonlinear oscillators.