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.

Figure 1

(a) Plot of $f$ vs $I_{\mathrm{dc}}$ with amplitude shown in a linear color scale from 0 (black) to $100{\mathrm{nV}}^2/\mathrm{Hz}$ (light) with (b) corresponding $dV/dI$ curve without ac drive. Inset: Device and measurement schematic. (c) Device output power vs $I_{\mathrm{dc}}$ without ac drive signal in the same color scale. (d),(e) Same as in (a),(b) but with an ac drive at 10.86 GHz, $410\mu {\mathrm{A}}^{\mathrm{rms}}$. (f) Plot of $V_{\mathrm{rect}}$ vs $I_{\mathrm{dc}}$. Vertical lines indicate the region of locking.

Figure 2

(a) Time-domain measurement of device output at $I_{\mathrm{dc}}=7.6\mathrm{mA}$ along with a sinusoidal fit (line). (b) Spectral measurement of the device output with the same bias $I_{\mathrm{dc}}$ along with a fit to a Lorentzian function.

Figure 3

(a) Time-domain measurements of the device output as a function of dc current bias. The data are offset for clarity. (b) Relative phase shift between the device output and the external drive signal. An overall phase of 100° has been subtracted from the data.

Figure 4

(a) Plot showing the $f$ vs $I_{\mathrm{dc}}$ relation for several different amplitudes of drive at 10.86 GHz. The solid line is the predicted oscillation frequency for the drive of $330\mu \mathrm{A}$, as discussed in the text. (b) Plot showing the locking range as a function of ac drive amplitude (ac voltage across the device) along with a linear fit to the data.