Mutual phase locking in high-frequency microwave nano-oscillators as a function of field angle

We perform a qualitative analysis of phase locking in a double point-contact spin–valve system by solving the Landau–Lifshitz–Gilbert–Slonzewski equation using a hybrid-finite-element method. We show that the phase-locking behaviour depends on the applied field angle. Starting from a low field angle, the locking-current difference between the current through contact A and B increases with increasing angle up to a maximum of 14 mA at 30°, and it decreases thereafter until it reaches a minimum of 1 mA at 75°. The tunability of the phase-lock frequency with current decreases linearly with increasing out-of-plane angle from 45 to 21 MHz/mA.