Linear Phase Tuning of Spin Torque Oscillators Using In-Plane Microwave Fields

We demonstrate numerically and analytically that a nano-pillar spin torque oscillator (STO), operating either with in-plane or out-of-plane free-layer precession, locks to a microwave field (H_ac) having the same frequency as the STO. By varying the spatial direction of the microwave field, we further show the preferred phase shift (ΔΦ₀) between the STO and H_ac can be tuned in a linear fashion. We explain this phenomenon by using a magnetic-energy-based analysis. Our results provide a way to synchronize serially connected STOs by tuning the phase shift of each individual STO with external microwave field, which may enhance the locking efficiency, the locking range, and the output power of the serially connected STOs.