Abstract
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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</sub> ) having the same frequency as the STO. By varying the spatial direction of the microwave field, we further show the preferred phase shift (ΔΦ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ) between the STO and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ac</sub> 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.
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