Model for acoustic locking of Spin Torque Oscillator

This paper presents a model for locking Spin Torque Oscillator (STO) to an out-of-plane AC strain generated using a mechanical transducer like High-Overtone Bulk Acoustic Resonator (HBAR). We model the magnetization dynamics of the free layer magnet in the STO using the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation modified to include magneto-elastic coupling term. Locking is clearly demonstrated from the simulated frequency spectrum of the acoustically-locked STO which has a narrower linewidth and higher signal power as compared to a free running STO. We have shown locking of different modes of the STO and compare the amplitude of out-of-plane AC strain needed to achieve lock. Acoustic locking illustrated here can be used for locking multiple STOs to a common strain transducer and is a potential platform for developing hybrid magneto-acoustic oscillator systems.