  This paper introduces a novel oscillator that combines the tunability of spin
Hall-driven nano oscillators with the high quality factor (Q) of high overtone
bulk acoustic wave resonators (HBAR), integrating both reference and tunable
oscillators on the same chip with CMOS. In such magneto acoustic spin Hall
(MASH) oscillators, voltage oscillations across the magnetic tunnel junction
(MTJ) that arise from a spin-orbit torque (SOT) are shaped by the transmission
response of the HBAR that acts as a multiple peak-bandpass filter and a delay
element due to its large time constant, providing delayed feedback. The
filtered voltage oscillations can be fed back to the MTJ via a) strain, b)
current, or c) magnetic field. We develop a SPICE-based circuit model by
combining experimentally benchmarked models including the stochastic
Landau-Lifshitz-Gilbert (sLLG) equation for magnetization dynamics and the
Butterworth Van Dyke (BVD) circuit for the HBAR. Using the self-consistent
model, we project up to $\sim$ 50X enhancement in the oscillator linewidth with
Q reaching up to 52825 at 3 GHz, while preserving the tunability by locking the
STNO to the nearest high Q peak of the HBAR. We expect that our results will
inspire MEMS-based solutions to spintronic devices by combining attractive
features of both fields for a variety of applications.
