Theory of Spin-Acoustic Resonance for Spin-3/2 Si Vacancy with $C_{3v}$ Site Symmetry in Silicon Carbide

Motivated by the recent acoustically driven spin resonance studies applied to silicon vacancy centers in silicon carbide, we theoretically investigate the spin–strain interaction characterized by the defect spin-$3\mathrm{/}2$ quadrupole components coupled to strain fields. Considering the $C_{3v}$ symmetry of the vacancy site beyond the spherical approximation, we clarify the effect of a deviation from the spherical symmetry on spin resonance transition rate, which can be changed by rotating a static magnetic field. The ratios of spin–strain coupling parameters can be evaluated from the anisotropic field-direction dependence of the transition rate using a standing or traveling surface acoustic wave. We also discuss the effect of the propagation direction of the acoustic wave tilted from the crystallographic mirror plane reflecting the $C_{3v}$ symmetry. The results presented here reveal the quadrupole properties inherent in spin-3/2 states and will promote the realization of the acoustically driven strain control of spin.