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A theory of magnetoacoustic resonance is proposed to measurequadrupole-strain couplings in a spin-triplet state with the $C_{3v}$ pointgroup symmetry, considering the spin-strain interaction in a diamondnitrogen-vacancy (NV) center. Based on the Floquet theory, we demonstrate howthe single- and two-phonon transition probabilities depend on the change in thelongitudinal and transverse quadrupole couplings, which can be controlled byrotating an applied magnetic field, around the threefold axis. The obtainedquadrupole dynamics results are useful for realizing mechanical or acstrain-control of the NV spin as an alternative to the conventional magneticcontrol by spin resonance.

Magnetoacoustic Resonance to Probe Quadrupole-Strain Coupling in a Diamond Nitrogen-Vacancy Center as a Spin-Triplet System