  Hybrid quantum systems exhibiting coupled optical, spin, and mechanical
degrees of freedom can serve as a platform for sensing, or as a bus to mediate
interactions between qubits with disparate energy scales. These systems are
also creating opportunities to test foundational ideas in quantum mechanics,
including direct observations of the quantum regime in macroscopic objects.
Here, we make use of angular momentum conservation to study the dynamics of a
pair of paramagnetic centers featuring different spin numbers in the presence
of a properly tuned external magnetic field. We examine the interplay between
optical excitation, spin evolution, and mechanical motion, and theoretically
show that in the presence of continuous optical illumination, inter-spin
cross-relaxation must induce rigid rotation of the host crystal. The system
dynamics is robust to scattering of spin-polarized phonons, a result we build
on to show this form of angular momentum transfer should be observable using
state-of-the-art torsional oscillators or trapped nanoparticles.
