Mechanical rotation via optical pumping of paramagnetic impurities

The microscopic understanding of magneto-mechanical processes — involving the inter-conversion between magnetization and angular momentum in a solid — has long been hampered by the complex dynamics governing the spin polarized electrons of a ferromagnetic material, collectively coupled via quantum exchange. Here we use a rotationally invariant Hamiltonian to study the spin dynamics of a pair of paramagnetic centers in an insulator — namely, the so-called P1 and NV centers in diamond — close enough to each other to interact via the dipolar coupling. We examine the interplay between magnetic and mechanical degrees of freedom, and theoretically show that in the presence of continuous optical illumination, cross-relaxation between the NV and P1 spins leads to a rigid rotation of the diamond crystal along with the generation of spin-polarized phonons. The effect should be observable using state-of-the-art torsional oscillators.