Spin angular momentum transfer in the Einstein-de Haas effect

Abstract: We investigate spin angular momentum transfer in the Einstein-de Haas effect within prototypical magnetic crystals, focusing on its partition between phonons and rigid-body rotation. Using the Eckart frame to decouple local vibrations (phonons) from rigid-body rotation, we demonstrate that spin angular momentum is simultaneously transferred into both phonons and rigid-body rotation in an asymmetric way: rigid-body rotation acquires the dominant share of angular momentum, while phonons absorb most of the resulting kinetic energy. This divergent transfer of angular momentum and energy identifies phonons as direct and indispensable participants in the Einstein-de Haas dynamics. Furthermore, we find that pseudo-dipolar anisotropy and Dzyaloshinskii-Moriya interaction exert distinct control over the angular momentum transfer. Stronger pseudo-dipolar anisotropy increases the total amount of transferred angular momentum, whereas stronger Dzyaloshinskii-Moriya interaction accelerates the transfer rate and increases the proportion of phonon angular momentum. Our work clarifies the microscopic picture of the Einstein-de Haas effect and enables targeted angular-momentum control in magneto-mechanical devices.