Einstein-de Haas effect at radio frequencies in and near magnetic equilibrium

The Einstein-de Haas (EdH) effect and its reciprocal, the Barnett effect, are fundamental to magnetism and uniquely yield measures of the ratio of magnetic moment to total angular momentum. These effects, small and generally difficult to observe, are enjoying a resurgence of interest as contemporary techniques enable new approaches to their study. The high mechanical resonance frequencies in nanomechanical systems offer a tremendous advantage for the observation of EdH torques in particular. At radio frequencies, the EdH effect can become comparable to or even exceed in magnitude conventional cross-product magnetic torques. In addition, the rf-EdH torque is expected to be phase shifted by 90 degrees relative to cross-product torques, provided the magnetic system remains in quasistatic equilibrium, enabling separation in quadratures when both sources of torque are operative. Radio-frequency EdH measurements are demonstrated through the full hysteresis range of micrometer-scale, monocrystalline yttrium iron garnet disks. Equilibrium behavior is observed in the vortex state at low bias field. Barkhausen-like features emerge in the in-plane EdH torque at higher fields in the vortex state, revealing magnetic disorder too weak to be visible through the in-plane cross-product torque. Beyond vortex annihilation, peaks arise in the EdH torque versus bias field, and these together with their phase signatures indicate additional utility of the Einstein-de Haas effect for the study of rf-driven spin dynamics.