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The Einstein-de Haas (EdH) effect is a fundamental, mechanical consequence ofany temporal change of magnetism in an object. EdH torque results fromconserving the object's total angular momentum: the angular momenta of all thespecimen's magnetic moments, together with its mechanical angular momentum.Although the EdH effect is usually small and difficult to observe, it increasesin magnitude with detection frequency. We explore the frequency-dependence ofEdH torque for a thin film permalloy microstructure by employing a ladder offlexural beam modes (with five distinct resonance frequencies spanning from 3to 208 MHz) within a nanocavity optomechanical torque sensor via magnetichysteresis curves measured at mechanical resonances. At low DC fields thegyrotropic resonance of a magnetic vortex spin texture overlaps the 208 MHzmechanical mode. The massive EdH mechanical torques arising from thisco-resonance yield a fingerprint of vortex core pinning and depinning in thesample. The experimental results are discussed in relation to mechanicaltorques predicted from both macrospin (at high DC magnetic field) andfinite-difference solutions to the Landau-Lifshitz-Gilbert (LLG) equation. Aglobal fit of the LLG solutions to the frequency-dependent data reveals astatistically significant discrepancy between the experimentally observed andsimulated torque phase behaviours at spin texture transitions that can bereduced through the addition of a time constant to the conversion betweenmagnetic cross-product torque and mechanical torque, constrained by experimentto be in the range of 0.5 - 4 ns.

Einstein-de Haas torque as a discrete spectroscopic probe allows nanomechanical measurement of a magnetic resonance