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Magnetization dynamics and spin pumping induced by standing elastic waves

The magnetization dynamics induced by standing elastic waves excited in a thin ferromagnetic film is described with the aid of micromagnetic simulations taking into account the magnetoelastic coupling between spins and lattice strains. The simulations have been performed for the 2 nm thick Fe81Ga19 film dynamically strained by longitudinal and transverse standing waves with various frequencies, which span a wide range around the resonance frequency nu_res of coherent magnetization precession in unstrained Fe81Ga19 film. It is found that standing elastic waves give rise to complex local magnetization dynamics and spatially inhomogeneous dynamic magnetic patterns. The spatio-temporal distributions of the magnetization oscillations in standing elastic waves have the form of standing spin waves with the same wavelength. Remarkably, the amplitude of magnetization precession does not go to zero at the nodes of these spin waves, which cannot be precisely described by simple analytical formulae. In the steady-state regime, the magnetization oscillates with the frequency of elastic wave, except for the case of longitudinal waves with frequencies well below nu_res, where the magnetization precesses with a variable frequency strongly exceeding the wave frequency. The precession amplitude at the antinodes of standing spin waves strongly increases when the frequency of elastic wave becomes close to nu_res. The results obtained for the magnetization dynamics driven by elastic waves are used to calculate the spin current pumped from the dynamically strained ferromagnet into adjacent paramagnetic metal. Importantly, the transverse charge current created by the spin current via the inverse spin Hall effect is high enough to be measured experimentally.