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Spin-rotation coupling, which is responsible for angular momentum conversion between the electron spin and rotational deformations of elastic media, is exploited for generating spin current. This method requires neither magnetic moments nor spin-orbit interaction. The spin current generated in nonmagnets is calculated in presence of surface acoustic waves. We solve the spin diffusion equation, extended to include spin-rotation coupling, and find that larger spin currents can be obtained in materials with longer spin lifetimes. Spin accumulation induced on the surface is predicted to be detectable by time-resolved Kerr spectroscopy.

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