Einstein-de Haas phase shifts in surface acoustic waves

We demonstrate the phase shift of the Rayleigh-type surface acoustic wave (RSAW) in a ferromagnetic ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ film based on the gyromagnetic Einstein--de Haas (EdH) torque that can be attributed to the back action of spin-wave excitation. The EdH torque modulates the transverse velocity of the bulk acoustic wave that causes the bipolar phase shift of RSAW. When compared with a magnetoelastic torque, the phase shift can be more prominently enhanced by increasing the frequency. The gyromagnetic torque in the RSAW paves the way for controlling spin-mechatronics devices without magnetoelastic torque which is specific to a certain material.