Elastodynamically Induced Spin and Charge Pumping in Bulk Heavy Metals

Analogous to the spin-Hall effect (SHE), ab initio electronic structure calculations reveal that acoustic phonons can induce charge (spin) current flowing along (normal to) its propagation direction. Using the Floquet approach we have calculated the elastodynamically induced charge and spin pumping in bulk Pt and demonstrate that (i) the longitudinal charge pumping originates from the Berry curvature, while the transverse pumped spin current is an odd function of the electronic relaxation time and diverges in the clean limit. (ii) The longitudinal charge current is of nonrelativstic origin, while the transverse spin current is a relativistic effect that to lowest order scales linearly with the spin-orbit coupling strength. (iii) Both charge and spin pumped currents have parabolic dependence on the amplitude of the elastic wave.