  Analogous to the Spin-Hall Effect (SHE), {\it ab initio} electronic structure
calculations reveal that acoustic phonons can induce charge (spin) current
flowing along (normal to) its propagation direction. Using Floquet approach we
have calculated the elastodynamical-induced charge and spin pumping in bulk Pt
and demonstrate that: (i) While the longitudinal charge pumping is an intrinsic
observable, the transverse pumped spin-current has an extrinsic origin that
depends strongly on the electronic relaxation time; (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.
