Nonlocal spin-charge conversion via Rashba spin-orbit interaction

We show theoretically that conversion between spin and charge by spin-orbit interaction in metals occurs even in a nonlocal setup where magnetization and spin-orbit interaction are spatially separated if electron diffusion is taken into account. Calculation is carried out for the Rashba spin-orbit interaction treating the coupling with a ferromagnet perturbatively. The results indicate the validity of the concept of effective spin gauge field (spin motive force) in the nonlocal configuration. The inverse Rashba-Edelstein effect observed for a trilayer of a ferromagnet, a normal metal and a heavy metal can be explained in terms of the nonlocal effective spin gauge field.