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We show theoretically that conversion between spin and charge by spin-orbitinteraction in metals occurs even in a non-local setup where magnetization andspin-orbit interaction are spatially separated if electron diffusion is takeninto account. Calculation is carried out for the Rashba spin-orbit interactiontreating the coupling with a ferromagnet perturbatively. The results indicatethe validity of the concept of effective spin gauge field (spin motive force)in the non-local configuration. The inverse Rashba-Edelstein effect observedfor a trilayer of a ferromagnet, a normal metal and a heavy metal can beexplained in terms of the non-local effective spin gauge field.

Non-local Spin-charge Conversion via Rashba Spin-Orbit Interaction