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

## TL;DR

This paper theoretically demonstrates that spin-charge conversion via Rashba spin-orbit interaction can occur non-locally in metals with spatially separated magnetization and spin-orbit regions, considering electron diffusion effects.

## Contribution

It introduces a theoretical framework for non-local spin-charge conversion via Rashba spin-orbit interaction, emphasizing the role of electron diffusion and effective spin gauge fields.

## Key findings

- Non-local spin-charge conversion is possible with spatial separation.
- Effective spin gauge field concept is valid in non-local setups.
- The inverse Rashba-Edelstein effect can be explained by this non-local framework.

## Abstract

We show theoretically that conversion between spin and charge by spin-orbit interaction in metals occurs even in a non-local 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 non-local 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 non-local effective spin gauge field.