# Boundary conditions for spin and charge diffusion in the presence of interfacial spin-orbit coupling

## TL;DR

This paper develops generalized boundary conditions for spin and charge diffusion at interfaces with spin-orbit coupling, enabling better understanding and detection of spin currents in hybrid structures.

## Contribution

It introduces a symmetry-based theoretical framework to incorporate interfacial spin-orbit coupling effects into diffusion equations.

## Key findings

- Predicts an 'ISOC-gating' effect for detecting spin currents.
- Provides a classification of spin-charge conversion effects due to ISOC.
- Offers a method to analyze spin transport in nonmagnetic hybrid structures.

## Abstract

Breaking of the inversion symmetry at the interface between different materials may dramatically enhance spin-orbit interaction in the vicinity of the interface. We incorporate the effects of this interfacial spin-orbit coupling (ISOC) into the standard drift-diffusion theory by deriving generalized boundary conditions for diffusion equations. Our theoretical scheme is based on symmetry arguments, providing a natural classification and parametrization of all spin-charge and spin-spin conversion effects that occur due to ISOC at macroscopically isotropic interfaces between nonmagnetic materials. We illustrate our approach with specific examples of spin-charge conversion in hybrid structures. In particular, for a lateral metal-insulator structure we predict an "ISOC-gating" effect which can be used to detect spin currents in metallic films with weak bulk SOC.