# Theory of Spin Injection in Two-dimensional Metals with Proximity-Induced Spin-Orbit Coupling

## TL;DR

This paper develops a comprehensive theory for spin injection and coupled spin-charge transport in two-dimensional materials with proximity-induced spin-orbit coupling, accounting for uniform and random SOC components.

## Contribution

It introduces a realistic model of spin-charge diffusion in 2D systems with proximity-induced SOC, including various charge-to-spin conversion mechanisms and their experimental signatures.

## Key findings

- Dominant spin-charge conversion mechanisms can be identified via nonlocal resistance measurements.
- The theory applies to 2D electron gases in heterostructures with adatoms and imperfections.
- Analysis helps distinguish between different spin-orbit coupling effects in experiments.

## Abstract

Spin injection is a powerful experimental probe into a wealth of nonequilibrium spin-dependent phenomena displayed by materials with spin-orbit coupling (SOC). Here, we develop a theory of coupled spin-charge diffusive transport in two-dimensional spin-valve devices. The theory describes a realistic proximity-induced SOC with both spatially uniform and random components of the SOC due to adatoms and imperfections, and applies to the two dimensional electron gases found in two-dimensional materials and van der Walls heterostructures. The various charge-to-spin conversion mechanisms known to be present in diffusive metals, including the spin Hall effect and several mechanisms contributing current-induced spin polarization are accounted for. Our analysis shows that the dominant conversion mechanisms can be discerned by analyzing the nonlocal resistance of the spin-valve for different polarizations of the injected spins and as a function of the applied in-plane magnetic field.