# Stationary states and screening equations in the spin-Hall effect

## TL;DR

This paper analyzes stationary states in the spin-Hall effect using a two spin-channel model, revealing two types of bulk states and deriving screening equations for charge accumulation near edges.

## Contribution

It introduces a distinction between two definitions of stationary states in the spin-Hall effect and derives screening equations for charge accumulation considering spin-orbit coupling.

## Key findings

- Two types of bulk stationary states: zero transverse spin-current and non-zero pure spin-current.
- Screening equations describe electric charge accumulation due to spin-orbit coupling.
- Spin-flip scattering and spin-Hall accumulation are independent effects under certain conditions.

## Abstract

The characterization of the stationary states in the spin-Hall effect is discussed within the framework of the phenomenological two spin-channel model. It is shown that two different definitions of the stationary states can be applied in the spin-Hall effect, leading to two different types of state in the bulk: zero transverse spin-current or non-zero pure spin-current. This difference is due to the treatment of the region near the edges, in which electric charge accumulation occurs. The screening equations that describe the accumulation of electric charges due to spin-orbit coupling are derived. The spin-accumulation associated to spin-flip scattering and the spin-Hall accumulation due to spin-orbit coupling are two independent effects if we assume that the screening length is small with respect to the spin-diffusion length. The corresponding transport equations are discussed in terms of the Dyakonov-Perel equations.