Screening effect in Spin-Hall Devices

TL;DR

This paper investigates the screening effects in Spin-Hall devices using a variational approach, deriving analytical expressions for spin-accumulation and spin-currents considering different spin-flip scattering regimes.

Contribution

It introduces a variational method that includes non-equilibrium screening effects to analyze spin-Hall devices, providing analytical solutions for spin-accumulation and currents under various scattering conditions.

Findings

Spin-accumulation is linear across the device and with electric field.

Derived analytical expressions for spin-currents in different scattering regimes.

Spin-accumulation inversely proportional to temperature in non-degenerate conductors.

Abstract

The stationary state of the spin-Hall bar is studied in the framework of a variational approach that includes non-equilibrium screening effects. The minimization of the power dissipated in the system is performed with taking into account the spin-flip relaxation and the global constrains due to the electric generator and global charge conservation. The calculation is performed in both approximations of negligible spin-flip scattering and strong spin-flip scattering. In both cases, the expressions of the spin-accumulation and the longitudinal and transverse pure spin-currents are derived analytically. Due to the small value of the Debye-Fermi screening length, the spin-accumulation is shown to be linear in $y$ (across the device), linear in the electric field imposed by the generator, and inversely proportional to the temperature for non-degenerate conductors.