Spin accumulation from non-equilibrium first principles methods

TL;DR

This paper presents a first-principles computational approach to directly calculate spin accumulation at metallic surfaces caused by the spin Hall effect, comparing semiclassical and quantum methods with experimental data.

Contribution

It introduces a fully relativistic, non-equilibrium density functional theory framework to predict surface spin accumulation due to the spin Hall effect, bridging theory and experiment.

Findings

Good agreement between semiclassical and quantum calculations.

Theoretical predictions match experimental trends across elements.

Deviations linked to Fermi surface complexity.

Abstract

For the technologically relevant spin Hall effect most theoretical approaches rely on the evaluation of the spin-conductivity tensor. In contrast, for most experimental configurations the generation of spin accumulation at interfaces and surfaces is the relevant quantity. Here, we directly calculate the accumulation of spins due to the spin Hall effect at the surface of a thin metallic layer, making quantitative predictions for different materials. Two distinct limits are considered, both relying on a fully relativistic Korringa-Kohn-Rostoker density functional theory method. In the semiclassical approach, we use the Boltzmann transport formalism and compare it directly to a fully quantum mechanical non-equilibrium Keldysh formalism. Restricting the calculations to the spin Hall induced, odd in spatial inversion, contribution in the limit of the relaxation time approximation we find good agreement between both methods, where deviations can be attributed to the complexity of Fermi surfaces. Finally, we compare our results to experimental values of the spin accumulation at surfaces as well as the Hall angle and find good agreement for the trend across the considered elements.