Current-induced spin polarization at the surface of metallic films: a theorem and an ab initio calculation

TL;DR

This paper proves a theorem showing how electric currents induce surface spin polarization in metallic films due to spin-orbit interaction, and supports it with ab initio calculations to determine a key material parameter.

Contribution

It introduces a theorem relating bulk current to surface spin polarization and provides ab initio calculations to determine the interfacial spin-orbit coupling parameter.

Findings

Surface spin density is proportional to the cross product of current and surface normal.

The theorem applies universally to semi-infinite jellium models.

Ab initio calculations enable determination of the material-specific spin-orbit coupling parameter.

Abstract

The broken inversion symmetry at the surface of a metallic film (or, more generally, at the interface between a metallic film and a different metallic or insulating material) greatly amplifies the influence of the spin-orbit interaction on the surface properties. The best known manifestation of this effect is the momentum-dependent splitting of the surface state energies (Rashba effect). Here we show that the same interaction also generates a spin-polarization of the bulk states when an electric current is driven through the bulk of the film. For a semi-infinite jellium model, which is representative of metals with a closed Fermi surface, we prove as a theorem that, regardless of the shape of the confinement potential, the induced surface spin density at each surface is given by ${\bf S} =-\gamma \hbar {\bf \hat z}\times {\bf j}$, where ${\bf j}$ is the particle current density in the bulk, ${\bf \hat z}$ the unit vector normal to the surface, and $\gamma=\frac{\hbar}{4mc^2}$ contains only fundamental constants. For a general metallic solid $\gamma$ becomes a material-specific parameter that controls the strength of the interfacial spin-orbit coupling. Our theorem, combined with an {\it ab initio} calculation of the spin polarization of the current-carrying film, enables a determination of $\gamma$, which should be useful in modeling the spin-dependent scattering of quasiparticles at the interface.