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

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 $\mathbf{S}=-\gamma \hslash \hat{\mathbf{z}}\times \mathbf{j}$, where $\mathbf{j}$ is the particle current density in the bulk, $\hat{\mathbf{z}}$ the unit vector normal to the surface, and $\gamma =\frac{\hslash }{4m{c}^2}$ 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.

arXiv comment5 pages, 2 figures

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• Quantitative comparison of electrically induced spin and orbital polarizations in heavy-metal/3d-metal bilayers
• Strong influence of spin-orbit coupling on magnetotransport in two-dimensional hole systems
• Boundary conditions for spin and charge diffusion in the presence of interfacial spin-orbit coupling
• Theory of bilinear magneto-electric resistance from topological-insulator surface states
• Dynamical current-induced ferromagnetic and antiferromagnetic resonances
• Spin-orbit induced equilibrium spin currents in materials
• Interfacial mechanism in the anomalous Hall effect of Co/Bi${}_2$O${}_3$ bilayers
• Quantum unidirectional magnetoresistance
• Current-induced spin polarization at metallic surfaces from first-principles
• Electron Interactions in Rashba Materials
• Promoted current-induced spin polarization in inversion symmetry broken topological insulator thin films
• Large spin-charge interconversion induced by interfacial spin-orbit coupling in a highly conducting all-metallic system
• Quantification of interfacial spin-charge conversion in metal/insulator hybrid structures by generalized boundary conditions