Nonlocal magnetolectric effects in diffusive conductors with spatially inhomogeneous spin-orbit coupling

Physical Review B 100, 195406 (2019)

Nonlocal magnetolectric effects in diffusive conductors with spatially inhomogeneous spin-orbit coupling

C. Sanz-Fernández, J. Borge, I. V. Tokatly, F. S. Bergeret

We present a theoretical study of nonlocal magnetoelectric effects in diffusive hybrid structures with an intrinsic linear-in-momentum spin-orbit coupling (SOC) which is assumed to be spatially inhomogeneous. Our analysis is based on the SU(2)-covariant drift-diffusion equations from which we derive boundary conditions at hybrid interfaces for SOC of any kind. Within this formulation, the spin current is covariantly conserved when the spin relaxation is only due to the intrinsic SOC. This conservation leads to the absence of spin Hall (SH) currents in homogeneous systems. If, however, extrinsic sources of spin relaxation (ESR), such as magnetic impurities and/or a random SOC at nonmagnetic impurities, are present the spin is no longer covariantly conserved, and SH currents appear. We apply our model to describe nonlocal transport in a two-dimensional system with an interface separating two regions: one normal region without intrinsic SOC and one with a Rashba SOC. We first explore the inverse spin-galvanic effect, i.e., a spin polarization induced by an electric field. We demonstrate how the spatial behavior of such spin density depends on both the direction of the electric field and the strength of the ESR rate. We also study the spin-to-charge conversion, and compute the charge current and the distribution of electrochemical potential in the whole system when a spin current is injected into the normal region. In systems with an inhomogeneous SOC varying in one spatial direction, we find an interesting nonlocal reciprocity between the spin density induced by a charge current at a given point in space, and the spatially integrated current induced by a spin density injected at the same point.

Additional Information

Download
Preprint - 1.5 MB
Doi
http://dx.doi.org/10.1103/PhysRevB.100.195406
arxiv
http://arxiv.org/abs/arXiv:1907.11688

Related Projects

Related Research Areas