On the Evaluation of the Spin Galvanic Effect in Lattice Models with Rashba Spin-Orbit Coupling

Götz Seibold,Marco Grilli,Sergio Caprara,Roberto Raimondi

doi:10.3390/condmat3030022

Abstract

The spin galvanic effect (SGE) describes the conversion of a non-equilibrium spin polarization into a charge current and has recently attracted renewed interest due to the large conversion efficiency observed in oxide interfaces. An important factor in the SGE theory is disorder which ensures the stationarity of the conversion. Through this paper, we propose a procedure for the evaluation of the SGE on disordered lattices which can also be readily implemented for multiband systems. We demonstrate the performance of the method for a single-band Rashba model and compare our results with those obtained within the self-consistent Born approximation for a continuum model.

Highlights

Spin-orbit coupling (SOC) lies at the heart of spin-to-charge conversion [1], which is a major issue for future spintronics technologies [2,3]
For small Rashba SOC (RSOC) α/B, the Drude response agrees with the expected result from the continuum model, Equation (16), with the mass given by m = 1/(2t) = 2/B
Such an approach has recently been used [22] for the computation of the spin galvanic effect (SGE) in a three-band model for oxide interfaces related to the observation of a large spin-to-charge conversion in these materials [13,14,15]

Summary

Introduction

Spin-orbit coupling (SOC) lies at the heart of spin-to-charge conversion [1], which is a major issue for future spintronics technologies [2,3]. The standard impurity technique involves a three-step procedure: (a) calculation of the irreducible self-energy in the self-consistent Born approximation for the determination of the single-particle Green function; (b) calculation of the vertex corrections for the charge current by solving the corresponding Bethe-Salpeter equations; and (c) computation of the response function from a convolution of the Green functions and the vertices This procedure has been successfully applied for the evaluation of the inverse spin galvanic effect [23], anisotropy magnetoresistance [24,25], and the spin Hall effect [26] in single-band Rashba models. One could diagonalize directly the microscopic Hamiltonian on finite lattices and induce disorder by a suitable distribution of local and/or intersite potentials and evaluate the Kubo response function numerically from the eigenvalues and eigenstates This approach has been previously followed in [22] for the evaluation of the SGE in a multiband model for oxide interfaces.

Response Functions

Disorder Limit

Conclusions