Semiclassical spin transport in LaO/STO system in the presence of multiple Rashba spin-orbit couplings

Abstract

The interaction between the linear and cubic spin-orbit coupling with magnetic moments and mobile spin-polarized carriers in the LaO/STO system provides new avenues for spin transport applications. We study the interplay between linear and cubic Rashba spin orbit coupling (RSOC) on in-plane magnetic moments in the LaO/STO system using the Boltzmann transport theory based on the relaxation time approximation (RTA) and the more refined Schliemann-Loss (SL) delta-potential scattering model. In general, both methods yield a linear (quadratic) relationship between the spin accumulation (spin current) when one of the three RSOC strengths is varied and the other two fixed. The simultaneous presence of multiple types of RSOC with distinct angular dependences is a key ingredient in breaking the k-space symmetry of the Fermi surface, thus ensuring a finite spin accumulation upon integration over the entire Fermi surface. While the oft-used RTA method is sufficiently accurate for spin accumulation calculations, the more refined SL model is required for spin current calculations because the RTA method neglects the anisotropy of the Fermi contour arising from the cubic RSOC terms. Based on the refined SL model and under optimal tuning of the RSOC parameters, the spin charge conversion values in LaO/STO is predicted to reach a remarkable efficiency of 30%.

Second-order charge and spin transport in LaO/STO system in the presence of cubic Rashba spin orbit couplings

“…For all the numerical results that follow, we take J H M = 10 meV and ϵ F = 30 meV from the band bottom of the le − band, at which equation ( 32) is a good description of the electronic behavior of the LaO/STO system [29]. Because our focus here is on elucidating the general qualitative effects of the interplay between the three types of RSOC on the second-order spin and charge responses rather than to replicate the findings of any specific experiment, the SOC strengths α, β 3 , and η 3 in equation ( 32) are treated as free parameters owing to x is indicated by whether its corresponding point on the blue curve lies within (negative value) or outside the Fermi surface (positive value), and its relative magnitude by the separation between that point and the Fermi surface. )…”

“…In particular, the cubic-momentum RSOC terms reflect the perturbative effects of the higher-energy he and le + bands on the low-energy le − bands modelled by equation (32). The three RSOC terms have distinct spin textures and effects on the Fermi surfaces in k space, which are described in more detail in our previous work [29]. Their effects on the energy spectra are illustrated in figure S2 of the supplementary materials.…”

“…where R i is the spatial location of the impurity, V 0 its scattering strength, and a 0 is a quantity with the physical dimensions of area introduced for dimensional consistency [29]. Denoting the number density (i.e.…”

“…In going from equation (29) to equation (30), we made use of the fact that the integration limits of k span from…”

“…In our earlier study [29], we investigated the first-order spin current and spin accumulation responses (i.e. the responses are linear in the applied electric field) in the LaO/STO system.…”