Intrinsic Spin Hall Effect at Oxide Interfaces: a Simple Model

TL;DR

This paper models the intrinsic spin Hall effect at oxide interfaces using a simple asymmetric triangular potential well, revealing non-zero spin Hall conductivity influenced by well symmetry and spin-orbit coupling.

Contribution

It demonstrates that an asymmetric triangular well supports a non-vanishing intrinsic spin Hall effect, contrasting with wedge-shaped wells where it vanishes due to vertex corrections.

Findings

Spin Hall conductivity increases as the well becomes more symmetric.

Conductivity is proportional to the square of the spin-orbit coupling constant.

At low carrier density, conductivity depends on effective mass renormalization.

Abstract

An asymmetric triangular potential well provides the simplest model for the confinement of mobile electrons at the interface between two insulating oxides, such as LaAlO_3 and SrTiO_3 (LAO/STO). These electrons have been recently shown to exhibit a large spin-orbit coupling of the Rashba type, i.e., linear in the in-plane momentum. In this paper we study the intrinsic spin Hall effect due to Rashba coupling in an asymmetric triangular potential well. Besides splitting each subband into two branches of opposite helicity, the spin-orbit interaction causes the wave function in the direction perpendicular to the plane of the quantum well (the z direction) to depend on the in-plane wave vector k. In contrast to the extreme asymmetric case, i.e., the wedge-shaped quantum well, for which the intrinsic spin Hall effect vanishes due to vertex corrections, we find that the asymmetric well supports a non-vanishing intrinsic spin Hall conductivity, which increases in magnitude as the well becomes more symmetric. The spin Hall conductivity is found to be proportional to the square of the spin-orbit coupling constant and, in the limit of low carrier density, depends only on the effective mass renormalization associated with the k-dependence of the wave functions in the z direction. Its origin lies in the non-vanishing matrix elements of the spin current between subbands corresponding to different states of quantized motion perpendicular to the plane of the well.