Staggered spin Hall conductivity

TL;DR

This paper introduces a method to compute position-dependent intrinsic spin Hall conductivity in materials with lower local symmetry, revealing staggered components relevant for spintronics.

Contribution

It presents a general computational approach for position-dependent spin Hall conductivity and applies it to specific materials, uncovering staggered spin current components.

Findings

Applied method to 1T'-WTe₂ revealing conventional and staggered spin Hall components.

Found that staggered components are comparable in magnitude to experimental spin-orbit torques.

Demonstrated larger spin conductivity in orthorhombic PbTe.

Abstract

The intrinsic spin Hall effect plays an important role in spintronics applications, such as spin-orbit torque-based memory. The bulk space group symmetry determines the form of the bulk spin current conductivity tensor. This paper considers materials for which the local point group symmetry of individual atoms is lower than the global (bulk) symmetry. This enables a position-dependent spin current response, with additional tensor components allowed relative to the bulk response. We present a general method to compute the position-dependent intrinsic spin Hall conductivity, with similar computational effort relative to computing the bulk spin Hall conductivity. We also present the general symmetry-constrained form of the position-dependent spin current response. We apply this method to 1T'-WTe$_2$, which exhibits a conventional spin Hall conductivity tensor component $\sigma^y_{xz}$ and a staggered unconventional component $\sigma^z_{xz}$. The magnitude of these two components, around 100 and 20 $(\rm \Omega\cdot cm)^{-1}$, respectively, are comparable to the spin-orbit torque exerted on adjacent ferromagnets in experiments. We then consider orthorhombic PbTe, in which both uniform and staggered spin current conductivity are one order of magnitude larger.