English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The substantial amount of recent research into spin torques has beenaccompanied by a revival of interest in the spin-Hall effect. This effectcontributes to the spin torque in many materials, including topologicalinsulator/ferromagnet devices, Weyl semimetals, and van der Waalsheterostructures. In general the relative sizes of competing spin torquemechanisms remain poorly understood. Whereas a consensus is beginning to emergeon the evaluation of a conserved spin current, the role of extrinsic disordermechanisms in the spin-Hall effect has not been clarified. In this work wepresent a comprehensive calculation of the extrinsic spin Hall effect whilefocussing on the bulk states of topological insulators as a prototype systemand employing a fully quantum mechanical formalism to calculate the proper spincurrent. Our calculation of the proper spin current employs a 4x4 k.pHamiltonian describing the bulk states of topological insulators. At the sametime, we provide a qualitative explanation of the proper spin currentscalculated based on an effective $2\times2$ Hamiltonian obtained via aSchrieffer-Wolf transformation. We find that the extrinsic contribution to theproper spin current, driven by side jump, skew scattering and relatedmechanisms, is of a comparable magnitude to the intrinsic contribution, makingit vital to take such disorder effects into account when seeking to understandexperiments. Among the scattering effects considered, side jump scattering isthe primary contributor to the extrinsic spin Hall effect. The total spinsusceptibility calculated here is too small to explain experimentally measuredspin torques, hence we expect the spin Hall effect to make a negligiblecontribution to the spin torque in topological insulator structures.

Spin-Hall effect due to the bulk states of topological insulators: Extrinsic contribution to the conserved spin current