Origin of the Magnetic Spin Hall Effect: Spin Current Vorticity in the Fermi Sea

TL;DR

This paper explains the magnetic spin Hall effect (MSHE) as arising from spin current vorticity in the Fermi sea, providing a symmetry-based framework and models to understand its occurrence in magnetic materials with strong spin-orbit coupling.

Contribution

It introduces a symmetry-based explanation for the MSHE, linking it to spin current vorticity and identifying minimal conditions for its occurrence in magnetic materials.

Findings

MSHE is related to spin current vorticity in the Fermi sea.

MSHE occurs in ferromagnets with large spin-orbit coupling.

Models confirm the vortex-based interpretation of MSHE.

Abstract

The interplay of spin-orbit coupling (SOC) and magnetism gives rise to a plethora of charge-to-spin conversion phenomena that harbor great potential for spintronics applications. In addition to the spin Hall effect, magnets may exhibit a magnetic spin Hall effect (MSHE), as was recently discovered [Kimata \textit{et al.}, Nature \textbf{565}, 627-630 (2019)]. To date, the MSHE is still awaiting its intuitive explanation. Here we relate the MSHE to the vorticity of spin currents in the Fermi sea, which explains pictorially the origin of the MSHE. For all magnetic Laue groups that allow for nonzero spin current vorticities the related tensor elements of the MSH conductivity are given. Minimal requirements for the occurrence of a MSHE are compatibility with either a magnetization or a magnetic toroidal quadrupole. This finding implies in particular that the MSHE is expected in all ferromagnets with sufficiently large SOC. To substantiate our symmetry analysis, we present various models, in particular a two-dimensional magnetized Rashba electron gas, that corroborate an interpretation by means of spin current vortices. Considering thermally induced spin transport and the magnetic spin Nernst effect in magnetic insulators, which are brought about by magnons, our findings for electron transport can be carried over to the realm of spincaloritronics, heat-to-spin conversion, and energy harvesting.