Effective Model Analysis of Intrinsic Spin Hall Effect with Magnetism in the Stacked Kagome Weyl Semimetal Co3Sn2S2

We theoretically study the spin Hall effect in a simple tight-binding model of the stacked kagome Weyl semimetal ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2}{\mathrm{S}}_{2}$ with ferromagnetic ordering. We focus on the two types of spin Hall current: one flowing in the in-plane direction with respect to the kagome lattice (in-plane spin Hall current), and the other flowing in the stacking direction (out-of-plane spin Hall current). We show that the spin Hall conductivities for those spin currents drastically change depending on the direction of the magnetic moment. In particular, the out-of-plane spin Hall current may induce surface spin accumulations, which are useful for magnetization switching via spin-orbit torque.