Topological spin Hall effect in antiferromagnets

We investigate topological Hall effects in a metallic antiferromagnetic (AFM) thin film and/or at the interface of an AFM insulator-normal metal bilayer with a single skyrmion in the diffusive regime. To determine the spin and charge Hall currents, we employed a Boltzmann kinetic equation with both spin-dependent and spin-flip scatterings. The interaction between conduction electrons and static skyrmions is included in the Boltzmann equation via the corresponding emergent magnetic field arising from the skyrmion texture. We compute intrinsic and extrinsic contributions to the topological spin Hall effect and spin accumulation, induced by an AFM skyrmion. We show that although the spin Hall current vanishes rapidly outside the skyrmion, the spin accumulation can be finite at the edges far from the skyrmion, provided the spin diffusion length is longer than the skyrmion radius. In addition, We show that in the presence of a spin-dependent relaxation time, the topological charge Hall effect is finite and we determine the corresponding Hall voltage. Our results may help to explore antiferromagnetic skyrmions by electrical means in real materials.Comment: 6 pages, 3 figure

Bilinear planar Hall effect in topological insulators due to spin-momentum locking inhomogeneity

We study the effect of spin-momentum locking inhomogeneity on the planar Hall effect in topological insulators (TIs). Using the minimal model describing surface states of 3D TIs and semiclassical Boltzmann formalism, we have derived the planar Hall conductivity within the generalized relaxation time approximation. We have found that the total planar Hall conductivity is a sum of linear and nonlinear to the external electric field components. The linear term is a conventional planar Hall conductivity which scales quadratically with an external magnetic field, whereas the nonlinear term reveals bilinear behaviour, i.e., changes its sign when either charge current density or in-plane magnetic field orientation is reversed. We have shown that the emergent nonlinear planar Hall effect is a consequence of spin-momentum locking inhomogeneity in the TIs with isotropic energy dispersion and dominates under the conventional planar Hall effect.Comment: 5 pages, 1 figur