  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.
