Topological Spin Hall Effect due to Magnetic Skyrmions

The intrinsic spin Hall effect (SHE) originates from the topology of the Bloch bands in momentum space. The duality between real space and momentum space calls for a spin Hall effect induced from a real space topology in analogy to the topological Hall effect (THE) of skyrmions. We theoretically demonstrate the topological spin Hall effect (TSHE) in which a pure transverse spin current is generated from a skyrmion spin texture.