A Hall viscosity for skyrmion via magnon interaction

Hall viscosity is a universal transport coefficient that arises when parity symmetry is broken. MAgnetic field and Dzyaloshinskii-Moriya interaction (DMI) both break the symmetry. By time-averaging the magnon contribution in insulating magnets, we identify a Hall viscosity term in skyrmion motion directly from DMI. The viscosity term is proportional to the skyrmion charge. Skyrmion Hall angle shows significant dependence on the skyrmion shape and size, the ratio of exchange over DMI parameters, while roughly independent of the Gilbert damping parameter. We speculate a velocity-dependent Hall viscosity contribution that either come from the magnetic field or from DMI through indirect interaction to seek asymmetric Hall angles for the opposite skyrmion charges.