Hydrodynamics of three-dimensional skyrmions in frustrated magnets

We study the nucleation and collective dynamics of Shankar skyrmions [Shankar, J. Phys. 38, 1405 (1977)] in the class of frustrated magnetic systems described by a SO(3) order parameter, including multilattice antiferromagnets and amorphous magnets. We infer the expression for the spin-transfer torque that injects skyrmion charge into the system and the Onsager-reciprocal pumping force that enables its detection by electrical means. The thermally assisted flow of topological charge gives rise to an algebraically decaying drag signal in nonlocal transport measurements. We contrast our findings to analogous effects mediated by spin supercurrents.