  We study a robust topological transport carried by vortices in a thin film of
an easy-plane ferromagnetic insulator between two metal contacts. A vortex,
which is a nonlocal topological spin texture in two-dimensional magnets,
exhibits some beneficial features as compared to skyrmions, which are local
topological defects. In particular, the total topological charge carried by
vorticity is robust against local fluctuations of the spin order-parameter
magnitude. We show that an electric current in one of the magnetized metal
contacts can pump vortices into the insulating bulk. Diffusion and nonlocal
Coulomb-like interaction between these vortices will establish a steady-state
vortex flow. Vortices leaving the bulk produce an electromotive force at
another contact, which is related to the current-induced vorticity pumping by
the Onsager reciprocity. The voltage signal decays algebraically with the
separation between two contacts, similarly to a superfluid spin transport.
Finally, the vorticity and closely related skyrmion type topological
hydrodynamics are generalized to arbitrary dimensions, in terms of nonsingular
order-parameter vector fields.
