  Departing from the conventional view on superconducting vortices as a
parasitic source of dissipation for charge transport, we propose to use mobile
vortices as topologically-stable information carriers for spin transport. To
this end, we start by constructing a phenomenological theory for the
interconversion between spin and vorticity, a topological charge carried by
vortices, at the interface between a magnetic insulator and a superconductor,
by invoking the interfacial spin Hall effect therein. We then show that a
vortex liquid in superconductors can serve as a spin-transport channel between
two magnetic insulators by encoding spin information in the vorticity. The
vortex-mediated nonlocal signal between the two magnetic insulators is shown to
decay algebraically as a function of their separation, contrasting with the
exponential decay of the quasiparticle-mediated spin transport. We envision
that hydrodynamics of topological excitations, such as vortices in
superconductors and domain walls in magnets, may serve as a universal framework
to discuss long-range transport properties of ordered materials.
