Probing viscous regimes of spin transport with local magnetometry

It is now well-established, both theoretically and experimentally, that charge transport of metals can be in a hydrodynamic regime in which frequent electron-electron collisions play a significant role. Meanwhile, recent experiments have demonstrated that it is possible to inject spin currents into magnetic insulator films and explore the DC transport properties of spins. Inspired by these developments, we investigate the effect of viscosity, which naturally arises in the hydrodynamic regime, on DC spin transport. We show that viscosity gives rise to a sharp peak in the spatial profile of the out-of-plane stray magnetic field near the spin current injector. We propose that local magnetometers such as SQUIDs and nitrogen-vacancy centers can detect this viscosity-induced structure in the stray magnetic field. We also discuss the relevance of our results to yittrium iron garnet, a ferromagnetic insulator, and to Kagome spin liquids.