Anti-Poiseuille flow by spin Hall effect

Hydrodynamics is known to emerge in electron flow when the electron-electron interaction dominates over the other momentum-nonconserving scatterings. The hydrodynamic equation that describes the electric current includes viscosity, extending beyond the Ohmic flow. The laminar flow of such a viscous electron fluid in a sample with finite width is referred to as the Poiseuille flow, where the flow velocity is maximum at the center and decreases towards the edges of the sample. In this paper, we show a unique viscous electron fluid arising in electron systems exhibiting the spin Hall effect (spin Hall systems), where the charge and spin currents are coupled. Such a viscous electron fluid emerges even in noninteracting electron systems, and the current density exhibits a minimum at the center of a flow and a maximum at the edges, i.e. an anti-Poiseuille flow realizing. We also find that the spin accumulation by the spin Hall effect is connected to the electric current vorticity in two-dimensional (2D) spin Hall systems. Furthermore, we propose a novel guiding principle to manipulate topological magnetic textures from the hydrodynamic viewpoint. By solving the hydrodynamic equation in a 2D spin Hall system with a cavity and employing micromagnetic simulations for an attached chiral magnetic insulator, we demonstrate that spin accumulation near the cavity's boundary leads to creating a magnetic skyrmion. Our research illuminates new aspects of electron hydrodynamics and spintronics, contributing significant insights to the fields.