Phenomenological Theory of Spin Hydrodynamic Generation
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In a recent experiment, it was found that mercury (Hg) flowing through a pipe lined with platinum (Pt) strips generated electrical voltage across the strips. This is thought to be due to spin hydrodynamic generation (SHG) from the coupling between the fluid vorticity and internal spins of the particles that make up the fluid, such as the electron's spin. A theory for this coupling is developed in a phenomenological manner from irreversible thermodynamics, and hydrodynamical modes and simple spin density solutions for flows between plates and inside pipes are obtained. These spin density solutions are then applied to the experimental setting motivating our research in order to investigate interface effects. We find and confirm that the spin current generated inside the viscous fluid induces spin transport across the Hg-Pt interface, and, by means of the inverse spin Hall effect, an electrical potential. We also discuss an alternative interpretation based on momentum, rather than spin, transfer.