Spin imaging of Poiseuille flow of a viscous electronic fluid

Recent progress in fabricating high-quality conductors with small densities of defects has initiated studies of a viscous electron fluid and has motivated the search for evidence of a hydrodynamic regime of electron transport. In this Letter we come up with the spin imaging technique, which can allow to attest to the emergence of electron hydrodynamic flows. Using numerical calculations, we examine specific inhomogeneous distributions of the electron spin density injected in a sample with a Poiseuille flow of a viscous electron fluid. We also demonstrate that the Hanle curves (the dependencies of the electron spin on magnetic field) at different positions across the channel acquire relative phase shifts resulting from the space variation of the hydrodynamic velocity. The studied effects can be employed to detect and map a viscous electron fluid noninvasively.