Extracting current-induced spins: spin boundary conditions at narrow Hall contacts

We consider the possibility to extract spins that are generated by an electric current in a two-dimensional electron gas with Rashba - Dresselhaus spin - orbit interaction ( R2DEG) in the Hall geometry. To this end, we discuss boundary conditions for the spin accumulations between a spin - orbit (SO) coupled region and a contact without SO coupling, i.e. a normal two-dimensional electron gas (2DEG). We demonstrate that in contrast to contacts that extend along the whole sample, a spin accumulation can diffuse into the normal region through finite contacts and be detected by e.g. ferromagnets. For an impedance-matched narrow contact the spin accumulation in the 2DEG is equal to the current induced spin accumulation in the bulk of R2DEG up to a geometry-dependent numerical factor.