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 impedancematched narrow contact the spin accumulation in the 2DEG is equal to the current induced spin accumulation in the bulk of R2DEG up to a geometrydependent numerical factor.