Onsager relations and the detection of current-induced spins by Ferromagnetic contacts

The recent prediction of intrinsic spin Hall currents raised many questions about methods of detection. We focus on the theoretical issues related to the detection of spin currents and accumulations via ferromagnetic contacts. Along the way, based on Onsager-like relations for the conductance, we show the unfeasibility of detecting spin current from a non-magnetic conductor in a two probe geometry within linear response. It is nevertheless possible to detect spin current in a four probe geometry, in which the spin current flowing into the ferromagnet leads to a potential difference between the Hall contacts. We calculate the Hall conductivity and compare this effect to the Anomalous Hall effect. Work done in collaboration with G.E.W. Bauer and B.I. Halperin