  A nonlocal electric response in the spin-Hall regime, resulting from spin
diffusion mediating charge conduction, is predicted. The spin-mediated
transport stands out due to its long-range character, and can give dominant
contribution to nonlocal resistance. The characteristic range of nonlocality,
set by the spin diffusion length, can be large enough to allow detection of
this effect in materials such as GaAs despite its small magnitude. The
detection is facilitated by a characteristic nonmonotonic dependence of
transresistance on the external magnetic field, exhibiting sign changes and
decay.
