We study the depinning of domain walls by pure diffusive spin currents in a nonlocal spin valve structure based on two ferromagnetic permalloy elements with copper as the nonmagnetic spin conduit. The injected spin current is absorbed by the second permalloy structure with a domain wall and from the dependence of the wall depinning field on the spin current density we find an efficiency of 6*10^{-14}T/(A/m^2), which is more than an order of magnitude larger than for conventional current induced domain wall motion. Theoretically we reproduce this high efficiency, which arises from the surface torques exerted by the absorbed spin current that lead to efficient depinning.
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