We theoretically study the current-driven domain wall motion in the presence
of both the spin Hall effect and an extrinsic pinning potential. The spin Hall
effect mainly affects the damping ratio of the domain wall precession in the
pinning potential. When the pinning potential is not too strong, this results
in a significant reduction of a threshold current density for the depinning of
a domain wall with certain polarity. We also propose one way to distinguish the
spin Hall effect induced spin-transfer torque from the one induced by the
Rashba spin-orbit coupling experimentally
