We present a theoretical study of the influence of magnetic viscosity on
current-driven domain wall dynamics. In particular we examine how domain wall
depinning transitions, driven by thermal activation, are influenced by the
adiabatic and nonadiabatic spin-torques. We find the Arrhenius law that
describes the transition rate for activation over a single energy barrier
remains applicable under currents but with a current-dependent barrier height.
We show that the effective energy barrier is dominated by a linear current
dependence under usual experimental conditions, with a variation that depends
only on the nonadiabatic spin torque coefficient beta.Comment: 8 pages, 4 figure