feels a torque because it absorbs the component of an incident spin current that is polarized transverse to its magnetization. The same idea generalizes to systems with continuously non-uniform magnetization. [@Berger:1978; @Bazaliy:1998] This realization has generated a flurry of experimental [@expt] and theoretical work [@Waintal:2004; @Tatara:2004; @Zhang:2004; @Thiaville:2005; @Barnes:2005] focused on current-driven motion of domain walls in magnetic thin films.

The experiments cited just above employ Néel-type domain walls with widths $w\approx 100$ nm. This length is very large compared to the characteristic length scales of the processes that determine the local torque.[@Stiles:2002; @Zhang:2002] Therefore, it is appropriate to adopt an adiabatic approximation where the spin current is assumed to lie parallel to the local magnetization. [@Berger:1978; @Bazaliy:1998] Surprisingly, the adiabatic prediction for the current dependence of the domain wall velocity [@Berger:1986; @Tatara:2004; @Thiaville:2004] agrees very poorly with experiment. This has led theorists [@Waintal:2004; @Tatara:2004; @Zhang:2004; @Thiaville:2005; @Barnes:2005] to consider non-adiabatic effects and experimenters [@Klaui:2005; @Ravelosona:2005] to study systems with domain wall widths that are much shorter ($w\approx 10$ nm) than those studied previously.

Two groups [@Zhang:2004; @Thiaville:2004] have studied the effect on domain wall motion of a distributed spin-transfer torque represented by a sum of gradients of the local 