the positive $z$ axis, $\phi(x)$ is the azimuthal angle in the $x$-$y$ plane, and $M_s$ is the saturation magnetization. We begin with the spin current and spin torque for an infinite spin spiral with constant pitch. This system turns out to be perfectly adiabatic; the torque is described by Eq. (\[lt\]) with $c_2=0$. The same is true for realistic domain walls of the sort usually encountered in experiment. Non-adiabatic effects appear only for very narrow walls. In that case, the torque is non-local and cannot be written in the form Eq. (\[lt\]). The non-adiabatic torque decreases exponentially as the wall width increases for all realistic domain wall profiles. Finally, our analysis casts doubt on the existence of a non-adiabatic contribution to the torque due to spin-flip scattering proposed recently by Zhang and Li.[@Zhang:2004].

The remainder of the paper is organized as follows. Section \[models\] describes our Stoner model and the methods we use to calculate the spin current and spin-transfer torque. Section \[spinspiral\] reports our results for an infinite spin spiral and Section \[domainwalls\] does the same for one-dimensional domain walls that connect two regions of uniform magnetization. Section \[other\] relates these calculations to previous work by others. Section \[scattering\] 