magnetizations. Hence, this analysis argues against the existence of the resulting contribution to the “non-adiabatic” torque from spin flip scattering.

Scattering
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We do not explicitly treat scattering in any of our calculations. However, the distribution function in Eq. (\[eqn:spinandcurrent\]), a shifted Fermi distribution, is an approximate solution of the Boltzmann equation in certain limits. First, the electric field must be small enough that the transport is in the linear regime. Then, the appropriate limits are determined by three important length scales, the Fermi wavelength, the mean free path, and the characteristic length of the structure, either the pitch of the spin spiral or the width of the domain wall. In all cases, we consider the limit in which the Fermi wavelength is short compared to the mean free path. This limit allows the description of the states of the system in terms of the eigenstates of the system in the absence of scattering. Different limits apply to the cases of domain walls and of spin spirals because the distribution functions are interpreted differently for these two structures.

We use the Boltzmann equation in two different ways. When the mean free path is much longer than the characteristic size of 