magnetization with constant coefficients. For a one-dimensional magnetization ${\bf
M}(x)$, the torque function can be written in terms of two vectors perpendicular to the magnetization $$\label{lt}
    {\bf N}_{\rm st}(x) = c_1\partial_x\hat{\bf M}  
+ c_2\hat{\bf M}\times\partial_x\hat{\bf M}.$$ In general, the coefficients $c_1$ and $c_2$ are functions of position. The well-established adiabatic piece of the torque is the first term in Eq. (\[lt\]) with a constant coefficient. Consistent with usage in the literature, we call all deviations from the adiabatic torque non-adiabatic. Any contributions of the second term are then called non-adiabatic. Zhang and Li [@Zhang:2004] derive a contribution along this second direction in Eq. (\[lt\]) from a consideration of magnetization relaxation due to spin-flip scattering in the context of an s-d exchange model of a ferromagnet. [@Berger:1986; @Zhang:2002] Their arguments lead them to the estimate $c_2/c_1\approx 0.01$. The authors of Ref.  report that a similar value of $c_2/c_1$ produces agreement with experiment when Eq. (\[lt\]) is used in micromagnetic simulations.

In this paper, we study the applicability of Eq. (\[lt\]) to a free-electron Stoner model with one-dimensional magnetization distributions of the form $$\label{eqn:magnetization}
    {\bf M}(x) = M_s{\left( \sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta \right)}.$$ In Eq. (\[eqn:magnetization\]), the polar angle $\theta(x)$ is measured from 