  We use a matrix Boltzmann equation formalism to test the accuracy of
Slonczewski's theory of spin-transfer torque in thin-film heterostructures
where a non-magnetic spacer layer separates two non-collinear ferromagnetic
layers connected to non-magnetic leads. When applicable, the model predictions
for the torque as a function of the angle between the two ferromagnets agree
extremely well with the torques computed from a Boltzmann equation calculation.
We focus on asymmetric structures (where the two ferromagnets and two leads are
not identical) where the agreement pertains to a new analytic formula for the
torque derived by us using Slonczewski's theory. In almost all cases, we can
predict the correct value of the model parameters directly from the geometric
and transport properties of the multilayer. For some asymmetric geometries, we
predict a new mode of stable precession that does not occur for the symmetric
case studied by Slonczewski.
