Boltzmann test of Slonczewski’s theory of spin-transfer torque

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 nonmagnetic spacer layer separates two noncollinear ferromagnetic layers connected to nonmagnetic 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 an 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 mode of stable precession that does not occur for the symmetric case studied by Slonczewski.