Boltzmann Test of Slonczewski's Theory of Spin Transfer Torque

TL;DR

This paper tests the accuracy of Slonczewski's spin-transfer torque theory in thin-film heterostructures using a Boltzmann equation approach, finding excellent agreement and predicting new precession modes in asymmetric structures.

Contribution

It introduces a matrix Boltzmann formalism to validate and extend Slonczewski's theory, especially for asymmetric multilayer structures.

Findings

Excellent agreement between model predictions and Boltzmann calculations.

Derived a new analytic formula for torque in asymmetric structures.

Predicted a new stable precession mode in asymmetric geometries.

Abstract

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.