Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Boltzmann Test of Slonczewski's Theory of Spin Transfer Torque



J Xiao, A Zangwill, Mark D. Stiles


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.
Physical Review B (Condensed Matter and Materials Physics)


Xiao, J. , Zangwill, A. and Stiles, M. (2004), Boltzmann Test of Slonczewski's Theory of Spin Transfer Torque, Physical Review B (Condensed Matter and Materials Physics), [online], (Accessed April 23, 2024)
Created November 11, 2004, Updated October 12, 2021