A numerical method to solve the Boltzmann equation for a spin valve
Abstract
We present a numerical algorithm to solve the Boltzmann equation for the electron distribution function in magnetic multilayer heterostructures with non-collinear magnetizations. The solution is based on a scattering matrix formalism for layers that are translationally invariant in plane so that properties only vary perpendicular to the planes. Physical quantities like spin density, spin current, and spin-transfer torque are calculated directly from the distribution function. We illustrate our solution method with a systematic study of the spin-transfer torque in a spin valve as a function of its geometry. The results agree with a hybrid circuit theory developed by Slonczewski for geometries typical of those measured experimentally.
Keywords
Cite
@article{arxiv.cond-mat/0701385,
title = {A numerical method to solve the Boltzmann equation for a spin valve},
author = {Jiang Xiao and A. Zangwill and M. D. Stiles},
journal= {arXiv preprint arXiv:cond-mat/0701385},
year = {2011}
}
Comments
13 pages, 8 figures