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A Numerical Method to Solve the Boltzmann Equation for a Spin Valve
Published
Author(s)
J Xiao, A Zangwill, Mark D. Stiles
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.
Xiao, J.
, Zangwill, A.
and Stiles, M.
(2007),
A Numerical Method to Solve the Boltzmann Equation for a Spin Valve, European Physical Journal B
(Accessed November 29, 2023)