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 May 20, 2025)
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A Numerical Method to Solve the Boltzmann Equation for a Spin Valve
Published
Author(s)
, ,
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.Citation
European Physical Journal B
Volume
59
Issue
4
Pub Type
Journals
Keywords
Boltzmann equation, drift-diffusion, magnetic multilayer, spin current, spin transport, spin vlave, spin-transfer torque
Citation
Issues
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Created September 30, 2007, Updated October 12, 2021