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A numerical method to solve the Boltzmann equation for a spin valve

Jiang Xiao·A. Zangwill·M. D. Stiles
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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.

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Jiang Xiao, A. Zangwill, M. D. Stiles. 2007-01-16. A numerical method to solve the Boltzmann equation for a spin valve. https://doi.org/10.1140/epjb%2Fe2007-00004-0

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