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Publication Citation: A Numerical Method to Solve the Boltzmann Equation for a Spin Valve

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Author(s): J Xiao; A Zangwill; Mark D. Stiles;
Title: A Numerical Method to Solve the Boltzmann Equation for a Spin Valve
Published: October 01, 2007
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
Pages: pp. 415 - 427
Keywords: Boltzmann equation,drift-diffusion,magnetic multilayer,spin current,spin transport,spin vlave,spin-transfer torque
Research Areas: Nanomagnetics