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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|
|Pages:||pp. 415 - 427|
|Keywords:||Boltzmann equation,drift-diffusion,magnetic multilayer,spin current,spin transport,spin vlave,spin-transfer torque|