The European Physical Journal B

, Volume 59, Issue 4, pp 415–427 | Cite as

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

  • J. Xiao
  • A. Zangwill
  • M. D. StilesEmail author
Topical Issue on New Trends in Spin Transfer Physics


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.


85.75.-d Magnetoelectronics; spintronics: devices exploiting spin polarized transport or integrated magnetic fields 75.47.De Giant magnetoresistance 


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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.School of Physics, Georgia Institute of TechnologyAtlantaUSA
  2. 2.Electron Physics Group, National Institute of Standards and TechnologyGaithersburgUSA

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