https://doi.org/10.1140/epjb/e2007-00004-0
A numerical method to solve the Boltzmann equation for a spin valve
1
School of Physics, Georgia Institute of Technology, Atlanta, GA, 30332-0430, USA
2
Electron Physics Group, National Institute of Standards and Technology, Gaithersburg, MD, 20899-8412, USA
Corresponding author: a mark.stiles@nist.gov
Received:
7
September
2006
Revised:
3
November
2006
Published online:
10
January
2007
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.
PACS: 85.75.-d – Magnetoelectronics; spintronics: devices exploiting spin polarized transport or integrated magnetic fields / 75.47.De – Giant magnetoresistance
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007