Topical Issue on New Trends in Spin Transfer Physics

The European Physical Journal B

, Volume 59, Issue 4, pp 415-427

First online:

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

  • J. XiaoAffiliated withSchool of Physics, Georgia Institute of Technology
  • , A. ZangwillAffiliated withSchool of Physics, Georgia Institute of Technology
  • , M. D. StilesAffiliated withElectron Physics Group, National Institute of Standards and Technology Email author 

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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