Physical Review B 72(21), 212410 (2005)
In perpendicular-transport structures with magnetic and non-magnetic layers, there is a resistance associated with changes in the value of current polarization throughout the structure. Starting from a Boltzmann equation Valet and Fert derived macroscopic transport equations to describe this effect. Their derivation is formally justified in the limit that the spin diffusion length is long compared to the mean free path, but appears to agree with experiment well beyond this limit. Here, numerical studies of the Boltzmann equation verify that their approach is valid beyond that limit. In addition, we have examined the case of non-isotropic spin flip scattering. For reasonable parameters there is only a small difference in the resistance from the isotropic case.
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