Theory of the perpendicular magnetoresistance in magnetic multilayers

TLDR

The study calculates transport properties of magnetic multilayers for perpendicular currents using the Boltzmann equation. The model incorporates volume and interface spin‑dependent scattering within a Boltzmann‑equation framework. The analysis shows that macroscopic equations hold when the spin‑diffusion length exceeds the mean free path, but Johnson’s additive interface assumption fails; accounting for interface interplay yields results consistent with experiments and enables separation of volume and interface spin‑dependent scattering contributions.

Abstract

By starting with the Boltzmann equation, we calculate the transport properties of magnetic multilayers for currents perpendicular to the layers. Our model takes into account both volume and interface spin-dependent scattering. We show that the macroscopic equations already used by Johnson et al. or van Son et al. are justified if the spin-diffusion length is much longer than the mean free path, even for individual layer thicknesses of the order of the mean free path. But, second, we show that Johnson's assumption of additive effects from independent interfaces in multilayers is incorrect and we obtain different results by taking into account the interplay between successive interfaces. The simple expressions derived for individual thicknesses much shorter than the spin-diffusion length are in agreement with the analysis of experimental results already proposed. It turns out that data on the perpendicular magnetoresistance can be used to separate clearly the volume and interface contributions to the spin-dependent scattering.