3-dimensional distribution of spin-polarized current: application to (Cu/Co) pillar structures

We present a formalism determining spin-polarized current and electrochemical potential inside arbitrary electric circuit within diffusive regime for parallel/antiparallel magnetic states. When arbitrary nano-structure is expressed by 3-dimensional (3D) electric circuit, we can determine 3D spin-polarized current and electrochemical potential distributions inside it. We apply this technique to (Cu/Co) pillar structures, where pillar is terminated either by infinitely large Cu layer, or by Cu wire with identical cross-sectional area as pillar itself. We found that infinitely large Cu layers work as a strong spin-scatterers, increasing magnitude of spin-polarized current inside the pillar twice and reducing spin accumulation nearly to zero. As most experimentally studied pillar structures are terminated by such a infinitely large layers, we propose modification of standard Valet-Fert formalism to simply include influence of such infinitely large layers.