Three-dimensional distribution of the spin-polarized current inside nanostructures

We present a formalism to determine the three-dimensional (3D) distribution of the spin-polarized current and electrochemical potential inside arbitrary nanostructures such as magnetic/nonmagnetic layered pillars, etc. The model is based on dividing the nanostructure into a 3D electric circuit of spin-dependent-resistor elements, inside each of which the propagation is treated as a one-dimensional problem. The solutions presented here are calculated in the diffusive transport regime for the parallel/antiparallel magnetic states.