Charge estimation due to band mismatch in CPP GMR

We modify the macroscopic equations proposed by Valet and Fert for current perpendicular to the plane of a magnetic bilayer. Considering different spin bands for the spin-up and spin-down electrons, we calculate the charge accumulation near the interface along with the spin accumulation. This gives rise to a voltage drop at the interface, and causes the resistance to depend on the relative degree of magnetization of the two layers. We obtain expressions for the spatial distribution of charge and the accompanying electric field across the interface between the magnetic layers. An additional resistance caused by the potential step at the interface is added to get a better estimate of the magnetoresistance.