Charge and spin currents in magnetic multi layers in the presence of both electric field and spin dynamics

The number and the spin angular momentum of electrons on each site, and the charge and the spin currents between adjacent sites are theoretically studied. Considering one dimensional electronic system including impurity atoms with some density, the static electric field (represented by an electric potential) and the s-d interaction with spin dynamics are treated perturbatively. We show that the effect of the applied electric field can be understood from the ideas of the drift by the field and the band shift due to the electric potential.