Calculation of Giant Magnetoresistance in Laterally Confined Multilayers

We have studied the Giant Magnetoresistance (GMR) for laterally confined multilayers, e.g., layers of wires, using the classical Boltzmann equation in the current-in-plane (CIP) geometry. For spin-independent specularity factors at the sides of the wires we find that the GMR due to bulk and surface scattering decreases with lateral confinement. The length scale at which this occurs is of order the film thickness and the mean free paths. The precise prefactor depends on the relative importance of surface and bulk scattering anisotropies. For spin-dependent specularity factors at the sides of the wires the GMR can increase in some cases with decreasing width. The origin of the change in the GMR in both cases can be understood in terms of lateral confinement changing the effective mean free paths within the layers.