Magnetoresistance of magnetic multilayers: understanding Ohmʹs law

The magnetic-field dependence of the magnetoresistance MR(H) of magnetic multilayers in the CPP mode (current perpendicular to the layers) was recently measured for two samples that differ only in the ordering of the layers: [Fe/Cu/Co/Cu]N and [Fe/Cu]N[Co/Cu]N, where N denotes the number of repeats. Ohmʹs law states that MR(H) should be the same for these two samples because in a series circuit, the resistance is independent of the ordering of the resistors. However, the measured MR(H) curves were found to be completely different for the two samples. We show that this unexpected result can be explained as follows. The mean free path is sufficiently long that MR(H) is due to the scattering of electrons by pairs of neighbouring magnetic layers, which differ for the two samples. To confirm these ideas, we carried out calculations of MR(H) and obtained quantitative agreement with experiment.