Oscillations with Co and Cu thickness of the current-perpendicular-to-plane giant magnetoresistance of a Co/Cu/Co(001) trilayer

The results of a rigorous quantum calculation of the current-perpendicular-to-plane giant magnetoresistance (CPP GMR) of a Co/Cu/Co(001) trilayer without impurity scattering are reported. The conductances per spin in the ferromagnetic (FM) and antiferromagnetic (AF) configurations of the magnetic layers are computed from Kubo formula. The electronic structure of the Cu and Co layers is described by fully realistic s,p,d tight-binding bands fitted to ab initio band structures of Cu and ferromagnetic fee Co. Depending on Co thickness, the CPP GMR ratio can be as high as 90%. The whole calculated effect is due solely to quantum reflections of electrons from perfectly fiat Co/Cu interfaces. The CPP GMR ratio is found to oscillate both with Co and Cu thickness, the respective oscillation amplitudes being 12 and 6% of the average GMR. The resistances in each spin channel per unit cross-sectional area of the trilayer range from 3 to 7 f Omega and oscillate with an amplitude similar to 0.5 f Omega. An analytic asymptotic formula for resistance oscillations originating from the Cu Fermi surface is applied to analyze the numerical results. It is found that the resistance oscillations for majority electrons in the FM configuration have periods dominated by the extremal radii of the Cu Fermi surface. These are the same periods as observed in the oscillatory exchange coupling. However, the amplitude of resistance oscillations with the Fermi-surface periods is negligibly small for the minority electrons in the FM configuration and for electrons of either spin orientation in the AF configuration. The resistance oscillations of these electrons are dominated instead by periods determined by cutoffs of the conductance due to a mismatch between the Co and Cu bands across the Co/Cu interfaces.