  We predict that current perpendicular to the plane (CPP) giant
magnetoresistance (GMR) in a phase-coherent magnetic multilayer is suppressed
when one of the contacts is superconducting. This is a consequence of a
superconductivity-induced magneto-resistive (SMR) effect, whereby the
conductance of the ferromagnetically aligned state is drastically reduced by
superconductivity. To demonstrate this effect, we compute the GMR ratio of
clean (Cu/Co)_nCu and (Cu/Co)_nPb multilayers, described by an ab-initio spd
tight binding Hamiltonian. By analyzing a simpler model with two orbitals per
site, we also show that the suppression survives in the presence of elastic
scattering by impurities.
