We report on x-ray magneto-optical reflectivity investigations of Co/Cu multilayers with circularly polarized synchrotron light. The individual layer thicknesses of the samples were tuned to the second maximum of the giant magnetoresistance. An external magnetic field was applied parallel to the sample surface and the scattering plane utilizing the longitudinal magneto-optical Kerr effect. The reflectometry curves measured at the Co L3 absorption edge clearly show antiferromagnetic (AFM) coupling of the Co layers by half-integer-order Bragg peaks of magnetic origin, which disappear for nonresonant excitation. Whereas the first-order magnetic peak overlaps with strong charge scattering contributions, the higher-order magnetic peaks are more pronounced and sensitive to magnetic effects. In an applied field, the magnetic peaks are suppressed due to a reduction of the AFM layer coupling, and an additional intensity modulation occurs due to asymmetry effects. Measurements of the photon energy dependence of the Bragg peak positions were employed close to the Co L2,3 edges to determine the dispersive part of the magneto-optical constants of the Co/Cu multilayer. © 2003 American Institute of Physics.