A laminated magnetic recording medium for data storage uses a magnetic recording layer having at least two antiferromagnetically-coupled (AFC) layers spaced apart by a nonferromagnetic spacer layer. Each AFC layer is formed as two ferromagnetic films antiferromagnetically coupled together across an antiferromagnetically coupling film that has a composition and thickness to induce antiferromagnetic coupling of the second film to the first film. The magnetic moments of the two antiferromagnetically-coupled films in each AFC layer are oriented antiparallel, and thus the net remanent magnetization-thickness product (Mrt) of each AFC layer is the difference in the Mrt values of the two ferromagnetic films. The nonferromagnetic spacer layer between neighboring AFC layers has a composition and thickness to prevent any antiferromagnetic coupling of the ferromagnetic films of one AFC layer with the ferromagnetic films of the neighboring AFC layer.