  It is shown that interlayer spin-singlet Cooper pairing is induced by
magnetic interactions in a metallic antiferromagnet of stacked conductive
layers in which each layer is ferromagnetically polarized and they order
antiferromagnetically in stacking direction. As a result, the antiferromagnetic
long-range order and superconductivity coexist at low temperatures. It is shown
that T_AF > T_c except for in a very limited parameter region unless T_AF = 0,
where T_AF and T_c denote the antiferromagnetic and superconducting transition
temperatures, respectively. It is found that the exchange field caused by the
spontaneous staggered magnetization does not affect superconductivity at all,
even if it is very large. The resultant superconducting order parameter has a
horizontal line node, and is isotropic in spin space in spite of the anisotropy
of the background magnetic order. We discuss the possible relevance of the
present mechanism to the antiferromagnetic heavy fermion superconductors
UPd_2Al_3 and CePt_3Si.
