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It is shown that a non-magnetic metallic band in the presence of anantiferromagnetic background coupled only by the exchange interaction developsa superconducting instability similar to the one described by BCS theory plusadditional terms that strongly renormalize the spin excitation spectra. ABardeen-Pines-like hole-hole interaction Hamiltonian, mediated by magneticexcitations, is deduced from a microscopic model of a fermion band and a spinband that interact with each other only via the exchange interaction. Thetheory shows the appearance of an attractive interaction when the Fermivelocity in the non-magnetic band is larger than the magnon velocity in themagnetic band. The electron-magnon scattering is suppressed by the appearanceof a spin gap simultaneously with the superconducting state. Although thismodel may well describe a general class of materials to be discovered, thepossibility that this theory could describe superconducting cuprates isdiscussed.

Superconducting instability of a non-magnetic metallic band in an antiferromagnetic background