  The ground state of K$_{0.8+x}$Fe$_{1.6+y}$Se$_2$ and other iron-based
selenide superconductors are doped antiferromagnetic semiconductors. There are
well defined iron local moments whose energies are separated from those of
conduction electrons by a large band gap in these materials. We propose that
the low energy physics of this system is governed by a model Hamiltonian of
interacting electrons with on-site ferromagnetic exchange interactions and
inter-site superexchange interactions. We have derived the effective pairing
potential of electrons under the linear spin-wave approximation and shown that
the superconductivity can be driven by mediating coherent spin wave excitations
in these materials. Our work provides a natural account for the coexistence of
superconducting and antiferromagnetic long range orders observed by neutron
scattering and other experiments.
