  We study theoretically a three-dimensional correlated and spin-orbit coupled
system, the half-filled extended Fu-Kane-Mele-Hubbard model on a diamond
lattice, focusing on the topological magnetoelectric response of the
antiferromagnetic insulator phase. In the antiferromagnetic insulator phase,
the Dirac-like low-energy effective Hamiltonian is obtained. Then the theta
term, which results in the magnetoelectric response, is derived as a
consequence of the chiral anomaly. The realization of the dynamical axion field
in our model is discussed. The relation with a symmetry broken phase induced by
interactions in lattice quantum chromodynamics is also discussed.
