Magnetoelectric Response of the Antiferromagnetic Insulator Phase in a Correlated and Spin-Orbit Coupled System

The magnetoelectric response of the antiferromagnetic insulator phase in a three-dimensional correlated and spin-orbit coupled system, the half-filled extended Fu-Kane-Mele-Hubbard model on a diamond lattice, is studied within the mean-field approximation. 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. A possible mechanism that generates small deviations of the value of $\theta$ from $0$ or $\pi$ is also discussed.