Axion mass in antiferromagnetic insulators

We calculate axion potential in antiferromagnetic insulators from path integral. It is derived from the effective potential for the order parameter of the antiferromagnetic phase in insulators. Static and dynamical axions are defined consistently from the potential. Consequently antiferromagnetic/paramagnetic and topological/normal orders are classified. The dynamical axion is predicted in all phases and its mass turns out to be various values up to eV scale.