  We search for dynamical magnetoelectric phenomena in three-dimensional
correlated systems with spin-orbit coupling. We focus on the antiferromagnetic
insulator phases where the dynamical axion field is realized by the fluctuation
of the antiferromagnetic order parameter. It is shown that the dynamical chiral
magnetic effect, an alternating current generation by magnetic fields, emerges
due to the time dependences of the order parameter such as antiferromagnetic
resonance. It is also shown that the anomalous Hall effect arises due to the
spatial variations of the order parameter such as antiferromagnetic domain
walls. Our study indicates that spin excitations in antiferromagnetic
insulators with spin-orbit coupling can result in nontrivial charge responses.
Moreover, observing the chiral magnetic effect and anomalous Hall effect in our
system is equivalent to detecting the dynamical axion field in condensed
matter.
