Chiral Magnetic Effect and Anomalous Hall Effect in Antiferromagnetic Insulators with Spin-Orbit Coupling

We search for dynamical magnetoelectric phenomena in three-dimensional correlated systems with spin-orbit coupling. In the antiferromagnetic insulator phase, 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, arises 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.