Electromagnetic effects induced by time-dependent axion field

We studied the dynamics of the so-called $\theta$-term, which exists in topological materials and is related to a hypothetical field predicted by Peccei-Quinn in particle physics, in a magnetic superlattice constructed using a topological insulator and two ferromagnetic insulators, where the ferromagnetic insulators had perpendicular magnetic anisotropies and different magnetic coercive fields. We examined a way to drive the dynamics of the $\theta$-term in the magnetic superlattice through changing the inversion symmetry (from an anti-parallel to a parallel magnetic configuration) using an external magnetic field. As a result, we found that unconventional electromagnetic fields, which are magnetic field-induced charge currents and vice versa, are generated by the nonzero dynamics of the $\theta$-term.