  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.
