  Axion insulator is an exotic magnetic topological insulator with zero Chern
number but a nonzero quantized Chern-Simons magnetoelectric coupling. A
conclusive experimental evidence for axion insulators is still lacking due to
the small signal of topological magnetoelectric effect (TME). Here we show that
the dynamical magnetoelectric coupling can be induced by the
\emph{out-of-plane} surface magnetization dynamics in axion insulator thin
films, which further generates a polarization current in the presence of an
external magnetic field in the same direction. Such a current is finite in the
bulk and increases as the film thickness $d$ decreases, in opposite to TME
current which decreases as $d$ decreases. Remarkably, the current in thin films
at magnetic resonance is at least ten times larger than that of TME, and thus
may serve as a smoking gun signature for axion insulators.
