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Layered perovskites $A_3M_2$O$_7$ are known to exhibit the so-called hybridimproper ferroelectricity. Despite experimentally confirmed cases (e.g.nonmagnetic $M$=Ti and Sn), the ferroelectricity in magnetic Ca$_3$Mn$_2$O$_7$remains a puzzle. Here, the structural, ferroelectric, magnetoelectric, andoptical properties of Ca$_3$Mn$_2$O$_7$ are systematically investigated.Switchable polarization is directly measured, demonstrating itsferroelectricity. In addition, magnetoelectric response is also evidenced,implying the coupling between magnetism and ferroelectricity. Furthermore,strong visible light absorption is observed, which can be understood from itselectronic structure. Its direct and appropriate band gap, as well as wideconducting bands, makes Ca$_3$Mn$_2$O$_7$ a potential candidate forferroelectric photoelectric applications.

Direct observation of ferroelectricity in Ca$_3$Mn$_2$O$_7$ and its prominent light absorption