Hybrid improper ferroelectricity and magnetoelectric coupling in a two-dimensional perovskite oxide

Unlike van der Waals materials, perovskite oxide may undergo structural reconstruction when reduced to two dimensions. Therefore, it is still an open question whether some of the ferroelectric mechanisms and magnetoelectric coupling effects found in perovskite bulks can be maintained at the two-dimensional (2D) limit. Here we demonstrate that the ferroelectricity induced by octahedral rotation and the magnetoelectric coupling mechanism dependent on Dzyaloshinskii-Moriya (DM) interaction exist in a proposed perovskite bilayer. Although the octahedral rotation distortion of the ${\mathrm{Ca}}_{3}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ bilayer is reconstructed with respect to its layered bulk phase, tensile strain can induce the same octahedral rotation type as its bulk phase, resulting in the emergence of ferroelectric phase. We show that the modulation of the DM vector by octahedral rotation distortion provides a coupling between polarization and the induced magnetization. In ferroelectric switching, the polarization is reversed by a ${180}^{\ensuremath{\circ}}$ rotation of the tilt axis within the $ab$ plane, which also results in a reversal of magnetization. This work is expected to provide a guidance for realizing electric-field control of magnetization direction in 2D perovskite oxides.