Stacking-dependent ferroicity of a reversed bilayer: Altermagnetism or ferroelectricity

Altermagnetism, as a new branch of magnetism independent of traditional ferromagnetism and antiferromagnetism, has attracted extensive attention recently. At present, researchers have proved several kinds of three-dimensional altermagnets, but research on two-dimensional (2D) altermagnets remains elusive. Here, we propose a method for designing altermagnetism in 2D lattices: bilayer reversed stacking. This method could enable altermagnetism-type spin splitting to occur intrinsically and the spin splitting could be controlled by crystal chirality. We also demonstrate it through a real material of bilayer $\mathrm{Pt}{\mathrm{Br}}_{3}$ with AB\ensuremath{'} stacking order. Additionally, the combination of stacking order and slidetronics offers opportunities for electrical writing and magnetic reading of electronic devices. In the case of ${\mathrm{AC}}^{\ensuremath{'}}$ stacking, interlayer sliding results in reversible spontaneous polarization. This unique combination of antiferromagnetism and sliding ferroelectricity leads to polarization-controlled spin splitting, thus enabling magnetoelectric coupling, which can be detected by magneto-optical Kerr effect even without net magnetization. Our research highlights that reversed stacking provides a platform to explore rich physical properties of magnetism, ferroelectricity, and spin splitting.