Ferroelastic-ferroelectric multiferroics in a bilayer lattice

Two-dimensional multiferroics, combined with ferroelastic and ferroelectric orders, enable unprecedented exploration of applications, such as high-density multistate storage. However, current ferroelastic-ferroelectric-multiferroic research is based on the paradigm of unique symmetry in a single-layer lattice, which restricts ferroelastic ferroelectricity to being rarely explored. Here, going beyond the existing paradigm, we report a design principle for realizing ferroelastic ferroelectricity using the van der Waals interaction as perturbation in a bilayer lattice. Using first principles, we show that, through layer-stacking, bilayer ${\mathrm{ZrI}}_{2}$ not only possesses 120 \ifmmode^\circ\else\textdegree\fi{} ferroelasticity due to its crystal symmetry but also holds out-of-plane and in-plane polarizations caused by interlayer charge redistribution, thereby achieving ferroelastic-ferroelectric multiferroics in a bilayer lattice. The switch of out-of-plane polarization relates to interlayer sliding, while in-plane polarization reversal correlates with 120 \ifmmode^\circ\else\textdegree\fi{} ferroelastic switching. Based on this fact, we propose the six-logic-state multiferroicity. This paper illustrates a tantalizing scheme for achieving and developing two-dimensional ferroelastic ferroelectricity.