Insights into the origin of multiferroicity and large in-plane piezoelectricity in AlXY ( X=S,Se ;

Understanding the interplay of properties in two-dimensional (2D) multiferroic materials is of paramount importance for crafting the blueprint of cutting-edge functional devices in the next generation. In the present study, we report a family of stable multiferroics $\mathrm{Al}\mathit{XY}$ ($X=\mathrm{S},\mathrm{Se}$; $Y=\mathrm{Cl},\mathrm{Br},\mathrm{I}$) with the coexistence of ferroelectricity and ferroelasticity, using density functional theory (DFT) calculations. The $\mathrm{Al}\mathit{XY}$ monolayers (MLs) exhibit large in-plane ferroelectric polarization (${P}_{y}$) ranging from 148 to 177 pC/m with a moderate switching barrier of 0.102--0.192 eV/atom. The polarization in these MLs owes its origin to the repositioning of Al atoms, actuated by soft ${B}_{2u}$ phonon mode in the paraelectric phase (Pmmn). These MLs exhibit robust ferroelasticity with a large reversible strain of 38%--45.1% and moderate switching barriers of 0.175--0.213/eV/atom. The ferroelectric and ferroelastic (FA) phases differ in the electric polarization direction by ${90}^{\ensuremath{\circ}}$ rotation. Besides a strong anisotropy in mechanical properties, in-plane piezoelectricity and carrier mobilities are observed in the $\mathrm{Al}\mathit{XY}$ MLs. Moreover, FA switching provides a highly effective way for finely tuning these anisotropic properties of $\mathrm{Al}\mathit{XY}$ MLs. Complementing these findings, we devised an empirical predictive model built on descriptors derived from linear regression analysis, linking atomic polarizability, Bader charge, lattice constant ($b$), layer thickness ($h$), bandgap, and effective mass of electron in order to estimate polarization (${P}_{y}$) and in-plane piezoelectric constants (${d}_{22},\phantom{\rule{0.16em}{0ex}}{d}_{21}$) of $\mathrm{Al}\mathit{XY}$ MLs, which is in excellent agreement (${R}^{2}=0.95\ensuremath{-}0.98$) with results obtained from DFT.