Multiferroic ScLa X 2 ( X = P , As, and Sb) monolayers: Bidirectional negative Poisson's ratio effects and phase transformations driven by rare-earth (main-group) elements

The combination of auxetic property, ferroelasticity, and ferroelectricity in two-dimensional materials offers new avenues for next-generation multifunctional devices. However, two-dimensional materials that simultaneously exhibit those properties are rarely reported. Here, we present a class of two-dimensional Janus-like structures $\mathrm{ScLa}{X}_{2}$ ($X=\mathrm{P}$, As, and Sb) with a rectangular lattice based on first-principles calculations. We predict that those $\mathrm{ScLa}{X}_{2}$ monolayers are stable semiconductors with both intrinsic in-plane and out-of-plane auxetic properties, showing a bidirectional negative Poisson's ratio effect. The value of the out-of-plane negative Poisson's ratio effect can reach \ensuremath{-}2.28/\ensuremath{-}3.06/\ensuremath{-}3.89. By applying uniaxial strain engineering, two transition paths can be found, including the VA main group element path and the rare-earth metal element path, corresponding to the ferroelastic and the multiferroic (ferroelastic and ferroelectric) phase transition, respectively. For the $\mathrm{ScLaS}{\mathrm{b}}_{2}$ monolayer, the external force field can not only control the ferroelastic phase transition, but it can also lead to the reversal of the out-of-plane polarization, exhibiting potential multiferroicity. The coupling between the bidirectional negative Poisson's ratio effect and multiferroicity makes the $\mathrm{ScLa}{X}_{2}$ monolayers promising for future device applications.