. The nonzero and independent C ij in Voigt notation of FE MOX 2 monolayers are given in the Table , and they also are positive (i.e., C 11 , C 22 , C 12 , C 66 > 0 ). Indicating their mechanical stability, our orthorhombic monolayers clearly satisfy the Born elastic stability criteria : C 11 C 22 -C 2 12 > 0. We nd large d 11 for the MOX 2 monolayers but small d 12 , although still d 12 of TiOCl 2 or TiOBr 2 is quite comparable with that of 1H-MoS 2 (3.73 pm/V) or 1H-VS 2 (4.104 pm/V) . TiOBr 2 has the largest d 11 (37.758 pm/V), which is 210 times larger than that of 1H-type monolayers ] (e.g., d 11 of 1H-MoS 2 and 1H-CrTe 2 is 3.65 pm/V and 13.45pm/V, respectively ). This be- ; and also about 7 times higher than d 33 of w -AlN (5.1 pm/V) . Note that group-IV monochalcogenide monolayers have relatively smaller indicating their softness C 11 and C 22 than MOX 2 monolayers. As VOCl 2 and VOBr 2 monolayers have AFM ground state, we also study how their piezo-response will change in response to AFM-to-FM phase transition, which can be possible under an external magnetic eld . Note that FM-to-AFM transition can be a challenge in experiments. We nd that AFM1-to-FM transition somewhat increases the elastic constants especially C 22 thus slightly decrease d 11 . Interestingly, such hardening of C 22 is intrinsic to AFM1-to-FM transition as we see that it comes from mere magnetic order change even if the lat-tice parameters and atomic positions are xed at AFM1 (see Table ). There is a signicant decrease in d 12 (see Table ). Interestingly, d 12 changes sign under AFM1to-FM transition for VOBr 2 monolayer, indicating that subject to an external electric eld the monolayer can shrink or expand depending on the presence of a magnetic eld. This can allow us to control piezoelectricity by magnetism, which may nd applications in realizing multifunctional nano-devices. We believe that other magnetic piezoelectrics especially 2D multiferroelectric can exhibit such coupling between piezo-response and magnetic order.