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Out-of-plane high-temperature ferromagnetic monolayer CrSCl with large vertical piezoelectric response

For two-dimensional (2D) material, piezoelectric ferromagnetism (PFM) with large out-of-plane piezoresponse is highly desirable for multifunctional ultrathin piezoelectric device application. Here, we predict that Janus monolayer CrSCl is an out-of-plane ferromagnetic (FM) semiconductor with large vertical piezoelectric response and high Curie temperature. The predicted out-of-plane piezoelectric strain coefficient $d_{31}$ is -1.58 pm/V, which is higher than ones of most 2D materials (compare absolute values of $d_{31}$). The large out-of-plane piezoelectricity is robust against electronic correlation and biaxial strain, confirming reliability of large $d_{31}$. Calculated results show that tensile strain is conducive to high Curie temperature, large magnetic anisotropy energy (MAE) and large $d_{31}$. Finally, by comparing $d_{31}$ of CrYX (Y=S; X=Cl, Br I) and CrYX (Y=O; X=F, Cl, Br), we conclude that the size of $d_{31}$ is positively related to electronegativity difference of X and Y atoms. Such findings can provide valuable guidelines for designing 2D piezoelectric materials with large vertical piezoelectric response.