Large out-of-plane piezoelectric effect in a Janus ferromagnetic semiconductor monolayer of CrOFBr

The exploitation of piezoelectric ferromagnetism in two-dimensional (2D) materials with large out-of-plane piezoelectric response is motivated not only by technological applications but also scientific interest. In this study, the $\mathrm{CrO}NM$ monolayer family $(N=\text{F,}\phantom{\rule{4.pt}{0ex}}\text{Cl};$ $M=\text{Br,}\phantom{\rule{4.pt}{0ex}}\text{Cl})$ was investigated using first-principles calculations, revealing that the Janus CrOFBr monolayer exhibits intrinsic ferromagnetic semiconductor behavior along with a significant out-of-plane piezoelectric effect. The calculated out-of-plane piezoelectric strain coefficients ${d}_{31}$ and ${d}_{32}$ are up to 1.21 and 0.63 pm/V, respectively. These values are greater than those of the majority of 2D materials. Furthermore, our findings demonstrate that applying tensile strain can enhance the out-of-plane piezoelectric response, leading to a respective 27% and 67% augmentation in the piezoelectric strain coefficients ${d}_{31}$ and ${d}_{32}$ compared to the unstrained configurations. This discovery holds great potential for propelling the field of nanoelectronics forward and facilitating the development of multifunctional semiconductor spintronic applications. Finally, by comparing ${d}_{31}$ and ${d}_{32}$ of the $\mathrm{CrO}NM$ monolayer family $(N=\text{F,}\phantom{\rule{4.pt}{0ex}}\text{Cl};$ $M=\text{Br,}\phantom{\rule{4.pt}{0ex}}\text{Cl})$, we find that the magnitudes of ${d}_{31}$ and ${d}_{32}$ are correlated with the electronegativity difference ratio. These findings provide valuable insights for the design of 2D piezoelectric materials with enhanced vertical piezoelectric responses.