Large out-of-plane piezoelectric response in ferromagnetic monolayer NiClI

The combination of piezoelectricity and ferromagnetic (FM) order in a two-dimensional (2D) material, namely 2D piezoelectric ferromagnetism (PFM), may open up unprecedented opportunities for novel device applications. Here, we predict an in-plane FM semiconductor Janus monolayer NiClI with considerably large magnetic anisotropy energy (MAE) of 1.439 meV, exhibiting dynamic, mechanical and thermal stabilities. The NiClI monolayer possesses larger in-plane piezoelectricity ($d_{11}$$=$5.21 pm/V) comparable to that of $\mathrm{MoS_2}$. Furthermore, NiClI has huge out-of-plane piezoelectricity ($d_{31}$$=$1.89 pm/V), which is highly desirable for ultrathin piezoelectric device application. It is proved that huge out-of-plane piezoelectricity is robust against electronic correlation, which confirms reliability of huge $d_{31}$. Finally, being analogous to NiClI, PFM with large out-of-plane piezoelectricity can also be achieved in the Janus monolayers of NiClBr and NiBrI, with the predicted $d_{31}$ of 0.73 pm/V and 1.15 pm/V, respectively. The predicted huge out-of-plane piezoelectric response makes Janus monolayer NiClI a good platform for multifunctional semiconductor spintronic applications, which is also compatible with the bottom/top gate technologies of conventional semiconductor nanoelectronic devices.