In-plane strain tuning multiferroicity in monolayer van der Waals NiI$_{2}$

Multiferroic order with the engineered levels of strain in monolayer NiI$_{2}$ is explored based on density functional theory calculations and Monte Carlo simulations. Through the investigation of strain-free monolayer NiI$_{2}$, we find that the first nearest neighbor and third nearest neighbor exchange interactions play an essential role in the formation of its magnetic phase diagrams. The competition of these interactions induces magnetic frustration, leading to the formation of proper-screw helimagnetic ground state. We further show that these conclusions drawing from the strain-free monolayer can be well generalized to the cases within our engineered range of strains. Notably, our calculations show that with 6% tensile strain on the $a$-axis and 8% compressive strain on the $b$-axis, the N\'{e}el temperature $T_N$ can be significantly enhanced to 101 K, about 5 times larger than that of the strain-free one. The strength of spontaneous electric polarizations can also be more than doubled under 8% uniform compressive strain on both axis. Our work suggests that strain is a promising way to tune multiferroic orders in the monolayer NiI$_{2}$, with the potential to signicantly promote its transition temperatures and electric polarizations, therefore broaden the prospect of its applications in spintronics devices.