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.

中文翻译：

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单层范德华 NiI$_{2}$ 中的面内应变调谐多铁性

基于密度泛函理论计算和蒙特卡罗模拟，探索了单层 NiI$_{2}$ 中具有工程应变水平的多铁顺序。通过对无应变单层NiI$_{2}$的研究，我们发现第一近邻和第三近邻交换相互作用在其磁相图的形成中起着至关重要的作用。这些相互作用的竞争引起磁挫折，导致形成适当的螺旋磁基态。我们进一步表明，从无应变单层得出的这些结论可以很好地推广到我们设计的菌株范围内的情况。值得注意的是，我们的计算表明，$a$ 轴上的拉伸应变为 6%，$b$ 轴上的压缩应变为 8%，N\' {e}el 温度 $T_N$ 可以显着提高到 101 K，大约是无应变温度的 5 倍。在两个轴上 8% 的均匀压缩应变下，自发电极化的强度也可以增加一倍以上。我们的工作表明，应变是调整单层 NiI$_{2}$ 中多铁性顺序的一种有前途的方法，具有显着提高其转变温度和电极化的潜力，因此拓宽了其在自旋电子器件中的应用前景。