We study lanthanum mononitride LaN by first-principles calculations. The commonly reported rock-salt structure of $\mathit{Fm}\overline{3}m$ symmetry for rare-earth monopnictides is found to be dynamically unstable for LaN at zero temperature. Using density functional theory and evolutionary crystal prediction, we discover a new, dynamically stable structure with $P1$ symmetry at 0 K. This $P1$-LaN exhibits spontaneous electric polarization. Our ab initio molecular dynamics simulations of finite-temperature phonon spectra further suggest that LaN will undergo ferroelectric and structural transitions from $P1$ to $\mathit{Fm}\overline{3}m$ symmetry, when temperature is increased. Moreover, $P1$-LaN will transform to a tetragonal structure with $P4/\mathit{nmm}$ symmetry at a critical pressure $P=18$ GPa at 0 K. Electronic structures computed with an advanced hybrid functional show that the high-temperature rock-salt LaN can change from a trivial insulator to a strong topological insulator at $P~14$ GPa. Together, our results indicate that when $P=14-18$ GPa, LaN can show simultaneous temperature-induced structural, ferroelectric, and topological transitions. Lanthanum monopnictides thereby provide a rich playground for exploring novel phases and phase transitions driven by temperature and pressure.

我们通过第一性原理计算研究了单氮化镧 LaN。常见的岩盐结构$\mathit{调频}\overline{3}米$发现稀土单核元素的对称性对于 LaN 在零温度下是动态不稳定的。使用密度泛函理论和进化晶体预测，我们发现了一种新的动态稳定结构$磷1$ 在 0 K 处对称。这 $磷1$-LaN 表现出自发电极化。我们对有限温度声子光谱的ab initio分子动力学模拟进一步表明，LaN 将从$磷1$ 到 $\mathit{调频}\overline{3}米$对称性，当温度升高时。此外，$磷1$-LaN 将转变为四方结构 $磷4/\mathit{纳米}$ 临界压力下的对称性 $磷=18$ GPa at 0 K. 使用高级混合函数计算的电子结构表明，高温岩盐 LaN 可以在 $磷~14$GPa。总之，我们的结果表明，当$磷=14——18$GPa、LaN 可以同时显示温度引起的结构、铁电和拓扑转变。因此，镧系元素为探索由温度和压力驱动的新相和相变提供了丰富的游乐场。