Optical spectroscopy, x-ray diffraction measurements, density functional theory (DFT), density functional theory + embedded dynamical mean-field theory ($\mathrm{DFT}+eDMFT$), and crystal-field calculations have been used to characterize structural and electronic properties of hexagonal $M_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ $\left(M=\mathrm{Fe},\mathrm{Mn}\right)$ polar magnets. Our experimental data are consistent with the room-temperature structure belonging to the space group $P{6}_{3}mc$ for both compounds. The experimental structural and electronic properties at room temperature are well reproduced within $\mathrm{DFT}+eDMFT$ method, thus establishing its predictive power in the paramagnetic phase. With decreasing temperature, both compounds undergo a magnetic phase transition, and we argue that this transition is concurrent with a structural phase transition (symmetry change from $P{6}_{3}mc$ to $P{6}_3$) in the Fe compound and an isostructural transition (no symmetry change from $P{6}_{3}mc$) in the Mn compound.

中文翻译：

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光谱和第一原理DFT + eDMFT研究M2Mo3O8（M = Fe，Mn）极性磁体的复杂结构，电子和振动特性

光谱学，x射线衍射测量，密度泛函理论（DFT），密度泛函理论+嵌入式动态平均场理论（$\mathrm{DFT}+电子数据交换$），并且晶体场计算已用于表征六方晶的结构和电子性质 ${\mathrm{中号}}_2{莫}_3{\mathrm{Ø}}_8$ $（\mathrm{中号}=铁，锰）$极性磁铁。我们的实验数据与属于空间群的室温结构一致$P{6}_3米C$对于这两种化合物。室温下的实验结构和电子性能在$\mathrm{DFT}+电子数据交换$方法，从而建立其在顺磁阶段的预测能力。随着温度的降低，两种化合物都经历了磁性相变，我们认为这种转变与结构相变同时发生（$P{6}_3米C$ 至 $P{6}_3$铁化合物中的）和等构相变（ $P{6}_3米C$）在Mn化合物中。