We report on the structural and spectroscopic characterization of the multiferroic ${\mathrm{Fe}}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$. Synchrotron x-ray and neutron diffraction as well as thermal expansion measurements reveal a lattice anomaly at $T_{\mathrm{N}}\simeq 60\mathrm{K}$ but do not show any symmetry lowering in the magnetically ordered state. The lattice parameter $c$ exhibits a nonmonotonic behavior with a pronounced minimum around 200 K, which is also reflected in an anomalous behavior of some of the observed infrared-active optical excitations and parallels the onset of short-range magnetic order. The infrared reflectivity spectra measured between 5 and 300 K in the frequency range of $100\text{–}8000{\mathrm{cm}}^{-1}$ reveal most of the expected phonon modes in comparison with the eigenfrequencies obtained by density-functional calculations. The $A_1$ phonons show an overall hardening upon cooling, whereas a nonmonotonic behavior is observed for some of the $E_1$ modes. These modes also show a strongly increased phonon lifetime below $T_{\mathrm{N}}$, which we associate with the quenched direction of the orbital moment in the magnetically ordered state. A similar increase is observed in the lifetime of the higher-lying $d\text{−}d$ excitations of the tetrahedral ${\mathrm{Fe}}^{2+}$ site that become clearly visible below $T_{\mathrm{N}}$ only.

中文翻译：

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Fe2Mo3O8中的结构，声子和轨道自由度

我们报告了多铁性的结构和光谱表征 ${铁}_2{莫}_3{\mathrm{Ø}}_8$。同步加速器的X射线和中子衍射以及热膨胀测量表明在${Ť}_{\mathrm{ñ}}\simeq 60\mathrm{ķ}$但在磁有序状态下不显示任何对称性降低。晶格参数$C$呈现出非单调行为，其最小最小值在200 K附近，这也反映在一些观察到的红外活性光激发的异常行为中，并且与短程磁阶的发生平行。在5-300 K之间的频率范围内测得的红外反射光谱$100\text{–}8000{\mathrm{厘米}}^{-\mathrm{1个}}$与通过密度泛函计算获得的本征频率相比，揭示了大多数预期的声子模式。的${\mathrm{一种}}_{\mathrm{1个}}$ 声子在冷却时显示出整体硬化，而在某些情况下观察到非单调行为 ${Ë}_{\mathrm{1个}}$模式。这些模式还显示，在以下情况下，声子寿命大大增加${Ť}_{\mathrm{ñ}}$，它与处于磁有序状态的轨道矩的淬灭方向相关联。在高处的生命周期中观察到类似的增加$d\text{-}d$ 四面体的激发 ${铁}^{2+}$ 在下面变得清晰可见的网站 ${Ť}_{\mathrm{ñ}}$ 只要。