Spectroscopic and first principle DFT+eDMFT study of complex structural, electronic, and vibrational properties of M2Mo3O8 ( M=Fe , Mn) polar magnets

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 ${M}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ $(M=\mathrm{Fe},\mathrm{Mn})$ 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.