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.

• Received 1 August 2019
• Revised 18 July 2020
• Accepted 25 August 2020

DOI:https://doi.org/10.1103/PhysRevB.102.115139