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Spectroscopic and first principle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>DFT</mml:mi><mml:mo>+</mml:mo><mml:mo>eDMFT</mml:mo></mml:mrow></mml:math> study of complex structural, electronic, and vibrational properties of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Mo</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>8</…
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 …