Calculation of the Phonon Spectrum of PbMnBO4 Crystal Using Density Functional Theory

The phonon dispersion and Raman spectrum of the PbMnBO4 ferromagnetic crystal have been calculated within the density functional theory. Imaginary phonon branches have been observed at the points Y, Z, and CYRILLIC CAPITAL LETTER GHE and along the X-S direction of the Brillouin zone, which indicates structural instability and a possible phase transition with variation in external factors (temperature and pressure). The shapes of vibrations and symmetry types of the normal modes of the crystal at the center of the Brillouin zone have been determined. The calculation results are compared with the experimental and theoretical spectra from other studies. It is shown that the vibrational mode of highest intensity at 692.5 cm(-1) in the spectrum and the mode at 272.3 cm(-1), corresponding to the experimental modes at 690.5 and 224.7 cm(-1), are bending vibrations of oxygen atoms in distorted MnO6 octahedra.