Phonons in the cubic phase of Co₃B₇O₁₃X (X=Cl, Br, and I) boracites

The phonon structure in the cubic paraelectric phase (F4̅ 3c) of Co₃B₇O₁₃X (X=Cl,Br,I) boracites has been studied theoretically by density-functional theory and experimentally by Raman spectroscopy. The calculated Raman frequencies are in good agreement with those determined from the polarized Raman spectra. In addition to the four Raman-allowed phonons of A₁ symmetry, a low-frequency broadband of same symmetry is observed in the spectra of Co₃B₇O₁₃Cl and Co₃B₇O₁₃Br. The position and width of this band correspond to those of the partial phonon density of states of the halogen vibrations: an indication for disorder and instability of the halogen sublattice. In the case of Co₃B₇O₁₃I, an even greater number of spectral features reflecting the underlying phonon density of states are observed. An “instability” F₂ mode that involves displacements of the X atoms along ⟨111⟩ and of the Co atoms along ⟨100⟩ directions is also identified. It is shown that this mode is closely related to the halogen and metal sublattice instabilities, which trigger the cubic to orthorhombic transition at lower temperature.