Calculating the Lattice Dynamics in the RFe3(BO3)4 Crystals in the Quasi-Harmonic Approximation

Abstract

The frequencies of lattice vibrations in the RFe₃(BO₃)₄ (R = Pr, Nd, Tb, Dy, or Ho) crystals in the high-temperature R32 phase and their temperature dependence have been calculated using the quasi-harmonic approximation. It has been found that, at the boundary point Λ of the Brillouin zone, the frequency of the unstable vibration mode the structural phase transition R32 → P3₁21 is related to strong changes with temperature in the TbFe₃(BO₃)₄, DyFe₃(BO₃)₄, and HoFe₃(BO₃)₄ crystals. With increasing temperature, the frequency of the soft mode stabilizes and takes a real value. No significant changes in the phonon spectra, including the boundary point Λ, with increasing temperature for the PrFe₃(BO₃)₄ and NdFe₃(BO₃)₄ crystals have been observed.