Effect of a Rare-Earth Ion on the Structural Instability in RFe3(BO3)4 Crystals

The dynamics of the crystal lattice of RFe3(BO3)4 (R = Pr, Nd, Sm, Gd, Tb, Dy, and Ho) compounds in the high-symmetry R32 phase has been calculated. Significant changes in spectra of compounds with various rare-earth ions have been obtained only near the edge Λ point of the Brillouin zone (qΛ = 1/3(−2b1 + b2 + b3, where b1, b2, and b3 are the reciprocal lattice vectors) for acoustic oscillation branches. A decrease in the frequency of an acoustic mode at the point Λ has been revealed in all studied compounds. This frequency depends on the type of rare-earth ion and decreases from a compound with Pr to a compound with Ho down to imaginary values. Such a behavior of the frequency of the unstable acoustic mode is in good agreement with experimental data on the dependence of the temperature of the R32 → P3121 structural phase transition on the type of rare-earth ion in ferroborates.