Structure and lattice dynamics of rare-earth ferroborate crystals: Ab initio calculation

The ab initio calculation of the crystal structure and the phonon spectrum of crystals $R$Fe$_{3}$(BO$_{3}$)$_{4}$ ($R$ = Pr, Nd, Sm) has been performed in the framework of the density functional theory. The ion coordinates in the unit cell, the lattice parameters, the frequencies and the types of fundamental vibrations, and also the intensities of lines in the Raman spectrum and infrared reflection spectra have been found. The elastic constants of the crystals have been calculated. For low-frequency $A_{2}$ mode in PrFe$_{3}$(BO$_{3}$)$_{4}$, a “seed” vibration frequency that strongly interacts with the electronic excitation on a praseodymium ion was found. The calculation results satisfactory agree with the experimental data.