Lattice dynamics of rare-earth titanates with the structure of pyrochlore R$_2$Ti$_2$O$_7$ (R = Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu): Ab initio calculation

The ab initio calculation has been performed for the crystal structure and the phonon spectrum of titanates with the structure of pyrochlore R$_2$Ti$_2$O$_7$ (R = Gd–Lu). The frequencies and types of fundamental vibrations have been found. For R = Tb, Tm, and Yb, this calculation has been carried out for the first time; furthermore, there is no available information on experimental studies of the phonon spectrum for Tm and Yb. The influence of hydrostatic pressure to 35 GPa on the structure, dynamics, and elastic properties of the Gd$_2$Ti$_2$O$_7$ lattice has been investigated. The dependence of the phonon frequencies on the pressure has been obtained. The calculations have predicted that the relative change in the pyrochlore structure volume during compression at pressures to 35 GPa is well described by the third-order Birch-Murnaghan equation of states. The results of the calculations agree with the available experimental data. It has been shown that the structural, dynamic, and elastic properties of the R$_2$Ti$_2$O$_7$ crystal lattice can be adequately described in the case where the inner shells of the RE ion up to 4$f$ are replaced by the pseudopotential.