Ab initiocalculations of phonons inLiNbO3

Abstract

Using the ab initio method within the local-density approximation with ultrasoft pseudopotentials and plane-wave basis, calculating the Hellmann-Feynman forces and applying the direct method, the phonon-dispersion relations for ferroelectric and paraelectric rhombohedral phases of ${\mathrm{LiNbO}}_{3}$ crystal have been derived. The calculated phonon frequencies for the ferroelectric phase at the $\ensuremath{\Gamma}$ point are compared with Raman, infrared, and neutron-scattering measurements, and they agree very well. The phonon frequencies at the Z, L, and F high-symmetry points are also calculated. It is disclosed that the force constants involving lithium ions are an order of magnitude smaller than the force constants between niobium and oxygen ions. As a consequence, the lithium ions do not contribute to high-frequency optical vibrations. In the paraelectric phase the phonon-dispersion curves show a soft branch with the soft mode of symmetry ${A}_{2u}$ at the $\ensuremath{\Gamma}$ point. This soft mode leads to the observed paraelectric-ferroelectric phase transition. The LO/TO splitting is considered by assuming formal values of ionic charges, and by fitting the longitudinal infrared active modes to the experimental data.