Jahn-Teller effect in the phonon properties of defective SrTiO ₃ from first principles

Using a hybrid density functional theory method combined with linear combination of atomic orbitals basis set and periodic supercell approach, the atomic, electronic structure, and phonon properties were calculated for SrTiO ₃ containing either Fe4 ⁺ substituting host Ti4 ⁺ ions or neutral oxygen vacancies V _o. For both defects, the Jahn-Teller effect occurs, thus reducing the cubic symmetry of a perfect crystal and leading to the appearance of both Raman- and infrared-active vibrational modes. The calculated phonon densities of states and group-theoretical analysis of defect-induced phonon frequencies were used for the interpretation of the relevant experimental data, once defect-induced local modes are identified. The temperature dependence of the V _o formation energy based on the calculated Gibbs free energy was also compared with experiments, and the phonon contribution therein estimated.