Temperature dependence of Ti 1s near-edge spectra in Ti-based perovskites: theory and experiment

Ti 1s near-edge spectra (around 4970~eV) in SrTiO$_3$ and PbTiO$_3$ reveal electric-dipole and quadrupole transitions to Ti 3d, 4p and mixed 3d-4p states. Crystal field-split “pre-edge” features attributed to 1s$\rightarrow$3d transitions are small compared to the main “edge jump” at the onset of the Ti 4s/4p continuum. Pre-edge and subsequent near-edge features are predicted to be weaker than what is observed, unless one accounts for ferroelectric polarization in PbTiO$_3$ and thermal motion in both compounds. Using density-functional theory molecular dynamics simulations at various temperatures (including sampling two phases of PbTiO$_3$), we capture the statistically averaged root-mean-square deviations of Ti$^{4+}$ ions from the centers of their oxygen cages. By sampling appropriate snapshots of atomic configurations and averaging Ti 1s absorption spectra computed within a Bethe-Salpeter Equation framework, we obtain absorption spectra that agree well with experiment~[ R.V. Vedrinskii et al., J. Phys. IV France 7, C2-107 (1997), J.C. Woicik et al., Phys. Rev. B 75, 140103(R) (2007)], including details related to ferroelectric polarization, phase transitions, and fluctuations of atomic coordinates.