Electron-phonon-interaction-driven anharmonic mode-mode coupling in ferroelectrics: The origin of acoustic-mode anomalies

Ferroelectric oxides are modeled by a two-dimensional nonlinear lattice model with harmonic electron-phonon interactions and higher-order density multiphonon terms. This model is solved exactly for arbitrary q in order to study q-dependent anomalies in the phonon dispersion, as observed experimentally in, e.g., SrTiO₃. It is found that the acoustic mode in the 〈11〉 direction flattens anomalously at small q values, and the anomaly becomes more pronounced with decreasing temperature. The origin of this finding can be attributed to highly anharmonic unperiodic oxygen ion displacements which are driven by electron-density multiphonon interactions.