Electron-phonon coupling in dielectrics

Abstract

The instability of certain vibrational modes in ionic dielectrics such as BaTiO₃ is theoretically studied by taking account of electron-vibration coupling. It is found that the vibronic interactions in the elementary units e.g. Ti-O-Ti or TiO₆ octahedra render the polar modes unstable. This provides a microscopic description of the origin of ferroelectric phase transition. The temperature dependence of the frequency of the soft (the unstable transverse optical) mode is then investigated by considering the collective oscillations of a lattice of such elementary units after including anharmonic interactions. The stabilization of the soft mode, beyond a certain temperature T_c, occurs as a result of fourth order anharmonic interaction involving the acoustic and the transverse optical mode. The temperature dependence of the effective frequency, namely, ω _eff² (transverse optical) α (T-T_c) is similar to the relation found by Silverman. The agreement with available experimental results is satisfactory.