Nonlinear electronic polarizations and anharmonic phonon couplings in ferroelectric perovskite compounds

Based on the least action principle, we use first-principles calculations to analyze continuous switching paths of the ferroelectric modes in ferroelectric perovskite compounds at zero macroscopic electric field. We find that the posteriori linearity of the polarization as a function of the ferroelectric mode is followed in BaTiO3 while it fails in PbTiO3. The nonlinearity of the polarization reflects the direction change of the ferroelectric mode. Such direction changes in both ferroelectric and cubic cells arise from the anharmonic coupling of the optical phonons, which is described by the sum of the eigenvectors of the soft Γ15 mode and two high-frequency Γ15 modes. The anharmonic coupling of the phonon modes contributes to the nonlinearity of polarization, especially the nonlinearity of the electronic part of the polarization. The uncovering approach of continuous switching paths is expected to provide a deep understanding of the polarization switching process and ferroelectric phase transitions.