POLARIZATION GRADIENT COEFFICIENTS AND THE DISPERSION SURFACE OF THE SOFT MODE IN PEROVSKITE FERROELECTRICS

The gradient coefficients in the Landau-Ginzburg theory are crucial for quantitative description of domain walls in ferroelectrics. The magnitude of these gradient coefficients are a measure of nonlocal coupling strength of the polarization. In this paper, we intend to explain the physical meaning of these gradient coefficients in terms of lattice dynamics and give some relationships between these gradient coefficients and the dispersion surface of the soft mode. The implications for the study of over damped soft modes are also discussed.