Unified description of the soft and the relaxational mode in the dielectric response of ferroelectrics

We present a quantum-mechanical calculation of the temperature dependence of the dielectric susceptibility of displacive, order-disorder, and intermediate ferroelectrics. The ferroelectric is modeled as a lattice of coupled quantum-mechanical anharmonic oscillators. The coupling of the oscillators is described in a mean-field approximation. For all ferroelectrics the dielectric response consists of two contributions. The first contribution is formed by the response of the vibrational transitions. This response is calculated using a new equation for the dielectric susceptibility of low-frequency vibrational transitions. The second contribution to the response results from vibrational population transfer between levels with different mean displacements. The coupling of the two dielectric responses via the mean field leads to a rise of a strong low-frequency dielectric response close to the phase-transition temperature.