Dynamical response of ferroelectries in terms of a classical anharmonic-oscillator model

The author's earlier work on dynamical response of ferroelectrics [Prog. Theor. Phys. 44 (1970) 1477] is extended to incorporate relaxational response into the anharmonic-oscillator model. Dynamical polarizability of an oscillator in a double-minimum potential inevitably possesses a vanishing imaginary component proportional to iomegadelta(omega) because of the non-ergodicity of its motion. When the oscillator is allowed to hop between the two minima through thermal contact with the reservoir, the above delta-function will acquire a broadening with characteristic hopping frequency. The resulting formula properly describes coexistence of soft modes and relaxational modes. It is thus explicitly shown that the unified model of ferroelectricity covers from the extreme limit of displacive ferroelectrics where only soft modes appear to the other limit of order-disorder ones where only Debye-type relaxation is observed.