Phase Transition of Perovskite-Type Ferroelectrics

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Abstract
Using the Hartree and time-dependent Hartree approximations, static and dynamic properties of a model for a perovskite-type ferroelectric near its transition temperature are calculated. In this model only one ion per unit cell is treated dynamically. The influence of the rigid frame of the other ions is idealized by an essentially anharmonic single-particle potential. The ions in different cells interact via the dipole-dipole force plus a repulsive force of shorter range. This model gives a phase transition of second order. The temperature dependence of the "soft" modes, of the Debye-Waller factor, of the displacement correlation functions, and of the specific heat is calculated, and the connection with static properties, such as the Curie constants, is established. The critical transverse modes are split in the presence of the spontaneous or an externally induced polarization. Finally, the model and the results are discussed.