Calculations of the lattice dynamics and spontaneous polarization for thin ferroelectric films of disordered solid solutions PbB′_1/2 B″_1/2O₃ (B′ = Sc, Ga, In, Lu; B″ = Nb, Ta)

Abstract

The lattice dynamics and spontaneous polarization in thin ferroelectric films of disordered solid solutions PbB′_1/2 B″_1/2 O₃ (B′ = Sc, Ga, In, Lu; B″ = Nb, Ta) are calculated in terms of the generalized Gordon-Kim model. It is found that all the compounds under investigation contain an unstable polar mode, the frequencies of this mode for all the compounds are close in magnitude, and the eigenvectors of the soft polar mode are different in character for different types of surfaces (PbO and 〈B〉O₂, where 〈B〉 is the average ion in the virtual crystal approximation). The frequency of the soft polar mode, the dynamic Born charges, and the rf permittivity are calculated as functions of the film thickness. It is demonstrated that, as the film thickness increases, all the above quantities tend to corresponding values for the bulk compound. The spontaneous polarization of the monoclinic phase distorted along the eigenvector of the soft mode is calculated as a function of the film thickness and in individual layers of the film for different types of surfaces.