Phase Diagram of Modulated Structures in Ferroelectric Crystals Based on Quantum Ising Model with Third-Neighbor Interactions

Abstract

Incommensurate–commensurate phase transitions are analyzed using a model derived from the normal coordinate Hamiltonian for a crystal lattice. The Hamiltonian consists of a local self-potential and effective third-neighbor interactions. Free energies of various modulated phases are calculated with a mean-field approximation under the condition that two quantum states within the local potential are important at low temperature. It is demonstrated that the quantum effect works to stabilize the incommensurate phase rather than the commensurate phase. Even at zero temperature, the incommensurate phase can occupy a finite region in the phase diagram. This situation is similar to quantum paraelectricity in some ferroelectrics, and can be expected as a general feature of modulated structures of dielectric crystals. The phase diagram for ferroic first- and third-neighbor interactions but antiferroic second-neighbor interactions is constructed theoretically and is discussed in detail to explain qualitatively the l...