Self-Consistent Anharmonic Theory and Its Application to BaTiO3 Crystal

Abstract

Because phase transition is important in solid state physics, numerous attempts have thus far been made to study the nature of phase transitions in magnets, superconductors, ferroelectrics, and so on. For ferroelectrics, both phenomenological and microscopic approaches have been adopted to study phase transitions. Generally, it is considered that at high temperatures, the general phenomenological theory and first-principles calculations appears to be almost mutually exclusive. It is well known that the phenomenological Landau theory of phase transitions can provide a qualitatively correct interpretation of the soft mode of ferroelectrics at the Curie temperature (L.D.Landau & E.M.Lifshitz, 1958); however, this theory cannot explain the mechanism of ferroelectric phase transition. Furthermore, the coefficients of the expansion terms of the Gibbs potential cannot be explained by the essential parameters derived by first-principles calculations. The first principles calculations were performed to determine the adiabatic potential surface of atoms, and the potential parameters were determined to recreate the original adiabatic potential surface. This procedure ensures a highly systematic study of ferroelectric properties without any reference to the experimental values. In order to study the phase transition, Gillis et al. discussed first the instability phenomena in crystals, on the basis of a self-consistent Einstein model (N. S. Gills et al., 1968, 1971). In this model each atom is assumed to perform harmonic oscillation with the frequency which is self-consistently determined from the knowledge of interatomic potential in crystal and the averaged motions of all atoms. The effect of anharmonicity comes in through the selfconsistent equations. T. Matsubara et al. applied this method to a simple one-dimensional model to discuss anharmonic lattice vibration, which is enhanced on and near the surface than in the interior (T. Matsubara & K. Kamiya,1977). On the other hand, the combination of the results derived from first-principles calculations with the effective Hamiltonian method implemented by means of a Monte Carlo simulation (W. Zhong et al.,1995), seems to successfully explain the lattice strain change in BaTiO3 at high temperatures. However, the abovementioned approach cannot explain the behavior of the dielectric property of materials at high temperatures during the phase transitions in the soft mode.