Microscopic calculations of ferroelectric instability in perovskite crystals

First-principles calculations are performed relating to the stability of a series of perovskite crystals with respect to transition to the ferroelectric and the antiferroelectric state. The calculations employ the generalized Gordon-Kim method, in which the total charge density of an ionic crystal is represented as a superposition of the densities of the individual ions. In the spirit of the nonequilibrium thermodynamics of Leontovich the charge density of an individual ion is calculated in the presence of external auxiliary fields which deform this density. Multipole deformations up to quadrupole are taken into account. The actual magnitude of the deformation is found by minimizing the total energy of the crystal in the Thomas-Fermi-Dirac approximation. The calculated values of the ion shifts in the ferroelectric phase for BaTiO₃, and also the electron contribution to the dielectric constant ε _∞ and the dynamic Born effective charges Z ^eff are found to be in good agreement with the experimental data. The proposed method allows one to obtain an analytical expression for ε _∞, Z ^eff, and the dynamic vibration matrix. It is shown that these expressions formally coincide with the expressions arising in the phenomenological models of the polarized and deformed ion. Analysis of the expressions obtained confirms the validity of the classical theory of ferroelectrics of displacement type for perovskite crystals. Zh. éksp. Teor. Fiz. 114, 333–358 (July 1998)