First-principles accurate total energy surfaces for polar structural distortions ofBaTiO3,PbTiO3, and

Takeshi Nishimatsu

¹

,

M. Iwamoto²,

Yoshiyuki Kawazoe³

et al.

Abstract

Specific forms of the exchange correlation energy functionals in first-principles density functional theory-based calculations, such as the local density approximation (LDA) and generalized-gradient approximations (GGA), give rise to structural lattice parameters with typical errors of −2 % and 2 %. Due to a strong coupling between structure and polarization, the order parameter of ferroelectric transitions, they result in large errors in estimation of temperature dependent ferroelectric structural transition properties. Here, we employ a recently developed GGA functional of Wu and Cohen [Phys. Rev. B, 73, 235116 (2006)] and determine total-energy surfaces for zone-center distortions of BaTiO3, PbTiO3, and SrTiO3, and compare them with the ones obtained with calculations based on standard LDA and GGA. Confirming that the Wu and Cohen functional allows better estimation of structural properties at 0 K, we determine a new set of parameters defining the effective Hamiltonian for ferroelectric transition in BaTiO3. Using the new set of parameters, we perform molecular-dynamics (MD) simulations under effective pressures p = 0.0 GPa, p = −2.0 GPa, and p = −0.005T GPa. The simulations under p = −0.005T GPa, which is for simulating thermal expansion, show a clear improvement in the cubic to tetragonal transition temperature and c/a parameter of its ferroelectric tetragonal phase, while the description of transitions at lower temperatures to orthorhombic and rhombohedral phases is marginally improved. Our findings augur well for use of Wu-Cohen functional in studies of ferroelectrics at nano-scale, particularly in the form of epitaxial films where the properties depend crucially on the lattice mismatch.

Accuracy of first-principles interatomic interactions and predictions of ferroelectric phase transitions in perovskite oxides: Energy functional and effective Hamiltonian

“…6), which is similar to the dispersion obtained in earlier simulations using WC-GGA-based parameters 7 . The short-range interaction gives the most unstable mode at the X point ( see FIG.…”

“…Instead, an approximate approach is adopted that uses an effective Hamiltonian, which focuses on the low-energy structural configurations in MD or MC simulations 7,8 . Thus, there are two sources of errors in first-principles description of ferroelectric transitions: (a) ones arising from the choice of DFT functional, and (b) ones arising from the truncation of the set of configurations through the effective Hamiltonian.…”

Molecular Dynamics Simulations of Chemically Disordered Ferroelectric (Ba,Sr)TiO3 with a Semi-Empirical Effective Hamiltonian

“…17, we perform first-principles calculations to determine a set of parameters of H eff for SrTiO 3 (See Table I). We averaged the parameters of H eff of BaTiO 3 in Ref.…”

“…We averaged the parameters of H eff of BaTiO 3 in Ref. 17 and those of H eff of SrTiO 3 (See Table I). It is found that this set of parameters indeed reproduces the three transition temperatures of (Ba 1/2 Sr 1/2 )TiO 3 as depicted in Fig.…”

“…Temperaturedependent negative effective pressure p = −0.005T GPa for BaTiO 3 , which was applied in Ref. 17 to mimic thermal expansion, is not applied in present work.…”