First-principles accurate total energy surfaces for polar structural distortions of BaTiO 3 , PbTiO 3 , and SrTiO 3 : Consequences for structural transition temperatures

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 $\ensuremath{-}2\mathrm{%}$ 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 ${\text{BaTiO}}_{3}$, ${\text{PbTiO}}_{3}$, and ${\text{SrTiO}}_{3}$ 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 set of parameters defining the effective Hamiltonian for ferroelectric transition in ${\text{BaTiO}}_{3}$. Using the new set of parameters, we perform molecular-dynamics simulations under effective pressures $p=0.0\text{ }\text{GPa}$, $p=\ensuremath{-}2.0\text{ }\text{GPa}$, and $p=\ensuremath{-}0.005T\text{ }\text{GPa}$. The simulations under $p=\ensuremath{-}0.005T\text{ }\text{GPa}$, 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 nanoscale, particularly in the form of epitaxial films where the properties depend crucially on the lattice mismatch.