First-principles modeling of structural and electronic properties in ferroelectric compounds

We present applications of density-functional theory to ferroelectric systems. We investigate the ground-state structure and dynamical properties of SrTiO₃, as well as the perturbed ferroelectric and piezoelectric properties of ferroelectrics with a broken inversion symmetry. We also develop a formalism, within the framework of density-functional perturbation theory, to study the effect of an applied static homogeneous electric field on the structure and polarization of polar insulators.; With a classical treatment of the ionic positions, we investigate the ferroelectric (FE) and anti-ferrodistortive (AFD) structural instabilities in the tetragonal phase of SrTiO₃. Phonon frequency anisotropies of the AFD modes, and of the polarized FE modes in the AFD state, are calculated and yield good agreement with experiment. Contributions to the FE instabilities and the anisotropy from different structural distortions are identified.; The effects of compositionally broken inversion symmetry on FE instabilities are explored in double-cell (AA′)( BB′)O₃ and triple-cell ( AA′A″) BO₃ and A(BB ′B″)O₃ perovskite structures. In these systems, different cation layers alternate along the FE direction. While isovalent cation substitutions are strong enough to permit self-poling of the material, heterovalent substitutions result in an enormously stronger symmetry breaking that destroys the double-well energy landscape. In model systems Ba(Ti − δ,Ti, Ti + δ)O₃ and (Ba,Sr)(Ti − δ,Ti + δ)O₃, where δ is a composition parameter that can be continuously tuned between 0 and 1, the leading term of the strength of symmetry breaking is found to scale with δ 3 and δ, respectively. Effects of the symmetry breaking on piezoelectric coefficients are studied in detail.; We consider the thermodynamic potentials E(R, η, $E$) and F(R, η, P), whose minimization with respect to the internal structural parameters R and unit cell strain η yields the equilibrium structure at fixed electric field $E$ and polarization P, respectively. First-order expansion of E(R, η, $E$) in $E$ leads to a useful approximation in which F( P) can be obtained by simply minimizing the zero-field internal energy with respect to structural coordinates subject to the constraint of a fixed spontaneous polarization P. To illustrate the formalism, we study effects of the applied electric field on structural response, linear and non-linear dielectric response, and field-induced phase transition in ferroelectric systems.