Intrinsic local symmetry breaking in nominally cubic paraelectric BaTiO3

Whereas at low-temperatures ferroelectrics have a well understood ordered spatial dipole arrangement, the fate of these dipole configurations in the higher temperature paraelectric (PE) phase remains poorly understood. Using density functional theory (DFT), we find that, unlike the case in nonpolar $AB{\mathrm{O}}_{3}$, perovskites such as cubic $\mathrm{BaZr}{\mathrm{O}}_{3}$ that do not lower their energy by any form of positional symmetry breaking, the origin of distribution of the $B$-site off-centering in cubic PE such as $\mathrm{BaTi}{\mathrm{O}}_{3}$ is an intrinsic, energy lowering due to symmetry breaking. Minimizing the internal energy ${E}_{0}$ of a constrained cubic phase represented by a large enough supercell to accommodate symmetry breaking already reveals the presence of a distribution of local displacements (i.e., a polymorphous network) that (i) locally mimics the symmetries of the low temperature phases, while (ii) being the precursors of what finite temperature density functional theory (DFT) molecular dynamics (MD) finds as thermal motifs when equilibrating the free energy ${E}_{0}\ensuremath{-}TS$. Analyzing the DFT-derived configurations of the PE cubic supercell by projecting its displacements onto irreducible representations reveals that it is best described as a temperature-dependent superposition of numerous modes, including ferroelectric $({{\mathrm{\ensuremath{\Gamma}}}_{4}}^{--})$ and antiferroelectric (${{M}_{2}}^{--}$ and ${{X}_{5}}^{+}$), rather than a single mode, (e.g., ${{X}_{5}}^{+}$) representing a well-defined long-range ordered configuration. This suggests that the electronic and dielectric properties of such PE phases are best calculated from a polymorphous distribution of interrelated local motifs in large supercells rather than from either purely disordered or long-range ordered models. In this respect, PE phases share a common feature with paramagnetic (PM) and paraelastic (PEL) perovskite phases whose central feature is a polymorphous distribution of local motifs---dipole moments in PE, magnetic moments in PM, and ordinary octahedral distortion modes in PEL---all computable by DFT supercells and useable in calculating electronic and magnetic properties of paraphases.