Local symmetry breaking in different phases of BaTiO₃

Macroscopically, the different phases of BaTiO₃ have been generally understood by considering an averaged structure with the ordered local dipole or without the local dipole. However, microscopically, the local dipole configurations (LDC) in different phases remain poorly understood except for the ground state BaTiO₃. Experimental local probes, e.g., pair distribution function (PDF), and frequency-dependent structure factor S(q,w), as well as density functional theory (DFT) calculations[1] reveal that the LDC in their averaged crystal structures, especially in cubic, does not describe well the system. Here, using DFT including in finite T Molecular Dynamics and minimizing the energy (E=U-TS) in supercells, we find the existence of LDC in all the phases of BaTiO₃ before & after temperature sets in. Except for ground state BaTiO₃, the calculated and measured LDC in different phases differentiates from the ordered LDC or no LDC from their averaged structures. Further direct comparisons between the calculated PDF and S(q,w) based on the DFT minimized structures and the experimental measured PDF and S(q, w) confirm that local symmetry breaking due to LDC in different phases of BaTiO₃. Our work bridges the theoretical simulation to the experimentally local measurement.