Spatio-temporal distribution of relative Ti-O₆ displacements in cubic BaTiO₃

BaTiO₃ is often considered a model ferroelectric material in which the dielectric properties are defined by the displacements of Ti ions with respect to surrounding oxygen atoms. However, despite the decades of a dedicated research, certain controversies have remained as to the description of collective movements of the Ti ions. We approached this problem using nonoscale-oriented X-ray scattering methods and large-scale atomistic simulations [1]. Together these allowed us to show that the Ti dynamics can be exhaustively explained by phonons excited on a timescale of picoseconds.

Fig. 1: One component of the relative Ti-O₆ displacement is mapped within one layer of the material using different time averages (a-c) which clearly shows that chain correlations exist on a timescale of picoseconds. The displacements averaged over the simulation time and all unit cells of the crystal have a cuboidal distribution with shallow minima along diagonal directions.

Reference:
[1] M. Paściak, T. R. Welberry, J. Kulda, S. Leoni, and J. Hlinka, Dynamic Displacement Disorder of Cubic BaTiO₃, Phys. Rev. Lett. 120, 167601 (2018).