Quantifying Local and Cooperative Components in the Ferroelectric Distortion of BaTiO<sub>3</sub>: Learning from the Off-Center Motion in the MnCl<sub>6</sub><sup>5–</sup> Complex Formed in KCl:Mn<sup>+</sup>
The delicate balance between cooperative and local contributions in the ferroelectric distortions of BaTiO3 is explored by means of ab initio calculations. As a salient feature, it is found that a single Ti4+ ion in BaTiO3 is not allowed to move off-center at ambient pressure, while this is no longer true if the lattice is expanded by only ∼5%, stressing the high sensitivity of the local contribution to chemical and hydrostatic pressures. In order to further understand the effect of local contributions on the phase transition mechanism of ferroelectrics, we have investigated the surprising C3v → C4v → Oh local transformations occurring in the 10–50 K temperature range for the MnCl65– complex formed in KCl:Mn+ that mimic the behavior of BaTiO3. From Boltzmann analysis of the vibronic levels derived from ab initio calculations and considering decoherence introduced by random strains, the present calculations reproduce the experimental phase sequence and transition temperatures. Furthermore, our calculations show that the off-center instability in KCl:Mn+ would be suppressed by reducing by only 1% the lattice parameter, a situation that then becomes comparable to that found for BaTiO3 at ambient pressure. The present results thus stress the deep link between the structural phase transitions of ferroelectric materials and local phase transitions displayed by transition-metal impurities in insulators.