The impurity ion off-center behavior induced by a localized vibronic Frenkel exciton in a soft-mode crystal

The 3d-4p Frenkel exciton localized at a Mn⁴⁺ impurity ion in BaTiO₃ is considered. The electron and hole of this exciton are correlated, degenerate, and involved in the pair Jahn-Teller effect. Such an exciton is characterized by the significant contribution of indirect electron-hole attraction through lattice (in particular, soft) vibrations to the coupling energy, which is comparable with the Coulomb attraction. Thus, the exciton under consideration is both Coulomb and vibronic excitation. The vibronic contribution increases when approaching the point of soft phonon condensation. It is shown that a vibronic Frenkel exciton allows the off-center behavior of an impurity ion, which is significantly enhanced when approaching the point of soft phonon condensation. As a result, the vibronic Frenkel exciton is a low-lying excitation.