Multiple instabilities inBi4Ti3O12: A ferroelectric beyond the soft-mode paradigm

The Aurivillius compound ${\mathrm{Bi}}_4{\mathrm{Ti}}_3{\mathrm{O}}_{12}$ exhibits a single phase transition from a tetragonal high-temperature phase to a ferroelectric state. By means of first-principles calculations guided by a complete symmetry analysis of the experimental distortion, we confirm $B1a1$ as the (monoclinic) symmetry of the room-temperature phase but show that the transition involves a complex interplay of six different normal modes belonging to four different irreducible representations. Three of them are necessary for the observed symmetry break. We do not find any feature in the energy landscape that would force the simultaneous condensation of these three order parameters and cause such an avalanche transition, so we suggest that further experimental work might be able to detect intermediate phases. On the other hand, the necessary condensation of pairs of normal modes of the same symmetry already puts ${\mathrm{Bi}}_4{\mathrm{Ti}}_3{\mathrm{O}}_{12}$ outside the standard soft-mode paradigm and has important structural implications. In particular, the approximate rigidity of the $\mathrm{Bi}{\mathrm{O}}_6$ octahedra is due to anharmonic couplings of these modes. In addition, a comparison of the energy calculations and the behavior of the bond-valence global instability index is presented.