On the terahertz dielectric response of cubic BaTiO3: Coexistence of displacive and order-disorder dynamics

Two distinct modes with frequencies below 150 cm−1 were recently observed in cubic BaTiO3 (Ponomareva I. et al., Phys. Rev. B, 77 (2008) 012102). One of these modes perfectly softens to zero while the other saturates at about 60 cm−1 as the ferroelectric transition is approached. In the present work, we interpret these modes employing two widely recognized elements: nano-size tetragonal precursors forming in the cubic phase and an eight-well potential model for Ti ions due to Comes, Lambert and Guinier (Solid State Commun., 6 (1968) 715). We show that the frequency squared of the saturating mode (SM), which exists in the cubic phase, and that of an E-symmetry mode (EM), which exists in the tetragonal phase, fall on a single curve, ~33 cm−2K−1(T − T*), thereby suggesting connections between the lattice dynamics across the ferroelectric transition. T* is predicted and confirmed to coincide with the tetragonal-orthorhombic transition temperature of 290 K. The perfectly softening mode (PSM) is argued to be associated with the re-orientational motions of tetragonal precursors. The complex dielectric function is calculated without free inputs and the result agrees satisfactorily with measurements. The SM is characterized as a resonant mode, whereas the PSM as a relaxational mode, confirming that both order-disorder and displacive dynamics coexist in cubic BaTiO3.