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

Department of Applied Physics, The Hong Kong Polytechnic University - Hung Hom, Kowloon, Hong Kong

Received: 3 September 2012
Accepted: 1 October 2012

Abstract

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.