Coexistence of the Phonon and Relaxation Soft Modes in the Terahertz Dielectric Response of Tetragonal BaTiO₃

The dielectric response to infrared waves polarized along the tetragonal axis of a ferroelectric single-domain crystal of BaTiO₃ was determined by time-domain THz spectroscopy and Fourier-transform infrared reflectivity techniques. In addition to the three well-known polar lattice modes, the experiment shows an additional mode of the relaxation type in the THz spectral region, which accounts for the Curie-Weiss behavior of the c-axis dielectric constant. A comparison of experimental results with ab initio based effective-Hamiltonian simulations allows us to elucidate its relation to the order-disorder model of Comes, Lambert, and Guinier [ Solid State Commun. 6 715 (1968)].