Electronic and optical properties of BaTiO₃ across tetragonal to cubic phase transition: An experimental and theoretical investigation

Temperature dependent diffuse reflectance spectroscopy measurements were carried out on polycrystalline samples of BaTiO₃ across the tetragonal to cubic structural phase transition temperature (T_P). The values of various optical parameters such as band gap (E_g), Urbach energy (E_u), and Urbach focus (E₀) were estimated in the temperature range of 300 K to 480 K. It was observed that with increasing temperature, E_g decreases and shows a sharp anomaly at T_P. First principle studies were employed in order to understand the observed change in E_g due to the structural phase transition. Near T_P, there exist two values of E₀, suggesting the presence of electronic heterogeneity. Further, near T_P, E_u shows metastability, i.e., the value of E_u at temperature T is not constant but is a function of time (t). Interestingly, it is observed that the ratio of E_{u (t=0)}/E_{u (t = tm)}, almost remains constant at 300 K (pure tetragonal phase) and at 450 K (pure cubic phase), whereas this ratio decreases close to the transition temperature, which confirms the presence of electronic metastability in the pure BaTiO₃. The time dependence of E_u, which also shows an influence of the observed metastability can be fitted with the stretched exponential function, suggesting the presence of a dynamic heterogeneous electronic disorder in the sample across T_P. First principle studies suggest that the observed phase coexistence may be due to a very small difference between the total cohesive energy of the tetragonal and the cubic structure of BaTiO₃. The present work implies that the optical studies may be a sensitive probe of disorder/heterogeneity in the sample.