Understanding the High Temperature Thermoelectric Properties of La$_{0.82}$Ba$_{0.18}$CoO$_{3}$ Compound using DFT+U Method

Normally, understanding the temperature dependent transport properties of strongly correlated electron systems remains challenging task due to complex electronic structure and its variations (around E$_{F}$) with temperature. Here, we report the applicability of DFT+U in explaining thermopower ($\alpha$) and electrical conductivity ($\sigma$) in high temperature region. We have measured temperature dependent $\alpha$ and $\sigma$ in the 300-600 K range. The non-monotonic temperature dependent behavior of $\alpha$ and metallic behavior of $\sigma$ were observed. The value of $\alpha$ at 300 K was $\sim$15.80 $\mu$V/K and it decreases upto $\sim$477 K ($\sim$11.6 $\mu$V/K) and it further increases with temperature to the $\sim$14.8 $\mu$V/K at 600 K, whereas the values of $\sigma$ were found to be $\sim$1.42 $\times$10$^{5}$ $\Omega$$^{-1}$ m$^{-1}$ and $\sim$0.20 $\times$10$^{5}$ $\Omega$$^{-1}$ m$^{-1}$ at 300 and 600 K, respectively. Combining the WIEN2k and BoltzTraP code, the electronic structure and temperature dependent transport coefficients were calculated. The ferromagnetic ground state electronic structure with half-metallic character obtained from the DFT+U calculations, U = 3.1 eV, provides better explanation of high-temperature transport behavior. Two current model was used for calculation of $\alpha$ and $\sigma$ where the temperature dependent values of relaxation time ($\tau$), almost linear for up-spin, $\tau$$_{up}$, and non-linear for dn-spin, $\tau$$_{dn}$, were used and estimated values were found to be in good agreement with experimentally reported values.