The Small Polaron Problem with an Application to Optical and DC Data of Reduced Barium Titanate

Reflectivity data from 1 to 12 μm for four samples of reduced BaTiO3 with dc conductivities between 20 and 240 (Ωcm)−1 are analysed in terms of small a polaron theory. Quantitative agreement between theory and experiment is found except for the sample with the highest conductivity. By fitting the optical data it is found that the parameters of the theory the average frequency of the optical phonons, Ω0, and the number η of phonons in the polarization cloud, have the values Ω0 = 1.265 × 1014 s−1 and η = 7. These parameters also determine the temperature dependence of the dc mobility. A weak temperature dependence of the mobility is found theoretically and is in agreement with the experimental data.