Infrared absorption in oxides in the presence of both large and small polarons

Infrared conductivity in oxides when two types of polaron are present is discussed, and experiments on ${\mathrm{Pr}}_2$ ${\mathrm{NiO}}_{4.22}$ in the ab plane are analyzed in detail. Infrared reflectivity spectra on a crystal of this material between 30 and 20 000 ${\mathrm{cm}}^{\mathrm{-}1}$ have been obtained from 77 K up to room temperature. The low-energy region (up to 1000 ${\mathrm{cm}}^{\mathrm{-}1}$) can be interpreted as phonon spectra screened by a plasmon. Thermal evolution of the screening of phonons shows the semiconducting behavior of this material. Conductivity data obtained from Kramers-Kronig transformations for frequencies between 1000 and 16 000 ${\mathrm{cm}}^{\mathrm{-}1}$ are fitted by a theory involving the simultaneous presence of large and small polarons. Due to expectations of relatively large effects of disorder and of Coulomb interactions on properties of large polarons, one contribution to the absorption, that for which the initial and final state is in the wide (large-polaron) band, is approximated as a Gaussian with adjustable center position and width. The other three contributions, involving at least one of the initial or final states in the narrow (small-polaron) band are treated by modifications of previously published theories for small concentrations of polarons. In all there are seven parameters in the theory. After preliminary fits in which each parameter is treated as adjustable at each temperature, the phonon energy was fixed at 0.064 eV, with the other parameters determined by fitting. The fits are approximately as good as the estimated accuracy of the conductivity data, and the fitted values occur in ranges expected from the theory. Values of parameters associated with small polarons imply a large contribution to binding energies from short-range forces. Combining results for parameters with the conductivity data of Allançon et al. enables estimates to be made of the approximate position of the mobility edge in the wide band and of orders of magnitude of concentrations of mobile carriers. Plasma frequencies are inferred to be very low below room temperature, and highly temperature dependent.