Colossal magnetoresistanace using the small polaron picture with finite bandwidth effects

We present a small polaron picture and show that finite bandwidth effects a re important to understand colossal magnetoresistance. Besides the polaron size parameter, we show that there is another parameter (adiabaticity param eter) that is relevant to studying magnetoresistance. We find that for fixe d values of the polaron size parameter an increase in the adiabaticity para meter increases the magnetoresistance. The magnetic transition is studied w ithin a mean-field approach. We point out important oversights in the liter ature. We find that for the reported values of the bandwidth (based on band -structure calculations) and for experimentally determined values of activa tion energy and Debye frequency, the calculated values of the magnetoresist ance compare favorably with experimental ones. We calculate the optical con ductivity too and find that there is reasonable agreement with experiment.