Colossal Magnetoresistance using the Small Polaron Picture with Finite   Bandwidth Effects
  We present a small polaron picture and show that finite bandwidth effects are important to understand colossal magnetoresistance. Besides the polaron size parameter, we show that there is another parameter (adiabaticity parameter) that is relevant to studying magnetoresistance. We find that for fixed values of the polaron size parameter an increase in the adiabaticity parameter increases the magnetoresistance. The magnetic transition is studied within a mean field approach. We point out important oversights in the literature. We find that for the reported values of the bandwidth (based on band structure calculations) and for experimentally determined values of activation energy and Debye frequency, the calculated values of the magnetoresistance compare favorably with experimental ones. We calculate the optical conductivity too and find that there is reasonable agreement with experiment. 
Sudhakar Yarlagadda