Small polaron hopping in spinel manganates

The temperature dependence of small polaron hopping conduction in ceramic spinel NiMn2O4+ thermistor material has been investigated. We used a theoretical framework based on a random resistor network model to describe small polaron nearest-neighbor hopping NNH and variable range hopping VRH , following the principles of Shklovskii and Efros. We find that in printed thick films and in pressed pellets resistivity is described best by a VRH model of the form T2p exp T0 /T p, whereas in thin NiMn2O4+ films resistivity is better described by NNH, T exp T0 /T . Steady state dc resistance vs temperature measurements for NiMn2O4+ thick films, thin films, and pellets have been carried out and the parameters p and T0 determined. For thick films p was found to be 0.5, indicating VRH with an approximately parabolic distribution of the density of states DOS around Fermi level. For pellets p was 0.65, and in thin films 1 indicating NNH. The increase of p was interpreted as an increase of disorder in the system, leading to strong electron localization effects and narrowing Mn3+/Mn4+ bandwidth. In thick films and pellets the DOS was determined by a parametrization related to the p value, giving 1020–1021 eV−1 cm−3. The characteristic temperature T0 was in the range of 2 105 K in thick films, 3 104 K in pellets, and 5 103 K in thin films.