Adiabatic and non-adiabatic small-polaron hopping conduction in La_1−xPb_xMnO_3+δ (0.0 ≤ x ≤ 0.5)-type oxides above the metal–semiconductor transition

Above the semiconductor-to-metallic transition (SMT) temperature (T_p), transport properties of the La_1−xPb_xMnO_3+δ (0 ≤ x ≤ 0.5)-type mixed valence oxides with T_p between 230 and 275 K (depending on x) have been thoroughly examined for a small-polaron hopping conduction mechanism of the carriers. Although the variable range hopping (VRH) model was used earlier to fit the entire conductivity data above SMT, we noticed two distinct regions (above and below θ_D/2; θ_D is the Debye temperature) where different types of conduction mechanisms are followed. The high temperature (T > θ_D/2) conductivity data of all the Pb-doped samples follow the adiabatic hopping conduction mechanism, while those of LaMnO₃ (x = 0) showing no SMT follow the non-adiabatic hopping conduction mechanism of Mott or Emin with reasonable values of polaron radius, hopping distance, polaron binding energy, activation energy, etc being different for different systems. The VRH model, however, fits the corresponding low temperature (T < θ_D/2) data of all the samples. Both resistivity ρ(T) and thermoelectric power S(T) follow a similar microscopic theory above T_p supporting the small-polaron hopping mechanism. Thermoelectric power also showed appreciable magnetic field dependence around SMT.