The effect of particle size on the transport properties (resistivity and thermopower) of La0.5Pb0.5MnO3 has been investigated both in the presence and in the absence of magnetic field B=0.0–1.5 T (maximum). Grain size, dc conductivity; and the metal–insulator transition temperature Tp of the sample increase with increasing annealing time. Grain size has, however, comparatively little effect on the Seebeck coefficient S. Magnetoresistance is higher for the samples with smaller grain sizes. dc magnetic susceptibility also increases with increasing grain size. High temperature (T>θD/2) resistivity data well fit the small polaron hopping model. Polaron hopping energy WH decreases but polaron radius rp increases with the increase of grain size. In the metallic regime (for T<Tp), resistivity data fit well with ρ=ρ0+ρ2.5 T2.5 and the transport mechanism is attributed mainly to the magnon-carrier scattering (∼T2.5). In all the samples with different grain sizes, S changes sign below Tp. In contrast to magnetoresistance, application of magnetic field increases S at low temperature (T<Tp) for these samples. Thermopower data in the metallic phase (both for B=0.0 and 1.5 T) can be analyzed by considering a spin-wave fluctuation term (∼T4) in addition to the magnon-scattering term similar to the case of resistivity data. Although the variable range hopping mechanism is supported from the resistivity data (for Tp>T>θD/2), it is hard to justify this model from the temperature dependent thermopower data.
Banerjee, A., Pal, S., Bhattacharya, S., Chaudhuri, BK., & Yang, HD. (2002). Particle size and magnetic field dependent resistivity and thermoelectric power of La0.5Pb0.5MnO3 above and below metal-insulator transition. Journal of Applied Physics, 91(8), . https://doi.org/10.1063/1.1459618