Variable-range hopping of small polarons in mixed-valence manganites

Mixed-valence manganites Ln(1-x)A(x)MnO(3) exhibit complicated transport behaviour resulting from complex interplays among charge, spin and lattice. In the paramagnetic phase, the carriers are trapped in localized states as small polarons due to the incorporation of three different localization features: ii) strong electron-phonon interaction, (ii) the variations in the Coulomb potential due to the presence of Ln(3+) and A(2+) ions in the lattice, (iii) the magnetic localization due to spin disorder on the interatomic scale. When the thermal energy is not enough for small polarons to hop between nearest-neighbour sites, the transport of small polarons could be accomplished by two steps: first, the small polaron is thermally activated into an intermediate stare in which the carrier is weakly localized; then it feels the potential fluctuation due to an electrical and magnetic disorder and transports by variable-range hopping. We term this kind of transport process as variable-range hopping of small polarons, and derive the expression of resistivity as rho = BT exp[E-a/kT + (T-0/T)(1/4)].