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

Abstract

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: (i) 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 state 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 ρ = BT exp[E a /kT + (T 0 /T )

On conduction mechanism in paramagnetic phase of Gd based manganites

“…In the case of small polarons (deeply trapped electrons), the thermal energy is not sufficient to overcome the deep potential well and to hop out of its site. Then the hopping is possible by a multiphonon assisted process (Sun et al 2000). That is, the electron is activated to an intermediate state first, which is still a localized state with higher energy.…”

“…At the same time, Mott and Davies used the variable range hopping mechanism (VRH) for the whole temperature range (Mott 1990;Mott and Davies 1971). Coey et al (1999) and Sun et al (2000) used VRH in a temperature interval T C < T < T D /2 and small polaron hopping mechanism for temperature T > T D /2, where T D is the Debye temperature. The small polaron hopping mechanism appears to be most suited to manganites with smaller ionic radii rare earth ions because small polarons result from the structural distortions because of the lower ionic radii.…”

Small polaron hopping in spinel manganates

“…Generally, the use of VRH models in manganese oxides is quite widely accepted. [37][38][39][40] A problem with the application of a VRH model to NiMn 2 O 4+␦ is the fact that the scaling factor a needs to be estimated to calculate g͑ ͒, or vice versa. A theoretical study would be useful to calculate a in spinel manganates; the calculation or measurement of both, a and g͑ ͒, would allow even better in-depth analysis.…”

Insulator-to-metal transition in(R,Ca)VO3

“…By using T 0 and a reasonable value for ␣ of 0.2 Å −1 ͑␣ −1 is the decay rate of the wave function associated with the charge carriers and is commonly of the order of ϳ5 Å in transition metal oxides, corresponding in our case to the approximate distance between next-nearest-neighbor V atoms͒, [28][29][30][31] N͑E F ͒ can be extracted. As expected, N͑E F ͒ rapidly increases with doping ͑Tables I and III͒.…”