Variable-range hopping conductivity in (x = 0.5; y = 0, 0.02, 0.1)

Abstract

The temperature dependences of the resistivity ρ(T) of ceramic samples at x = 0.5, and y = 0, 0.02 and 0.10 are investigated in the temperature range of 5-300 K in magnetic field B up to 1 T. It was found that dependences ρ(T) with x = 0.5; y = 0.02, and 0.10 obey the Shklovskii–Efros-like variable-range hopping conductivity law This behavior is governed by generation of a soft Coulomb gap Δ ≈ 0.3 eV in the density of localized states, as well as a rigid gap ≈ 0.20 and 0.17 eV at y = 0.02 and y = 0.10, respectively. The obtained values of the rigid gap at y = 0.02 indicate the presence of charge ordering. It was shown that a decrease in the width of the rigid gap when y is increased, is accompanied by both a growing disorder attributed to the presence of Fe and a decrease in lattice distortions caused by charge ordering at y = 0.02. It is shown that the pre-exponential factor of resistivity follows the law where m changes from 9/2 at y = 0.02 to 5/2 at y = 0.10. This confirms that doping with Fe enhances microscopic disorder by introducing an additional fluctuating short-range potential. The calculated values of the carrier localization radius α ≈ 5.1 and 2.7 Å at y = 0.02 and y = 0.10, respectively, satisfy the condition for the formation of small polarons.