Variable-Range Hopping of Spin Polarons: Magnetoresistance in a Modified   Mott Regime
  We analize electrical conductivity controlled by hopping of bound spin polarons in disordered solids with wide distributions of electron energies and polaron shifts (barriers). By means of percolation theory and Monte Carlo simulations we have shown that in such materials at low temperatures, when hopping occurs in the vicinity of the Fermi level, a hard polaron gap does not manifest itself in the transport properties. This happens because as temperature decreases the hopping polaron trades the decreasing electron and polaron barriers for increasing hopping distance. As a result, in the absence of the Coulomb correlation effects, in this variable-range variable-barrier hopping regime, the electrical resistivity as a function of temperature obeys a non-activation law, which differs from the standard Mott law. 
M. Foygel, R. D. Morris, and A. G. Petukhov