Conductivity and isotope effect in the colossal magnetoresistance

The diffusion of nearly localized electrons is considered in the presence o f the spin-dependent and multiple scattering on the randomly oriented and/o r distributed magnetic moments of scatterers. The spin diffusion coefficien t in the case of the exchange interaction between the diffusive but nearly localized electrons is evaluated. It is shown that the electron localizatio n leads to the vanishing of the spin diffusion and hence the ferromagnetic phase transition. The isotope effect in the Curie temperature in the case o f the electron-phonon inelastic relaxation is obtained, as experimentally o bserved in the manganese oxides by Zhao and co-workers.(11) The strong spin -polaron effect caused by the interaction of the diffusive electrons with t he diffusive paramagnons significantly reduces conductivity near the Curie temperature. The temperature dependence of conductivity in the absence and presence of an external magnetic field is discussed as well.