Intermediate-valence model for the colossal magnetoresistance inTl2Mn2O7

The colossal magnetoresistance exhibited by ${\mathrm{Tl}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ is an interesting phenomenon, as it is very similar to that found in perovskite manganese oxides, although the compound differs both in its crystalline structure and electronic properties from the manganites. At the same time, other pyrochlore compounds, though sharing the same structure with ${\mathrm{Tl}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7,$ do not exhibit the strong coupling between magnetism and transport properties found in this material. Mostly due to the absence of evidence for significant doping into the Mn-O sublattice and the tendency of Tl to form conduction bands, the traditional double-exchange mechanism mentioned in connection with manganites does not seem suitable to explain the experimental results in this case. We propose a model for ${\mathrm{Tl}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7$ consisting of a lattice of intermediate-valence ions fluctuating between two magnetic configurations, representing Mn $3d$ orbitals, hybridized with a conduction band, which we associate with Tl. This model had been proposed originally for the analysis of intermediate-valence Tm compounds. With a simplified treatment of the model we obtain the electronic structure and transport properties of ${\mathrm{Tl}}_2{\mathrm{Mn}}_2{\mathrm{O}}_7,$ with good qualitative agreement with experiments. The presence of a hybridization gap in the density of states seems important to understand the reported Hall data.