Ferromagnetic transition in the double - exchange model on the pyrochlore lattice

The double-exchange model, which has been extensively studied in the context of colossal magneto-resistance in perovskite manganese oxides, is known to exhibit a ferromagnetic metallic state at low temperatures because of the interplay between localized moments and itinerant electrons through the Hund’s-rule coupling. Here we investigate numerically the ferromagnetic transition in the double-exchange model defined on the frustrated pyrochlore lattice as a simple model for ferromagnetic pyrochlore oxides. We demonstrate that the finite-size corrections are largely reduced by implementing averages over the twisted boundary conditions in the Monte Carlo simulation, which enables to estimate the ferromagnetic transition temperature in relatively small size clusters. The estimate is compared with that for the nonfrustrated cubic lattice system.