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A two-site double exchange model with a single polaron is studied using aperturbation expansion based on the modified Lang-Firsov transformation. Theantiferromagnetic to ferromagnetic transition and the crossover from small tolarge polaron are investigated for different values of the antiferromagneticinteraction ($J$) between the core spins and the hopping ($t$) of the itinerantelectron. Effect of the external magnetic field on the small to large polaroncrossover and on the polaronic kinetic energy are studied. When the magnetictransition and the small to large polaron crossover coincide for some suitablerange of $J/t$, the magnetic field has very pronounced effect on the transport.Comment: REVTEX and ps files, accepted in the European Physical Jour.

Magnetic transition and polaron crossover in a two-site single polaron model including double exchange interaction