  A two-site double exchange model with a single polaron is studied using a
perturbation expansion based on the modified Lang-Firsov transformation. The
antiferromagnetic to ferromagnetic transition and the crossover from small to
large polaron are investigated for different values of the antiferromagnetic
interaction ($J$) between the core spins and the hopping ($t$) of the itinerant
electron. Effect of the external magnetic field on the small to large polaron
crossover and on the polaronic kinetic energy are studied. When the magnetic
transition and the small to large polaron crossover coincide for some suitable
range of $J/t$, the magnetic field has very pronounced effect on the transport.
