  We have studied the growth of Fe3O4 (111) epitaxial films on Al2O3 (001)
substrates using a pulsed laser deposition / thermal reduction cycle using an
{\alpha}-Fe2O3 target. While direct deposition onto the Al2O3 (001) substrates
results in an {\alpha}-Fe2O3 epilayer, deposition on the Fe3O4 (111) surface
results in a {\gamma}-Fe2O3 epilayer. The kinetics of the transitions between
Fe2O3 and Fe3O4 were studied by measuring the time constants of the
transitions. The transition from {\alpha}-Fe2O3 to Fe3O4 via thermal reduction
turns out to be very slow, due to the high activation energy. Despite the
significant grain boundaries due to the mismatch between the unit cells of the
film and the substrate, the Fe3O4 (111) films grown from deposition/thermal
reduction show high crystallinity.
