  We report on the finite size effects in the Verwey transition of stress-free
magnetite Fe3O4 thin films. A limit thickness of 20 nm is evidenced, above
which the transition temperature TV is constant and close to 120 K (bulk value)
and below which no genuine transition is observed. Field Cooled and Zero Field
Cooled measurements evidence irreversibilities for all thicknesses. This
irreversible behavior abruptly disappears around TV for the thicker films, when
the magnetic anisotropy vanishes. These behaviors are interpreted in terms of
assemblies of interacting magnetic Fe3O4 clusters, which are smaller than the
antiphase domains present in the films.
