  In ferromagnetic thin films, the Curie temperature variation with the
thickness is always considered as continuous when the thickness is varied from
$n$ to $n+1$ atomic planes. We show that it is not the case for Fe in Fe/Ir
superlattices. For an integer number of atomic planes, a unique magnetic
transition is observed by susceptibility measurements, whereas two magnetic
transitions are observed for fractional numbers of planes. This behavior is
attributed to successive transitions of areas with $n$ and $n+1$ atomic planes,
for which the $T_c$'s are not the same. Indeed, the magnetic correlation length
is presumably shorter than the average size of the terraces. Monte carlo
simulations are performed to support this explanation.
