  The scaling of antiferromagnetic ordering temperature of corundum-type
chromia films have been investigated. N\'eel temperature $T_N$ was determined
from the effect of perpendicular exchange-bias on the magnetization of a
weakly-coupled adjacent ferromagnet. For a thick-film case, the validity of
detection is confirmed by a susceptibility measurement. Detection of $T_N$ was
possible down to 1-nm-thin chromia films. The scaling of ordering temperature
with thickness was studied using different buffering materials, and compared
with Monte-Carlo simulations. The spin-correlation length and the corresponding
critical exponent were estimated, and they were consistent between experimental
and simulation results. The spin-correlation length is an order of magnitude
less than cubic antiferromagnets. We propose that the difference is from the
change of number of exchange-coupling links in the two crystal systems.
