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The scaling of antiferromagnetic ordering temperature of corundum-typechromia films have been investigated. N\'eel temperature $T_N$ was determinedfrom the effect of perpendicular exchange-bias on the magnetization of aweakly-coupled adjacent ferromagnet. For a thick-film case, the validity ofdetection is confirmed by a susceptibility measurement. Detection of $T_N$ waspossible down to 1-nm-thin chromia films. The scaling of ordering temperaturewith thickness was studied using different buffering materials, and comparedwith Monte-Carlo simulations. The spin-correlation length and the correspondingcritical exponent were estimated, and they were consistent between experimentaland simulation results. The spin-correlation length is an order of magnitudeless than cubic antiferromagnets. We propose that the difference is from thechange of number of exchange-coupling links in the two crystal systems.

Finite-size scaling effect on N\'eel temperature of antiferromagnetic Cr$_2$O$_3$-(0001) films in an exchange-coupled heterostructure