  Chromium(III) oxide is a classical collinear antiferromagnet with a linear
magnetoelectric effect. We are presenting the measurements of the
magnetoelectric susceptibility $\alpha$ of a sputter-deposited 500-nm film and
a bulk single-crystal of Cr$_\mathrm{2}$O$_\mathrm{3}$. We investigated the
magnetic phase-transition and the critical exponent $\beta$ of the sublattice
magnetization near N\'eel temperature. For the films, an exponent of 0.49(1)
was found below 293 K, and changed to 1.06(4) near the N\'eel temperature of
298 K. For the single-crystal, the exponent was constant at 0.324(4). We
investigated the reversal probability of antiferromagnetic domains during
magnetoelectric field cooling. For the sputtered films, reversal probability
was zero above 298 K and stabilized only below 293 K. We attribute this
behavior to formation of grains during film growth, which gives different
intergrain and intragrain exchange-coupling energies. For the single-crystal,
reversal probability was stabilized immediately at the N\'eel temperature of
307.6 K.
