  The linear magnetoelectric effect was measured in 500 nm Cr2O3 films grown by
rf sputtering on Al2O3 substrates between top and bottom thin film Pt
electrodes. Magnetoelectric susceptibility was measured directly by applying an
AC electric field and measuring the induced AC magnetic moment using
superconducting quantum interference device magnetometry. A linear dependence
of the induced AC magnetic moment on the AC electric field amplitude was found.
The temperature dependence of the magnetoelectric susceptibility agreed
qualitatively and quantitatively with prior measurements of bulk single
crystals, but the characteristic temperatures of the film were lower than those
of single crystals. It was also possible to reverse the sign of the
magnetoelectric susceptibility by reversing the sign of the magnetic field
applied during cooling through the N\'eel temperature. A competition between
total magnetoelectric and Zeeman energies is proposed to explain the difference
between film and bulk Cr2O3 regarding the cooling field dependence of the
magnetoelectric effect.
