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The linear magnetoelectric effect was measured in 500-nm Cr2O3 films grown by radio frequency sputtering on Al2O3 substrates between top and bottom thin film Pt electrodes. Magnetoelectric susceptibility was measured directly by applying an alternating current (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 Néel 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. [ABSTRACT FROM AUTHOR]