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Cr$_2$O$_3$ is the archetypal magnetoelectric (ME) material, which has alinear coupling between electric and magnetic polarizations. Quadratic MEeffects are forbidden for the magnetic point group of Cr$_2$O$_3$, due tospace-time inversion symmetry. In Cr$_2$O$_3$ films grown by sputtering, wefind a signature of a quadratic ME effect that is not found in bulk singlecrystals. We use Raman spectroscopy and magetization measurements to deduce theremoval of space-time symmetry, and corroborate the emergence of the quadraticME effect. We propose that meta-stable site-selective trace dopants remove thespace, time, and space-time inversion symmetries from the original magneticpoint group of bulk Cr$_2$O$_3$. We include the quadratic ME effect in a modeldescribing the switching process during ME field cooling, and estimate theeffective quadratic susceptibility value. The quadratic magnetoelectric effectin a uniaxial antiferromagnet is promising for multifunctionalantiferromagnetic and magnetoelectric devices that can incorporate optical,strain-induced, and multiferroic effects.

Quadratic magnetoelectric effect during field cooling in sputter grown Cr$_2$O$_3$ films