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Antiferromagnets are normally thought of as materials with compensatedmagnetic sublattices. This adds to their technological advantages butcomplicates readout of the antiferromagnetic state. We demonstratetheoretically the existence of a Dzyaloshinskii-Moriya interaction (DMI) whichis determined by the magnetic symmetry classes of Cr$_2$O$_3$ surfaces with anin-plane magnetic easy axis. The DMI explains a previously predictedout-of-plane magnetization at the nominally compensated surfaces of chromia,leading to a surface-localized canted ferrimagnetism. This is in agreement withmagnetotransport measurements and with density functional theory predictionswhich further allow us to quantify the strength of DMI. The temperaturedependence of the transversal resistance for these planes shows distinctbehavior in comparison with that of the Cr$_2$O$_3$ $c$ plane, which weattribute to the influence of DMI. Our work provides a framework to analyzesurface-driven phenomena in antiferromagnets, and motivates the use ofnominally compensated chromia surfaces for antiferomagnetic spintronics andmagnonics.

Surface-symmetry-driven Dzyaloshinskii--Moriya interaction and canted ferrimagnetism in collinear magnetoelectric antiferromagnet Cr$_2$O$_3$