Using symmetry theory we explore how symmetry breaking inevitably present in the vicinity of any surface gives rise to spontaneous surface piezomagnetic, piezoelectric, and magnetoelectric effects. The large surface-to-volume ratio makes the surface symmetry effects dominant in small enough nanosystems. As a result piezomagnetism, piezoelectricity, and strong size-dependent linear magnetoelectric coupling are predicted in nanomaterials, which are nonpiezomagnetic and/or nonpiezoelectric in the bulk, but belong to the one of the existing 90 bulk magnetic classes, e.g., among a wide class of cubic binary oxides such as MnO, FeO, CoO, NiO, EuO, PrO, and Er2O3.
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