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 ${\text{Er}}_2{\text{O}}_3$.

• Received 23 May 2010

DOI:https://doi.org/10.1103/PhysRevB.82.085408