Complete symmetry analyses of the surface-induced piezomagnetic, piezoelectric and linear magnetoelectric effects

The impact of the surface on the magnetic symmetry is studied. It is shown how symmetry breaking transforms the "seeding" 90 bulk magnetic classes, which include 66 piezomagnetic classes and 58 magnetoelectric classes, into the 21 surface-induced magnetic classes, which all are piezomagnetic, piezoelectric and 19 of them are linear magnetoelectric. So, the new piezomagnetic, piezoelectric properties and linear magnetoelectric coupling should appear in nanomaterials, which are absent in the bulk.