  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.
