  The symmetry breaking inevitably present in the vicinity of any surface,
namely an inversion center disappears in surface normal direction and only axes
and planes normal to the surface conserve, gives rise to the spontaneous
piezomagnetic, piezoelectric and magnetoelectric effects in nanosystems, while
the effects can be absent in a bulk material. All these phenomena are inherent
to nanos made of materials belonging to all ninety bulk magnetic classes.
Therefore the new linear magnetoelectrics should appear among nanomaterials,
nonpiezomagnetic and nonpiezoelectric in the bulk. To demonstrate this we
consider the typical cases of ultra-thin films, nanowires and nanospheres.
Coupled with a surface stress for nanoparticles and a mismatch strains for thin
films on substrates the surface piezomagnetic and piezoelectric effects lead to
the appearance of built-in magnetic and electric fields respectively. The
built-in fields play an important role in the appearance of self-magnetization
and self-polarization in the nanosystems paramagnetic and paraelectric in the
bulk and can lead to the appearance of some other interesting properties absent
in the bulk. We obtained analytical dependencies on sizes for the built-in
fields and magnetoelectric coupling coefficients. The values of the built-in
fields increase with the decrease of film thickness h or nanoparticles radii R
as ~1/h or 1/R2 respectively, while the magnetoelectric coupling is inversely
proportional to the sizes in both cases. This shows the strong influence of
sizes on the considered properties of nanos and so opens the ways to govern the
properties by the choice of the sizes and to create new multifunctional
nanomaterials.
