Inherent piezomagnetic, piezoelectric, linear magnetoelectric effects and built-in fields in nanos

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.