  Based on our analytical results [http://arxiv.org/abs/1006.3670], we predict
that undoped nanoparticles (size <10-100nm) of incipient ferroelectrics without
any magnetic ions can become ferromagnetic even at room temperatures due to the
inherent presence of a new type of magnetic defects with spin S=1, namely
oxygen vacancies, where the magnetic triplet state is the ground state in the
vicinity of the surface (magnetic shell), while the nonmagnetic singlet is the
ground state in the bulk material (nonmagnetic core). Consideration of randomly
distributed magnetic spins (S=1) had shown that magnetic properties of
incipient ferroelectric nanoparticles are strongly size and temperature
dependent due to the size and temperature dependence of their dielectric
permittivity and the effective Bohr radius proportional to permittivity. The
phase diagrams in coordinates temperature - particle radius are considered. In
particular, for particle radii less that the critical radius ferromagnetic
long-range order appears in a shell region of thickness 5 - 50 nm once the
concentration of magnetic defects exceeds the magnetic percolation threshold.
The critical radius is calculated in the mean field theory from the condition
of the magnetic defects exchange energy equality to thermal energy. For
particle radii higher than critical value only the paramagnetic phase is
possible. The conditions of the super-paramagnetic state appearance in the
assembly of nanoparticles with narrow distribution function of their sizes are
discussed also.
