Possible Mechanisms of Defects-Induced Ferromagnetic Order Near the Surface

5 Possible Mechanisms of Defects-Induced Ferromagnetic Order Near the Surface 

In this section, we discuss semi-quantitatively the possible mechanisms of ferromagnetic ordering in the defects ensemble near the surface. 

4 True Nanoferroics with the Properties Absent in Corresponding Bulk Samples 

It is seen from the table that for the small effective mass p, = 0.1 and 82 3 corresponding critical percolation concentrations and are quite reasonable (less than 1 %, which is less than 10 cm (3D case) or 10 cm (2D case)), while for the case p = 1 m . they may be very high (more than 20 % for 82 = 3 and more that 5 % for 82 = 10). Note, that in accordance with the results of Volnianska and Boguslawski [31] and Osorio-Guillen et al. [50] from the first principles calculations, the concentration of Ca vacancies in CaO percolation threshold is 4.9 % that agrees qualitatively with = 5.18 % in Table 4.1. We hope that for the values 82 and p characteristic for CaO the agreement could be better. 

The percolation critical concentration of surface defects is always several times higher that the bulk one as anticipated from the percolation theory [49]. Fortunately the concentration of defects at the surface may be much higher than far from it. We can estimate the increase of the vacancies concentration at the surface in comparison with a bulk of material using the results of the density functional calculations 

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