Using the quantum-mechanical approach combined with the image charge method, the lowest energy levels of the impurities and neutral vacancies with two electrons or holes located in the vicinity of flat surface of different solids were calculated. It was unexpectedly found that the magnetic triplet state was the ground state of the impurities and neutral vacancies in the vicinity of surface, while the non-magnetic singlet was the ground state in the bulk for He atoms, Li+, Be2+ ions, etc. The energy difference between the lowest triplet and singlet states depended strongly upon the electron (hole) effective mass μ, dielectric permittivity of the solid ε2 and the distance from the surface z0. For z0=0 and defect charge ∣Z∣=2 the energy difference was more than several hundreds of K at μ=(0.5−1)me and ε2=2–10, more than several tens of K at μ=(0.1−0.2)me and ε2=5–10, and not more than several K at μ<0.1me and ε2>15 (me was the mass of a free electron). Pair interaction of the identical surface defects (two doubly charged impurities or vacancies with two electrons or holes) revealed the ferromagnetic spin state with the maximal exchange energy at the definite distance between the defects (∼5–25nm). Estimates were made of the critical concentration of surface defects and transition temperature of ferromagnetic long-range order appearance in the framework of percolation and mean field theories, and the RKKY approach for semiconductors like ZnO. It was found that the non-magnetic singlet state was the lowest one for a molecule with two electrons formed by a pair of identical surface impurities (like surface hydrogen), while its next state with deep enough negative energy minimum was the magnetic triplet. The metastable magnetic triplet state appeared for such molecule at the surface indicated the possibility of metastable ortho-states of the hydrogen-like molecules, while they were absent in the bulk of material. The two series of spectral lines were expected due to the coexistence of ortho- and para-states of the molecules at the surface. It was hoped that the results obtained would provide an alternative mechanism for the room-temperature ferromagnetism observed in TiO2, HfO2 and In2O3 thin films with a contribution from oxygen vacancies. It was expected that both anion and cation vacancies near to the flat surface acted as magnetic defects because of their triplet ground state and Hund's rule. The theoretical forecasts were waiting for experimental justification allowing for the number of the defects in the vicinity of surface was much larger than in the bulk of as-grown samples.

Surface-Induced Magnetism of the Solids with Impurities and Vacancies. A.N.Morozovska, E.A.Eliseev, M.D.Glinchuk, R.Blinc: Physica B, 2011, 406[9], 1673-88