  We investigate the effect of low-coordinated surface atoms on the
defect-induced magnetism in MgO nanocrystallites using hybrid density
functional theory calculations. It has been demonstrated that when Mg vacancies
are introduced at the corners of cube-like MgO clusters, a magnetic state
becomes lower in total energy than the nonmagnetic singlet state by 1-2 eV,
resulting in the spin-polarized ground state. The spin density is not only
located at the surrounding O atoms neighbor to the corner Mg vacancy site but
is also extended to the distant (1 nm or longer) low-coordinated surface O
atoms along the <110> directions. This directional spin delocalization allows a
remote Mg vacancy-Mg vacancyinteraction, eventually leading to a spontaneous
long-range ferromagnetic interaction.
