We show through density functional theory calculations that extended magnetic
states can inherently occur in oxides as the size of the crystals is reduced
down to the nanometer scale even when they do not explicitly include intrinsic
defects. This is because in nanoscale systems crystallographically perfect
crystallites paradoxically result in nonstoichiometric compositions owing to
the finite number of constituting atoms. In these structurally perfect but
stoichiometrically imperfect nanocrystallites, the spin-triplet state is found
to be more stable than the spin-singlet state, giving rise to an extended spin
distribution that expands over the entire crystal. According to this picture,
long-range magnetic order arises from the combined effect of crystal symmetry
and nonstoichiometry that can coexist exclusively in nanoscale systems. The
idea can also give reasonable explanations for the unprecedented ferromagnetic
features observed commonly in nanoscale oxides, including ubiquity, anisotropy,
and diluteness.Comment: 12 pages, 4 figure
