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.
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