Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry and Nonstoichiometry as Possible Origin of Ferromagnetism in
  Nanoscale oxides   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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The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph