  A single-atom vacancy defect and its array in graphene and graphite were
considered to be one candidate carrying the room-temperature ferromagnetism.
Applying density functional theory to a single-atom vacancy in
graphene-nano-ribbon (GNR), a detailed relationship between the
multiple-spin-state and the Jahn-Teller distortion was studied. An equilateral
triangle of an initial vacancy having six unpaired electrons had distorted to
isosceles triangle by the Jahn-Teller effect. Among capable spin-state of
Sz=6/2, 4/2 and 2/2, the most stable one was Sz=2/2. Total energy was 15.6
kcal/mol lower (stable) than that of the initial one and a sum of spin density
(magnetic moment) around one vacancy was 1.49 {\mu}B. Amazing result was
obtained in case of Sz=4/2. Initial flat ribbon turned to three dimensionally
curled one. There appears ferromagnetic spin distribution on GNR. Total energy
was -15.5kcal/mol, which was very close to that of Sz=2/2. Such calculation
suggested the coexistence of flat ribbon and curled ribbon by generating
vacancies. Bi-layered AB stacked GNR was analyzed in case of {\alpha}-site
vacancy and also \b{eta}-site one. The most stable spin state was Sz=2/2 in
both cases. These distorted vacancy triangle show 60 degree clockwise rotation
from beta- to alpha-site, which is consistent with several experimental
observations by using a scanning tunneling microscope.
