Jahn-Teller Distortion and Multiple-spin-state Analysis of Single-atom Vacancy in Graphene-nano-ribbon

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.