Mixed magnetic edge states in graphene quantum dots

Graphene quantum dots (GQDs) exhibit abundant magnetic edge states with promising applications in spintronics. Hexagonal zigzag GQDs possess a ground state with an antiferromagnetic (AFM) inter-edge coupling, followed by a metastable state with ferromagnetic (FM) inter-edge coupling. By analyzing the Hubbard model and performing large-scale spin-polarized density functional theory calculations containing thousands of atoms, we predict a series of new mixed magnetic edge states of GQDs arising from the size effect, namely mix-n, where n is the number of spin arrangement parts at each edge, with parallel spin in the same part and anti-parallel spin between adjacent parts. In particular, we demonstrate that the mix-2 state of bare GQDs (C6N2) appears when N ≥ 4 and the mix-3 state appears when N ≥ 6, where N is the number of six-membered-ring at each edge, while the mix-2 and mix-3 magnetic states appear in the hydrogenated GQDs with N = 13 and N = 15, respectively.