Intrinsic ferromagnetism in two-dimensional carbon structures: Triangular graphene nanoflakes linked by carbon chains

Using density functional theory (DFT) we show that intrinsic ferromagnetism in two-dimensional (2D) carbon semiconducting structures can be achieved by linking triangular graphene nanoflakes (GNFs) with carbon chains containing an odd number of carbon atoms. The observed magnetism can be understood from the singlet-triplet rule of C chain, the anti-pattern rule for a magnetic bipartite C structure, and the Lieb-Mattis criterion. Monte Carlo (MC) simulations indicate that the 2D frameworks can display transitions from a high-spin state to a low-spin state and to a paramagnetic state as temperature increases.

Figure 1

Geometric structures of (a) GNF${}_5$-GNF${}_5$, (b) GNF${}_5$-C${}_1$-GNF${}_5$, (c) GNF${}_3$-GNF${}_3$, and (d) GNF${}_3$-C${}_1$-GNF${}_3$ along with their spin density (ρ${}_{\alpha }$ − ρ${}_{\beta }$) isosurface with value of 0.03 electron/Å${}^3$ in their own stable spin configurations, AFM and FM, respectively. Green and red represent positive and negative signs, respectively.

Figure 2

(a) Exchange energy ($E_{\mathrm{AFM}}$ − $E_{\mathrm{FM}}$) as a function of C chain index n. (b) Spin density of GNF${}_5$-C${}_5$-GNF${}_5$ in FM and GNF${}_5$-C${}_4$-GNF${}_5$ in AFM states. (c) Sketch of Ising model describing magnetic behavior with exchange parameters for odd and even n. (d) Simulated variation of $J_{\mathrm{GC}}$ and $J_{\mathrm{GG}}$ parameters with index n.

Figure 3

(a) Geometric structure and (b) spin density isosurface of 2D periodic GNF${}_3$-C${}_3$-GNF${}_3$ framework. Blue-dashed rhombus denotes the simulated unit cell.

Figure 4

Variation of magnetization per unit cell of 2D periodic (a) GNF${}_3$-C${}_3$-GNF${}_3$ and (b) GNF${}_5$-C${}_7$-GNF${}_5$ as a function of temperature.