Effect of edges on the stability and magnetic interaction of Co atoms embedded in zigzag graphene nanoribbons

We report the results of first-principles calculations for the atomic, electronic, and magnetic properties of the Co atoms embedded in divacancy defects in graphene nanoribbons with zigzag-shaped edges. We find that the edges play an important role in the stabilization of a Co-divacancy complex near the edge, where the edge C atoms undergo large relaxations, resulting in a tilted-edge structure. When Co is positioned in the middle of the ribbon, the edge C atoms generally remain on the sheet, forming a flat-edge structure due to the small edge effect. The spin polarization of the edges is determined by two bipartite lattices separated by the Co atom. When a Co-divacancy pair is formed near the same edge, the edge structure is significantly modified. The magnetic interaction between the Co atoms is either ferromagnetic or antiferromagnetic, depending on the relative positions of the Co atoms, and its magnetic ordering can be described by the combined effect of the bipartite lattices formed around individual Co atoms.

Figure 1

(a), (b) The atomic structures of a pristine GNR with zigzag-shaped edges and zigzag GNR with a single Co atom embedded in the divacancy, where the dangling bonds of the edge C atoms are passivated by hydrogen (red balls at the edges). The numbers denote possible positions of the divacancy. The spin densities of the Co-embedded GNR are compared for (c) dUd and (d) uUu spin configurations. Red and blue clouds represent the spin densities of spin-up and spin-down electrons, respectively. (e) The $b$/$a$ values of the C${}_4$ pore for different positions of Co, where $a$ and $b$ are perpendicular and parallel to the missing C dimer, respectively. (f) The relative energies and the average values of the Co-C bond lengths of the Co-DV complexes in their lowest-energy spin configurations for different positions of Co.

Figure 2

The projected densities of states (PDOS) onto the Co $d$ states for the Co-DV complexes in different spin and edge structures. (a) The Co $d$ bands are compared for the uUu and dUd spin configurations of the Co-DV complex in the flat-edge structure at site 0. The PDOS are compared for the Co-DV complexes in the dUd spin configuration, which form (b), (c) the flat-edge structure at sites 0 and 5, respectively, and (d) the tilted-edge structure at site 5. Red, blue, green, brown, and orange lines represent the Co $d_{\mathrm{xz}}$, $d_{\mathrm{yz}}$, $d_{\mathrm{xy}}$, $d_{x^2-y^2}$, and $d_{z^2}$ states, respectively. Black solid and dashed lines stand for the PDOS onto the C${}_4$-pore $p$ and edge C${}_t$ p states, respectively, and the C${}_t$ p states are six times enlarged for clarity.

Figure 3

The atomic structures of the (a) flat-edge and (b) tilted-edge structures of the Co-DV complex, where Co is positioned at site 5 near the edge.

Figure 4

(a)–(c) Various configurations for the relative positions of the two Co atoms in the Co-DV pair. Red and blue segments denote the ferromagnetic and antiferromagnetic states of the Co-DV pair, respectively. In (b) and (c), one Co atom is fixed at the site marked by a yellow circle, whereas the other Co position is represented by red and blue segments. (d) The energies of the Co-DV pairs relative to the configuration $n$ for the configurations considered, which have different Co-Co distances.

Figure 5

The atomic structures of the Co-DV pairs in the configurations (a) $f$, (b) $g$, (c) $h$, (d) $i$, (e) $j$, and (f) $k$, where θ represents the alignment angle between the two $M_{\mathrm{v}}$ lines. Note that, in the configuration $f$, the pentagons are squashed due to large compressive strain between the two Co atoms.

Figure 6

Schematic diagrams of the spin densities of (a) the single Co-DV complex and (b)–(d) the Co-DV pair, where Co is positioned at site 5 near the edge. In (b), the two $M_{\mathrm{v}}$ lines are parallel, whereas the alignment angles between the two $M_{\mathrm{v}}$ lines are ±60° in (c), (d). Large ellipses represent the Co atoms embedded in the divacancy, and $A$ and $B$ denote the sublattice sites of graphene. Red and blue colors indicate the spin densities of spin-up and spin-down electrons, respectively.