Effects of random atomic disorder on the magnetic stability of graphene nanoribbons with zigzag edges

We investigate the effects of randomly distributed atomic defects on the magnetic properties of graphene nanoribbons with zigzag edges using an extended mean-field Hubbard model. For a balanced defect distribution among the sublattices of the honeycomb lattice in the bulk region of the ribbon, the ground-state antiferromagnetism of the edge states remains unaffected. By analyzing the excitation spectrum, we show that while the antiferromagnetic ground state is susceptible to single spin-flip excitations from edge states to magnetic defect states at low defect concentrations, its overall stability is enhanced with respect to the ferromagnetic phase.

Figure 1

(a) Graphene nanoribbon lattice structure with 10 010 atoms and randomly generated 1% defect concentration equally distributed within the A sublattice (downward pointed triangles) and the B sublattice (upward pointing triangles). (b) AFM (ground state) and (c) FM spin density profile of a portion of the ribbon. (d) and (e) Average magnetization along the ribbon length for the AFM and FM phases.

Figure 2

Mean-field energy per atom as a function of total spin $S_z$ for the clean and the 1%, 3%, and 5% defect concentration cases. For the clean case, the ground state is AFM edges with $S_z=0$, and the FM phase occurs at $S_z=69$. The FM-AFM gap increases with increasing defect concentration.

Figure 3

Mean-field DOS for the AFM phase for the (a) clean, (b) 1% concentration, (c) 3% concentration, and (d) 5% defect concentration cases. Edge and defect state contributions are plotted with dotted and dot-dashed lines, respectively. Energy gap values of the total DOS are given for each case.

Figure 4

Average (a) single edge magnetization, (b) AFM-FM energy gap, and (c) AFM energy gap, over ten randomly generated disorder configurations, as a function of defect concentration. Bars and symbols represent standard errors over the ten random configurations.