Suppression of spin polarization in graphene nanoribbons by edge defects and impurities

Graphene nanoribbons (GNRs) have attracted much re­ cent interest because of their unique electronic properties and potential for device applications.1-11 Of particular interest are those GNRs with zigzag edges, which are shown to have a spin-polarized ground state.4"'’'8 The spin polarization origi­ nated from the edge states that introduce a high density of state at the Fermi energy. It can be qualitatively understood in terms of the Stoner magnetism of sp electrons (in analogy to conventional d electrons) occupying a very narrow edge band to render instability of spin-band splitting.12 The spins are found to be localized on the ribbon edges, with ferromag­ netic coupling within each edge and antiferromagnetic cou­ pling between the two edges. Because the magnetism in GNRs resulted from the highly degenerate edge states, it must require a perfect edge struc­ ture. However, real samples of GNRs (Ref. 9) are unlikely to have perfect edges but contain structural defects and impuri­ ties of foreign atomic species. Thus, one important question is how robust the spin state is in the presence of edge defects and impurities. The answer to this question not only is sci­ entifically interesting to better understand the physical mechanisms of spin polarization in GNRs but also has im­ portant technological implications if GNRs are to be realized as a new class of spintronic materials. Some existing studies-'’ seemed to suggest that the spins in GNRs are robust against the formation of edge defects at certain concentrations. How­ ever, in this Brief Report, we show that the spins can be completely removed by edge defects or impurities at concen­ trations accessible in real samples, which renders a practical difficulty in realizing spin polarization in GNRs. We have performed a systematic study of the stability and degree of spin polarization in GNRs as a function of the concentration of edge defects and impurities by using firstprinciples density-functional-lheory (DFT) calculations. We chose vacancy and substitutional boron (B) atom as typical examples of a structural edge defect and impurity, respec­ tively, since vacancies are expected to be the most abundant defects in a roughened edge and B atoms are a common choice of electronic dopants.7-6 Our calculations show that the spin is completely suppressed at the defect (impurity) sites, while it may preserve on those sites away from defects (impurities) when the defect (impurity) concentration is low. The stability of the spin state and its “average” magnetic moment continuously decreases with increasing the defect (impurity) concentration. Typically, independent of the rib­ bon width, the system becomes nonmagnetic at the critical concentration of one edge defect (impurity) per —10 A, which is a concentration shown to be accessible in real samples based on thermodynamic considerations. The mag­ netism can also be locally “dead” in between two defects (impurities) as long as they are closer than the third nearestneighbor (NN) positions. The spin suppression closely cor­ relates with the reduction and removal of edge states at the Fermi energy. Our calculations are performed using the DFT pseudopo­ tential plane-wave method within the local spin-density approximation.13 The plane-wave cut-off energy is set as 450 eV. The structure optimization has been performed until the residual atomic forces are less than 0.01 eV/A. We cal­ culated GNRs with H-terminated zigzag edges with two dif­ ferent widths, namely, the (2.5,2.5) and (1.5,1.5) “armchair” ribbons,7 by using a nomenclature in analogy to armchair carbon nanotubes that would unfold into corresponding ribbons with zigzag edges. Vacancies or impurities are introduced into the edge by removing edge C-H pairs or replacing C with B, respectively. Their concentrations are varied from 0.034 to 0.136 A""1 along the edge, and both uni­ form and nonuniform distributions of defects (impurities) are considered. Figure 1 (a) shows the calculated ground-state spin distri­ butions of a (2.5,2.5) GNR at an edge vacancy concentration of 0.034 A-1. The spin polarization is mostly localized on the edges with the top and bottom edge spins antiferromag­ netic coupled with each other. One notices that spin is locally absent at the vacancy sites and it increases as one moves away from the vacancy along the edge. Figure 1(b) shows the ground-state spin distributions at a higher vacancy con­ centration of 0.068 A-1. Overall, the spins exhibit an identi­ cal distribution pattern, but their magnitude is reduced in comparison to those in Fig. 1(a). At an even higher vacancy concentration of 0.136 A-1, Fig. 1(c) shows that the spins are completely suppressed at all the atomic sites and the GNR becomes nonmagnetic. Almost identical results are obtained for B impurities, as shown in Figs. 1(d)-1(f). In Fig. 1(g), we plot the magnetic moments on the top edge as a function of edge positions at four different vacancy