Ferromagnetism at the edges of the stacked graphitic fragments: an ab initio study

We carry out first-principles density functional calculations to investigate electronic and magnetic structures of the stacked graphitic fragments. Ferromagnetically ordered ground states are found to be stable in the zigzag edges of an isolated graphene, regardless of whether or not the edges are passivated with hydrogen atoms. However, the localized moments in the hydrogen-terminated edge vanish upon stacking the graphite fragments. Interlayer and inter-edge interactions are investigated in detail, and it is found that dangling bonds are indispensable to the formation of the ferromagnetism at the edges of the stacked graphitic fragments. 2004 Elsevier B.V. All rights reserved. The observations of magnetic signals in the doped fullerenes [1] and in the highly oriented pyrolytic graphite (HOPG) [2], have prompted numerous research works toward understanding as well as synthesizing the carbon-based magnetic systems [1,3]. Diverse experimental results include spin-glass-like state [4], paramagnetic state [5], and ferromagnetic (FM) state [2,6,7]. Among them, the observation of the stable ferromagnetism in the glassy carbon [7] as well as in the polymerized C60 s [8] have revived the long-pending questions about the intrinsic ferromagnetism in the carbon systems. Meanwhile, researchers have investigated the ferromagnetism of graphite nodule in meteorite [6] and cautioned that some of the carbon ferromagnetism claimed so far might have extrinsic origins. The recent report of ferromagnetism in the proton-irradiated graphites [9] is thought to be another piece of evidence for the possible 0009-2614/$ see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.09.069 * Corresponding author. Fax: +82 2 884 3002. E-mail address: [email protected] (J. Yu). magnetic ordering in a graphitic sample without magnetic impurities. In parallel with experimental findings, there have been a series of theoretical studies on the magnetism in carbon systems, especially in the graphitic fragments. An earlier work based on the p-orbital tight-binding model [10] revealed the localized states at the zigzag edge, which leads to flat bands at the Fermi level. Subsequent first-principles calculations [11–13] demonstrated that the Fermi instability, arising solely from the localized p-orbital states, could result in the magnetically ordered edge states. It was shown that the ferromagnetically ordered spins along one edge have the opposite direction to the direction of spins at the other edge [12]. However, it remains as an open question whether these edge-localized spins could make a measurable contribution to the bulk magnetism. In this Letter, we carry out ab initio calculations to study the stacking effect on the magnetism localized at the graphitic edges. We show that the presence of dangling bonds is a crucial factor in the formation of a magnetic moment in pure carbon systems. While the 208 H. Lee et al. / Chemical Physics Letters 398 (2004) 207–211 magnetic ground states are found to be most stable in the hydrogen-terminated edges of the isolated graphene sheet, it is shown that the localized spin moment in these edges disappears upon stacking of the graphitic fragments. Nevertheless, the interlayer interactions between the edges with dangling bonds are found to favor ferromagnetic ordering of the edge magnetic moments. We perform ab initio calculations based on the density-functional theory (DFT) [14,15] by using the planewave basis set with PWSCF package [16]. The ultrasoft pseudopotentials [17] are employed for the ionic potential and the local spin density approximation (LSDA), parameterized by Perdew and Wang [18], is used for the exchange-correlation potential. The kinetic energy cutoff for the plane-wave basis is set to 30 Ry throughout the calculations. For the graphitic fragment, we choose a one-dimensional strip as a model geometry as illustrated in Fig. 1. The graphitic strip is chosen to have the zigzag shape at both sides of the edges [19] and a periodically repeated unit-cell, which is so-called a supercell method commonly used in the electronic structure calculations. In order to allow for an antiferromagnetic ordering along the edge of the strip, we choose the unitcell along the x-direction as twice the minimal unitcell of the strip, as indicated by the dashed lines in Fig. 1. Along the directions perpendicular to the strip direction (i.e., yand z-directions in Fig. 1) the unit-cell dimensions are set to be large enough that the smallest distance between atoms in the neighboring cells, i.e., the length of the vacuum region is larger than 10 Å. In the later part, we perform the calculation for the stacked fragments by fixing the interlayer distance (along z) to 3.335 Å, which corresponds to the inter-layer separation of bulk graphite. For the finite number of stacked layers, we also include a vacuum region (larger than 10 Å) between the stacked fragments along the z-direction. The width of a strip is denoted by the number of zigzag chains parallel to the strip direction (i.e., the x-direction). In Fig. 1, we have the strip of width W = N where the zigzag chains are numbered from left to right. The