Structural, magnetic, and electronic properties of Nin and Fen nanostructures (n=1–4) adsorbed on zigzag graphene nanoribbons

Extensive ab initio density-functional calculations were performed to investigate the structural, magnetic, and electronic properties of systems comprising Nin and Fen nanostructures n=1–4 adsorbed on hydrogenpassivated zigzag graphene nanoribbons GNRs . Both Ni and Fe atoms were most strongly bound at GNR edge sites and neither altered whether the GNR was metallic or semiconducting. However, Nin nanostructures were more strongly bound than Fen nanostructures, and their atoms had much smaller spin magnetic moments; Nin /GNR systems, like the pristine GNR, always had lowest energy with antiparallel edge spins, whereas among Fen /GNR systems this was only found for oneor two-atom adstructures at subedge or near-subedge atop sites; and zigzag Ni3 and Ni4 chains placed at GNR hole sites retained close contact with the GNR upon relaxation, whereas the analogous Fe chains adopted geometries similar to those of free-standing Fe clusters, with one or more atoms lifted away from the GNR.


I. INTRODUCTION
Identification of Kroto et al. 1 of the truncated icosahedral structure of C 60 in 1985 spurred intense research on the properties of fullerenes and other all-carbon nanostructures, especially carbon nanotubes ͑CNTs͒ 2,3 and the graphene sheet. [4][5][6][7][8][9] The latter is a zero-gap two-dimensional semiconductor with striking properties of interest for nanoelectronics; in particular, it has extremely high carrier mobility due to the linear band dispersion around the Fermi point. 5 CNTs, obtained conceptually by rolling up a strip of graphene sheet, are uniquely specified by their diameter and winding angle, which together determine not only their structure but also other properties, such as whether they behave electronically as conductors or semiconductors. 3 A carbon nanostructure that has attracted considerable attention of late is the graphene nanoribbon ͑GNR͒, an ͑unrolled͒ graphene strip.  Just as the structures and electronic properties of CNTs are determined by their diameter and winding angle, so those of GNRs are determined by their width and by the direction-dependent configuration of atoms along their long edges, which can range from zigzag ͑the edges run perpendicular to one of the bond directions͒ to armchair ͑the edges run parallel to one of the bond directions͒. In particular, zigzag GNRs with hydrogen-passivated edges, in which all the spins are the same along each edge, are metallic or semiconducting depending on whether the two edges have the same or opposite spins 24 ͓the latter configuration, Ferro-A, is marginally more stable than the former, Ferro-F, in which antiferromagnetic ͑AFM͒ coupling between nearest neighbors is frustrated at the center of the ribbon͔. 17,29 CNTs can be obtained with the catalytic aid of late transition metals ͑TMs͒, notably Ni. 3,[32][33][34] For this and other reasons, there has been considerable research on nanostructures composed of C and TM atoms. It is found, for example, that systems with early TMs differ markedly from those with late TMs. Thus early TMs do not catalyze CNT formation, and early 3d metals ͑Ti, V, and Cr͒ preferentially form "met-cars" [35][36][37][38][39][40][41] ͑clusters with TM 8 C 12 stoichiometry and remarkable stability͒, while late 3d metals ͑Co and Ni͒ do not. 41 Knowledge of how TM-C interactions depend on where the TM atoms bind is of fundamental importance for understanding not only catalytic CNT growth, the mechanism of which is still controversial, 33,42 but also the magnetic and other electronic properties of carbon nanostructures with adsorbed or embedded TM atoms. For example, GAUSSIAN03 43 calculations have predicted that the electron tunneling current in Ni-C 60 -Ni is greater when the Ni atoms occupy hole sites than in the more stable structure 44 in which they occupy bridge sites. 45 Of course, non-TM atoms can also alter electronic properties: hydrogen-passivated zigzag GNRs with boron-doped ferromagnetically coupled edges have been shown theoretically to be semiconductors with spin-sensitive transmittance. 24 Ab initio calculations using SIESTA 46 and TRANSAMPA 47 have shown that the most stable configuration of a hydrogenpassivated zigzag GNR with a single adsorbed Ni atom features the adatom at an edge site, that the adsorption process reduces the magnetic moments of both the Ni and its neighboring C atoms due to the hybridization of Ni 3d orbitals with C 2p orbitals, and that the electronic transmittance along the GNR is, as in the case of B-doped zigzag GNRs, 24 spin dependent. 29 To contribute to a better understanding of the behavior of TM/GNR systems, in the work described here we performed SIESTA calculations to compare the structural, magnetic, and electronic behaviors of Ni n and Fe n structures ͑n =1-4͒ that were supported on hydrogenpassivated zigzag GNRs. The Ni n / GNR and Fe n / GNR systems proved to differ significantly in many respects. The essential technical details of the method used are sketched in Sec. II, our results are discussed in Sec. III, and in Sec. IV we summarize our main conclusions.

II. DETAILS OF THE COMPUTATIONAL PROCEDURE
The computational method employed has been described in detail in Ref. 46. Briefly, it is a density-functional theory ͑DFT͒ approach using numerical pseudoatomic orbitals as basis sets to solve the single-particle Kohn-Sham equations. For the exchange and correlation potential we used the Perdew-Burke-Ernzerhof form of the generalized gradient approximation ͑GGA͒. 48 The atomic cores were described by nonlocal norm-conserving Troullier-Martins pseudopotentials 49 factorized in the Kleinman-Bylander form. 50 The pseudopotentials for Ni and Fe were generated using the valence configurations 4s 1 3d 9 and 4s 1 3d 7 and have been validated in previous work on Ni-C and Fe-C clusters. [51][52][53] For both TM and C atoms, valence states were described using triple-doubly polarized basis sets. The energy cutoff used to define the real-space grid for the numerical calculations involving the electron density was 250 Ry ͑in a few calculations performed as a check with a 500 Ry energy cutoff, the results were virtually the same as those obtained with the smaller cutoff͒. Using a conjugate gradient method, 54 all the structures were fully relaxed, without any geometry or spin constraints, until the interatomic forces were smaller than 0.005 eV/ Å.
Most calculations concerned a 9.83ϫ 50ϫ 10 Å supercell containing four unit cells of a hydrogen-passivated ͗10, 0͘ zigzag GNR ͑80 C atoms together with 8 H atoms saturating the dangling bonds at the edges͒ 55 together with Ni or Fe adatoms. Periodic boundary conditions were applied in all directions to make infinite copies of an endless adatomspattered GNR 22.08 Å wide in the y direction, with copies separated by 10 and 50 Å in the z and y directions, respectively. For the largest TM nanostructures, eight unit cells of GNR were included in the supercell as a check on accuracy. For some TM nanostructures, calculations were also performed in which the dangling bonds were passivated with alternating H atoms and methylene groups, 17 but the results were the same as with H-only passivation. A Monkhorst-Pack 56 grid of 9 ϫ 1 ϫ 1 k points was used along the GNR growth direction ͑x direction͒ for integration in the Brillouin zone; calculations performed with a 15ϫ 1 ϫ 1 grid gave virtually the same results.

III. RESULTS AND DISCUSSION
We started our calculations by reproducing known results for pristine hydrogen-passivated zigzag GNRs, i.e., zigzag GNRs with no TM atoms. We found the energy of Ferro-A to be just 0.014 eV/unit cell lower than that of Ferro-F. Note that Pisani et al. 17 showed that although different exchange and correlation functionals can afford slightly different predictions of the magnetic configuration of GNRs, the qualitative features of the results are robust with respect to changes of functional. This should also hold for the results obtained in this paper for Ni n / GNR and Fe n / GNR systems.
Following the above preliminaries, we performed extensive calculations on single-adatom Ni/GNR and Fe/GNR systems to investigate, as possible adsorption sites, the central hole site ͑CHS͒ of the GNR unit cell, a subcentral bridge site ͑SCBS͒, and a subedge "atop" site ͑SEAS͒ ͓see Figs. 1͑a͒-1͑c͔͒. In each case, we also investigated magnetic behavior; magnetic differences between the Ni/GNR and Fe/ GNR systems were expected because the Fe atom has three unpaired d electrons and the Ni atom has only one. Due to space limitations, we present here only part of our results for these and other Ni n / GNR and Fe n / GNR systems ͑n =2-4͒; for the remainder, see the supplementary material. 57 FIG. 1. ͑Color online͒ Lower panels: spin density distributions of the systems ͑a͒ Fe͑CHS͒/Ferro-F, ͑b͒ Ni͑SCBS͒/Ferro-A, and ͑c͒ Fe͑SEAS͒/Ferro-F after full relaxation, calculated by taking the difference between the spin-up and spin-down densities and integrating along the z direction ͑Ref. 59͒. Upper panels: spin magnetic moments of all atoms in a band perpendicular to the x axis which contains the adatom ͑white, hydrogen; yellow, carbon; red, Fe; and blue, Ni; triangles and dashed lines correspond to pristine GNR and circles and continuous lines correspond to TM/GNR͒. The entries for n = 1 in Tables I and II list the predicted adsorption energies of Ni and Fe on Ferro-A and Ferro-F, together with the spin magnetic moments of the adatom and of the nearest C atoms of the two edges ͑for each n, magnetic moments were in fact calculated for all atoms in a band perpendicular to the x direction that contained the adatoms͒. For both metals, the most stable structure featured the adatom at a Ferro-A SEAS, which in the case of Ni/GNR agrees with the results of Rigo et al. 29 Unlike Rigo et al., however, we found that adsorption at an SCBS was also stable for Ni ͓Ni͑SCBS͒/Ferro-A being slightly more stable than Ni͑SCBS͒/Ferro-F͔ though not for Fe. This result for Ni is consistent with the stability of C 60 with Ni adsorbed at bridge sites. 44,45 When adsorption occurred at the CHS, Ni͑CHS͒/Ferro-A was again slightly more stable than Ni͑CHS͒/Ferro-F, but adsorption of Fe reversed the spin preference of the pristine GNR, Fe͑CHS͒/Ferro-F being much more stable than Fe͑CHS͒/Ferro-A. For all configura- n Name n Name maining results are included in the supplementary material. 57 At the CHS, the magnetic moment of the Ni atom in Ni͑CHS͒/Ferro-A was zero due to hybridization between the Ni 3d and nearest-neighbor C 2p orbitals, although in the less stable Ni͑CHS͒/Ferro-F it had a small magnetic moment with AFM coupling to the edge C atoms ͑see Table I͒. By contrast, the Fe atom had an appreciable magnetic moment in both Fe͑CHS͒/Ferro-A and Fe͑CHS͒/Ferro-F ͓see Table II and Fig. 1͑a͔͒, with ferromagnetic ͑FM͒ coupling to the edge C atoms in the latter. The energetic disadvantage of Fe͑CHS͒/Ferro-A would seem to be due to the Fe atom not being able to couple ferromagnetically to both edges; of course, no such frustration can occur in Ni͑CHS͒/Ferro-A, in which the magnetic moment of the Ni atom is zero. At an SCBS, an Ni adatom had a slightly larger magnetic moment than at the CHS due to a lesser degree of hybridization and coupled ferromagnetically to the nearest edge in both Ni͑SCBS͒/Ferro-A and Ni͑SCBS͒/Ferro-F ͓see Table I and Fig. 1͑b͔͒; however, both these structures were less stable than their CHS analogs. The most stable single-adatom con-figurations featured the Ni or Fe atoms at SEAS, and in both cases Ferro-A was just marginally more stable than Ferro-F.  Table II and Fig. 1͑c͔͒. Figure 2 shows the projected density of states ͑PDOS͒ of Ni and Fe atoms adsorbed on Ferro-A at the CHS and at a SEAS. At the CHS, the Ni PDOS below the Fermi level E F is composed of d-type states resulting from hybridization between the 3d orbitals of the Ni adatom and the nearestneighbor C 2p orbitals, which lowers the lower limit of the effective d band to approximately 4 eV below E F . Equal spin-up and spin-down densities give a zero spin magnetic moment. At the SEAS, there are unoccupied spin-down d-type states in an energy range of about 0-2 eV above E F , in consonance with the nonzero spin magnetic moment of the Ni adatom at this position. Moreover, the unoccupied p orbitals are now delocalized ‫ء‬ orbitals. When the adatom is Fe at the CHS, delocalized unoccupied ‫ء‬ orbitals are accompanied by significant unoccupied spin-up and spin-down d-type state densities around 0.8 and 0.0 eV above E F , respectively, while at the SEAS the two main d-type peaks of the spin-up and spin-down densities are located within windows about 2 eV wide around 2.4 and 0 eV below E F , respectively.
The five two-adatom configurations investigated had adatoms at the CHS and at a neighboring hole site closer to one of the edges of the ribbon ͑CHS+ NHS͒, at a SEAS and a neighboring atop site closer to the center of the ribbon ͑SEAS+ NAS͒, at two neighboring SEAS ͑2SEAS͒, at a single SEAS, in a double-decker configuration with one of the two adatoms atop the other ͑DD-SEAS͒, and in a similar double-decker configuration at the CHS ͑DD-CHS͒. These last two configurations were included to allow comparison with the finding of Johll et al. 58 that TM dimers on graphene bind most stably in DD-CHS-like configurations. Tables I  and II  In all five Ni pair configurations, the Ferro-A configuration of the GNR was slightly more stable than the Ferro-F configuration. In the CHS+ NHS configuration, both Ni atoms behaved similarly to single Ni atoms at the CHS, with zero or very small magnetic moments; in the SEAS+ NAS configuration, both had appreciable magnetic moments ͑though somewhat smaller than those of a solitary Ni atom at a SEAS͒, while in the 2SEAS configuration ͑the most stable͒, one of the Ni atoms had a larger magnetic moment than in the SEAS+ NAS configuration ͑Ϸ0.7 B ͒ and the other had a smaller ͑note that the 2SEAS configuration did not lie parallel to the x axis after full relaxation͒. The double-decker configuration DD-CHS was somewhat more stable than CHS+ NHS, but DD-SEAS was less stable than 2SEAS ͑though more so than SEAS+ NAS͒. In both the doubledecker configurations, the top adatom retained more than half the magnetic moment of the isolated Ni atom ͑2 B ͒, but the bottom adatom did not.
When the two adatoms were Fe, the Ferro-A configuration of the GNR was marginally the more stable with the Fe pair in the configurations SEAS+ NAS, DD-SEAS and 2SEAS, but the reverse held for DD-CHS, and Fe 2 ͑CHS + NHS͒ / Ferro-F was about 0.5 eV more stable than Fe 2 ͑CHS+ NHS͒ / Ferro-A. The stabilities of the various configurations increased in the same order as for Ni: CHS + NHS Ͻ DD-CHS Ͻ SEAS + NAS Ͻ DD-SEAS Ͻ 2 SEAS, though the energy difference between these last two was much smaller than for the Ni analogs. In CHS+ NHS configuration, both Fe atoms had magnetic moments Ͼ3.0 B ͓one had a magnetic moment as large as 3.521 B in Fe 2 ͑CHS+ NHS͒ / Ferro-F͔, and the greater stability of the Ferro-F configuration is attributable to both its Fe atoms coupling ferromagnetically to the edge carbons, whereas in Fe 2 ͑CHS+ NHS͒ / Ferro-A there is FM coupling between the CHS atom and one edge, and AFM coupling between this atom and the other edge, between the NHS atom and its nearest edge, and between the two Fe atoms. In the SEAS + NAS configuration, both Fe atoms had magnetic moments of about 3.4 B regardless of the GNR configuration, and in the 2SEAS configuration ͑the most stable͒, both always had magnetic moments of about 3.44 B . The magnetic moments of the two adatoms in the double-decker configurations were much more similar than in the case of Ni, but differed more than in the other configurations ͑by 0.8 B in DD-SEAS͒.
Note that in DD-CHS configuration, both Ni 2 / Ferro-F and Fe 2 / Ferro-F had adsorption energies and magnetic moments similar to those reported for a double-decker configuration at a hole site of graphene: 3.58 eV, 1.29 B and 0.73 B for Ni, and 3.0 eV, 3.48 B and 2.76 B for Fe. 58 The three-and four-adatom configurations investigated were, before relaxation, linear and zigzag chains ͑LCs and ZZCs͒ with an atom at the CHS and the other atoms at neighboring hole sites or ͑for Fe ZZCs͒ an atom at a SEAS and the other atoms at atop sites nearer the center of the GNR ͓see Figs. 4͑a͒, 4͑b͒, and 5 and the supplementary material 57 ͔. Ferromagnetically coupled ZZCs are the most stable configurations of free-standing Ni and Fe chains of infinite length. 60 Note that, in view of the preference of Fe and Ni dimers for the 2SEAS configuration, none of the three-or four-adatom structures studied is likely to be the ground state structure for that number of adatoms. It seems probable that the adatoms of the ground state structures all occupy SEASs, and for a study of such structures to prevent interactions between the adstructure and its images in neighboring supercells it would be necessary to use a supercell much larger than four unit cells. The structures we were able to examine in the present study nevertheless enable comparison between LCs and ZZCs and between Fe ZZCs in more central and more lateral locations, as well as comparison of Fe with Ni. Tables I and II list  boid corresponding approximately to a graphene unit cell. CHS-ZZCs were more stable than CHS-LCs, and, in keeping with the results for Ni/GNR and Ni 2 / GNR, Ferro-A was more stable than Ferro-F.
Like their Ni analogs, Fe 3 and Fe 4 CHS-LCs retained their structures upon relaxation, and like their centrally located Fe and Fe 2 homologs were more stable as Ferro-F than as Ferro-A. Ferro-F was also the more stable GNR configuration in Fe 3 and Fe 4 ZZCs, but the Fe atoms of these ZZCs adopted geometries that were similar to the triangle and tetrahedron of free-standing Fe 3 4 ͑SEAS-ZZC͒ / Ferro-F ͑Fig. 5͒, which were more stable than their CHS-ZZC and CHS-LC analogs and had atomic spin magnetic moments even closer to those of the free-standing clusters. Thus the geometries of the most stable Fe 3 / GNR and Fe 4 / GNR structures that were investigated were not imposed by the planar geometry of the GNR but by those of the free Fe clusters, which underlines the weakness of the Fe-GNR interactions in comparison with the Fe-Fe interaction. That the atomic spin magnetic moments are so much larger in the Fe nanostructures than in their Ni analogs is attributable to the former, but not the latter, having a large excess of spin-down d-type states above E F , as is illustrated in Fig. 6 by the cases of Ni n ͑CHS-ZZC͒ / Ferro-A and Fe n ͑CHS-ZZC͒ / Ferro-F ͑n =3,4͒.
As was indicated in Sec. I, the carbon atoms of each edge of a hydrogen-passivated zigzag GNR all have the same spin, and the GNR is metallic or semiconducting depending on whether the spins at the two edges are parallel ͑Ferro-F͒ or antiparallel ͑Ferro-A͒. 24 In both cases, there are flat energy bands near E F that correspond to the and ‫ء‬ orbitals of the edge atoms. After computing the electronic band structure of Ni/GNR systems with the Ni atom at various different adsorption sites, Rigo et al. 29 reported that the electronic character of the GNR is not altered by adsorption of a single Ni atom, although its presence does perturb the energy bands. In this study we found that the same holds when two, three, or four Ni or Fe atoms are adsorbed, at least when the initial adsorption configurations are as in this study, as is shown in Figs. 7͑a͒ and 7͑b͒ for the cases of Ni 2 ͑SEAS+ NAS͒ / Ferro-A, Ni 4 ͑CHS-ZZC͒ / Ferro-A, Fe 2 ͑SEAS+ NAS͒ / Ferro-A, and Fe 4 ͑CHS-ZZC͒ / Ferro-F. Note that, as is expected given the computed PDOS ͓see Fig.  6 for the cases of Ni 4 ͑CHS-ZZC͒ / Ferro-A and Fe 4 ͑CHS-ZZC͒ / Ferro-F͔, the Fe n / GNR systems show more splitting indicative of interaction between spin-up and spindown bands and that the flat sections of the energy bands near E F in Ni n / Ferro-A configurations extend to higher wave numbers as the number of adatoms increases, at the same time slightly reducing the gap between the states above and below E F .

IV. SUMMARY AND CONCLUSIONS
In this work, using the computational package SIESTA 46 with standard nonlocal norm-conserving pseudopotentials 49 and the GGA to exchange and correlation, 48 we performed extensive ab initio DFT calculations to investigate the structural, magnetic, and electronic properties of Ni n and Fe n nanostructures ͑n =1-4͒ that were adsorbed on hydrogenpassivated ͗10, 0͘ zigzag GNRs. Ni n clusters were more strongly bound than Fe n clusters, and their atoms had much smaller spin magnetic moments. The difference in binding energies also explains why zigzag Ni 3 and Ni 4 chains placed at GNR hole sites retained close contact with the GNR upon relaxation, whereas the analogous Fe chains adopted geometries similar to those of free-standing Fe clusters, with one or more atoms lifted away from the GNR. An extensive study of adsorbed dimers shows that although, for both Ni 2 and Fe 2 , the perpendicular DD-CHS and DD-SEAS configu-rations are, respectively, more stable than the epitaxial CHS+ NHS and SEAS+ NAS configurations, the most stable configurations of the dimers are those with the two atoms at adjoining SEASs. Like the pristine GNR, Ni n / GNR systems were more stable in Ferro-A than in Ferro-F configuration, whereas among Fe n / GNR systems this was only found for one-or two-atom adstructures at subedge or near-subedge atop sites. The conductivity type of the GNR ͑metallic in Ferro-F configuration, semiconducting in Ferro-A configura-tion͒ was unaltered by adsorption of up to four Ni or Fe atoms.
The results presented in this paper show that, as in other TM/all-carbon systems, 3,32-41,51-53 the structural, magnetic, and electronic properties of TM/GNR systems depend to a large extent on the nature of the TM atom. Accordingly, further simulations, as well as theoretical and experimental work, will be necessary for satisfactory understanding of the behavior of TM/GNR systems in general.