Functionalization of edge reconstructed graphene nanoribbons by H and Fe: A density functional study
Soumyajyoti Haldar, Sumanta Bhandary, Satadeep Bhattacharjee, Olle Eriksson, Dilip Kanhere, Biplab Sanyal
aa r X i v : . [ c ond - m a t . m e s - h a ll ] O c t Functionalization of edge reconstructed graphene nanoribbons by H and Fe: a density functional study
Soumyajyoti Haldar, Sumanta Bhandary, Satadeep Bhattacharjee, Olle Eriksson, Dilip Kanhere, and BiplabSanyal Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala,Sweden Department of Physics, Central University of Rajasthan, Bander Sindri Campus, Dist-Ajmer,Rajasthan-305801, India
In this paper, we have studied functionalization of 5-7 edge-reconstructed graphene nanoribbons by ab initiodensity functional calculations. Our studies show that hydrogenation at the reconstructed edges is favorablein contrast to the case of unreconstructed 6-6 zigzag edges, in agreement with previous theoretical results.Thermodynamical calculations reveal the relative stability of single and dihydrogenated edges under differenttemperatures and chemical potential of hydrogen gas. From phonon calculations, we find that the lowestoptical phonon modes are hardened due to 5-7 edge reconstruction compared to the 6-6 unreconstructed hy-drogenated edges. Finally, edge functionalization by Fe atoms reveals a dimerized Fe chain structure along theedges. The magnetic exchange coupling across the edges varies between ferromagnetic and antiferromagneticones with the variation of the width of the nanoribbons.
I. INTRODUCTION
Graphene is a wonder material with many extraordi-nary electronic, mechanical and optical properties to beused in future technology . Moreover, the similaritybetween its properties and the phenomena observed inhigh energy physics has created enormous possibilitiesto test fundamental theories in quantum electrodynam-ics by table-top experiments. Apart from exploring thebeautiful physics associated with the Dirac cones in theBrillouin zone, a perpetual interest exists in the chemicalfunctionalization of graphene to realize new properties.One of the routes of chemical functionalization is throughthe creation of defects in graphene and hence, modifica-tion of its properties . The other notable effort is toattach chemical species (H, F etc.) to graphene to openup band gaps by altering sp bonds to sp ones between Catoms . Very recently, it has also been shown thata combination of boron nitride and carbon in a two di-mensional network can yield interesting electronic prop-erties, e.g., opening of band gaps in an otherwise zeroband gap semiconducting situation in pure graphene.Graphene nanoribbons (GNRs) have attracted a lotof attention in the last few years as they are poten-tial candidates for future nanoelectronics. It is well-known that armchair nanoribbons are semiconductorswhile the zigzag GNRs (ZGNRs) have magnetic edgescoupled to each other antiferromagnetically to open upa gap. Band gap engineering as a function of the thick-ness of GNRs is an important study towards realizingtunable electronics . Also, chemical functionalization ofGNR edges to achieve novel properties is another strongmotivation to study GNRs. Recent theoretical studieshave reported the possibility of realizing zigzag and arm-chair type nanoribbons at the interface of graphene andgraphane (hydrogenated graphene) demonstratingan interesting way of generating nanoribbons.It has been proposed that apart from realizing theconventional and most abundant GNR edges, viz., zigzag and armchair, one may consider self reconstructededges where the hexagonal rings at the edges recon-struct to form pentagon-heptagonal pairs (reczag). Thisis similar to what has been observed as 5-7-5 Stone-Wales defects in bulk graphene. Calculations suggestthat the total energy of a reconstructed edge is 0.35eV/˚A lower than that of a zigzag one. The presenceof a reconstructed edge geometry has been confirmedin experiments using aberration corrected high reso-lution transmission electron microscopy. A recent reviewarticle has discussed about the formation of defectiveedges along with the folded ones where the adjacent edgesof multilayered graphene can join to form closed loops.The discussions on the zigzag and reconstructed edgesis very important from the point of view of magnetismat the GNR edges, which is a debatable issue. Recentdensity functional calculations suggest that the singleedge reconstructed GNRs show magnetism with metallicedges although the reconstructions allowed at both edgesdo not show any magnetism. Rodrigues et al. havestudied reconstructed zigzag nanoribbons decorated byStone-Wales defects by tight-binding theory with the pa-rameters extracted from first principles electronic struc-ture calculations.From the above discussions, it is clear that the forma-tion of reconstructed edges can modify the properties ofGNRs drastically. So, a thorough understanding of theproperties of the edges is essential along with the possi-bilities of realizing novel properties due to chemical func-tionalization by adatoms or molecules . The motivationof this present work is to study of the properties of edge-functionalized reconstructed GNRs by ab initio calcula-tions. We have focussed on the geometries and electronicstructures of reczag edges of varying thicknesses, theirstability at finite temperatures under hydrogenation. Fi-nally, we have exploited the possibility of realizing mag-netism by decorating the edges with Fe atoms. In thisregard, electronic structure, magnetic exchange couplingacross the edges and the stable geometries of Fe chains1t the edges have been studied. II. COMPUTATIONAL DETAILS
First principles spin-polarized density functional cal-culations were performed using a plane-wave projectoraugmented wave (PAW) method based code, VASP .The generalized gradient approximation (GGA) as pro-posed by Perdew, Burke and Ernzerhof (PBE) was usedfor the exchange-correlation functional. We have consid-ered different sizes of double edged reczag, which wereinfinite along the y axis. To create a sufficient vacuum inorder to avoid the interactions within adjacent cells, unitcell dimensions along x and z axis were considered as 50˚A and 16 ˚A respectively. The electronic wave functionswere expanded using plane waves up to a kinetic energyof 500 eV. The electron smearing used was Fermi smear-ing with a broadening of 0.05 eV. The energy and theHellman-Feynman force thresholds were kept at 10 − eVand 0.005 eV/˚A respectively. All atomic positions wereallowed to relax and the elemental cell was kept at a con-stant size during the optimization. For all electronic andionic calculations, we used a 1 × × k Monkhorst-Pack k-point mesh, whereas for phonon calculations, a1 × × .A few selected calculations for the geometry optimiza-tions and electronic structures were repeated by using theQuantum Espresso code using plane wave basis sets andpseudopotentials within GGA-PBE. We tested the con-vergence with respect to the basis-set cutoff energy anda value of 80 Ry. was considered for all results shown inthis paper. The other parameters were similar to thoseused in VASP calculations. We found out that the resultsobtained by the two codes are quite similar.In all our calculations, we have kept the unit cell vec-tors fixed. However, we have tested cell relaxation for4-rows 2H terminated reczag GNR, as in this case, theeffect of cell relaxation is expected to be the largest.From our calculations, we find that the change in unitcell length along the periodic direction (y) is less than3 % and along x direction, it is 0.7 %. The maximumchange in the C-C bond length is 1.8 % whereas themaximum change in the H-C-H bond angle is only 0.2%. Our results are not affected by these changes due tocell relaxation. III. RESULTSA. Edge termination by H
The dangling bonds of edge carbon atoms are ex-tremely reactive and need to be saturated. Among theseveral possible ways of edge termination, we concentrateon hydrogen termination at the edges as this seems to beone of the most stable configurations due to its planar structure. We have considered the reczag edge termina-tion by one (1H) and two (2H) hydrogen atoms attachedto each edge carbon atom for nanoribbons of width 4 to12 rows. Figure 1 shows the optimized geometry of areczag edge with 2H termination.The C atoms in the middle of the ribbons rearrangethemselves after geometry optimization and the bondlengths come out to be very close to the C-C bond dis-tances of bulk graphene (1.42 ˚A). However, the creationof edge reconstruction and H termination significantlychanges the C-C bond distances near the edge. In abare reczag edge without H termination, the edge car-bon atoms form a triple bond with a bond length of 1.25˚A. When this edge is terminated by 1H, this bond lengthincreases to 1.43 ˚A. Both bare reczag edge and the 1Hterminated one have planar structures. In the case of 2Htermination, the sp planar structure becomes buckled,making an sp like structure with an angle 102 ◦ betweenthe H and edge carbon atoms. The C-C bond length in-creases further to 1.58 ˚A. However, the C-C bond lengthof 1.42 ˚A in sp bonded graphene is recovered in the mid-dle of the ribbon.The edge carbon atoms are displacedfrom the plane of the ribbon with one C atom shiftingupwards and one downwards. H atoms attached to thesetwo carbon atoms also change their orientation to giverise to a twisted geometry as shown in figure 1. To in-vestigate the reason of twisting we have done Γ point(long wavelength) phonon calculations of 2H terminatedreczag edge using frozen phonon method . We find thatthe structure with 2 H atoms vertically placed on oneanother and connected to the edge C atom is not stable,showing two unstable modes involving the displacementof H atoms away from the vertical position. For 2H ter-mination, we therefore relaxed the structure again withthese two unstable modes frozen. The relaxed structurewas stable and a twisted geometry (shown in figure 1)was obtained due to the freezing of the above mentionedmodes. It is obvious that the edge sp structure has sub-stantial effects on the whole part of ribbons with smallerwidths whereas the structural distortion is not prominentin the middle of the wider ribbons.For the termination of edges with 2 H atoms per C, theformation energies have been defined as E f = E ( G H ) − [ E ( G H ) + n ∗ E ( H )], where E ( G H ) and E ( G H ) arethe total energies for reconstructed graphene nanorib-bons’ edges terminated with 1H and 2H atoms per edge,respectively. E ( H ) is the calculated energy for a H molecule in the gas phase and n is the number of H molecules used to compensate the uneven number of Hatoms.The calculated formation energies indicate that 2H ter-minated edge is probable to form. Also it is observed(data not shown) that the formation energies saturateafter a width of eight rows as reported before for a unre-constructed edge zigzag nanoribbon. Moreover, our cal-culation shows that the termination with H atoms will bespontaneous at T=0K. We have done test calculations byfreezing the edge carbon bond lengths. The edge hydro-2 a)(b)FIG. 1. (Color online) (a) Reconstructed edge GNR with 2H termination. Brown (dark in print) balls are C atoms and white(light in print) balls indicate H atoms. The close-up of the edge structure is also shown; (b) Gibbs free energy calculated for12 rows-reczag. Both 1H and 2H terminations with respect to bare reczag are presented. In the inset, transition pressures asa function of temperatures are shown. P is the reference pressure taken to be 0.1 bar. genation seems to be difficult if the C-C bond lengths arenot allowed to relax. Once the full geometry optimiza-tion is allowed, edge hydrogenation becomes probable.For the reconstructed edges, we find that a spontaneousformation of 2H terminated edges is possible rather thanthe 1H terminated ones for all widths. This is in sharpcontrast with the hydrogenation at the unreconstructedZGNRs studied earlier .In order to investigate the influence of finite tempera-ture/elevated gas pressure, we have calculated Gibbs freeenergies as a function of the chemical potential of the hy-drogen molecule, according to the following formula givenby Wassmann et al. . G H = 12 L [ E H − ( N H µ H ] G H = 12 L [ E H − ( N H µ H ] E H = E ( G H ) − [ E ( G H ) + 4 E ( H )] E H = E ( G H ) − [ E ( G H ) + 2 E ( H )] µ H = H ( T ) − H (0) − T S ( T ) + k B T ln ( PP )In the above equations, µ H , H , S , P and k B arethe chemical potential, enthalpy, entropy, pressure andBoltzmann constant respectively and N H is the numberof H atoms attached at the edge. The values for the en-tropies and enthalpies are taken from the tabular datapresented in Ref. . P is the reference pressure takento be 0.1 bar according to the tabular data. E ( G H ), E ( G H ) , E ( G H ) and E ( H ) are total energies for 2H,1H and bare reconstructed nanoribbons and hydrogenmolecule respectively. The results are shown in figure 13or 300 K. The Gibbs free energy is normalized by 2L,where L is unit cell length. The stability of 2H and 1Hterminated reconstructed nanoribbons is shown with re-spect to bare reconstructed nanoribbons . The zero tem-perature calculation shows that they are always favoredcompared to the bare nanoribbons. Also, 2H terminatedribbons are more stable than the 1H ones. With the in-clusion of temperature and pressure effects, it is observedthat at low pressure, 1H terminated edge can be stabi-lized over 2H terminated edge but after a certain pres-sure, 2H edge becomes more stable. We call this crossover point as the transition point. The pressure requiredto reach this transition point increases with temperatureas shown in the inset of figure 1. The values of transitionpoint pressures also suggest the possibility of the forma-tion of a 2H terminated reczag edge at room temperatureand ambient pressure. FIG. 2. (Color online) Zone center phonon DOSs plottedas a function of frequency for (a) 1H terminated ZGNR andreczag structures and (b) 2H terminated ZGNR and reczagstructures.
The calculated electronic structures (data not shown)for 1H and 2H terminations show the presence of finitedensity of states at Fermi energy originating mostly fromthe p z orbitals of the C atoms next to the edge C atoms.However, the magnetic moment is lost due to the satura-tion of C-C bonds at the edges, as seen earlier . Un-reconstructed ZGNR with 1H and 2H terminated edgeshave finite magnetic moments and metallicity . Incontrast to those, both 1H and 2H terminated reczagedges are non magnetic in the present case.Now, we show the comparison of the phonon densitiesof states of 1H and 2H terminated unreconstructed andreconstructed edge structures. The results are shown infigure 2 where only optical phonons are displayed. Fromthe figure it is clear that due to edge reconstruction, thelowest optical phonon modes are hardened. This hard-ening is however enhanced in the case when the edge is terminated with 2H compared to that of 1H. B. Edge termination with Fe Γ Xk-points-3-2-1012 E - E f ( e V ) Γ Xk-points 5 10 15DOS (states/eV)-3-2-1012 up up-dos down down-dos -0.4-0.200.20.4 p z p x p y -0.4-0.200.20.4 p z p x p y -5 -4 -3 -2 -1 0 1 2 3 E - E f (eV) -4-2024 d xy d yz d z - r d xz d x - y (i) (ii)(iii) D O S ( s t a t e s / e V ) FIG. 3. (Color online) (left) Total DOSs and band structuresfor an Fe decorated 12 rows reczag edge. Both spin-up andspin-down states are shown. (Right) Spin-polarized site andorbital projected DOSs for (a) C atoms in the middle of theribbon, (b) edge C atoms and (c) Fe atom.
The edge reconstruction destroys the magnetism of Catoms at the edges as the flat bands near or on Fermi levelfor unreconstructed GNRs are now highly dispersive dueto increased hybridization. To introduce magnetism andalso to observe magnetic interaction through graphenelattice, we decorated the edges with Fe atoms. Our ge-ometry optimization shows that the Fe atom placed inbetween two heptagons is favorable over top-hexagon ortop-pentagon positions by at least 27 meV/C atom. The4alculated formation energies of Fe terminated reczagedge are around 2.6 eV when the chemical potential ofFe is taken as the same as bulk bcc Fe. The formationenergy E f of a metal atom at the edge, is defined as E f = E ( M et N + reczag ) − [ N ∗ E ( M et ) + E ( reczag )],where E ( M et N + reczag ) is the total energy of geometryoptimized Metal+reconstructed edge graphene nanorib-bon, E ( reczag ) is the total energy for the optimized ge-ometry of reconstructed edge GNR and E ( M et ) is thechemical potential of the metal calculated in its bulkphase. N is the number of metal atoms in the unit cell. Itshould be noted that a recent paper reports a negativeformation energy (indication of spontaneous formation)for Fe decoration at the zigzag or armchair edges whenthe chemical potential is taken from Fe in the atomicphase. So, the formation of Fe decorated edges highlydepends on the Fe reference level. FIG. 4. (Color online) (top) Inter-edge exchange coupling(total energy difference between FM and AFM coupling acrossthe edges) plotted as a function of ribbon width, (bottom)Spin density isosurfaces of 8-rows Fe doped reczag edge for aFM coupling across the edges. Red and blue colors representspin-up and spin-down densities respectively.
Figure 3 shows the band structure and DOSs for anFe edge-decorated 12 rows reczag edge. The spin downchannel shows a localized peak in the total DOS (nondispersive band in the band structure plot) just belowthe Fermi level, contributed by Fe. The orbital projectedDOSs on Fe (shown in panel (c) at the right of Figure3) clearly indicate that this localized peak has a d z − r character in the spin-down channel. The spin-up channelof Fe is completely filled and has a negligible contributionwithin 2 eV below the Fermi level. The dispersive statesin this energy range in the band structure arise mainlyfrom edge C atoms. Projected DOSs on C atoms at theedge (panel (b)) are quite different from the ones in themiddle (panel (a)) of the nanoribbon. The dominance of p z character within a considerable energy range aroundFermi level in panel (a) is similar to what is observed forbulk graphene. The edge C atoms are spin-polarized anda strong contribution of in-plane p x and p y orbitals areseen in the similar energy range.If we look at the structural changes owing to the ad-dition of Fe atoms, it has effect on heptagons only as wehave seen for the hydrogenated reczag edges. But theeffect of Fe on the graphene lattice is longer ranged asevident from the spin density isosurfaces shown in fig-ure 4. The local moment on Fe is around 3.5 µ B forall widths considered. The Fe moments are quite ro-bust and they are independent of width as well as on theexchange coupling (FM or AFM) across the two edgesof the nanoribbons. The closest C atoms, to which Feis bonded, have induced moments antiparallel to the Feones and same for their same sublattice carbons, whereasother sublattice carbon atoms have in phase magnetiza-tion. As we travel towards the center of the ribbon, thiseffect is decreased. The opposite magnetization in dif-ferent sublattices is clearly visible throughout the ribbonfor the AFM coupled edges whereas for FM coupling, themagnetization disappears in the middle of the nanorib-bon due to the cancellation of induced moments.We have done a calculation to check the possibilityof monohydrogenation of a 12 rows reczag GNR alreadyfunctionalized with Fe. We have found that it’s com-paratively less favorable (formation energy of -0.29 eVcompared to -0.63 eV in the absence of Fe) to have a 1Htermination in the presence of Fe. This is expected as Feis already bonded at the edge and the H atom does nothave enough room for bonding as it was possible in theabsence of Fe. FIG. 5. (Color online) The structures of two dimerized chainsindicated as Dimer 1 (left) and Dimer 2 (right) in Table I.In the figure, red and yellow balls indicate Fe and C atomsrespectively.
The exchange coupling (measured by the total energydifference between FM and AFM coupling across the5 imer ∆ E (eV) Fe-Fe Fe-Fe momentdistance 1 (˚A) distance 2 (˚A) ( µ B )1 -0.23 2.61 2.30 2.942 -0.29 2.77 2.14 2.94TABLE I. Formation energies (∆ E ) of two types of Fe dimersin the chain with respective to non-dimerized structure. Thecorresponding bond lengths (short and long) of the Fe dimersare shown for the two structures shown in figure 5 along withthe local magnetic moments at Fe sites. edges) is plotted against the width of the nanoribbonand is shown in Figure 4. For 4 rows, there is a rela-tively strong FM coupling. With the increase in width,this coupling decreases and changes to an AFM one af-ter 8 rows. The AFM coupling tends to decrease after-wards. Interesting features of interedge coupling has beenreported recently for Fe and Co decorated armchairnanoribbons, where an oscillatory exchange coupling hasbeen observed. The analogy with interlayer exchangecoupling in case of magnetic multilayers coupled throughnonmagnetic layers was made in that paper. The pe-riod of the coupling was analyzed in connection to Fermisurface nesting vectors.Finally, we discuss the possibility of the formation of adimerized Fe chain along the edges of the nanoribbons asthis issue has been explored in case of unreconstructed6-6 nanoribbons . This situation is different from theabove discussions where the density of edge Fe atomswas considered to be lower. Here we allow the Fe atomsto bind to the edge C atoms of the heptagon in contrastto the previous case, where one Fe atom was allowed tosit in between the heptagons and hence, the Fe atomswere far enough to have the possibility of dimerization.To study the dimerization, we started the geometry op-timization from two different configurations of Fe dimersand have obtained the ground state geometries as shownin figure 5. One can observe two types of dimer struc-tures, one formed between the Fe atoms connected to thecarbon atoms of a heptagon (second structure of figure 5)and the second type is formed between the Fe atoms con-nected to carbon atoms belonging to adjacent heptagons.Both the dimers are stable with respect to non-dimerizedFe termination. Table I shows the energetics, structureand magnetism for the two cases. It is evident that Fedimers connected to the same heptagon is favorable overthe other one by an energy of 0.06 eV. The bond lengthof this dimer comes out to be 2.14 ˚A whereas the otherstructure yields a bond length of 2.3 ˚A. The local mag-netic moments on Fe are same for these two structuresand are close to 3 µ B . It is interesting to note that themoments are reduced compared to the non-dimerized Fechains, where the hybridization between the Fe-d orbitalswas weaker due to larger separations. The electronicstructure and corresponding magnetic exchange couplingfor these dimerized structures will be discussed in a fu-ture communication. IV. CONCLUSIONS
In this paper, chemical functionalization at the edgesof reconstructed zigzag graphene nanoribbons has beenstudied by ab initio density functional theory. Recon-structed edges do not show any magnetism and have ametallic behavior. From our calculations, it is seen thatboth single and dihydrogenated reczag edges are prob-able to form, as observed in previous theoretical calcu-lations.. Unlike unreconstructed ZGNRs, dihydrogena-tion is always favorable over monohydrogenated reczagedges, independent of the width of the nanoribbons un-der ambient conditions. We have also shown that at finitetemperatures, the hydrogen pressure dictates the forma-tion of mono- or di- hydrogenated edges. Our phononcalculations reveal a peculiar geometry at the dihydro-genated edges. Moreover, it has been found that thelowest optical phonon modes are hardened due to edgereconstruction. To render magnetism in reczag edges, wehave decorated the edges by Fe chains. The interedgemagnetic coupling varies between ferromagnetic and an-tiferromagnetic ones with the variation of the width ofthe nanoribbons with robust localized moments residingat the Fe sites. Finally, we show that the Fe atoms in thechain along an edge prefer to be in a dimerized configu-ration.
ACKNOWLEDGEMENTS
SH would like to acknowledge Indo-Swiss grant for fi-nancial support (No: INT/SWISS/P- 17/2009). BS ac-knowledges Swedish Research Links programme underVR/SIDA, G¨oran Gustafssons Stiftelse, Carl TryggersStiftelse and KOF initiative by Uppsala University for fi-nancial support. We thank SNIC-UPPMAX, SNIC-NSCand SNIC-HPC2N computing centers under Swedish Na-tional Infrastructure for Computing (SNIC) for grantingcomputer time. O.E. acknowledges support from ERCand the KAW foundation.
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