Journal ofMaterials Chemistry C

PAPER

Publ

ishe

d on

15

Febr

uary

201

3. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 26

/10/

2014

02:

02:0

7.

View Article OnlineView Journal | View Issue

aDepartment of Chemistry, Clark Atlanta Uni

Atlanta, GA 30314, USAbDepartment of Physics, Clark Atlanta Univ

Atlanta, GA 30314, USA. E-mail: xwang@ca

Cite this: J. Mater. Chem. C, 2013, 1,2696

Received 3rd January 2013Accepted 15th February 2013

DOI: 10.1039/c3tc00020f

www.rsc.org/MaterialsC

2696 | J. Mater. Chem. C, 2013, 1, 26

A trigonal planar network in hydrogenated epitaxialgraphene: a ferromagnetic semiconductor

Duminda K. Samarakoon,a Rosi N. Gunasinghea and Xiao-Qian Wang*b

Hydrogenated epitaxial graphene has distinctive electronic properties compared to the two-sided

hydrogenated graphene referred to as graphane. Of particular interest is the experimentally observed

room-temperature ferromagnetic semiconducting property, which has remained elusive to theoretical

interpretation. Here, we present results of a density functional theory investigation into various

hydrogenation patterns. Our results indicate that the stability of a given hydrogenation pattern is

strongly influenced by the amount of sp2-hybridized bonding in the structures. A hydrogenation

pattern with a trigonal planar network is identified as an intrinsic ferromagnetic semiconductor, which

is in very good conformity with experimental observations. Our results provide insight into the

structural, electronic, and magnetic properties of hydrogenated epitaxial graphene.

Introduction

Graphene, a single-layer of an all-carbon network, has beenshown to display a variety of unique and exploitable electronicand physical properties,1 including the quantum Hall effect andextremely high electron mobility at room temperature.2–4 Thesespecial characteristics make graphene a candidate for use inmany different potential applications, including transistors,integrated circuits, and biosensors.5–10 To realize these tech-nologies, it is necessary to understand and control its extraor-dinary properties.11–15 For example, learning how to engineerand to tune magnetic properties could help realize graphene-based spintronic devices.16 There have been several approachesto explore the magnetic properties in graphene and its deriva-tives. These include exfoliating graphene into nanoribbons,applying an electrical bias to graphene nanoribbons, andchemical modication through adsorption of radicals on thesurface of graphene.17–31

Attaching radicals to the surface of graphene leads tochemical bonding with carbon atoms and results in a change ofthe hybridization from sp2 to sp3, thus removing conjuga-tion.17,18 Furthermore, functionalizing graphene by reversiblehydrogenation can change its electronic properties frommetallic to semiconducting owing to the induced changes inhybridization.31,32 The fully hydrogenated graphene–graphane isthe building block of various novel materials and has increas-ingly opened up novel possibilities in hydrogen storage in two-dimensional electronics.33,34 On the other hand, epitaxial

versity, 223 James P. Brawley Drive, S.W.,

ersity, 223 James P. Brawley Drive, S.W.,

u.edu

96–2703

graphene (EG) grown on SiC exhibits a coherent transportproperty that holds potential for novel carbon-based nano-electronic applications.35,36 Recent experimental studies suggestthat the interface between the buffer layer graphene and silicon-terminated SiC can strongly inuence the electronic propertiesof the graphene overlayer.37 The graphene layer grows epitaxi-ally on SiC(0001)-(6O3� 6O3)R30� and can be exposed to atomichydrogen in an effort to alter the electronic properties of EG in acontrolled manner.37 While the two-sided hydrogenation ofgraphene has been studied intensively, the hydrogenation of EGremains not fully understood.

Full hydrogenation of EG yields the disappearance of bothoccupied and unoccupied p orbitals of graphene, resulting in anonmagnetic semiconductor.37 However, partial hydrogenationpreserves a fraction of the delocalized p network. As a result,unpaired spins facilitate long range coupling through thepercolated p network.37 Experimentally, ferromagnetism wasobserved in partial hydrogenated EG, which is attributed to adisrupted p bonding induced by the formation of unpairedelectrons.39 The hydrogenation mechanism on EG and theroom-temperature ferromagnetism are subject to considerableinterest. For instance, in semi-hydrogenated graphene referredto as graphone,40,41 the formation of unpaired electrons caninduce ferromagnetism.40 A robust room-temperature ferro-magnetic semiconductor for hydrogenated EG opens up thepossibility of making highly tunable graphene-based spintronicnanodevices.42

To facilitate a fundamental understanding of hydrogenatedEG and the ferromagnetic properties, herein we investigate agraphone–graphene bilayer using the rst-principles density-functional calculations. The graphone–graphene bilayer servesas a simplied model for the hydrogenation of EG. Amongpossible conformations of the graphone–graphene bilayer, our

This journal is ª The Royal Society of Chemistry 2013

Paper Journal of Materials Chemistry C

Publ

ishe

d on

15

Febr

uary

201

3. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 26

/10/

2014

02:

02:0

7.

View Article Online

attention is directed to the relative stability of bonded and non-bonded congurations. In the absence of H, two pristine gra-phene sheets interact with each other with weak van der Waalsforces.18,31 However, since unsaturated C sites in the graphonesheet are reactive due to unpaired electrons, a graphene sheetcan bind to graphone to form semi-hydrogenated bilayergraphone (referred to as BL-graphone hereaer). The ferro-magnetic properties of the BL-graphone depend crucially on theexistence of interlayer bonding or not.31 Our results indicatethat a non-bonding BL-graphone conformation is energeticallypreferred. The corresponding zigzag dimer chains can form atrigonal planar pattern, which has an intrinsic ferromagneticfeature independent of hydrogen or carbon defects. Interest-ingly, the trigonal planar pattern is in very good agreement withexperimental STM observations. Therefore, the trigonal planarhydrogenation pattern is yet another graphone structure thatserves as an inherent ferromagnetic semiconductor. Theproposed ferromagnetism mechanism for hydrogenated EGprovides a timely clarication of the experimental ndings.

Fig. 1 Optimized structures of semi-hydrogenated bilayer graphene. Carbonand hydrogen atoms are colored with orange (top layer), blue (bottom layer), andwhite, respectively. Insets: the hydrogenation arrangement in different confor-mations of BL-graphone using U and 0 for with and without hydrogenation,respectively.

Results and discussion

The local adsorption structures of single-sided hydrogenatedgraphene at low hydrogen coverage can be classied intomonomers, and para-, ortho-, or elongated-dimers. From theo-retical calculations,43–45 ortho- and para-dimers observed on thesurface of hydrogenated EG were predicted to be nonmagnetic,while single hydrogen attachment was predicted to bemagnetic.39,40 The ortho- and para-dimers are energetically themost stable dimer congurations on the basal plane.43–45 Duringhydrogen exposure, the dimers are formed into favorablebinding patterns. Thermodynamically, the barriers to bind intodimers are lower compared to those for hydrogen adsorptioninto monomers.37,46 However, the ensuing geometrical defor-mation plays an important role in determining the chemicalreactivity of hydrogen on EG. There is a decrease in theadsorption barrier because hydrogenation is associated withhybridization changes of the carbon from sp2 to sp3, whichyields motion of the carbon atom toward the hydrogenadsorption.37,38 The reaction-induced relaxation costs elasticpotential energy, and thus the hydrogen can bind favorably tothe peaks of the modulated EG surface.37,38 At high hydrogencoverage, however, random adsorption into large hydrogenatedclusters were observed experimentally.37,38 While the low-coverage hydrogenation behavior can be readily understood, thestructure and electronic properties of high-coverage hydroge-nation remain a paucity of investigation.

Graphone is a one-sided hydrogenated graphene, which hasa ferromagnetic semiconducting state if the hydrogenated sideis of a chair pattern.40,41 The ferromagnetic state is due to partialbreaking of p bonds of pristine graphene and the formation ofan alternative sp2–sp3–sp2–. carbon hybridization pattern.34

However, the thermodynamic stability of the chair-graphone isa subject of open debate.31 In fact, conformations such as boat,stirrup, and twist-boat patterns20,41 are clearly lower in energythan the chair-graphone, by about 0.33, 0.20, and 0.34 eV percarbon atom, respectively.31,41 In order to preserve the

This journal is ª The Royal Society of Chemistry 2013

ferromagnetic semiconducting feature, a few proposals basedon the bilayer counterpart of chair-graphone were put forward.Using rst-principles density functional calculations, it wasdemonstrated that a proper one-sided desorption of hydrogencould retain the magnetic state due to unpaired spins.31

Furthermore, applying an electrical bias perpendicularlybetween the graphene layers opens a band gap that can betuned continuously.31 As the bias is increased, the band gapcollapses, leading to a transition from a semiconductor to ametallic state. These predictions support the possibility thatgraphene can be employed to create more exible nanodeviceswith a tunable band gap, such as lasers that change color orelectronic circuits having the ability to rearrange them.

Nevertheless, a reexamination of the energy order for the BL-graphone is necessary in order to identify the lowest energyconformation of the hydrogenated EG. We show in Fig. 1 theoptimized structures of rec-stirrup, twist-boat, rec-chair, boat,stirrup, and chair conformations.7,21,41,47 Labeling the hydroge-nated and non-hydrogenated sites as U and 0 in a hexagonalring,48 stirrup can be characterized as UUU000, twist-boat as0UU00U, chair as 0U0U0U, and boat as U0UU0U/0U00U0 (insetsof Fig. 1), respectively. In the stirrup (UUU000) conformation,hydrogenation adsorption is along the zigzag direction in theUUU pattern. The rec-stirrup conformation has one graphenelayer and one graphone layer bonded non-covalently. Thebottom layer consists of sp2 hybridized carbon while the top

J. Mater. Chem. C, 2013, 1, 2696–2703 | 2697

Journal of Materials Chemistry C Paper

Publ

ishe

d on

15

Febr

uary

201

3. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 26

/10/

2014

02:

02:0

7.

View Article Online

layer is alternating sp2 and sp3 carbon chains along the zigzagdirection.

For the stirrup graphone layered on top of the graphene, thelayer separation is 3.62 A without interlayer bonding. As aresult, the bottom graphene layer is at. The lack of bondingyields a stirrup graphone with alternating sp2 (red box in Fig. 1)and sp3 chains along the zigzag direction. The C–C bond lengthalong the sp2 zigzag chain is 1.42 A, while that along the sp3

zigzag chain is 1.51 A, which is slightly shorter than the usualcarbon–carbon sp3 length of 1.56 A. The C–C bond length of thegraphene layer is 1.43 A that is slightly longer than the typicalsp2 bond length of 1.42 A. The commensurate bilayer stackingleads to compressive strain in the rec-stirrup graphone layer andtensile strain in the graphene layer. As seen in Fig. 1, thegraphone layer shis 0.66 A along the armchair direction rela-tive to the AB stacked bilayer graphene. On the other hand,there is no shi in the zigzag direction. The interlayer non-bonding side pattern has 5–7 carbon rings, reminiscent of theM-carbon and the rec-chair bilayer graphone.21,40

In the twist-boat (0UU00U) conformation,20,49 hydrogenadsorption is alternative to the armchair and zigzag directions.As seen in Fig. 1, the twist-boat graphone layer shis as well,�0.56 A along the armchair direction relative to the AB stackedbilayer. Unlike the rec-stirrup or twist-boat, boat (U0UU0U/0U00U0) conformation in BL-graphone has covalent bondingbetween the layers.20 The interlayer bonding replaces sp2

hybridization with sp3 one. Similarly, rec-chair (U0U0U0) bilayergraphone also has bonding between two layers, but the bondingpattern is different from the boat BL-graphone. Instead ofhaving alternative sp2 and sp3 carbons along zigzag, rec-chairbilayer graphone alternate sp2 and sp3 carbon chains along thezigzag direction. The alternate sp2 and sp3 carbon chains makerec-chair bilayer graphone a directional conductor similar to therec-stirrup structure. AB-stacked-chair also consists of twobonded layers of carbons. Bernal-stacked chair has sp2 and sp3

carbon patterns like in bilayer graphone.We have calculated binding energy per atom (Eb) and the

energy gap (Eg) for semi-hydrogenated BL-graphone conforma-tions (Table 1). As seen from Table 1, rec-stirrup is energeticallyfavored over other structures. Among those structures in Fig. 1,rec-stirrup, rec-chair, twist-boat, and unreconstructed stirrupconformations show metallic behavior, while the boat

Table 1 Calculated binding energy per carbon atom Eb, the band gap Eg, andthe cell dimension a� b for chair, stirrup, boat, and twist-boat conformations andtheir reconstructed counterparts of semi-hydrogenated bilayer graphene

Structure Eb (eV) Eg (eV) a � b (A � A)

rec-Stirrup �9.97 0 4.26 � 2.49Twist-boat �9.90 0 4.98 � 4.56rec-Chair �9.89 0 4.29 � 2.51Boat-I �9.89 3.22 4.20 � 2.53Boat-II �9.79 2.73 4.57 � 2.58Stirrup-I �9.76 0 4.17 � 2.64Stirrup-II �9.58 0 4.17 � 2.64Chair-I �9.56 0.87 2.63 � 2.63Chair-II �9.53 0.90 2.63 � 2.63

2698 | J. Mater. Chem. C, 2013, 1, 2696–2703

conformations show semiconducting behavior. Both unrecon-structed chair conformations, chair-I and chair-II, are ferro-magnetic semiconductors. Among the 9 congurationsconsidered, rec-stirrup, twist-boat, rec-chair, and boat-I undergoa planar shi relative to the underlying graphene layer. Stirrup-I, stirrup-II, and chair-II are of AA stacking in that the C atomsin the graphone layer are on top of the C atoms in the graphenelayer. The only Bernal stacked pattern is chair-I, the well-dis-cussed ferromagnetic graphone conrmation on top of thegraphene layer.40

The resonance sp2 geometries, resulting in p-electron delo-calization along the zigzag chain, contribute to the stability of astructure. The more sp2 bonding in a structure, the greater thestability of that structure. In fact, this explanation aloneaccounts for the energy ordering of the conformations shown inFig. 1 (Table 1). The sp2–sp3 ratios are 1.5, 1.0 and 0.5 for the rec-stirrup (UUU000), the twist-boat (0UU00U), and rec-chair(U0U0U0) structures, respectively. The remaining structureshave half sp2 bonding regions in the graphene layer and are lessstable, according to our calculations. Interestingly, this impliesthat the stability of the hydrogenated zigzag chain is not limitedto the semi-hydrogenation coverage.

The stirrup (UUU000) conformation is the most stableconguration for BL-graphone (Table 1). For this energeticallypreferred structure, there is no bonding between the layers,along with greater sp2 bonding compared to the other struc-tures. The existence of delocalized p orbitals on the zigzag sp2

carbon chains stabilizes the corresponding conformations. Theconjugated chain in rec-stirrup results in a directional metallicbehavior. As such, the experimentally observed elongated dimerchain along the zigzag can be interpreted as being attributed tothe preferred conjugations in the hydrogenated EG.

We are now in a position to discuss electronic structurecharacteristics of these conformations. The rec-stirrup has twoseparate layers bonded non-covalently. The corresponding bandstructure (Fig. 2a) can be viewed as twomerged bands, one fromthe graphene layer and the other from the graphone layer. Fornoncovalently bonded layers, the “substrate” graphene layerpreserves its electronic characteristics. In the context of EG, thisimplies that the buffer layer of EG interacts weakly with thehydrogenated graphene layer. Consequently, the Dirac conesemimetallic feature as shown in Fig. 2 should be replaced withthe corresponding buffer layer contribution. In contrast, forbonded conformations, rec-chair, boat, stirrup and chair, themodication of sp2 to sp3 bonding leads to profound changes ofthe structural and electronic properties.

We depict in Fig. 3 the top layer contribution of the chargedensity of BL-graphone for conduction band minimum (CBM)and valence band maximum (VBM), respectively. For CBM, thecharges are predominantly conned at the sp3 sites. For VBM,alternative sp2 and sp3 features are clearly observable. Thedirectional metallic behavior is attributed to the conjugatedchain in rec-stirrup. As such, the experimentally observedelongated dimer chain along the zigzag may be attributed to thepreferred conjugations in the hydrogenated EG.

An important ramication of the stability of rec-stirrup isthat the elongated dimers forming along the zigzag direction is

This journal is ª The Royal Society of Chemistry 2013

Fig. 2 Calculated band structures for (a) rec-stirrup, (b) twist-boat, (c) rec-chair,and (d) boat conformations of semi-hydrogenated bilayer graphene. For rec-stirrup Y ¼ (0, p/2b), G ¼ (0, 0), and B ¼ (�p/2a, 0), where a ¼ 4.26 A and b ¼2.49 A. For twist-boat Y ¼ (0, p/2b1), G ¼ (0, 0), and B ¼ (p/2a1, 0), where a1 ¼4.56 A and b1 ¼ 4.98 A. For rec-chair Y ¼ (0, p/2b2), G ¼ (0, 0), and B ¼ (�p/2a2,0), where a2 ¼ 4.29 A and b2 ¼ 2.51 A. For boat Y¼ (0, p/2b3), G¼ (0, 0), and B¼(�p/2a3, 0), where a3¼ 4.20 A and b3¼ 2.53 A. The valence bandmaximum is setto 0 eV.

Fig. 3 Extracted charge density for semi-hydrogenated bilayer graphene of CBMand VBM in top and bottom panels, respectively. The isovalue is 0.05 a.u.

Fig. 4 Calculated band structures for rec-stirrup conformation of semi-hydro-genated bilayer graphene (a) with one H defect (red box in the inset), (b) with oneC defect (red box in the inset) in the top layer. G ¼ (0, 0), B ¼ (0, p/2b) and Y ¼(p/2a, p/2b), where a¼ 8.52 A and b¼ 4.97 A. The valence band maximum is setto 0 eV. Insets: calculated spin density. The isovalue is 0.03 a.u.

Paper Journal of Materials Chemistry C

Publ

ishe

d on

15

Febr

uary

201

3. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 26

/10/

2014

02:

02:0

7.

View Article Online

energetically preferred for high coverage of hydrogenation.Since there are three equivalent zigzag directions in EG, we caninfer that the elongated dimer patterns should be observed

This journal is ª The Royal Society of Chemistry 2013

experimentally. Closer scrutiny of the experimental STM imagesindeed reveals such elongated dimer conformations.37,38 Theelongated dimer chain is closely connected to themetallic chainbehavior of the rec-stirrup at high stoichiometry of hydrogena-tion (Fig. 3). In reality, the linear metallic behavior cannot bepreserved as hydrogenated zigzag chains are randomly distrib-uted among the three orientations. The linear metallic chain ismanifested in the band structures of rec-stirrup (Fig. 2a) and rec-chair (Fig. 2c) by a touching point at the band edge (Y). However,the origin of the semimetallic feature arises from the top andbottom layers for rec-stirrup and rec-chair, respectively. On theother hand, boat (U0UU0U/0U00U0) conformation has a largeband gap (Fig. 2c). Even though the boat conformation has sp2

hybridized carbons in the bottom graphene layer, the non-conjugated patterns yield localized electrons. The band gap of�3.1 eV in the boat BL-graphone (Fig. 2d) is in conformity withthe band gap of bilayer graphane of �2.92 eV.31

Ferromagnetism generated by monomers corresponds to avery low hydrogenation concentration,38,50 which is difficult tocontrol. Experimental studies have demonstrated ferromag-netic ordering, which was argued to be attributed to variousdefects on graphene structures, such as vacancy, topologicaldefects or frustration, and hydrogen chemisorptions.39,40,50–56

The defects to the rec-stirrup (UUU000) conformation can beeither from the H-defect or the C-defect. The former is missinghydrogenation along the zigzag chain, while the latter has a C-vacancy. Both defects lead to ferromagnetic properties of thehydrogenated EG (Fig. 4). However, the coupling between themagnetic moments is either ferromagnetic or antiferromag-netic, depending on whether the defects correspond to the same(AA) or to different (AB) hexagonal sublattices of graphene. Inboth cases of a pair of H-defects or a pair of C- and H-defects,antiferromagnetically coupled AB defects are energeticallyfavored. As such, the underlying mechanism of the ferromag-netic property of hydrogenated EG remains unsettled as yet.

Experimental works have demonstrated ferromagneticordering among various defects on graphene structures, such as

J. Mater. Chem. C, 2013, 1, 2696–2703 | 2699

Journal of Materials Chemistry C Paper

Publ

ishe

d on

15

Febr

uary

201

3. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 26

/10/

2014

02:

02:0

7.

View Article Online

vacancy, topological defects or frustration, and hydrogenchemisorptions. The defects to the rec-stirrup (UUU000)conformation can be either from the H-defect or the C-defect.The former is a missing hydrogenation along the zigzag chain,while the latter is from a C-vacancy. Both defects lead to ferro-magnetic properties of the hydrogenated EG. As shown in Fig. 4,both systems are in ferromagnetic states. The spin densitydistribution as shown in the insets of Fig. 4 indicates localizedmagnetism. The induced magnetic moment is close to 1 mB forboth cases. The energy cost for the H-defect is �2.74 eV, whilethe cost for the C-defect is much higher, about 11.34 eV. For apair of hydrogen defects that are �8 A apart from each other,the antiferromagnetically coupled defects (AB defects) are morestable than the ferromagnetically coupled defects (AA defects),with an energy difference of �0.58 eV. Comparing one C-defectwith one H-defect, the AB defect pair is�0.04 eV lower in energythan the AA counterpart. In both cases, antiferromagneticallycoupled AB defects are energetically favored.

Pursuing further the idea of elongated dimer chains alongzigzag, we build a trigonal planar network of stirrup patterns.Such a network can be constructed by expanding the rhombusunit cell of graphene along the two unit directions odd-numberof times simultaneously. Illustrated in Fig. 5a is the 7 � 7rhombus cell with 98 carbon atoms and 37 hydrogen atoms. Therhombus cell has a length of 17.22 A, and the unit cell contains38% hydrogen concentration. It is worth noting that theexperimental maximal concentration of hydrogenation is about40%.37,38,50 As such, the trigonal planar conformation appears tobe the densest network for hydrogenated EG.

Closer scrutiny of the experimental STM38 reveals that thereevidently exists trigonal planar conformation. The basins of thetriangular and rhombus cells have depths of 3.9 and 3.0 A,respectively. The basins correspond to the dark spots observedin the experimental STM.38 To demonstrate this effect, we

Fig. 5 (a) Top view of the trigonal planar patterned graphone and (b) theexperimental STM image adapted with permission from ref. 38. Copyright 2009American Chemistry Society. Bottom panels: side view of triangular- andrhombus-shaped resins. Hydrogen and carbon atoms are colored with yellow andred, respectively.

2700 | J. Mater. Chem. C, 2013, 1, 2696–2703

highlighted in Fig. 5a oval and round black spots in order tomimic the basin patterns. As seen from Fig. 5, there is a verygood agreement with the theoretically predicted trigonal planarpattern and the experimentally observed STM. Specically, thecell length is in conformity with each other, which stronglysupports the suggested trigonal planar pattern.

In contrast to the induced ferromagnetism due to C- andH-defects, the trigonal planar conformation has an inherentferromagnetic property. As seen in Fig. 6, the trigonal planarhydrogenated EG is a ferromagnetic semiconductor. The spingap is about 0.52 eV (a direct gap at K), and the magneticmoment is 1 mB (313 a-electrons and 312 b-electrons) per unitcell. This intrinsic ferromagnetic property is attributed to theimbalance of the a-electrons and b-electrons in A and B sub-lattices (inset of Fig. 6). It is also worth emphasizing that thetrigonal planar network is distinctive from the graphone in thatthe chair conformation is no longer energetically favored inone-sided hydrogenation. Furthermore, the building blocks ofthe trigonal planar conformation—stirrup dimer chains—correspond to the most energetically stable conformation.17,18

The experimentally observed elongated chains are a few carbonatoms long, and two or three carbon chains are slanted to eachother, which supports our theoretical results that the conjuga-tion associated with the stirrup conformation yields preferredhydrogenation patterns.37,38 In general, the trigonal planarnetwork has another type of “defects” in that the missingH-pairs are inevitable. However, the missing H-pairs do notchange the intrinsic ferromagnetism property, which arisesfrom the inherent difference of the hydrogenation on A and Blattices, which is associated with the unique trigonal planarpattern. In fact, the quasilocalized feature of the near-gap states

Fig. 6 Calculated band structures for trigonal planar conformation. G ¼ (0, 0), K¼ (�p/3a, 2p/3a, 0) and M ¼ (0, p/2a), where a ¼ 17.22 A. The valence bandmaximum is set to 0 eV. Inset: calculated spin density (a-electrons and b-electronsare colored with blue and orange, respectively) with an isovalue of 0.01 a.u.

This journal is ª The Royal Society of Chemistry 2013

Fig. 7 Extracted charge density of near-gap states for trigonal planar confor-mation (a-electrons and b-electrons are colored with blue and purple, respec-tively) with an isovalue of 0.01 a.u.

Paper Journal of Materials Chemistry C

Publ

ishe

d on

15

Febr

uary

201

3. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 26

/10/

2014

02:

02:0

7.

View Article Online

is reminiscent of the relative at dispersions of the bandstructure (Fig. 6).

We illustrate in Fig. 7 the extracted charge density distribu-tions near the Fermi level. As seen in Fig. 7, the splitting of thespin states leads to nonidentical charge density for the corre-sponding states. It is worth noting that the near gap states arepretty at, indicating that the charges are conned in specicregions. The charge connement is depicted by spotted regionsof the charge density distribution.

Conclusions

In summary, our calculations reveal that the itinerant magne-tism can be triggered by a trigonal planar network in EG, whichis stable over the wide range of concentrations. The trigonalplanar pattern has an intrinsic ferromagnetic property. It isworth noting that ferromagnetic ordering is the only possibilityfor the magnetism originating from quasilocalized statesinduced by the differences of the hydrogenation of A and Bsublattices and the exchange coupling is characterized by theindirect spin-polarization effect. As such, the proposed trigonalplanar pattern is distinct from defect-induced ferromagnetismin that the ferromagnetic coupling is actually thermodynami-cally stable. At this point, it is worth noting that a recentexperimental study on the interaction of hydrogen plasma withmonolayer and multilayer graphene deposited on SiO2 revealedextremely high monolayer selectivity toward a hydrocarbon-forming reaction with hydrogen radicals and ions.60 The reac-tions result in random, continuously nucleating isotropic holes,

This journal is ª The Royal Society of Chemistry 2013

rather than well-organized patterns observed in experimentsusing an atomic hydrogen beam source.39 On the other hand, Hfrustration plays a role in the hydrogenation patterns as well.61

However, the frustration effect is more predominant for two-sided hydrogenations than one-sided hydrogenation.61 Never-theless, the formation of large domains of perfect trigonalnetworks was evidently demonstrated in various experimentalinvestigations. In fact, the stirrup dimer chains and the trigonalplanar pattern appear to be a typical feature of the ferromag-netic coupling in a large class of chemical functionalized EG.36

We hope the advocated trigonal planar network can stimulatefurther experimental work in this direction.

Computational session

The structural and electronic properties were investigated usingthe rst-principles density functional theory approach asimplemented in the DMol3 package.57 Our rst-principlescalculations are based on spin polarized dispersion correcteddensity functional theory with a general gradient approximation(GGA) for exchange–correlation potential.58 We employed thedispersion correction with the GGA using the Tkatchenko–Scheffler (TS) scheme, which exploits the relationship betweenpolarizability and volume.59 The TS dispersion correctionaccounts for the relative variation in dispersion coefficients ofdifferently bonded atoms by weighing values taken from thehigh-quality rst-principles database with atomic volumesderived from partitioning of the self-consistent electronicdensity.59 Our calculations reveal that the dispersion correctedGGA with the exchange correlation of Perdew–Burke–Ernzerhof(PBE)58 approximates the interlayer distance in bilayer graphenebetter than the GGA PBE itself and the local density approxi-mation (LDA) approach. A kinetic energy change of 3 � 10�4 eVin the orbital basis and appropriate Monkhorst�Pack k-pointgrids of 6 � 6 � 1 were sufficient to converge with the integra-tion of the charge density.57 The optimization of the atomicpositions proceeds until the change in energy is less than 1 �10�5 eV per cell. A supercell with a vacuum space of 16 A normalto the graphene plane was used.

The incorporation of the dispersion correction is importantfor accurately describing the interlayer van der Waals interac-tions. The employed scheme has been tested for various non-covalent functionalized graphene systems. It is well-known,however, that the density-functional approach underestimatesthe band gaps. Since our primary goal was to identify theferromagnetic properties, a spin-polarized calculation wasemployed. A semi-local approximation can be utilized to rectifythe band gaps. The semi-local calculation is, however, compu-tationally intensive for the trigonal planar conformations. Therectication of the band gap is thus le for future investigation.

Acknowledgements

This work was supported by the National Science Foundationunder Grant DMR-0934142 and the Air Force Office of ScienticResearch under Grant FA9550-10-1-0254.

J. Mater. Chem. C, 2013, 1, 2696–2703 | 2701

Journal of Materials Chemistry C Paper

Publ

ishe

d on

15

Febr

uary

201

3. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 26

/10/

2014

02:

02:0

7.

View Article Online

Notes and references

1 A. K. Geim and K. S. Novoselov, Nat. Mater., 2007, 6, 183.2 Y. Zhang, Y. W. Tan, H. L. Stormer and P. Kim, Nature, 2005,438, 201.

3 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang,S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, Science, 2004,306, 666.

4 C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud,D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad,P. N. First and W. A. de Heer, Science, 2006, 312, 1191.

5 W. A. de Heer, C. Berger, M. Ruan, M. Sprinkle, X. Li, Y. Hu,B. Zhang, J. Hankinson and E. H. Conrad, Proc. Natl. Acad.Sci. U. S. A., 2011, 108, 16900.

6 Y. Zhang, Z. Jiang, J. P. Small, M. S. Purewal, Y.-W. Tan,M. Fazlollahi, J. D. Chudow, J. A. Jaszczak, H. L. Stormerand P. Kim, Phys. Rev. Lett., 2006, 96, 136806.

7 X. Wang, L. Zhi and K. Mullen, Nano Lett., 2008, 8, 323.8 S. Gilje, S. Han, M. Wang, K. L. Wang and R. B. Kaner, NanoLett., 2007, 7, 3394.

9 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang,M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos andA. A. Firsov, Nature, 2005, 438, 197.

10 F. Schwierz, Nat. Nanotechnol., 2010, 5, 487.11 R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov,

T. J. Booth, T. Stauber, N. M. R. Peres and A. K. Geim,Science, 2008, 320, 1308.

12 F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake,M. I. Katsnelson and K. S. Novoselov, Nat. Mater., 2007, 6,652.

13 A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan,F. Miao and C. N. Lau, Nano Lett., 2008, 8, 902.

14 Q. Shao, G. Liu, D. Teweldebrhan and A. A. Balandin, Appl.Phys. Lett., 2008, 92, 204308.

15 A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake,M. I. Katsnelson and K. S. Novoselov, Nat. Mater., 2007, 6,652.

16 Y. Wang, Y. Huang, Y. Song, X. Zhang, Y. Ma, J. Liang andY. Chen, Nano Lett., 2009, 9, 220.

17 S. Ryu, M. Y. Han, J. Maultzsch, T. F. Heinz, P. Kim,M. L. Steigerwald and L. E. Brus, Nano Lett., 2008, 8,4597.

18 L. Ci, Z. Xu, L. Wang, W. Gao, F. Ding, K. F. Kelly,B. I. Yakobson and P. M. Ajayan, Nano Res., 2008, 1, 116.

19 Z. Chen and X.-Q. Wang, Phys. Rev. B: Condens. Matter Mater.Phys., 2011, 83, 081405.

20 D. K. Samarakoon, Z. Chen, C. Nicolas and X.-Q. Wang,Small, 2011, 7, 965.

21 J. Zhou, Q. Wang, Q. Sun and P. Jena, Appl. Phys. Lett., 2011,98, 063108.

22 J. Sivek, O. Leenaerts, B. Partoens and F. M. Peeters, J. Phys.Chem. C, 2012, 116, 19240.

23 R. Zboril, F. Karlicky, A. B. Bourlinos, T. A. Steriotis,A. K. Stubos, V. Georgakilas, K. Safarova, D. Jancik,C. Trapalis and M. Otyepka, Small, 2010, 6, 2885.

24 M. A. Ribas, A. K. Singh, P. B. Sorokin and B. I. Yakobson,Nano Res., 2011, 4, 143.

2702 | J. Mater. Chem. C, 2013, 1, 2696–2703

25 L. Zhu, H. Hu, Q. Chen, S. Wang, J. Wang and F. Ding,Nanotechnology, 2011, 22, 185202.

26 L. A. Chernozatonskii, P. B. Sorokin, A. A. Kuzubov,B. P. Sorokin, A. G. Kvashnin, D. G. Kvashnin, P. V. Avramovand B. I. Yakobson, J. Phys. Chem. C, 2011, 115, 132.

27 A. A. Avetisyan, B. Partoens and F. M. Peeters, Phys. Rev. B:Condens. Matter Mater. Phys., 2010, 81, 115432.

28 Y. Zhang, T.-T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl,M. F. Crommie, Y. R. Shen and F. Wang, Nature, 2009, 459,820.

29 Z. Zhang, C. Chen, X. C. Zeng and W. Guo, Phys. Rev. B:Condens. Matter Mater. Phys., 2010, 81, 155428.

30 B. Sahu, H. Min and S. K. Banerjee, Phys. Rev. B: Condens.Matter Mater. Phys., 2010, 82, 115426.

31 D. K. Samarakoon and X.-Q. Wang, ACS Nano, 2010, 4,4126.

32 D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V. Morozov,P. Blake, M. P. Halsall, A. C. Ferrari, D. W. Boukhvalov,M. I. Katsnelson, A. K. Geim and K. S. Novoselov, Science,2009, 323, 610.

33 K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg,L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Rohrl,E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weberand Th. Seyller, Nat. Mater., 2009, 8, 203.

34 A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic,M. S. Dresselhaus and J. Kong, Nano Lett., 2009, 9, 30.

35 H. Zhang, E. Bekyarova, J. W. Huang, Z. Zhao, W. Bao,F. Wang, R. C. Haddon and C. N. Lau, Nano Lett., 2011, 11,4047.

36 J. Hong, E. Bekyarova, P. Liang, W. A. de Heer, R. C. Haddonand S. Khizroev, Sci. Rep., 2012, 2, 624.

37 N. P. Guisinger, G. M. Rutter, J. N. Crain, P. N. First andJ. A. Stroscio, Nano Lett., 2009, 9, 4.

38 R. Balog, B. Jørgensen, J. Wells, E. Lægsgaard, P. Hofmann,F. Besenbacher and L. Hornekær, J. Am. Chem. Soc., 2009,131, 8744.

39 L. Xie, X. Wang, J. Lu, Z. Ni, Z. Luo, H. Mao, R. Wang,Y. Wang, H. Huang, D. Qi, R. Liu, T. Yu, Z. Shen, T. Wu,H. Peng, B. Ozyilmaz, K. Loh, A. T. S. Wee, Ariando andW. Chen, Appl. Phys. Lett., 2011, 98, 193113.

40 L. Pisani, B. Montanari and N. M. Harrison, New J. Phys.,2008, 10, 033002.

41 J. Zhou, Q. Wang, Q. Sun, X. S. Chen, Y. Kawazoe and P. Jena,Nano Lett., 2009, 9, 3867.

42 D. K. Samarakoon and X.-Q. Wang, ACS Nano, 2009, 3, 4017.43 N. Tombros, C. Jozsa, M. Popinciuc, H. T. Jonkman and

B. J. Wees, Nature, 2007, 448, 571.44 S. Casolo, O. M. Lovvik, R. Martinazzo and G. F. Tantardini,

J. Chem. Phys., 2009, 130, 54704.45 L. Hornekaer, Z. Sljivancanin, W. Xu, R. Otero, E. Rauls,

I. Stensgaard, E. Lægsgaard, B. Hammer andF. Besenbacher, Phys. Rev. Lett., 2006, 96, 156104.

46 Y. Ferro, D. Teillet-Billy, N. Rougeau, V. Sidis, S. Morissetand A. Allouche, Phys. Rev. B: Condens. Matter Mater. Phys.,2008, 78, 8.

47 O. Leenaerts, B. Partoens and F. M. Peeters, Phys. Rev. B:Condens. Matter Mater. Phys., 2009, 80, 245422.

This journal is ª The Royal Society of Chemistry 2013

Paper Journal of Materials Chemistry C

Publ

ishe

d on

15

Febr

uary

201

3. D

ownl

oade

d by

Mon

ash

Uni

vers

ity o

n 26

/10/

2014

02:

02:0

7.

View Article Online

48 X.-D. Wen, L. Hand, V. Labet, T. Yang, R. Hoffmann,N. W. Ashcro, A. R. Oganov and A. O. Lyakhov, Proc. Natl.Acad. Sci. U. S. A., 2011, 108, 6833.

49 D. K. Samarakoon and X.-Q. Wang, Nanoscale, 2011, 3,192.

50 Y. Wang, Y. Huang, Y. Song, X. Zhang, Y. Ma, J. Liang andY. Chen, Nano Lett., 2009, 9, 220.

51 D. W. Boukhvalov, M. I. Katsnelson and A. I. Lichtenstein,Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 77,035427.

52 O. V. Yazyev and L. Helm, Phys. Rev. B: Condens. MatterMater. Phys., 2007, 75, 125408.

53 P. Ruffieux, O. Groning, P. Schwaller, L. Schlapbach andP. Groning, Phys. Rev. Lett., 2000, 84, 4910.

54 H. A. Mizes and J. S. Foster, Science, 1989, 244, 559.

This journal is ª The Royal Society of Chemistry 2013

55 P. Ruffieux, M. Melle-Franco, O. Groning, M. Bielmann,F. Zerbetto and P. Groning, Phys. Rev. B: Condens. MatterMater. Phys., 2005, 71, 153403.

56 V. M. Pereira, F. Guinea, J. M. B. Lopes dos Santos,N. M. R. Peres and A. H. Castro Neto, Phys. Rev. Lett., 2006,96, 036801.

57 DMol3, Accelrys Soware Inc., San Diego, CA, 2011.58 J. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996,

77, 3865.59 A. Tkatchenko and M. Scheffler, Phys. Rev. Lett., 2009, 102,

073005.60 G. Diankov, M. Neumann and D. Goldhaber-Gordon, ACS

Nano, 2013, 7, 1324.61 M. Z. S. Flores, P. A. S. Autreto, S. B. Legoas and D. S. Galvao,

Nanotechnology, 2009, 20, 465704.

J. Mater. Chem. C, 2013, 1, 2696–2703 | 2703