Physics Letters A 372 (2008) 5492–5497

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Physics Letters A

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Metal-free spin channels in graphitic boron–nitrogen nanostructures

Sérgio Azevedo a,∗, Jorge Kaschny a, F. Moraes b

a Departamento de Física, Universidade Estadual de Feira de Santana 44031-460, Feira de Santana, BA, Brazilb Departamento de Física, CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970 João Pessoa, PB, Brazil

a r t i c l e i n f o a b s t r a c t

Article history:Received 3 March 2008Received in revised form 19 June 2008Accepted 21 June 2008Available online 3 July 2008Communicated by V.M. Agranovich

PACS:85.75.-d75.75.+a71.15.-m

Keywords:Spin-polarizationBoron nitrideFirst-principles

Evidence is given for the existence of metal-free spin channels in an insulating medium. First-principlescalculations indicate the presence of an unpaired spin, in a ground state boron–nitrogen nanostructurewith a carbon zig–zag chain generated by the inclusion of a disclination with either negative or positiveGaussian curvature. The spin-polarized states are delocalized on the carbon chain suggesting possiblespintronics applications.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

Mobile spins are an important issue in the developing field ofspintronics [1,2]. Separation of spin and electrical charge, a rarephenomenon that appears, for instance, in trans-polyacetylene[3–6], may be an extra advantage for developing spin circuits. Inthis Letter, we applied first-principles calculations to present apossible way of building metal-free spin channels in an insulatingmedium. Starting with graphitic boron nitride, with the inclusionof topological defects, which introduce either a boron or a nitro-gen zig–zag chain and, substituting those by carbon atoms, we findstrong spin delocalization on the carbon chain. Since the wholestructure is neutral there is no net electrical charge associated tothe delocalized spin. The structural stability of the BN nanoconeand its insulating properties make it a template for designing spincircuits.

Boron–nitride (BN) and carbon can be found in similar struc-tures, from the diamond and graphite bulk forms, to nanostruc-tures such as nanotubes [7–10], fullerenes [11,12], and conicalsheets [13,14]. However, unlike carbon, BN structures can containthree types of covalent bonds, namely B–N, N–N, and B–B [15,16].This leads to a qualitative difference between BN and carbon in theformation of the graphite-derived curved surfaces that are found

* Corresponding author. Tel.: +557532248206.E-mail address: sazevedo@uefs.br (S. Azevedo).

0375-9601/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.physleta.2008.06.076

in nanostructures such as fullerenes and nanotube caps. Recently,Wu and coworkers [17], using density functional theory, found un-paired electronic magnetic moment in BN nanotubes doped witha carbon atom. In this work we are also interested in a combinedBN and carbon structure such that we have basically an insulat-ing BN structure which contains a carbon chain like polyacetylene(which provides delocalization) ending in an odd-membered ringwhich provides the unpaired spin.

In recent works, both experiments [18,19] and theory [20–23]indicate that carbon materials can exhibit spin polarization with-out impurities. Park and coworkers [22], using the ab initio spindensity functional theory, found that carbon in compounds withnegative Gaussian curvature carry a net magnetic moment in theground state. In fact, starting from the graphene sheet, which isplanar, interchanging a six-membered carbon ring by a seven-membered ring introduces not only negative Gaussian curvaturebut also an extra trivalent carbon atom which is the source of anunpaired spin. In this case, the corresponding state is delocalizedover the entire structure and not confined to the ring. It is our ideato have only a single carbon chain in a BN structure, restrictingthus the delocalization of the unpaired spin to this carbon chan-nel.

In this Letter, we investigate the electronic properties of BNnanostructures, both of positive (cone) and negative (saddle) cur-vature, with antiphase boundaries (APB). The curved structuresare obtained from the planar graphite-like BN network by theintroduction of disclinations [15]. Our first-principles results in-

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Fig. 1. Topological construction of ±60◦ disclinations in a BN sheet. Nitrogen and boron atoms are represented by black and white circles, respectively. Hydrogen atoms(smaller black circles) saturate the dangling bonds at the wedges. (a) Flat BN sheet; (b) BN sheet with 60◦ wedge removed; (c) identification of the edges introduces +60◦disclination (cone) in the BN sheet with zig–zag APB of Nitrogen (Zig-N); (d) insertion of 60◦ wedge in the BN sheet; (e) identification of the edges introduces −60◦disclination (saddle) in the BN sheet with zig–zag APB of Nitrogen (Zig-N).

dicate that structures involving full carbon incorporation at theAPB, independently of the curvature sign, present a single un-paired electron in the ground state. We find that the origin of theunpaired spin in the BN network with disclinations is similar tothat of previous reports [24,25], which related the spin polariza-tion at a graphite wedge to the presence of two-fold coordinatedcarbon atoms. In Ref. [22] it was suggested that unpaired spinsmay be introduced by carbon radicals, rather than undercoordi-nated atoms. In the case studied here, the polarization is due tothe carbon doping of the APB introduced by the disclination in theBN sheet.

Our attention focuses on BN compounds with disclination an-gles of ±60◦ since they are the most energetically stable de-fects [26]. Fig. 1 illustrates the “cut and glue” topological process of

introducing such defects. Depending on where the cut is made theAPB may have either boron or nitrogen atoms in a zig–zag chain.In either case, further substitution of the zig–zag atoms by carbonleads to the zig-CB or zig-CN structures.

Our calculation is based on the density functional theory[27] as implemented in the SIESTA program [28]. We make useof non-conserving Troullier–Martins pseudopotentials [29] in theKleinmann–Bylander factorized form [30] and a double-ζ basis setcomposed of numerical atomic orbitals of finite range. Polarizationorbitals are included for nitrogen, boron, and carbon atoms, andwe use the generalized gradient approximation [31] (GGA) for theexchange-correlation potential. All the geometries are fully relaxed,with residual forces smaller than 0.1 eV/Å. When the maximumdifference between the output and the input on each element of

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Fig. 2. Density of states showing spin polarization for the boron–nitrogen graphitic sheet with conic defects. The corresponding graphs for the saddles are qualitatively thesame.

the density matrix in a SCF cycle is 10−4, then the selfconsistencyhas been achieved.

The density of states (DOS) for the cone and saddle with molec-ular APB’s of boron (Mol-B), nitrogen (Mol-N), carbon–boron (Mol-CB), and carbon–nitrogen (Mol-C) are shown in the Fig. 2. Besidesthis, it is also shown the DOS for the zig–zag APB’s of carbon–boron (zig-CB) and carbon–nitrogen (zig-CN). Notice that the Mol-B and Mol-N structures should not exhibit net spin polarization.This is due to the fact that, in both cases, either boron or nitro-gen, respectively, form trivalent bonds. In a similar way, Mol-CBand Mol-CN form tetravalent bonds yielding no net spin polariza-tion as can be verified by inspection of Fig. 1. Looking at Figs. 1(c)and 1(e) one can see that by substitution of the N atoms by car-bon at the zig–zag, one always ends with one of the carbon atomstrivalent. This fact justifies the results for zig-CB and zig-CN de-picted in Fig. 2, which shows net spin polarization of the groundstate explicitly. Also, from Fig. 2, we can obtain the value for theexchange splitting, separating the spin-up from spin-down states,which can be compared with results obtained in other geometries[22,32].

In Fig. 3 is depicted the spacial distribution of the electronicdensity of the gap states. In particular, Fig. 3(a) shows that, whenthe structure is Mol-B (Fig. 3(b)), there is localization of the elec-tronic states on the boron atoms on the APB but the wavefunctionextends over the network. However, such structure does not dis-play spin polarization, according to Fig. 2. In the C–N and C–Bzig–zags (Figs. 3(d) and 3(f)) the localization on the APB is strongerboth for the negative and positive curvature disclinations (Figs. 3(c)and 3(e)). From Fig. 2 we see that the spin polarized states are gapstates. Consequently, these states are associated to the carbon de-fect line as verified in Figs. 3(c) and 3(e). The explanation for theoccurrence of unpaired spins in these compounds is therefore theintroduction of carbon atoms in the BN network even in the ab-sence of the defect.

In pure carbon structures containing defects, i.e., rings with ei-ther 5 or 7 carbon atoms, unpaired spins appear associated to thedefects [33]. Here we notice that such defects in the pure B–N

structure do not present spin polarization. This appears only whencarbon atoms are introduced. The introduction of carbon atomsin the B–N structure turns one of the carbon atoms in the zig–zag trivalent. What the defect brings about is a zig–zag chain andthe consequent mobility of the magnetic moment over the carbonchain, reminiscent of neutral solitons in trans-polyacetylene [3,5].This may be important for spintronics applications.

The appearance of a unpaired magnetic moment in these struc-tures is justified by the fact that the boron or nitrogen atomsare connected to three neighbors by three single bonds, thereforeall electrons in the molecular or zig–zag APB’s should be pairedand the structure should not present spin polarization. Regardingcarbon-doped disclinations, we find that incorporation of carbonat the zig–zag APB’s leads to spin polarization in the ground state.However, carbon incorporation at the APB’s for the Mol structures,does not lead to spin polarization. Namely, as the carbon atom isconnected to three neighbors by one double and two single bonds,in the molecular APB, Fig. 3(b), the double bonds are associated toAPB (C–C), and the single bonds are associated to a boron (C–B) ora nitrogen (C–N) atom. In this case, all electrons should be pairedand the structure. For the carbon-substituted zig–zag APB cases,Fig. 3(d) and (f), one carbon at the zig–zag is trivalent, and there-fore is the source of spin polarization.

The density of states indicates that there exists polarization ofspin, for BN nanostructures, with incorporation of carbon at thezig–zag APB’s. From the density of states, Fig. 2, we conclude thatsuch spins are energetically localized in the region of the gap.

It is shown in Fig. 4 the total density of states for the C–N, B–Band C–B structures, respectively. For the C–N and C–B structures(Figs. 4(a) and 4(e)) spin polarization appears, and the localiza-tion on the zig–zag occurs, independently of the disclination being±60◦ . For the B–B structure, where there is no net spin polar-ization, the electronic density is weakly localized. From this, weconclude that there exists a stronger localization of states in theregion of the APB’s.

Our results show that the electrons, which are the source ofthe spin polarization, are mobile but confined to the APB’s. This

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Fig. 3. (a), (c), (e) Gap states electronic density corresponding to the structures (b), (d), (f), respectively. The arrows indicate the antiphase boundaries. (b) and (d) correspondto a −60◦ disclination with B–B molecular APB and C–N zig–zag, respectively. (f) Corresponds to a 60◦ disclination with C–N zig–zag.

is clearly seen in Fig. 5, where it is exhibited the difference be-tween the spin-up and spin-down charge densities on the zig–zagC–B structure. Notice that the charge density shown is equally dis-tributed on the Carbon atoms. Besides this, we can infer from theshape of charge density depicted in Fig. 5 that it is associated topz orbitals of the Carbon atoms. Such localization leads to a con-siderable spin-splitting at the Fermi level. For the neutral chargestate, the difference between the highest-occupied molecular state(which has majority spin), Fig. 2, and the lowest-unoccupied one(which has minority spin) is ≈ 0.6 eV. That is comparable towhat was found by ab initio plane-wave calculations for dopedcomposite nanotubes [32] and to the results obtained by calcu-lations based in spin density functional theory [22]. Fig. 4 con-firms that the spin polarization associated to the zig–zag is welllocalized on the carbon atoms and, at the same time, delocal-ized over the carbon network. The spin-splitting appears onlyfor structures with even number of C–C bonds at the zig–zagAPB, a result that raises the interesting question on what hap-

pens in the case of multiple defects, either cones or saddles, orboth.

In summary, we used first-principles calculations to studycarbon-doped BN nanostructures with disclinations. We showedthat negatively or positively curved boron–nitride surfaces withodd-numbered rings, containing carbon atoms at the zig–zag APB’s,display polarization of spin in the electronic ground state, gener-alizing the results of [22]. Differently from the case, where BNstructures were doped with a carbon atom [17], the defected net-work presents delocalization of the unpaired spin over the APB.This suggests the use of the BN matrix, with the incorporation ofcarbon atoms at zig–zag chains formed by topological defects, as asubstrate for spintronics circuits. In conclusion, the delocalized un-paired spin in the structure studied here appears in a way similarto that shown in reference [33]. The difference is that in their casethe defect in an all-carbon structure generates the unpaired spin,while in our case, it is the introduction of carbon atoms in the BNnetwork that does it.

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Fig. 4. (a), (c), (e) Total electronic density corresponding to the structures (b), (d), (f), respectively. (b) and (d) correspond to a −60◦ disclination with C–N zig–zag and B–Bzig–zag, respectively. (f) Corresponds to a 60◦ disclination with C–B zig–zag.

Fig. 5. Spin-up minus spin-down charge density on the Carbon APB.

Acknowledgements

This work has been supported by CNPq, PRONEX/FAPESQ-PB,CAPES/PROCAD and Fundação de Amparo a Pesquisa do Estado daBahia, FAPESB. We also thank Dionisio Bazeia e Claudio Furtado fora critical reading of the manuscript.

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