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The edge state of nanographene and the magnetism of the edge-state spins
Solid State Communications 149 (2009) 1144–1150
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The edge state of nanographene and the magnetism of the edge-state spins Toshiaki Enoki ∗ , Kazuyuki Takai Department of Chemistry, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8551, Japan
article
info
Article history: Received 7 November 2008 Accepted 25 February 2009 by the Guest Editors Available online 21 March 2009 PACS: 68.37.Ef 73.90.+f 75.50.Xx 75.75.+a
abstract Nanographene has unique edge-shape dependence of the electronic structure with non-bonding edge states being created in its zigzag edges. The presence of the edge state is experimentally confirmed in welldefined hydrogen-terminated zigzag edges by scanning tunneling microscopy/spectroscopy (STM/STS) observations. In the three-dimensional (3D) disordered network of nanographite domains in nanoporous carbon (activated carbon fibers), the localized edge-state spins are in a spin-glass-like ordered state at low temperatures with the aid of exchange interactions whose strengths varies randomly in space, when the strengths of inter-nanographene and nanographite interactions are tuned. Chemical and structural modifications of nanographene edges change the magnetism of edge-state spins through covalent bond formation and charge transfer. © 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Graphene D. Edge states
1. Introduction A prominent discovery of graphene prepared merely by micromechanical cleavage [1–3] has unveiled unconventional electronic features of graphene, which are explained essentially in terms of the massless Dirac fermion [1–13]. Interestingly, current works have provided us with new basic issues of condensed matter physics such as the unusual half-integer quantum Hall effect [3,4, 7], quantum spin Hall effect [5], quantum dots [10], etc. When the size of a graphene sheet decreases to nanodimensions, another interest arises as a consequence of the growing contribution of edges to the electronic structure; that is, the edge-shape effect on the electronic structure [14–27]. The circumference of an arbitrary shaped nanographene, which is defined as nano-sized graphene, is described in terms of a combination of armchair and zigzag edges (see Fig. 1(a) and (b)). According to theoretical suggestions [14–18], a non-bonding π electron state that is called an ‘‘edge state’’ is created in zigzag edges, in contrast to the absence of such a state in armchair edges. The edge state exists as a flat band at the Fermi level EF that is located at the Dirac point between the linear bands of bonding π and anti-bonding π ∗ -states. Therefore, it can play an important role in the electronic properties of nanographene. In particular,
∗
Corresponding author. E-mail addresses: [email protected], [email protected] (T. Enoki). 0038-1098/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2009.02.054
the localized spins of edge states give rise to unconventional magnetism in nanographene [16–19,21–27]. Interestingly, the presence of edge states in nanographene is relevant also to the organic chemistry issue of aromaticity in condensed polycyclic hydrocarbon molecules [28–34]. The electronic structure of benzene, which is the simplest and smallest molecule of this family, is described in terms of bonding π -states and anti-bonding π ∗ -states, between which a large HOMO–LUMO gap is present as a consequence of a large energy stabilization of resonance. When larger hydrocarbon molecules are formed by fusing benzene rings, the HOMO–LUMO gap decreases upon the increase in the number of benzene rings associated. The extreme case with an infinite number of benzene rings is graphene, whose electronic structure is that of a zero-gap semiconductor. However, the story from benzene to graphene is not so simple due to the presence of many branches on the way to graphene. What is the most important is the coexistence of Kekulé and non-Kekulé molecules. The Kekulé molecules are characterized merely by bonding π - and anti-bonding π ∗ -states. Here, the closed shell singlet electronic structure makes Kekulé molecules nonmagnetic. In contrast, there are non-bonding π -electron states as extra states at EF in the HOMO–LUMO gap in non-Kekulé molecules having an open shell structure. Consequently, the unpaired electrons in these states work to make the molecules magnetic, as the non-bonding π -states are half-filled at EF . Thus, the non-bonding π -state is caused by the same reason as the edge state in nanographene. The magnetic features of nanographene and non- Kekulé molecules vary depending on the structural details of the edges:
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the geometry of the edges and chemical modifications of the edges. This allows us to create a large variety of spin magnetism in nanographene. In this review article, we discuss the electronic structures of the edge state and the magnetic features of edge-state spins in nanographene and nanographite.
a
2. Nanographene and the edge state
b
One of the important criteria in examining whether hydrocarbon molecules have non-bonding π -states or not is Lieb’s theorem [35]. Here, we can classify the carbon sites into two subgroups in a molecule as shown in Fig. 2. The carbon sites, which are directly bonded to a site belonging to a subgroup (starred), belong to another subgroup (unstarred). According to Lieb’s theorem, the number of non-bonding states Nn is given by the difference in numbers of the starred and unstarred sites: Nn = |N∗ − Nun∗ |. The electrons occupying these non-bonding states degenerate at EF , obeying the Hund rule with a parallel spin arrangement. Hence, the half-filled non-bonding states that are populated around the peripheral region of the molecules have ferromagnetically coupled localized spins, thereby contributing to the occurrence of strong spin magnetism, in spite of the absence of spin magnetism in Kekulé molecules. Examples are given in Fig. 2 for (a) Kekulé and (b) non-Kekulé molecules, the former and the latter of which have and do not have non-bonding π -states, respectively. Here, no non-bonding π -state with Nn = 0 is present and this results in non-magnetic features with spin state S = 0 in benzene, naphthalene and anthracene that consist of one, two and three benzene rings, respectively, as shown in Fig. 2(a). In contrast, triangle-shaped molecules with three, six and ten benzene rings shown in Fig. 2(b) have one, two and three non-bonding π -states, respectively, which give rise to parallel spin arrangements (ferromagnetic) with S = 1/2, 1 and 3/2. An interesting feature we should note here is the spatial distribution of the non-bonding π -state as shown in Fig. 2(c). Indeed, the non-bonding π -state is strongly populated around the zigzag edges of the molecule [30]. The non-bonding π -state can exist also in linear molecules called acene and related molecules [23,32–34]. In linear molecules with the number of benzene rings smaller than six, the closed shell singlet structure is stabilized, giving rise to nonmagnetic features, as chemists know. When the number of benzene rings exceed the range 6–7, there is a crossover in the ground state from the close shell singlet state to open shell singlet [34]. Then parallel spin alignment on one zigzag edge side of the molecule is stabilized with that on the other zigzag edge side being antiparallel to the former. Fig. 3 demonstrates the antiferromagnetic spin arrangement of decacene, comprised of ten benzene rings arranged in a linear chain [32]. Therefore, linear molecules are categorized into a magnetic branch of hydrocarbon molecules showing an antiferromagnetic state in contrast to the ferromagnetic state in triangular shaped molecules. We should say that, in addition to these two branches having ferromagnetic and antiferromagnetic structures, there are a variety of magnetic molecules if zigzag edges are present. Here, their magnetic structure depends on how the zigzag edges are incorporated in the molecules. A similar situation arises in nanographene, as deduced by extrapolating the size of the molecule to nano-dimensions. As discussed in the Section 1, non-bonding edge states appear only in the zigzag edge region of the nanographene sheet, and not in the armchair edge region [14–17]. Fig. 4 shows a typical example of nanographene sheets comprising zigzag or armchair edges [14]. We can clearly observe an essential difference in the electron populations of the HOMO levels between the zigzag-edged and armchair-edged nanographene sheets. Indeed, the populations are
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c
Fig. 1. (a) Armchair edge, (b) zigzag edge, and (c) zigzag edge with all its edge-carbon atoms bonded to one additional carbon atom that participates in the π -conjugated system. (b) and (c) are called ‘‘Fujita edge’’ and ‘‘Klein edge’’, respectively.
Fig. 2. The spin states of (a) Kekulé molecules and (b) non-Kekulé molecules. The carbon sites, which are directly bonded to a site belonging to a subgroup (starred), belong to another subgroup (unstarred). The spin state is denoted by S. (c) The spatial distribution of the non-bonding π -state in a triangulene radical consisting of six benzene rings.
Fig. 3. The antiferromagnetic spin polarization of decacene, comprised of ten benzene rings fused in one dimension. The spins of the singly occupied orbital in the upper panel are in antiparallel to those in the lower panel. (Ref. [32]).
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Fig. 4. The spatial distributions of the populations of the HOMO level for nanographene with their edges having (a) armchair and (b) zigzag structures. (Ref. [14]).
homogeneously distributed in the entire region for the armchairedged nanographene (Fig. 4(a)), whereas the HOMO level, which is assigned to the singly occupied non-bonding edge state, has the largest populations in the edge region of the zigzag-edged nanographene sheet (Fig. 4(b)). This proves that zigzag edges have edge states that are well localized around the edge region. Chemical modification of zigzag edges with foreign species is predicted theoretically to give another variation of the magnetism [36–39]. A zigzag-edged nanographene ribbon with all the edge carbon atoms monohydrogenated on both sides of the ribbon has edge states well localized at the edges. This corresponds to the case of an antiferromagnetic state similar to that shown in Fig. 3. A monohydrogenated zigzag edge is called a Fujita edge. When all the edge carbon atoms of the zigzag edge on one side of a zigzagedged nanographene ribbon are dihydrogenated with those on the opposite side remaining monohydrogenated, a completely localized non-bonding state appears around EF , where all the carbon atoms are spin polarized even in the interior of the nanographene ribbon [38,39]. This is an interesting carbon-only ferromagnetism, in which all the carbon atoms are spin polarized ferromagnetically. The dihydrogenation of the zigzag-edge carbon atoms creates a modified zigzag edge (Klein edge) [36,37], whose structure is schematically shown as a beard zigzag edge in Fig. 1(c). In contrast to hydrogenation, fluorination of edges tends to suppress magnetism due to the tendency of forming a closed shell in fluorine [38, 39]. In a zigzag-edged nanographene ribbon with one edge side monofluorinated and the opposite side difluorinated, the spin polarization can survive only around the monofluorinated edge region. An interesting example is the oxidation of carbon atoms on one zigzag edge side. The oxidized edge forms electron conduction paths while the monohydrogenated edge works as a magnetic edge [38,39]. This means that the chemical modifications can give different roles to these two edges that are chemically modified in different fashions. Experimental efforts, which reinforce the above-mentioned theoretical suggestions on nanographene and graphene edges, are particularly important in order to take the issue on nanographene to reality. The presence of an edge state around zigzag edges is experimentally evidenced by ultra-high vacuum scanning tunneling microscopy/spectroscopy (STM/STS) observations of graphene edges whose carbon atoms are hydrogen terminated [40–42]. Fig. 5(a) shows the atomically resolved lattice image of a graphene edge that consists of zigzag and armchair edge regions. The bright spots distributed in the zigzag edge region are assigned to the large local density of states of the edge states around EF . The STS spectrum, which corresponds to the density of states as a function of energy, has a sharp peak assigned to the edge state at EF when we investigate the zigzag edge region. These two experimental findings are important evidence of edge states. On the other hand, in the armchair edge region, there are no bright spots of edge states,
Fig. 5. (a) Atomically-resolved ultra-high vacuum STM lattice image of the edge region (9 × 9 nm2 ) observed in the constant-height mode with a bias voltage of Vs = 0.02 V and a current I = 0.7 nA. (b) STS spectrum (dI /dVs vs. Vs ) around the zigzag edge. (Ref. [41]).
and the density of states can be explained in terms of only linear π - and π ∗ -bands, which touch each other at EF . It should be noted that armchair edges are generally long and defect-free, whereas zigzag edges tend to be short and defective, from STM observations. This suggests that zigzag edges are energetically less stable than armchair edges [43], similar to the trend in small non-Kekulé molecules. 3. Magnetic structure of nanographene and nanographite The edge states localized in the zigzag edge region have localized magnetic moments. Therefore, the magnetism of the edge-state spin system of nanographene is of particular interest in carbon-based magnetism. Interestingly, the magnetic moment is fractional and is estimated theoretically to be about 0.2 µB [16,34], which deviates from what is expected in the pure localized spin system with 1 µB (S = 1/2). The edge-state spins are arranged in parallel to each other in a zigzag edge with strong ferromagnetic interaction, whose strength is in the region of several 103 K [44]. This suggests that nanographene is expected to be a ferromagnetic material with a Curie temperature higher than iron, which is a popular ferromagnet. We employ here activated carbon fibers (ACFs) as a good model system for investigating the magnetism of edge-state spins. As schematically modeled in Fig. 6(a), ACFs are nanoporous carbon consisting of a three-dimensional (3D) disordered network of nanographite domains, each of which is a stack of 3–4 nanographene sheets with the mean in-plane size of about 3 nm. The magnetic investigations have given us detailed information on the magnetic structure of ACFs [45,46]. Fig. 6(b) gives the schematic view of the spin structure of an individual nanographene sheet in the nanographite domain. A nanographene sheet having
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changes in the inter-nanographene sheet interaction J2 and internanographite interaction J3 . Heat treatment at temperatures above the graphitization temperature (about 1500 ◦ C) makes nanographene sheets fuse with each other, resulting in successive disappearance of the nanographene edges and consequently the spin magnetism of nanographene. Therefore, heat treatment in a wide temperature range provides details of the magnetism of nanographene and nanographite. Here we summarize the electron transport in ACFs since it is well correlated to the magnetic feature. It is governed by the Coulomb-gap-type variable range hopping process between nanographite domains in the Anderson insulator regime [47]. The electrical conductivity σ obeys the following equation:
σ ∝ exp − (T0 /T )1/2 ,
Fig. 6. (a) The schematic structural model of activated carbon fiber (ACF). (b) The structure of an individual nanographene sheet in a nanographite domain of ACF, and the spatial distribution of edge-state spins.
an irregular shape is comprised of zigzag and armchair edges, which are distributed randomly in its periphery. Around the zigzag edges, the spins are arranged ferromagnetically through strong intra-zigzag-edge ferromagnetic exchange interaction J0 . The strength of each magnetic moment depends on the detailed geometry of the zigzag edges such as the edge length, and the environment surrounding the zigzag edge. The spins in a zigzag edge interact with the spins in the neighboring zigzag edge through π -conduction-electron-mediated indirect exchange interaction, which is the nanographene analogue of RKKY interaction in traditional metal magnets. These inter-zigzag interactions J1 have their strength in the range J1 /J0 = 10−1 –10−3 [44], and the signs of the interactions vary between plus (ferromagnetic) and minus (antiferromangetic) depending on the geometrical relation between the zigzag edges concerned. The cooperation of strong J0 and less strong J1 , and the spatial variation of the strengths of the magnetic moments bring about a ferrimagnetic structure with a finite net magnetic moment in a nanographene sheet. We need two more sorts of exchange interactions to take into account the magnetism of ACFs. The first one is the internanographene-sheet interaction J2 in a nanographite domain. The edge-state spins of adjacent nanographene sheets in a domain interact with each other with antiferromagnetic interaction J2 having an intermediate strength. Then the antiferromagnetic coupling J2 between the effective magnetic moments having different values in nanographene sheets results in the formation of a ferrimagnetic structure of an individual nanographite domain. The second one is the inter-domain antiferromagnetic interaction J3 , which is weak, in the range 2–3 K [45,46]. The behavior of the magnetic susceptibility in pristine ACFs, which apparently obeys a paramagnetic Curie–Weiss law with antiferromagnetic Weiss temperature (−2 to 3 K), is explained on the basis of the magnetic structure model as presented above [45,46]. The spin concentration is estimated as several spins per nanographite domain. The behavior of the ACF edgestate spin system is sensitive to the structural change induced by heat treatment. Indeed, the heat treatment up to 1500 ◦ C modifies the network structure of ACFs. This is owing to the
T0 =
6e2 4π 2 kB εξ
,
where ε and ξ are the dielectric constant of the medium and the localization length of the conduction electron wave function, respectively. This suggests that the electron hopping from one nanographite domain to the adjacent one is subjected to an electron–electron repulsive force. This also evidences the finite density of states at EF in the one-electron picture, consistent with the electronic structure of nanographite predicted theoretically. In pristine ACFs, the peripheries of nanographene sheets are covered with functional groups, which disturb the internanographite-domain electron transport. Heat treatment removes the functional groups, working to create coherent electron transport paths between nanographite domains. The development of coherent electron transport paths, which work as percolation path networks for electron transport, enhances the conductivity upon the elevation of the heat-treatment temperature (HTT). Eventually, metallic conductivity is achieved around an HTT of 1200 ◦ C, at which the percolation path network becomes infinite. The less temperature dependent conductivity above the insulator–metal transition of HTT ∼ 1200 ◦ C suggests an important contribution of structural disorder in the electron scattering process. The change in the conductivity is faithfully tracked by the magnetic susceptibility as given in Fig. 7(a). Namely, the Curie–Weiss behavior with localized edge-state spins in the Anderson insulator regime is converted to the less temperature dependent susceptibility of conduction electrons in the metallic regime, where the negative susceptibility is a combination of small positive Pauli paramagnetic and large negative orbital contributions. Interestingly, an anomalous feature appears in the vicinity of the insulator–metal transition; that is, the susceptibility has a cusp at about 7 K with a negative Weiss temperature (antiferromagnetic) of −2 to −3 K. This is reminiscent of the onset of an antiferromagnetic ordering. However, this is not the case, as a large field cooling effect on the susceptibility is evident in Fig. 7(b). Fig. 7(b) indicates that the susceptibility for the sample in the vicinity of the insulator–metal transition (HTT ∼ 1200 ◦ C) has a large field cooling effect, particularly around the temperature range in which the cusp emerges. The presence of a cusp and its large field cooling effect are the consequence of the development of quenched disordered magnetic structure like a spin glass state. In general, a spin glass state develops when the strengths of exchange interactions J vary randomly in space. From the magnetization curve analysis, a large randomness in the strengths of exchange interactions p is evident, the width of the distribution being estimated as h∆J i2 / hJ i ≈ 0.8, which is safely in the region of a spin glass. The occurrence of the insulator–metal transition drives the feature of electrons from a localized state to an itinerant one, since the mobile electrons are created at the expense of the localized edge-state spins as the fusion of nanographene sheets proceeds upon the elevation of the HTT in the metallic phase well above the insulator–metal transition.
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Fig. 8. A schematic model of the fluorination effect on nanographene.
Fig. 7. (a) The temperature dependence of the susceptibility for the ACF samples heat treated at different heat-treatment temperatures (HTT). Heat treatment was given for 15 min except 1500 (1 h), in which 1 h heat treatment was performed. (b) The field cooling effect on the susceptibility vs. temperature plots in the ACF samples heat treated at 1100 and 800 ◦ C, which are in the vicinity of the insulator–metal transition and far from the transition, respectively. Open and full circles represent the data for the zero field cooling (ZFC) and field cooling (FC) (H = 1 T) processes, respectively. (Ref. [46]).
However, a considerable amount of edge spins still survive in the vicinity of the transition. The coexistence of the localized edge-state spins and the conduction π -electrons in the disordered structure causes the anomalous magnetic state to appear in the insulator–metal transition region; that is, exchange interactions between the localized edge-state spins are mediated by the conduction electrons. The disordered structure of the nanographite network is responsible for the random spatial distribution in the strengths of the exchange interactions, resulting in the formation of a spin-glass-like disordered magnetic structure. Here, it should be noted that the range of exchange interaction is over 2–3 nm, in contrast to the ordinary short range feature of exchange interaction. Such long range nature of the exchange interaction adds uniqueness to the magnetism of the edge-state spins of nanographene. 4. Chemical modifications of nanographene and nanographite The edge state is susceptible to chemical modifications of nanographene edges [36–39,48–55] in addition to the sensitivity to structural changes [45,46,56–58]. For example, the termination of edge carbon atoms by two hydrogen atoms gives edge-state
populations that are different from that with one hydrogen atom [37–39,42]. Oxidation of edges strongly changes the feature of the edge state [38,39]. Here, let us investigate how the magnetism of the edge states changes when nanographene is subjected to chemical modifications with a halogen such as fluorine and bromine. Fluorine is the most chemically active species, and is strongly bonded to carbon atoms not only at the edges but also in the interior of a nanographene sheet [48,49]. Fig. 8 exhibits schematically how fluorine atoms attack the carbon sites in a nanographene sheet. In the initial stage of fluorination of nanographene in ACFs up to a fluorine concentration of F/C ∼ 0.4, the reaction with fluorine atoms takes place mainly around the edges due to the relatively strong chemical activity of edge carbon atoms, resulting in the formation of difluorinated edge carbon sites. In this fluorination process, the concentration of edge-state spins tends to decrease as the fluorine concentration is elevated. This means that the edge state is destroyed by chemical modification with fluorine atoms, consistent with theoretical suggestions [38,39,48]. After the fluorination is completed at the edges around F/C ∼ 0.4, a fluorine atom begins attacking a carbon atom in the interior of the nanographene sheet, breaking the π bond. This creates a σ -dangling bond having a localized spin at the carbon site bonded to the carbon atom that is fluorinated. The concentration of σ -dangling bond localized spins becomes maximized at a fluorine concentration of F/C ∼ 0.8, at which a half of carbon atoms in the interior of nanographene sheet are bonded to fluorine atoms. Finally, localized spins disappear at a saturated fluorine concentration of F/C ∼ 1.2, at which all the carbon atoms are bonded to fluorine atoms. Interestingly, the magnetic nature is different between the edge-state spins of π -electron origin and the σ -dangling bond localized spins, as clearly evident in Fig. 9. Fig. 9 shows the fluorine concentration dependence of the strength of the internal exchange field acting on the spins. In the low concentration range up to F/C ∼ 0.4, where the edgestate spins are dominant, a finite internal field is present and it is lowered upon the elevation of the fluorine concentration. This finding suggests that the edge-state spins are interacting with each other, consistent with the theoretical suggestion that the edge-state spins have features intermediate between localized and delocalized states, as discussed in Section 2 [16–18]. In contrast to the edge-state spins, the internal field is absent between the σ dangling bond localized spins above F/C ∼ 0.4; that is, σ -dangling bond localized spins are well isolated from each other. Bromine, which is a milder chemical species than fluorine, behaves differently from the latter in modifying the electronic structure of nanographene [50]. When ACFs are exposed to
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x 10 5
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3.0
< α > av (g.emu –1)
2.5
2.0
1.5
1.0
0.5
0
0
0.2
0.4
0.6
0.8
1.0
1.2
F/C Fig. 9. The mean molecular field coefficient hαiav as a function of F/C in fluorinated ACFs. (Ref. [49]).
bromine, three kinds of bromine species are generated; that is, charge transfer species, covalent bond species and physisorbed species. The charge transfer species are the same as those generated in the reaction with bulk graphite, as we know that graphite forms an intercalation compound with bromine where negatively charged bromine molecules working as acceptors are accommodated in the graphitic galleries through charge transfer from graphite to bromine [59]. The covalent species are bonded to the edge carbon atoms, similar to fluorine atoms reacting with the edge carbon atoms in the first stage of fluorination as explained above. The physisorbed species are accommodated through van der Waals interaction in the nanopores of ACFs. In nanographene, charge transfer and covalent bond species dominate the change in the electronic and magnetic properties of the edge state. Interestingly, in contrast to bulk graphite, covalent species overwhelm charge transfer species in nanographene. For example, at the composition ratio of Br/C = 0.27, 12% of bromine is charge transfer species while 42% is covalent bond species at the edges. These concentrations of the charge transfer and covalent bond species correspond to about 10 and 35 Br atoms in an individual nanographene sheet (3 nm in size) that includes about 300 carbon atoms in average. The two kinds of species change the magnetic properties in different manners. The charge transfer species taking charges from nanographene sheets shift the Fermi level downward, resulting in the generation of holes in the bonding π -bands just beneath the Dirac point. As the edge states are located around the Dirac point, vacancies are therefore created in the edge states upon the charge transfer. The amount of vacancies increases as the charge transfer is elevated. In pristine ACFs in the neutral state, the Fermi level is located at the middle of the edge states as they are half filled. In this case, the edge-state spin concentration is maximized. The charge transfer reduces the spin concentration successively as the charge transfer rate fc (charge per C atom) is elevated, the spin concentration extrapolated to the infinite fc being expected to be zero. However, the edge-state spin concentration behaves slightly differently from this expectation in spite of a semiqualitative agreement, as summarized in Fig. 10(a). This suggests inhomogeneity in the charge transfer reaction, dissimilar to that in bulk graphite, as schematically illustrated in Fig. 11. According to experimental results, a charge transfer reaction takes place in the low bromine concentration range, followed by the formation of covalent bonds with the edge carbon atoms in the higher
Fig. 10. The charge transfer rate fc dependence of (a) the localized spin density ns , (b) the Fermi energy and (c) the orbital susceptibility χorb in brominated ACF. The experimental data are denoted by full circles in (a) and (c). The horizontal dashed line in (a) is the charge-transfer-independent contribution of the localized spins. The solid curve in (a) is the fitting curve to the model with the coexistence of bounding and interior nanographene layers (see Fig. 11). The solid curve in (b) is obtained from the fitting (solid curve) in (a). The EF vs. fc plot in the case of the absence of the edge state is denoted as the dashed line in (b). The solid curve in (c) is the χorb at 300 K calculated with the results in (b) based on McClure’s theory. (Ref. [50]).
concentration [50]. In the low concentration range where the edges of nanographene sheets are covered by functional groups, bromine molecule intercalates cannot be accommodated in the graphitic galleries of the nanographite domain due to the blockade of functional groups as shown in Fig. 11. Only nanographene sheets exposed to the nanopores are subjected to the charge transfer reaction with bromine. Then the edge-state spins are killed on the outer nanographene sheets in this charge transfer process. The remaining edge-state spins in the higher charge transfer range are those surviving in the interior and protected by the blockade from the reaction. Here, it should be noted that the presence of the edge states at the Dirac point plays an important role in the charge-transfer-induced downshift of the Fermi level, as shown in Fig. 10(b). The edge state works as an electron reservoir, making the downshift of the Fermi level slow. The downshift of the Fermi energy drastically decreases the orbital susceptibility, but its trend is different from what we can expect with no edge states, as confirmed in Fig. 10(c). The covalent bond formation at the edge carbon atoms affects also the magnetism of the edge-state spins [50]. The g-value in the ESR signal gradually deviates from that in pristine nonadsorbed ACFs as the bromine concentration is elevated, while the line width is broadened linearly. This suggests the mixing of the electronic states of bromine atoms with the edge state, since these changes in the ESR signal are relevant to the contribution of the large spin–orbit interaction of bromine atoms. The bromine atoms bonded to the edge carbon atoms are considered to affect the electronic features of the edge state directly, though the charge transfer bromine species are partly responsible for these changes.
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References
Fig. 11. A schematic description of the inhomogeneous charge transfer between nanographite and bromine. BL and IL denote the bounding layers faced to bromine, and interior layers of nanographite, respectively. The edge-state spins disappear on the bounding layers due to the charge transfer. (Ref. [50]).
5. Summary Nanographene stands in a unique position in the nanocarbon family in relation to its unconventional electronic structure with unique geometry dependence owing to the presence of open edges. Here, in the zigzag edge, a non-bonding edge state is created in spite of the absence of such a state in an armchair edge. The presence of edge states in the zigzag edges has been confirmed by STM/STS observations of hydrogen-terminated samples. The edge state is relevant to the non-bonding π -state of radical structures of non-Kekulé molecules. As the edge states have localized spins, they can give a rich variety of magnetism in nanographene and nangraphite depending on their structure. From an experimental viewpoint, ACFs are an interesting model system in which the edge-state magnetism can be comprehensively investigated. Their structure consists of a 3D disordered network of nanographite domains, each of which is a stack of 3–4 nanographene sheets. The interplay of strong intra-zigzag-edge ferromagnetic interaction and inter-zigzag-edge interaction makes an individual nanographene sheet be in a ferrimagnetic state with a spontaneous magnetic moment. In pristine ACFs, the magnetism is described in terms of these magnetic moments in the insulating state. Heat treatment induces successive structural changes, which brings about an insulator– metal transition at HTT ∼ 1200 ◦ C, resulting in the enhancement of inter-nanographite domain electronic interactions. This induces a crossover in the magnetism from Curie–Weiss-type to Pauli-type paramagnetism at the transition. In the vicinity of the transition, a spin-glass-like disordered state is stabilized below about 7 K with a unique field cooling effect. The edge-state spins are susceptible to chemical and structural modifications of nanographene and nanographite. Fluorination takes place selectively at the edge-carbon atoms in the initial stage of the reaction, and proceeds to the interior of nanographene sheet. The edge state and its localized spins disappear in the fluorination of the edge carbon atoms. The fluorination of an interior carbon atom creates a σ -dangling bonds. The localized spins of the σ dangling-bonds thus created behave independently from each other, in contrast to the edge-state spins of π -electron origin interacting with each other through strong exchange interactions. Bromine atoms also modify the magnetism of the edge-state spins in two ways. Bromine atoms participating in charge transfer with nanographene works to reduce the concentration of the edge-state spins, while the state of bromine atoms covalently bonded to the edge carbon atoms is mixed with the edge state, the spin–orbit interaction being enhanced in the edge state. Acknowledgements The present work is supported by the Grant-in-Aid for Scientific Research No. 20001006 from the Japan Society for the Promotion of Science (JSPS).
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
The edge state of nanographene and the magnetism of the edge-state spins Toshiaki Enoki ∗ , Kazuyuki Takai Department of Chemistry, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8551, Japan
article
info
Article history: Received 7 November 2008 Accepted 25 February 2009 by the Guest Editors Available online 21 March 2009 PACS: 68.37.Ef 73.90.+f 75.50.Xx 75.75.+a
abstract Nanographene has unique edge-shape dependence of the electronic structure with non-bonding edge states being created in its zigzag edges. The presence of the edge state is experimentally confirmed in welldefined hydrogen-terminated zigzag edges by scanning tunneling microscopy/spectroscopy (STM/STS) observations. In the three-dimensional (3D) disordered network of nanographite domains in nanoporous carbon (activated carbon fibers), the localized edge-state spins are in a spin-glass-like ordered state at low temperatures with the aid of exchange interactions whose strengths varies randomly in space, when the strengths of inter-nanographene and nanographite interactions are tuned. Chemical and structural modifications of nanographene edges change the magnetism of edge-state spins through covalent bond formation and charge transfer. © 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Graphene D. Edge states
1. Introduction A prominent discovery of graphene prepared merely by micromechanical cleavage [1–3] has unveiled unconventional electronic features of graphene, which are explained essentially in terms of the massless Dirac fermion [1–13]. Interestingly, current works have provided us with new basic issues of condensed matter physics such as the unusual half-integer quantum Hall effect [3,4, 7], quantum spin Hall effect [5], quantum dots [10], etc. When the size of a graphene sheet decreases to nanodimensions, another interest arises as a consequence of the growing contribution of edges to the electronic structure; that is, the edge-shape effect on the electronic structure [14–27]. The circumference of an arbitrary shaped nanographene, which is defined as nano-sized graphene, is described in terms of a combination of armchair and zigzag edges (see Fig. 1(a) and (b)). According to theoretical suggestions [14–18], a non-bonding π electron state that is called an ‘‘edge state’’ is created in zigzag edges, in contrast to the absence of such a state in armchair edges. The edge state exists as a flat band at the Fermi level EF that is located at the Dirac point between the linear bands of bonding π and anti-bonding π ∗ -states. Therefore, it can play an important role in the electronic properties of nanographene. In particular,
∗
Corresponding author. E-mail addresses: [email protected], [email protected] (T. Enoki). 0038-1098/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2009.02.054
the localized spins of edge states give rise to unconventional magnetism in nanographene [16–19,21–27]. Interestingly, the presence of edge states in nanographene is relevant also to the organic chemistry issue of aromaticity in condensed polycyclic hydrocarbon molecules [28–34]. The electronic structure of benzene, which is the simplest and smallest molecule of this family, is described in terms of bonding π -states and anti-bonding π ∗ -states, between which a large HOMO–LUMO gap is present as a consequence of a large energy stabilization of resonance. When larger hydrocarbon molecules are formed by fusing benzene rings, the HOMO–LUMO gap decreases upon the increase in the number of benzene rings associated. The extreme case with an infinite number of benzene rings is graphene, whose electronic structure is that of a zero-gap semiconductor. However, the story from benzene to graphene is not so simple due to the presence of many branches on the way to graphene. What is the most important is the coexistence of Kekulé and non-Kekulé molecules. The Kekulé molecules are characterized merely by bonding π - and anti-bonding π ∗ -states. Here, the closed shell singlet electronic structure makes Kekulé molecules nonmagnetic. In contrast, there are non-bonding π -electron states as extra states at EF in the HOMO–LUMO gap in non-Kekulé molecules having an open shell structure. Consequently, the unpaired electrons in these states work to make the molecules magnetic, as the non-bonding π -states are half-filled at EF . Thus, the non-bonding π -state is caused by the same reason as the edge state in nanographene. The magnetic features of nanographene and non- Kekulé molecules vary depending on the structural details of the edges:
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the geometry of the edges and chemical modifications of the edges. This allows us to create a large variety of spin magnetism in nanographene. In this review article, we discuss the electronic structures of the edge state and the magnetic features of edge-state spins in nanographene and nanographite.
a
2. Nanographene and the edge state
b
One of the important criteria in examining whether hydrocarbon molecules have non-bonding π -states or not is Lieb’s theorem [35]. Here, we can classify the carbon sites into two subgroups in a molecule as shown in Fig. 2. The carbon sites, which are directly bonded to a site belonging to a subgroup (starred), belong to another subgroup (unstarred). According to Lieb’s theorem, the number of non-bonding states Nn is given by the difference in numbers of the starred and unstarred sites: Nn = |N∗ − Nun∗ |. The electrons occupying these non-bonding states degenerate at EF , obeying the Hund rule with a parallel spin arrangement. Hence, the half-filled non-bonding states that are populated around the peripheral region of the molecules have ferromagnetically coupled localized spins, thereby contributing to the occurrence of strong spin magnetism, in spite of the absence of spin magnetism in Kekulé molecules. Examples are given in Fig. 2 for (a) Kekulé and (b) non-Kekulé molecules, the former and the latter of which have and do not have non-bonding π -states, respectively. Here, no non-bonding π -state with Nn = 0 is present and this results in non-magnetic features with spin state S = 0 in benzene, naphthalene and anthracene that consist of one, two and three benzene rings, respectively, as shown in Fig. 2(a). In contrast, triangle-shaped molecules with three, six and ten benzene rings shown in Fig. 2(b) have one, two and three non-bonding π -states, respectively, which give rise to parallel spin arrangements (ferromagnetic) with S = 1/2, 1 and 3/2. An interesting feature we should note here is the spatial distribution of the non-bonding π -state as shown in Fig. 2(c). Indeed, the non-bonding π -state is strongly populated around the zigzag edges of the molecule [30]. The non-bonding π -state can exist also in linear molecules called acene and related molecules [23,32–34]. In linear molecules with the number of benzene rings smaller than six, the closed shell singlet structure is stabilized, giving rise to nonmagnetic features, as chemists know. When the number of benzene rings exceed the range 6–7, there is a crossover in the ground state from the close shell singlet state to open shell singlet [34]. Then parallel spin alignment on one zigzag edge side of the molecule is stabilized with that on the other zigzag edge side being antiparallel to the former. Fig. 3 demonstrates the antiferromagnetic spin arrangement of decacene, comprised of ten benzene rings arranged in a linear chain [32]. Therefore, linear molecules are categorized into a magnetic branch of hydrocarbon molecules showing an antiferromagnetic state in contrast to the ferromagnetic state in triangular shaped molecules. We should say that, in addition to these two branches having ferromagnetic and antiferromagnetic structures, there are a variety of magnetic molecules if zigzag edges are present. Here, their magnetic structure depends on how the zigzag edges are incorporated in the molecules. A similar situation arises in nanographene, as deduced by extrapolating the size of the molecule to nano-dimensions. As discussed in the Section 1, non-bonding edge states appear only in the zigzag edge region of the nanographene sheet, and not in the armchair edge region [14–17]. Fig. 4 shows a typical example of nanographene sheets comprising zigzag or armchair edges [14]. We can clearly observe an essential difference in the electron populations of the HOMO levels between the zigzag-edged and armchair-edged nanographene sheets. Indeed, the populations are
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c
Fig. 1. (a) Armchair edge, (b) zigzag edge, and (c) zigzag edge with all its edge-carbon atoms bonded to one additional carbon atom that participates in the π -conjugated system. (b) and (c) are called ‘‘Fujita edge’’ and ‘‘Klein edge’’, respectively.
Fig. 2. The spin states of (a) Kekulé molecules and (b) non-Kekulé molecules. The carbon sites, which are directly bonded to a site belonging to a subgroup (starred), belong to another subgroup (unstarred). The spin state is denoted by S. (c) The spatial distribution of the non-bonding π -state in a triangulene radical consisting of six benzene rings.
Fig. 3. The antiferromagnetic spin polarization of decacene, comprised of ten benzene rings fused in one dimension. The spins of the singly occupied orbital in the upper panel are in antiparallel to those in the lower panel. (Ref. [32]).
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Fig. 4. The spatial distributions of the populations of the HOMO level for nanographene with their edges having (a) armchair and (b) zigzag structures. (Ref. [14]).
homogeneously distributed in the entire region for the armchairedged nanographene (Fig. 4(a)), whereas the HOMO level, which is assigned to the singly occupied non-bonding edge state, has the largest populations in the edge region of the zigzag-edged nanographene sheet (Fig. 4(b)). This proves that zigzag edges have edge states that are well localized around the edge region. Chemical modification of zigzag edges with foreign species is predicted theoretically to give another variation of the magnetism [36–39]. A zigzag-edged nanographene ribbon with all the edge carbon atoms monohydrogenated on both sides of the ribbon has edge states well localized at the edges. This corresponds to the case of an antiferromagnetic state similar to that shown in Fig. 3. A monohydrogenated zigzag edge is called a Fujita edge. When all the edge carbon atoms of the zigzag edge on one side of a zigzagedged nanographene ribbon are dihydrogenated with those on the opposite side remaining monohydrogenated, a completely localized non-bonding state appears around EF , where all the carbon atoms are spin polarized even in the interior of the nanographene ribbon [38,39]. This is an interesting carbon-only ferromagnetism, in which all the carbon atoms are spin polarized ferromagnetically. The dihydrogenation of the zigzag-edge carbon atoms creates a modified zigzag edge (Klein edge) [36,37], whose structure is schematically shown as a beard zigzag edge in Fig. 1(c). In contrast to hydrogenation, fluorination of edges tends to suppress magnetism due to the tendency of forming a closed shell in fluorine [38, 39]. In a zigzag-edged nanographene ribbon with one edge side monofluorinated and the opposite side difluorinated, the spin polarization can survive only around the monofluorinated edge region. An interesting example is the oxidation of carbon atoms on one zigzag edge side. The oxidized edge forms electron conduction paths while the monohydrogenated edge works as a magnetic edge [38,39]. This means that the chemical modifications can give different roles to these two edges that are chemically modified in different fashions. Experimental efforts, which reinforce the above-mentioned theoretical suggestions on nanographene and graphene edges, are particularly important in order to take the issue on nanographene to reality. The presence of an edge state around zigzag edges is experimentally evidenced by ultra-high vacuum scanning tunneling microscopy/spectroscopy (STM/STS) observations of graphene edges whose carbon atoms are hydrogen terminated [40–42]. Fig. 5(a) shows the atomically resolved lattice image of a graphene edge that consists of zigzag and armchair edge regions. The bright spots distributed in the zigzag edge region are assigned to the large local density of states of the edge states around EF . The STS spectrum, which corresponds to the density of states as a function of energy, has a sharp peak assigned to the edge state at EF when we investigate the zigzag edge region. These two experimental findings are important evidence of edge states. On the other hand, in the armchair edge region, there are no bright spots of edge states,
Fig. 5. (a) Atomically-resolved ultra-high vacuum STM lattice image of the edge region (9 × 9 nm2 ) observed in the constant-height mode with a bias voltage of Vs = 0.02 V and a current I = 0.7 nA. (b) STS spectrum (dI /dVs vs. Vs ) around the zigzag edge. (Ref. [41]).
and the density of states can be explained in terms of only linear π - and π ∗ -bands, which touch each other at EF . It should be noted that armchair edges are generally long and defect-free, whereas zigzag edges tend to be short and defective, from STM observations. This suggests that zigzag edges are energetically less stable than armchair edges [43], similar to the trend in small non-Kekulé molecules. 3. Magnetic structure of nanographene and nanographite The edge states localized in the zigzag edge region have localized magnetic moments. Therefore, the magnetism of the edge-state spin system of nanographene is of particular interest in carbon-based magnetism. Interestingly, the magnetic moment is fractional and is estimated theoretically to be about 0.2 µB [16,34], which deviates from what is expected in the pure localized spin system with 1 µB (S = 1/2). The edge-state spins are arranged in parallel to each other in a zigzag edge with strong ferromagnetic interaction, whose strength is in the region of several 103 K [44]. This suggests that nanographene is expected to be a ferromagnetic material with a Curie temperature higher than iron, which is a popular ferromagnet. We employ here activated carbon fibers (ACFs) as a good model system for investigating the magnetism of edge-state spins. As schematically modeled in Fig. 6(a), ACFs are nanoporous carbon consisting of a three-dimensional (3D) disordered network of nanographite domains, each of which is a stack of 3–4 nanographene sheets with the mean in-plane size of about 3 nm. The magnetic investigations have given us detailed information on the magnetic structure of ACFs [45,46]. Fig. 6(b) gives the schematic view of the spin structure of an individual nanographene sheet in the nanographite domain. A nanographene sheet having
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changes in the inter-nanographene sheet interaction J2 and internanographite interaction J3 . Heat treatment at temperatures above the graphitization temperature (about 1500 ◦ C) makes nanographene sheets fuse with each other, resulting in successive disappearance of the nanographene edges and consequently the spin magnetism of nanographene. Therefore, heat treatment in a wide temperature range provides details of the magnetism of nanographene and nanographite. Here we summarize the electron transport in ACFs since it is well correlated to the magnetic feature. It is governed by the Coulomb-gap-type variable range hopping process between nanographite domains in the Anderson insulator regime [47]. The electrical conductivity σ obeys the following equation:
σ ∝ exp − (T0 /T )1/2 ,
Fig. 6. (a) The schematic structural model of activated carbon fiber (ACF). (b) The structure of an individual nanographene sheet in a nanographite domain of ACF, and the spatial distribution of edge-state spins.
an irregular shape is comprised of zigzag and armchair edges, which are distributed randomly in its periphery. Around the zigzag edges, the spins are arranged ferromagnetically through strong intra-zigzag-edge ferromagnetic exchange interaction J0 . The strength of each magnetic moment depends on the detailed geometry of the zigzag edges such as the edge length, and the environment surrounding the zigzag edge. The spins in a zigzag edge interact with the spins in the neighboring zigzag edge through π -conduction-electron-mediated indirect exchange interaction, which is the nanographene analogue of RKKY interaction in traditional metal magnets. These inter-zigzag interactions J1 have their strength in the range J1 /J0 = 10−1 –10−3 [44], and the signs of the interactions vary between plus (ferromagnetic) and minus (antiferromangetic) depending on the geometrical relation between the zigzag edges concerned. The cooperation of strong J0 and less strong J1 , and the spatial variation of the strengths of the magnetic moments bring about a ferrimagnetic structure with a finite net magnetic moment in a nanographene sheet. We need two more sorts of exchange interactions to take into account the magnetism of ACFs. The first one is the internanographene-sheet interaction J2 in a nanographite domain. The edge-state spins of adjacent nanographene sheets in a domain interact with each other with antiferromagnetic interaction J2 having an intermediate strength. Then the antiferromagnetic coupling J2 between the effective magnetic moments having different values in nanographene sheets results in the formation of a ferrimagnetic structure of an individual nanographite domain. The second one is the inter-domain antiferromagnetic interaction J3 , which is weak, in the range 2–3 K [45,46]. The behavior of the magnetic susceptibility in pristine ACFs, which apparently obeys a paramagnetic Curie–Weiss law with antiferromagnetic Weiss temperature (−2 to 3 K), is explained on the basis of the magnetic structure model as presented above [45,46]. The spin concentration is estimated as several spins per nanographite domain. The behavior of the ACF edgestate spin system is sensitive to the structural change induced by heat treatment. Indeed, the heat treatment up to 1500 ◦ C modifies the network structure of ACFs. This is owing to the
T0 =
6e2 4π 2 kB εξ
,
where ε and ξ are the dielectric constant of the medium and the localization length of the conduction electron wave function, respectively. This suggests that the electron hopping from one nanographite domain to the adjacent one is subjected to an electron–electron repulsive force. This also evidences the finite density of states at EF in the one-electron picture, consistent with the electronic structure of nanographite predicted theoretically. In pristine ACFs, the peripheries of nanographene sheets are covered with functional groups, which disturb the internanographite-domain electron transport. Heat treatment removes the functional groups, working to create coherent electron transport paths between nanographite domains. The development of coherent electron transport paths, which work as percolation path networks for electron transport, enhances the conductivity upon the elevation of the heat-treatment temperature (HTT). Eventually, metallic conductivity is achieved around an HTT of 1200 ◦ C, at which the percolation path network becomes infinite. The less temperature dependent conductivity above the insulator–metal transition of HTT ∼ 1200 ◦ C suggests an important contribution of structural disorder in the electron scattering process. The change in the conductivity is faithfully tracked by the magnetic susceptibility as given in Fig. 7(a). Namely, the Curie–Weiss behavior with localized edge-state spins in the Anderson insulator regime is converted to the less temperature dependent susceptibility of conduction electrons in the metallic regime, where the negative susceptibility is a combination of small positive Pauli paramagnetic and large negative orbital contributions. Interestingly, an anomalous feature appears in the vicinity of the insulator–metal transition; that is, the susceptibility has a cusp at about 7 K with a negative Weiss temperature (antiferromagnetic) of −2 to −3 K. This is reminiscent of the onset of an antiferromagnetic ordering. However, this is not the case, as a large field cooling effect on the susceptibility is evident in Fig. 7(b). Fig. 7(b) indicates that the susceptibility for the sample in the vicinity of the insulator–metal transition (HTT ∼ 1200 ◦ C) has a large field cooling effect, particularly around the temperature range in which the cusp emerges. The presence of a cusp and its large field cooling effect are the consequence of the development of quenched disordered magnetic structure like a spin glass state. In general, a spin glass state develops when the strengths of exchange interactions J vary randomly in space. From the magnetization curve analysis, a large randomness in the strengths of exchange interactions p is evident, the width of the distribution being estimated as h∆J i2 / hJ i ≈ 0.8, which is safely in the region of a spin glass. The occurrence of the insulator–metal transition drives the feature of electrons from a localized state to an itinerant one, since the mobile electrons are created at the expense of the localized edge-state spins as the fusion of nanographene sheets proceeds upon the elevation of the HTT in the metallic phase well above the insulator–metal transition.
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Fig. 8. A schematic model of the fluorination effect on nanographene.
Fig. 7. (a) The temperature dependence of the susceptibility for the ACF samples heat treated at different heat-treatment temperatures (HTT). Heat treatment was given for 15 min except 1500 (1 h), in which 1 h heat treatment was performed. (b) The field cooling effect on the susceptibility vs. temperature plots in the ACF samples heat treated at 1100 and 800 ◦ C, which are in the vicinity of the insulator–metal transition and far from the transition, respectively. Open and full circles represent the data for the zero field cooling (ZFC) and field cooling (FC) (H = 1 T) processes, respectively. (Ref. [46]).
However, a considerable amount of edge spins still survive in the vicinity of the transition. The coexistence of the localized edge-state spins and the conduction π -electrons in the disordered structure causes the anomalous magnetic state to appear in the insulator–metal transition region; that is, exchange interactions between the localized edge-state spins are mediated by the conduction electrons. The disordered structure of the nanographite network is responsible for the random spatial distribution in the strengths of the exchange interactions, resulting in the formation of a spin-glass-like disordered magnetic structure. Here, it should be noted that the range of exchange interaction is over 2–3 nm, in contrast to the ordinary short range feature of exchange interaction. Such long range nature of the exchange interaction adds uniqueness to the magnetism of the edge-state spins of nanographene. 4. Chemical modifications of nanographene and nanographite The edge state is susceptible to chemical modifications of nanographene edges [36–39,48–55] in addition to the sensitivity to structural changes [45,46,56–58]. For example, the termination of edge carbon atoms by two hydrogen atoms gives edge-state
populations that are different from that with one hydrogen atom [37–39,42]. Oxidation of edges strongly changes the feature of the edge state [38,39]. Here, let us investigate how the magnetism of the edge states changes when nanographene is subjected to chemical modifications with a halogen such as fluorine and bromine. Fluorine is the most chemically active species, and is strongly bonded to carbon atoms not only at the edges but also in the interior of a nanographene sheet [48,49]. Fig. 8 exhibits schematically how fluorine atoms attack the carbon sites in a nanographene sheet. In the initial stage of fluorination of nanographene in ACFs up to a fluorine concentration of F/C ∼ 0.4, the reaction with fluorine atoms takes place mainly around the edges due to the relatively strong chemical activity of edge carbon atoms, resulting in the formation of difluorinated edge carbon sites. In this fluorination process, the concentration of edge-state spins tends to decrease as the fluorine concentration is elevated. This means that the edge state is destroyed by chemical modification with fluorine atoms, consistent with theoretical suggestions [38,39,48]. After the fluorination is completed at the edges around F/C ∼ 0.4, a fluorine atom begins attacking a carbon atom in the interior of the nanographene sheet, breaking the π bond. This creates a σ -dangling bond having a localized spin at the carbon site bonded to the carbon atom that is fluorinated. The concentration of σ -dangling bond localized spins becomes maximized at a fluorine concentration of F/C ∼ 0.8, at which a half of carbon atoms in the interior of nanographene sheet are bonded to fluorine atoms. Finally, localized spins disappear at a saturated fluorine concentration of F/C ∼ 1.2, at which all the carbon atoms are bonded to fluorine atoms. Interestingly, the magnetic nature is different between the edge-state spins of π -electron origin and the σ -dangling bond localized spins, as clearly evident in Fig. 9. Fig. 9 shows the fluorine concentration dependence of the strength of the internal exchange field acting on the spins. In the low concentration range up to F/C ∼ 0.4, where the edgestate spins are dominant, a finite internal field is present and it is lowered upon the elevation of the fluorine concentration. This finding suggests that the edge-state spins are interacting with each other, consistent with the theoretical suggestion that the edge-state spins have features intermediate between localized and delocalized states, as discussed in Section 2 [16–18]. In contrast to the edge-state spins, the internal field is absent between the σ dangling bond localized spins above F/C ∼ 0.4; that is, σ -dangling bond localized spins are well isolated from each other. Bromine, which is a milder chemical species than fluorine, behaves differently from the latter in modifying the electronic structure of nanographene [50]. When ACFs are exposed to
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x 10 5
1149
3.0
< α > av (g.emu –1)
2.5
2.0
1.5
1.0
0.5
0
0
0.2
0.4
0.6
0.8
1.0
1.2
F/C Fig. 9. The mean molecular field coefficient hαiav as a function of F/C in fluorinated ACFs. (Ref. [49]).
bromine, three kinds of bromine species are generated; that is, charge transfer species, covalent bond species and physisorbed species. The charge transfer species are the same as those generated in the reaction with bulk graphite, as we know that graphite forms an intercalation compound with bromine where negatively charged bromine molecules working as acceptors are accommodated in the graphitic galleries through charge transfer from graphite to bromine [59]. The covalent species are bonded to the edge carbon atoms, similar to fluorine atoms reacting with the edge carbon atoms in the first stage of fluorination as explained above. The physisorbed species are accommodated through van der Waals interaction in the nanopores of ACFs. In nanographene, charge transfer and covalent bond species dominate the change in the electronic and magnetic properties of the edge state. Interestingly, in contrast to bulk graphite, covalent species overwhelm charge transfer species in nanographene. For example, at the composition ratio of Br/C = 0.27, 12% of bromine is charge transfer species while 42% is covalent bond species at the edges. These concentrations of the charge transfer and covalent bond species correspond to about 10 and 35 Br atoms in an individual nanographene sheet (3 nm in size) that includes about 300 carbon atoms in average. The two kinds of species change the magnetic properties in different manners. The charge transfer species taking charges from nanographene sheets shift the Fermi level downward, resulting in the generation of holes in the bonding π -bands just beneath the Dirac point. As the edge states are located around the Dirac point, vacancies are therefore created in the edge states upon the charge transfer. The amount of vacancies increases as the charge transfer is elevated. In pristine ACFs in the neutral state, the Fermi level is located at the middle of the edge states as they are half filled. In this case, the edge-state spin concentration is maximized. The charge transfer reduces the spin concentration successively as the charge transfer rate fc (charge per C atom) is elevated, the spin concentration extrapolated to the infinite fc being expected to be zero. However, the edge-state spin concentration behaves slightly differently from this expectation in spite of a semiqualitative agreement, as summarized in Fig. 10(a). This suggests inhomogeneity in the charge transfer reaction, dissimilar to that in bulk graphite, as schematically illustrated in Fig. 11. According to experimental results, a charge transfer reaction takes place in the low bromine concentration range, followed by the formation of covalent bonds with the edge carbon atoms in the higher
Fig. 10. The charge transfer rate fc dependence of (a) the localized spin density ns , (b) the Fermi energy and (c) the orbital susceptibility χorb in brominated ACF. The experimental data are denoted by full circles in (a) and (c). The horizontal dashed line in (a) is the charge-transfer-independent contribution of the localized spins. The solid curve in (a) is the fitting curve to the model with the coexistence of bounding and interior nanographene layers (see Fig. 11). The solid curve in (b) is obtained from the fitting (solid curve) in (a). The EF vs. fc plot in the case of the absence of the edge state is denoted as the dashed line in (b). The solid curve in (c) is the χorb at 300 K calculated with the results in (b) based on McClure’s theory. (Ref. [50]).
concentration [50]. In the low concentration range where the edges of nanographene sheets are covered by functional groups, bromine molecule intercalates cannot be accommodated in the graphitic galleries of the nanographite domain due to the blockade of functional groups as shown in Fig. 11. Only nanographene sheets exposed to the nanopores are subjected to the charge transfer reaction with bromine. Then the edge-state spins are killed on the outer nanographene sheets in this charge transfer process. The remaining edge-state spins in the higher charge transfer range are those surviving in the interior and protected by the blockade from the reaction. Here, it should be noted that the presence of the edge states at the Dirac point plays an important role in the charge-transfer-induced downshift of the Fermi level, as shown in Fig. 10(b). The edge state works as an electron reservoir, making the downshift of the Fermi level slow. The downshift of the Fermi energy drastically decreases the orbital susceptibility, but its trend is different from what we can expect with no edge states, as confirmed in Fig. 10(c). The covalent bond formation at the edge carbon atoms affects also the magnetism of the edge-state spins [50]. The g-value in the ESR signal gradually deviates from that in pristine nonadsorbed ACFs as the bromine concentration is elevated, while the line width is broadened linearly. This suggests the mixing of the electronic states of bromine atoms with the edge state, since these changes in the ESR signal are relevant to the contribution of the large spin–orbit interaction of bromine atoms. The bromine atoms bonded to the edge carbon atoms are considered to affect the electronic features of the edge state directly, though the charge transfer bromine species are partly responsible for these changes.
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References
Fig. 11. A schematic description of the inhomogeneous charge transfer between nanographite and bromine. BL and IL denote the bounding layers faced to bromine, and interior layers of nanographite, respectively. The edge-state spins disappear on the bounding layers due to the charge transfer. (Ref. [50]).
5. Summary Nanographene stands in a unique position in the nanocarbon family in relation to its unconventional electronic structure with unique geometry dependence owing to the presence of open edges. Here, in the zigzag edge, a non-bonding edge state is created in spite of the absence of such a state in an armchair edge. The presence of edge states in the zigzag edges has been confirmed by STM/STS observations of hydrogen-terminated samples. The edge state is relevant to the non-bonding π -state of radical structures of non-Kekulé molecules. As the edge states have localized spins, they can give a rich variety of magnetism in nanographene and nangraphite depending on their structure. From an experimental viewpoint, ACFs are an interesting model system in which the edge-state magnetism can be comprehensively investigated. Their structure consists of a 3D disordered network of nanographite domains, each of which is a stack of 3–4 nanographene sheets. The interplay of strong intra-zigzag-edge ferromagnetic interaction and inter-zigzag-edge interaction makes an individual nanographene sheet be in a ferrimagnetic state with a spontaneous magnetic moment. In pristine ACFs, the magnetism is described in terms of these magnetic moments in the insulating state. Heat treatment induces successive structural changes, which brings about an insulator– metal transition at HTT ∼ 1200 ◦ C, resulting in the enhancement of inter-nanographite domain electronic interactions. This induces a crossover in the magnetism from Curie–Weiss-type to Pauli-type paramagnetism at the transition. In the vicinity of the transition, a spin-glass-like disordered state is stabilized below about 7 K with a unique field cooling effect. The edge-state spins are susceptible to chemical and structural modifications of nanographene and nanographite. Fluorination takes place selectively at the edge-carbon atoms in the initial stage of the reaction, and proceeds to the interior of nanographene sheet. The edge state and its localized spins disappear in the fluorination of the edge carbon atoms. The fluorination of an interior carbon atom creates a σ -dangling bonds. The localized spins of the σ dangling-bonds thus created behave independently from each other, in contrast to the edge-state spins of π -electron origin interacting with each other through strong exchange interactions. Bromine atoms also modify the magnetism of the edge-state spins in two ways. Bromine atoms participating in charge transfer with nanographene works to reduce the concentration of the edge-state spins, while the state of bromine atoms covalently bonded to the edge carbon atoms is mixed with the edge state, the spin–orbit interaction being enhanced in the edge state. Acknowledgements The present work is supported by the Grant-in-Aid for Scientific Research No. 20001006 from the Japan Society for the Promotion of Science (JSPS).
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