DSpace at VNU: Electronic and magnetic properties of C-60-Fe-n-graphene intercalating nanostructures (n=1-6) predicted from first-principles calculations

Chemical Physics Letters 618 (2015) 127–131 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett Electronic and magnetic properties of C60 –Fen –graphene intercalating nanostructures (n = 1–6) predicted from first-principles calculations Hung M Le a,b,∗ , Wilson K.H Ng a , Hajime Hirao a,∗ a Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore b Faculty of Materials Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam a r t i c l e i n f o Article history: Received 10 September 2014 In final form 21 October 2014 Available online 30 October 2014 a b s t r a c t Graphene and C60 can establish coordination bonds with transition metal atoms/clusters Using firstprinciples modeling methods, we explore the C60 –Fen –graphene intercalating nanostructures (n = 1–6), which may have potential applications in, e.g., spintronics Twelve optimized configurations are found to possess good energetic stability (with binding energies of 4.22–20.54 eV) Eleven structures have different magnitudes of magnetism (2.00–12.75 ␮B /cell), whereas one is non-magnetic The magnetism is highly correlated with the bonding orientations between Fe atoms and C60 Seven nanostructures possess good half metallicity (with the spin polarization effects >0.8), while the non-magnetic structure is found to be insulating © 2014 Elsevier B.V All rights reserved Introduction Since the successful experimental synthesis of graphene, a material that features a two-dimensional carbon-made structure, many advanced technologies have been invented through its utilization At the nanometer scale, graphene has remarkable mechanical stability because of the fully sp2 -bonding arrangement of carbon atoms [1] Moreover, graphene is regarded as a zero-gap semiconductor that exhibits superconductivity and potentially offers useful applications in electronic devices [2] Reaction catalysis is another noticeable application because graphene can be employed as a hosting material to carry catalyzing metal atoms/clusters/complexes [3–5] For that reason, the chemistry of metal-bonding interactions of graphene is an important aspect that has been intensively investigated over the past few years [6–8] The metal–graphene contact is formed upon hybridization of d and p orbitals, similar to that in the intercalating structures of metal and benzene [9] The sp2 bonds are responsible for the formation of a graphene monolayer; however, the 2pz orbitals, which are not involved in the sp2 bonds, tend to interact with the vacant d shells of metal atoms and form coordination bonds So far, there have been a large number of experimental studies of metal–graphene nanostructures, such as those involving Ni [10], Au, Fe, Cr [11–13], ∗ Corresponding authors E-mail addresses: hung.m.le@hotmail.com (H.M Le), hirao@ntu.edu.sg (H Hirao) http://dx.doi.org/10.1016/j.cplett.2014.10.051 0009-2614/© 2014 Elsevier B.V All rights reserved or Ag [14] By employing electrolysis, Zhang et al [15] investigated the intercalating compounds of iron chloride on graphite In addition, there have been efforts to attach graphene on metal surfaces to derive interesting electronic properties [16] Theoretical and computational investigations of graphene– metal interactions have been conducted using density functional theory (DFT) calculations [17,18] Significant achievements in graphene research have been attained during the past few years, which have enhanced attention to the electronic and magnetic properties of graphene Importantly, Nakata and Ishii have provided theoretical evidence that 3d transition metals bind strongly to graphene [19] Moreover, the attachment of various types of ligands on graphene via a transition-metal atom bridge has been investigated in several previous studies [6,9,20,21] Recently, we have explored C60 –M–G nanostructures, in which buckminsterfullerene [22,23] (C60 ) was steadied on a graphene surface via one bridging transition-metal atom [4,24] Interestingly, when Cr, Mn, Fe, or Ni is used as a bridging metal atom, C60 –M does not stand upright on graphene; instead, we observe geometry distortions that correlate with spin polarization in the 3d orbitals and dispersion interactions between graphene and C60 We hypothesize that such a geometry distorting feature may be effectively exploited to design new nanostructures, in which multiple transition-metal atoms are arranged in a crown-like manner This strategy may allow one to construct more stable graphene–metal–C60 nanostructures that might find applications in spintronics or catalysis [25] In this Letter, we present a DFT investigation of bridging C60 and graphene using several Fe atoms (up to six atoms) 128 H.M Le et al / Chemical Physics Letters 618 (2015) 127–131 Table Binding energies, average Fe stabilization energies, MT and MA for the investigated nanostructures Fe distribution C60 –Fe–G Figure C60 steadied on graphene using six bridging Fe atoms Twelve configurations (pre-optimized) based on Fe allocations are suggested: (a) C60 –Fe–G, (b) C60 –Fe5 –G, (c) C60 –Fe6 –G, three C60 –Fe2 –G configurations, namely (d) (1,2), (e) (1,3), and (f) (1,4), three C60 –Fe3 –G configurations, namely (g) (1,2,3), (h) (1,2,4), and (i) (1,3,5), and three C60 –Fe4 –G configurations, namely (j) (1,2,3,4), (k) (1,2,3,5), and (l) (1,2,4,5) For convenience, the given nomenclatures are used to address the structures throughout the Letter Computational details DFT calculations are executed using the Quantum Espresso (QE) package [26] Specifically, we employ the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional [27,28] with the ultrasoft pseudopotentials [29,30] (USPP) The kinetic energy cutoff for plane-wave expansion is set to 45 Rydberg The empirical corrections for long-range dispersions are also included [31,32] To approximate the continuity of energy bands, we employ the Gaussian smearing technique with a small smearing width (0.002 Rydberg) Structural optimizations are performed with an energy-convergence criterion of 10−6 Rydberg/cell Initially, full structural optimizations are executed at the -point by relaxing the atomic positions and unit cells simultaneously Then, the final relaxed structures are determined by further relaxing the atomic positions with a k-point mesh of (6 × × 1) The theoretical models have two-dimensional characteristics and consist of three major building units: a periodic graphene monolayer (54 C atoms), bridging atoms (i.e Fen ), and C60 In those two-dimensional slabs, the length of c-axis is set to 40 Bohr ˚ to allow vacuum treatments in the z direction perpen(21.17 A) dicular to the graphene sheet In the C60 –Fe–G structure (Figure S2, Supplementary Material (SM)), C60 –Fe does not stand upright on the graphene sheet, and Fe interacts with only two C atoms in C60 In Figure 1, we show a complex structure with a maximum load of six Fe atoms, which fully interact with a honeycomb ring of C60 Also, all other possible structures of C60 –Fen –G (n < 6) are constructed For illustration purposes, the top and side views of all optimized C60 –Fen –G structures are presented in the SM After a geometry optimization, the binding energy of a complex nanostructure with n Fe atoms can be calculated using the following equation: Ebinding = EC60 + nEFe + EG − Estructure , Ebinding (eV) ES (eV) MT (␮B /cell) MA (␮B /cell) 4.22 4.22 2.00 3.09 7.62 6.78 6.83 3.81 3.39 3.42 4.11 0.00 4.05 6.33 0.00 5.40 C60 –Fe2 –G (1,2) (1,3) (1,4) C60 –Fe3 –G (1,2,3) (1,2,4) (1,3,5) 10.68 10.38 9.74 3.56 3.46 3.25 6.13 6.11 6.00 8.58 8.51 8.02 C60 –Fe4 –G (1,2,3,4) (1,2,3,5) (1,2,4,5) 13.88 13.98 14.05 3.47 3.49 3.51 8.50 8.14 8.09 11.31 10.55 11.30 C60 –Fe5 –G 17.73 3.55 10.36 14.12 C60 –Fe6 –G 20.54 3.42 12.75 16.60 Results and discussion As shown in Table 1, with a full load of six Fe atoms, the C60 –Fe6 –G nanostructure (Figure S3, SM) is highly stable with a binding energy of 20.54 eV On average, the stabilization energy arising from each Fe atom in this case is 3.42 eV, which indicates good stabilization of the nanostructure, although this stabilization energy is lower than that of C60 –Fe–G (4.22 eV) The DOS data allow us to estimate the total magnetization (MT ) and absolute magnetization (MA ) as reported in Table MT and MA of C60 –Fe6 –G are calculated as 12.75 and 16.60 ␮B /cell, respectively Such ferromagnetism is mainly produced by the strong spin polarization of the Fe atoms in the nanostructure (with the major contribution of d orbital polarization) Recall that in a previous work [24], with the use of one Fe atom, C60 –Fe–G was reported to exhibit a total magnetic moment of 2.00 ␮B /cell (Figure 2a), which is slightly smaller than one sixth (1) where EC60 , EFe , and EG are the total energies of C60 , an isolated Fe atom, and the periodic graphene layer, respectively, while Estructure denotes the total energy of the complex obtained from DFT calculations For fair comparisons among the investigated cases, we define average stabilization energy for a C60 –Fen –G nanostructure as ES = Ebinding n (2) Figure Spin-polarized total DOS (left panels) and PDOS of Fe atoms (right panels) in (a) C60 –Fe–G, (b) C60 –Fe4 –G (1,2,3,4), (c) C60 –Fe4 –G (1,2,3,5), (d) C60 –Fe4 –G (1,2,4,5), (e) C60 –Fe5 –G, and (f) C60 –Fe6 –G The Fermi level is positioned at H.M Le et al / Chemical Physics Letters 618 (2015) 127–131 Table Magnetic contributions (␮B ) from Fe atoms (and their 3d shells) and spin polarization effects for the investigated C60 –Fen –G nanostructures Fe distribution Fe magnetic contribution (␮B ) Total C60 –Fe–G P 3d 2.33 2.22 1.00 C60 –Fe2 –G (1,2) (1,3) (1,4) 4.81 0.00 3.68 4.75 0.00 3.57 1.00 – 0.87 C60 –Fe3 –G (1,2,3) (1,2,4) (1,3,5) 7.01 6.80 6.42 6.87 6.63 6.19 0.81 1.00 1.00 C60 –Fe4 –G (1,2,3,4) (1,2,3,5) (1,2,4,5) 9.46 8.27 9.32 9.30 8.10 9.16 0.61 0.76 0.68 11.91 14.27 11.75 14.14 0.39 0.89 C60 –Fe5 –G C60 –Fe6 –G of MT exhibited by C60 –Fe6 –G Interestingly, we observe an alternate pattern of Fe occupations in C60 –Fe6 –G: three are closer to C60 and possess slightly larger magnetic terms (2.50 ␮B ), whereas the other three are closer to graphene and possess smaller terms (2.25 ␮B ) as illustrated in Figure 2f Moreover, the Löwdin charge [33] analysis indicates that Fe2 , Fe4 , and Fe6 have smaller positive charges than the others (see Table S1, SM) The half-metallicity is an interesting feature that can be observed in several nanostructures In those nanostructures, while one electronic spin state (up) indicates insulation, the other spin state (down) is conductive In a typical case of perfect halfmetallicity, the spin-up DOS should completely vanish at the Fermi level Particularly in the C60 –Fe6 –G case, the spin-up DOS does not vanish at the Fermi level, but it is very small compared to the spin-down DOS as shown in the total DOS diagram (Figure 2f) Therefore, we regard this structure as an imperfect half metal The half-metallic property can be evaluated by the spin-polarization effect P [34,35]: P= ↑ (E ) − F ↑ (E ) + F ↓ (E ) F ↓ (E ) F , (3) where ↑ (EF ) and ↓ (EF ) represent the spin-up and spin-down DOS at the Fermi level, respectively If P is unity, the material can be regarded as a perfect half metal Indeed, the spin polarization effect of C60 –Fe6 –G is 0.89 In the C60 –Fe–G case, the spin polarization effect is determined to be unity, which indicates a good half-metal For convenience, we summarize the magnetic contributions from the metal atoms (and their 3d orbitals) and the calculated spin polarization effects of the investigated nanostructures in Table When five Fe atoms are used (C60 –Fe5 –G), the bonding interactions between the metal atoms and graphene change significantly From the top view (Figure S4, SM), it can be seen that those five Fe atoms constitute a pentagon-like structure Closer inspection shows that there are three types of Fe–graphene interactions with different degrees of spin polarization Two Fe atoms (2.52 ␮B /atom) interact with graphene via three Fe–C bonds, two Fe atoms (2.33 ␮B /atom) interact with full honeycomb units of graphene (but dislocated from the center of the honeycomb rings), and one Fe (2.24 ␮B /atom) is located above the center of a honeycomb ring The difference in Fe locations can also be observed from the PDOS of Fe (Figure 2e) The binding energy of C60 –Fe5 –G is 17.73 eV, while the stabilization energy for one Fe atom is 3.55 eV, slightly higher than that in C60 –Fe6 –G C60 –Fe5 –G possesses weak half metallicity because of its low spin-polarization effect (0.39) 129 As shown in Figure 1, three different C60 –Fe4 –G nanostructures are optimized When four Fe atoms are located at the (1,2,3,5) positions (Figure S5, SM), the structure has an intermediate binding energy (13.98 eV) and exhibits an intermediate magnetic moment (8.14 ␮B /cell) among the three possibilities In this structure, four Fe atoms fully interact with four corresponding honeycomb units from graphene Each of the first three metal atoms (Fe1 , Fe2 , Fe3 ) interacts with C60 via two Fe–C linkages, while the remaining Fe atom (Fe4 in Figure 2c) fully interacts with a five-membered pentagonal ring from C60 Indeed, this special Fe atom has the smallest spin polarization term (1.01 ␮B ) among the four and a negative charge (−0.06), while the other three Fe atoms have positive charges and exhibit greater magnetic moments of 2.31–2.64 ␮B The partial DOS (PDOS) profiles for Fe1 and Fe3 are very similar, and the highest polarization term originates from Fe2 Overall, this nanostructure has a spin polarization effect of 0.76 When four Fe atoms reside at the (1,2,3,4) positions (Figure S6, SM), the resulting structure has a binding energy of 13.88 eV (lowest of the three cases), while it has the strongest ferromagnetism of the three (8.50 ␮B /cell) In this case, the Fe atoms are observed to behave in slightly different manners (see Figure 2b) Each Fe atom has a positive charge and produces a strong ferromagnetic moment (higher than ␮B /atom) In the DOS plot (Figure 2b), it is observed that the (1,2,3,4) structure has a low spin polarization effect (0.61) Similar to the case of (1,2,3,4), there are two different types of Fe allocations in the (1,2,4,5) structure (Figure S7, SM), which has the largest binding energy (14.05 eV) of the three C60 –Fe4 –G cases All four atoms are found to shift slightly away from the center of the honeycomb rings in graphene and each Fe interacts with two C atoms from C60 , which results in a strong ferromagnetic moment (2.25–2.41 ␮B /atom) Consequently, a strong magnetic moment of 8.09 ␮B /cell is found (but the smallest of the three C60 –Fe4 –G cases) Like in the cases of (1,2,3,4) and (1,2,3,5), the (1,2,4,5) structure does not really possess the halfmetal characteristics, because there is still electron density in the spin-up state at the Fermi level (see the DOS plot in Figure 2d), and the spin polarization effect for the (1,2,4,5) structure is as low as 0.68 Additional validation calculations are executed using QE with the USPP and the Vienna Ab Initio Package [36–38] (VASP 4.6) with the projector-augmented-wave method for the inspection of ferromagnetic/anti-ferromagnetic states in C60 –Fe4 –G (1,2,4,5) and three other structures (Figure S1, SM) We conclude that neighboring Fe atoms favor the ferromagnetic spin alignment and not have opposing magnetic moments There are three possibilities to distribute two Fe atoms in C60 –Fe2 –G In those three cases, the two Fe atoms are observed to shift slightly away from the centers of the honeycomb units in graphene; however, the major distinctions come from various interacting schemes between Fe and C60 When two Fe atoms are placed in the (1,2) arrangement (Figure S8, SM) (resulting in an ˚ each Fe atom interacts with C60 via two Fe–Fe distance of 2.47 A), Fe–C linkages, receives a positive charge, and exhibits a large ferromagnetic moment (2.41 ␮B per each Fe atom) Overall, the (1,2) structure exhibits a total magnetic moment of 4.11 ␮B /cell From binding energy calculations, it is shown that the (1,2) structure is the most stable of the three C60 –Fe2 –G structures examined and the corresponding average stabilization energy is the largest (3.81 eV) of all structures reported in this study (excluding the C60 –Fe–G case) According to the DOS distribution (Figure 3a), the (1,2) structure can be regarded as a perfect half-metal with the P value of 1.00 (largest among three C60 –Fe2 –G cases) The (1,3) and (1,4) structures (Figures S9 and S10 in the SM, respectively) are less stable, with the binding energies being 6.78 and 6.83 eV, respectively It is seen from the DOS plots (Figure 3b and c) that the (1,3) nanostructure is a non-magnetic and insulating material, while (1,4) possesses half-metallicity with the 130 H.M Le et al / Chemical Physics Letters 618 (2015) 127–131 Figure Spin-polarized total DOS (left panels) and PDOS of Fe atoms (right panels) in (a) C60 –Fe2 –G (1,2), (b) C60 –Fe2 –G (1,3), (c) C60 –Fe2 –G (1,4), (d) C60 –Fe3 –G (1,2,3), (e) C60 –Fe3 –G (1,2,4), and (f) C60 –Fe3 –G (1,3,5) The Fermi level is positioned at spin-polarization effect estimated as 0.87 In the (1,3) case, two Fe atoms play similar roles in the bonding interaction with C60 , and each of them establishes bonding to C60 via three Fe–C linkages Interestingly enough, such an unusual interacting scheme causes the spin-up and spin-down DOS to cancel each other out and consequently produces a non-magnetic structure (illustrated in Figure 3b) The band gap of this insulating case is very narrow (0.09 eV) according to our band energy examination Both Fe atoms in the (1,3) case have negative charges On the other hand, two Fe atoms in the (1,4) case behave differently from each other While Fe1 (as denoted in Figure 3) makes bonds to a five-membered ring from C60 and exhibits a weak ferromagnetic term (1.30 ␮B ) with a negative charge (−0.04), Fe2 interacts with two C atoms and exhibits a stronger ferromagnetic moment (2.38 ␮B ) with a positive charge (0.13) Unlike the other magnetic structures where Fe atoms contribute ferromagnetic terms and C atoms contribute antiferromagnetic terms, the (1,4) structure is the sole case where Fe, C60 , and graphene jointly contribute ferromagnetism With the inclusion of three metal atoms, each Fe is found to interact fully with the honeycomb rings in graphene while binding to C60 via two Fe–C linkages When three metal atoms are located at the (1,2,3) positions (Figure S11, SM), Fe1 and Fe3 behave similarly in their interactions with graphene and C60 as proved by the PDOS of Fe1 and Fe3 (with a magnetic alignment of 2.23 ␮B /atom) Fe2 , on the other hand, exhibits a larger magnetic contribution (2.55 ␮B ) than the others The total ferromagnetic moment of the (1,2,3) structure (6.13 ␮B /cell) is actually observed to be the largest of all C60 –Fe3 –G cases In the next structure having the (1,2,4) arrangement for three Fe atoms (Figure S12, SM), the role of each metal atom is different from that of the others, as seen in the PDOS distribution in Figure 3e This structure exhibits a magnetic moment with an intermediate magnitude among three cases (6.11 ␮B /cell) In the last case, three Fe atoms are equally distributed on the graphene sheet (Figure S13, SM), so that they interact with C60 in an almost similar manner (see Figure 3f) As a result, they establish the same spin polarizations, which produce an approximate magnetic alignment of 2.14 ␮B /Fe atom The total magnetic moment given by this structure is 6.00 ␮B /cell It can be seen that the computed total magnetizations of three C60 –Fe3 –G structures vary in a small range Figure Charge density plots of the planes containing three Fe atoms in the (a) (1,2,3) and (b) (1,2,4) C60 –Fe3 –G nanostructures The Fe atoms are represented by red spheres (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) H.M Le et al / Chemical Physics Letters 618 (2015) 127–131 Notably, all the investigated C60 –Fe3 –G structures possess semimetallicity Among the three C60 –Fe3 –G nanostructures, the (1,2,3) structure has the lowest spin polarization effect (0.81) At the same time, this structure also has the largest binding energy and magnetic moment (shown in Table 1) In contrast, (1,2,4) and (1,3,5) have perfect spin polarization effects (1.00), while they are quite less stable (with binding energies of 10.38 and 9.74 eV, respectively) and exhibit smaller magnetic moments (6.11 and 6.00 ␮B /cell) The interactions between intercalated Fe atoms and graphene have large binding energies and thus can be regarded as strong coordination bonds Interestingly, this bonding interaction alters the electronic structure of graphene by doping electron density to build up the highest occupied bands in the ␤-spin Not only does this behavior result in magnetism, but it also causes halfmetallicity of most nanostructures, as can be seen in Figure S14 (SM) where we observe significant contributions of C60 –Fen groups at the highest occupied bands Semi-metallicity, which arises from the incorporation of the d-bands across the Fermi energy level, has also been found in other carbon materials intercalated with transition metal atoms [20,39] In cyclopentadienyl–Fe–carbon nanotube (Cp–Fe–CNT) [39], the magnetic moment of Fe is quenched to 0.00 or 0.97 ␮B /cell, whereas in benzene–Fe–graphene [20] and the current system, the magnetic moment of Fe remains large The smaller magnetic moment in Cp–Fe–CNT is due to the strong interactions and multiple chemical bonds between metal and CNT Another notable difference between previous studies and ours is the slant orientation of C60 in the one-Fe case, while the Cp ring and benzene remain flat and preserve the Á5 and Á6 hapticities, respectively In fact, Á2 hapticity in organometallic compounds containing a buckminsterfullerene ligand is common [40] It is of particular interest to inspect the Fe–Fe interactions, which may affect the stability of the nanostructures to some extent In order to verify the possible interactions between Fe atoms, we choose to examine charge density distributions in two C60 –Fe3 –G models: (1,2,3) and (1,2,4) In the (1,2,3) structure, there are two possible Fe–Fe bonds (with 2.37 A˚ in length), while in the (1,2,4) structure, we suspect that there is only one Fe–Fe interaction ˚ because one Fe is distant from the other two Fe atoms In (2.35 A) the two-dimensional charge density plots of the Fe atoms (Figure 4), we observe that there are actually two weak Fe–Fe interactions in the (1,2,3) case, while there is only one Fe–Fe interaction in (1,2,4) Such metal–metal interactions explain why the stabilization energy of (1,2,3) is the largest and the stabilization energy of (1,3,5) is the smallest The contribution of metal–metal interactions in structural stabilizations is also significant in C60 –Fe2 –G, because the (1,2) structure with a Fe–Fe distance of 2.47 A˚ has the largest stabilization energy a five-membered ring of C60 ) From the charge distribution plots (Figure 4), it is observed that there is a weak Fe–Fe interaction ˚ which contributes when the distance is relatively short (∼2.3 A), somewhat to the enhanced stabilization of Fe atoms in the structures Importantly, seven half-metals with spin polarization effects greater than 0.8 are found With the interesting magnetism and stability, the C60 –Fen –G nanostructures may find useful applications in spintronics, catalysis, etc Acknowledgments The authors thank the High-Performance Computing Centre at Nanyang Technological University and the Institute for Materials Research at Tohoku University, Japan (under VNU B2014-18-03) for computer resources This work is supported by a Nanyang Assistant Professorship and an AcRF Tier grant (RG3/13) Appendix A Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2014.10.051 References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] Conclusions In summary, the C60 –Fen –G nanostructures (n ≤ 6) investigated in this study are highly stable The nanostructures seem to be stabilized significantly with the average stabilization energies amounting to >3 eV Most structures exhibit ferromagnetism (except the C60 –Fe2 –G (1,3) case where magnetism vanishes and a narrow band gap of 0.09 eV is open) The magnetic alignment of each Fe atom exhibits dependency on the bonding situation between graphene and C60 For instance, when the metal atom is bound to C60 via two Fe–C linkages, the electron spin in 3d orbitals is highly polarized to produce a magnetization above ␮B Otherwise, the metal atom exhibits a weak magnetic moment (when it interacts fully with a five-membered ring from C60 ) or even becomes non-magnetic (when it interacts with three C atoms from 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(4.22 eV) The DOS data allow us to estimate the total magnetization (MT ) and absolute magnetization (MA ) as reported in Table MT and MA of C60 –Fe6 –G are calculated as 12.75 and 16.60 ␮B /cell,... is an interesting feature that can be observed in several nanostructures In those nanostructures, while one electronic spin state (up) indicates insulation, the other spin state (down) is conductive