Ferromagnetic Graphene Nanoribbons: Edge Termination with

Article pubs.acs.org/JPCC

Ferromagnetic Graphene Nanoribbons: Edge Termination with Organic Radicals Daeheum Cho,† Kyoung Chul Ko,† Heesoo Park,‡ and Jin Yong Lee*,† †

Department of Chemistry, Sungkyunkwan University, Suwon 440-746, Korea Department of Chemistry, Seoul National University, Seoul 151-742, Korea

‡

S Supporting Information *

ABSTRACT: The intramolecular magnetic exchange coupling of edge terminated zigzag graphene nanoribbon (ZGNR) was studied with density functional theory calculations. In order to examine the applicability of the spin alternation rule and a classification scheme for radicals and couplers on functionalized graphene nanoribbons, we investigated the magnetic behaviors of pristine zigzag graphene nanoribbon with eight zigzag chains (8ZGNR) and 8-ZGNRs terminated with trimethylenemethane (TMM) and 6-oxoverdazyl (OVER) radicals,that is, TMM-ZGNR-TMM (TZT), OVER-ZGNR-OVER (OZO), and TMM-ZGNR-OVER (TZO). As expected, only ZGNR terminated with different group radicals on each edge (TZO) had a ferromagnetic (high-spin) ground state with an energy gap of 39 meV/supercell (321.57 cm−1) relative to the low-spin state. This strongly supports the validity of the spin alternation rule and the classification scheme for radicals and couplers on extensively conjugated large graphene nanoribbons. TZT and OZO were found to have an antiferromagnetic (low-spin) ground state with magnetic coupling weaker than that of interedge antiferromagnetic superexchange of pristine 8-ZGNR. Based on the spin distribution pattern on magnetic ground states, GNR prefers to have each edge in antiferromagnetic order, which satisfies Lieb’s theorem on the Hubbard model and spin alternation rule. All of the terminated ZGNRs exhibited semiconducting properties with an energy gap of 0.06−0.21 eV. interactions in π-conjugated organic magnetic materials ranging from diradicals to polyradicals can be qualitatively understood using a spin polarization mechanism,15,16 spin alternation rule,17,18 and radical classification.19,20 The former two rules provide an accurate prediction of the ground spin state of πconjugated organic molecules in most cases. However, since application of the spin alternation rule may not apply to heteroatom-substituted radicals, such as nitronyl nitroxide and verdazyl, a classification scheme for radical units depending on the spin distribution on the radical moieties allows the first two rules to provide a more accurate prediction of the magnetic ground state. Intermolecular magnetic interactions occur when ferro- or antiferromagnetic molecules approach each other. Since organic crystals can contain a variety of packing patterns, some of the aggregated systems can interrupt cooperative magnetism. Thus, it is crucial to control the relative orientation of magnetic molecules in order to obtain high-spin materials. Although a single molecule has a ferromagnetic order, only a few of them produce macroscopic ferromagnetic order with appropriate intermolecular stacking associated with long-range (magnetic) interactions, while many of them will crystallize into an antiferromagnetically ordered phase.21−23 However, controlling the organic intermolecular magnetic interaction

1. INTRODUCTION Organic magnetic materials have been extensively studied over the past several decades. Contrary to conventional magnetic materials arising from spin interactions between partially filled d- or f-orbitals of inorganic compounds, organic magnetism arises from interactions between unpaired p-electrons of stable organic radicals. These novel materials have promising features such as photomagnetic behavior,1−3 spintronic properties,4,5 and superconductivity6,7 as well as advantages of lightweight and environmental friendliness. Despite these fascinating features, practical use of organic magnetic materials has been limited because most of them undergo magnetic ordering at low temperatures. Therefore, many efforts have been made to develop strongly coupled high-temperature organic magnetic materials whose magnetic ordering persists at temperatures above room temperature.8−14 Of course, a key to this is finding excellent combinations of radical-couplers and radicals that generate strong intra- and intermolecular magnetic interactions. Intra- and intermolecular spin−spin interactions in organic di- and polyradical systems are of great importance for the understanding and development of magnetism in pure organic materials. Intramolecular magnetic interaction determines the magnetic behavior of a single molecule containing at least two unpaired electrons. A vast number of experimental and theoretical studies were devoted to understanding these interactions and have presented several important results. Most of the through-bond-type intramolecular magnetic © XXXX American Chemical Society

Received: February 7, 2015 Revised: March 26, 2015

A

DOI: 10.1021/acs.jpcc.5b01288 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C Scheme 1. Spin Distribution on Each Edge of the 8-ZGNR

the chemical modification of ZGNR with organic radicals bearing magnetic moments in order to induce magnetic exchange interactions between them. It is worth examining the magnetic behaviors of ZGNR terminated with organic radicals, because it exhibits a significant change in thermal stability and electronic and magnetic properties due to edge functionalization.

remains challenging since pure organic molecules are only weakly bound to each other by π−π stacking or hydrogen bonds, and it is unlikely that inorganic crystals will have strong intra- and intermolecular coordinations.24,25 As an alternative to the control of intermolecular magnetic interactions, polymer-type high-spin magnetic materials containing a large number of unpaired electrons in a single molecule have the potential to generate cooperative magnetism, minimizing the chance of disjointed intermolecular stacks. Rajca et al.26 prepared a calix[4]arene-based macrocyclicpolyaryl-type high-spin material with a total spin S of up to 5000 showing ferro- or ferrimagnetic order at temperatures less than 10 K, where the highly cross-linked macrocyclic framework significantly reduced the chance of failure in spin−spin exchange coupling due to a chemical defect along the spin polarization pathway. More recently, Zaidi et al.13 presented a polyaniline-based tetracyanoquinodimethane (TCNQ) charge transfer salt with a Curie temperature higher than 350 K. Magnetism of polymer structures bearing stable neutral radicals, for example, nitroxide-based polyoxyimino radical27 and poly(phenyl methacrylate) pendant type 6oxoverdazyl radical,28 has also been reported. However, there is still a limited source of extensively π-conjugated polymer frameworks. In this context, we chose graphene nanoribbon (GNR), which is a nanometer-sized single atomic layer of graphite, as a polymer backbone in order to generate a pendant polyradical. This extraordinary two-dimensional material and its derivatives demonstrate excellent electron and spin transport properties with a very long spin coherence length through an sp2−pz carbon network and peculiar magnetic ordering.29−37 The extensively π-conjugated molecular framework is advantageous for delivering magnetic exchange coupling due to the existence of near infinite spin coupling pathways, reducing the chance of failure in spin coupling due to chemical defects,26,38 and the absence of heteroatoms, such as S, N, and O, which interrupt effective magnetic exchange.39,40 There are two types of GNR, depending on the edge shape, armchair (AGNR) and zigzag (ZGNR) types, which have a crucial influence on electronic and magnetic properties.41−43 The most salient difference between AGNR and ZGNR is the existence of magnetic order attributed to localized edge states, found exclusively in ZGNR.44−46 Localized edge states, which are coupled antiferromagnetic to each other (Scheme 1), play an active role in magnetic and spin transport properties of ZGNR, as distinguished from AGNR.47,48 It is also of great interest to tune and fabricate antiferromagnetic ZGNR into ferromagnetic material via chemical modifications.49−52 In this report, we investigated

2. COMPUTATIONAL DETAILS We performed our DFT calculations employing the Vienna Ab Initio Simulation Package (VASP)53 code with a spin-polarized generalized gradient approximation (GGA) with a Perdew− Burke−Ernzerhof (PBE)54 exchange-correlation functional and the projector-augmented wave (PAW)55 method. GGA was found to provide qualitatively accurate descriptions of magnetic materials, although it provides a somewhat overestimated magnetic coupling constant, that is, energy difference between high- and low-spin order solutions.56−58 We also performed ab initio nonlocal van der Waals density functional (vdW-DF)59,60 and semiempirical DFT-D261 calculations to evaluate the dispersion effect. Plane wave basis sets with an energy cut off of 400 eV and 25 × 1 × 1 Monkhorst−Pack k-point62 mesh were used for geometry optimization. A finer 100 × 1 × 1 k-point sampling scheme was used for calculation of band structure. It was reported that vacuum separation of 10−15 Å is enough to avoid interlayer interactions of carbon-based and other materials.63−66 Thus, we used vacuum layers about 12 Å, with a small variation depending on the systems investigated. 3. RESULTS AND DISCUSSION As mentioned in the Introduction, ZGNR has localized electronic edge states in ferromagnetic ordering and is antiferromagnetically coupled (Scheme 1). According to Lieb’s theorem for the Hubbard model in the bipartite lattice, the total spin of ZGNR is given by 2Sz = |NA − NB| = |NI| = 0, where Sz and NI represent total spin and sublattice imbalance, respectively.67,68 Magnetic structures of ZGNR were also confirmed by ab initio calculations and analytic formulations. One can deduce from Lieb’s theorem that introduction of nonzero sublattice imbalance (NI ≠ 0) induces a net spin magnetic moment on ZGNR. In accordance with this expectation, various chemical and physical functionalizations of the pristine ribbons such as chemical doping,49,50 vacancy generation,51 and adatoms52 were utilized to successfully trigger a nonzero Sz. On the other hand, the spin alternation rule,17,18,69 which is based on the spin polarization mechanism,15,16,70 also provides B


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The Journal of Physical Chemistry C

Scheme 2. Illustration of Design Strategy for Ferromagnetically Coupled ZGNR with Radical Termination and Radicals and Couplers Classified into Syn and Anti Groups

that this design strategy is applicable to any width of ZGNR, because magnetic orders of the localized edges are identical. Trimethylenemethane (TMM) and carbon-connected 6oxoverdazyl (OVER) were selected as a representative syn and anti radical, respectively. As shown in Figure 1, the signs of

chemical insight into aid in understand the magnetic properties of nanographites. According to this rule, neighboring carbon atoms in a π-conjugated system have opposing spins. Therefore, magnetic moments of carbon atoms lying on an edge with intervals of odd numbers of carbon atoms are in ferromagnetic order, while interedge magnetic coupling linked by an even number of carbon atoms is in antiferromagnetic order. Considering the spin distribution on ZGNR and spin alternation rule, it would be possible to rationally design a ZGNR-based magnetic material via chemical fabrication. Recently, our research group reported the classification scheme for organic radicals into syn and anti groups (previously called α and β groups), depending on the relative orientation of the magnetic moments between connected atoms and radical dot atoms.19,20,40,71 For syn radicals, connected atoms and radical dot atoms have parallel spin, while anti radicals have an antiparallel alignment (Scheme 2). This classification scheme proved to be useful for systematic design of ferromagnetic diradicals.19,20,40 In line with this, we classified couplers with terminal atoms in parallel/antiparallel spin order as a syn/anti coupler. Couplers with odd and even numbers of carbon atoms along the spin coupling pathway have parallel and antiparallel spins on the terminal carbons according to the spin alternation rule and are classified as syn and anti couplers, respectively. These syn/anti couplers yield ferromagnetic/antiferromagnetic ground states for the coupling between the same group radicals.40 Therefore, magnetic coupling between different radical groups linked through syn/anti couplers is ferromagnetic. Armed with this strategy in terms of classification of radicals and couplers, we designed ferromagnetically coupled organic radicals. According to our classification schemes, spin coupling along each edge of ZGNR belongs to a syn coupler (bold black lines in Scheme 1), while interedge coupling is assigned to an anti coupler (bold green lines in Scheme 1). Therefore, we anticipate obtaining ferromagnetic coupling by attaching the same radical groups on each edge and different radical groups to each other, as shown in Scheme 2. Because the majority of atomic spin densities reside on radical dot atoms, a net ferromagnetic state with edge states of ZGNR ordered antiferromagnetically to each other is produced. We emphasize

Figure 1. Structures and spin density maps of trimethylenemethane (syn group) and carbon-connected 6-oxoverdazyl (anti group); hollow circle, up spin; filled circle, down spin.

the atomic spin density at the connected atom and radical dot atom of TMM/OVER are identical (syn group)/opposite (anti group). Therefore, if we attach a TMM radical on the upper edge of ZGNR, spin density at the connected atom has to occur in the upward direction according to the spin alternation rule; thus, spin density at the radical dot atom of TMM should also be upward spin (see Scheme 2). On the contrary, when we terminate the bottom edge of ZGNR with OVER, spin density at the connected atom has to be a downward spin, resulting in upward spin on the radical dot atom. Likewise, terminated radicals of TMM-ZGNR-OVER have parallel spin, which leads to net ferromagnetism in ZGNR with antiferromagnetically ordered edge states. To test our hypothesis, we compared the magnetic properties of pristine 8-ZGNR, TMM-ZGNR-TMM (TZT), OVERZGNR-OVER (OZO), and TMM-ZGNR-OVER (TZO), as shown in Figure 2. The optimized geometry showed the torsion angle of 42.3° for TMM, whereas almost planar for OZO. Coupling of TMM C


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Figure 2. Calculated geometries of (a) 8-ZGNR, (b) TMM-ZGNRTMM (TZT), (c) OVER-ZGNR-OVER (OZO), and (d) TMMZGNR-OVER (TZO).

radical and ZGNR edge inevitably introduces torsion angle due to steric repulsion between hydrogen atoms. The rotational barrier by ∼20° at the equilibrium geometry for TMM was less than 2 kcal/mol. The torsional angle between radical and coupler may reduce the strength of magnetic coupling within pconjugated radical systems due to weak overlap. However, the spin alternation rule is still valid for the systems with torsion angle, for example, nitronyl nitroxide bisradicals, whose intramolecular magnetic interaction is fully describable within the spin alternation rule.40 The validity of spin alternation rule in the nanoribbon system with torsion angle can be seen from the alternant spin densities located at around TMM-edge contact in Figure 3, although spin polarization is weakened. Hereafter, we use “+/−” symbols to represent spin up/down configurations. Using this representation, “++” and “−+” denote ferromagnetic (FM) and antiferromagnetic (AFM) states of pristine 8-ZGNR, with the left symbol designating the spin moments on the upper edge. By terminating the upper and bottom edges of ZGNR with organic radicals, we expected to obtain several spin orders such as “++++”, “++−−”, “+−+−”, and so on, with the sequential symbol representing the spin moments on the upper radical/upper edge/bottom edge/ bottom radical on ZGNR. However, only magnetic states satisfying the spin alternation rule between radical-edge coupling were obtained through VASP calculations, because violation of the spin alternation rule between the edge state and the terminated radical drastically increases the total energy of the system by about 1200 meV/supercell, as reported in ref 72. For this reason, we only obtained the lowest two magnetic states for each system, “+−−+” (AFM1) and “+−+−” (AFM2) for TZT, “++++” (FM) and “−−++” (AFM) for OZO, and “+−++” (FM1) and “−+++” (FM2) for TZO, whose different spin density distributions are depicted in Figure 3. Considering the spin alternation rule and classification of radicals/couplers, TZT, OZO, and TZO were predicted to have AFM2, AFM, and FM ground states, respectively. Calculated electronic energies (eV), energy difference between the two lowest magnetic states ΔE = Elow‑spin − Ehigh‑spin (in eV and in cm−1 in the parentheses), net spin moment μs (μB, Bohr magneton), and band gap (eV) for each magnetic state of 8-ZGNR, TZT, OZO, and TZO calculated with a PBE-vdW-DF functional are summarized in Table 1 (see Table S1 for the PBE and PBD-D2 results). ΔE is the key parameter determining the magnetic behavior of the system, and a positive/negative value means that the functionalized ZGNR possess a ferromagnetic/antiferromagnetic ground state.

Figure 3. Spin difference distributions for (a) pristine 8-ZGNR, (b) TMM-ZGNR-TMM (TZT), (c) OVER-ZGNR-OVER (OZO), and (d) TMM-ZGNR-OVER (TZO). Yellow and cyan colors represent the up and down spin moments, respectively. Magnetic ground states are marked in green.

Since all the calculated results were consistent with small deviations for PBE, PBE-D2, and PBE-vdW-DF, only the results obtained for the PBE-vdW-DF functional are listed in Table 1, which was supposed to provide the most reliable data for dispersion interactions and total energy among the three functionals.73,74 For 8-ZGNR, the AFM state was found to be the ground spin state, 24 meV/supercell lower than the FM state, consistent with previous reports.44,45 The energy gap was smaller than that of 6-ZGNR reported by ref 72 due to weakened interedge magnetic coupling with larger widths.72,75,76 TZT and OZO, where both edges were terminated with same-group radicals (syn-syn and anti-anti radical combinations), were found to have a low-spin ground state with only 2 and 7 meV/supercell lower than the high-spin state, respectively. This indicates that radical termination weakened interedge magnetic interaction on the terminated ZGNR compared to interedge superexchange interaction of pristine ZGNR of 24 meV/supercell. As shown in Figure 3b, magnetic moments of both edges are noticeably diminished by termination of the TMM radical due to the inefficient spin polarization resulting from the dihedral angle between the radical and ribbon. Finally, for TZO terminated with different group radicals on each edge, the high-spin state (FM1) was found to be the ground state, 39 meV/supercell lower than lowspin state (FM2) corresponding to 462.68 K and 321.57 cm−1. The strong preference of high-spin state over low-spin state D


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Table 1. Calculated Electronic Energies (eV), Difference of Electronic Energies ΔE = Elow‑spin − Ehigh‑spin (in eV and in cm−1 in the parentheses), Net Spin Moment per Unit Cell μs (μB), and Band Gap (eV) for α and β Spin Components Calculated by PBE-vdW-DF Functional 8-ZGNR FM E (eV) ΔE μs (μB) band gap (eV)

TZT AFM

−492.3637 −492.3884 −0.02472 (−199.38) 2.1096 0.0000 0 0.4139 0 0.4144

AFM1

OZO AFM2

AFM

−636.0658 −636.0730 −0.00718 (−57.91) 4.0040 0.0000 0.1935 0.1680 0.0606 0.1676

FM1

FM2

−605.3050 −605.2651 0.03987 (321.57) 2.9996 1.0014 0.2295 0.1936 0.1234 0.0621

functional. This material is available free of charge via the Internet at http://pubs.acs.org.

allows the TZO to be utilized as a room temperature pure organic ferromagnet. Most importantly, our design strategy was confirmed to be correct by the fact that TZT and OZO have a low-spin ground state, while TZO has a high-spin ground state. TMM-ZGNRTMM (TZT) and OVER-ZGNR-OVER (OZO), which are ZGNRs terminated with same-group radicals on each edge, were in the low-spin (antiferromagnetic) ground state, while ZGNR terminated with different group radicals, TMM-ZGNROVER (TZO), had a high-spin (ferromagnetic) ground state. Due to the preference of AFM ordering in the ZGNR according to Lieb’s theorem and the spin alternation rule, magnetic states with antiparallel interedge coupling became the ground state in 8-ZGNR, TZT, OZO, and TZO. In this regard, we revealed that edge termination with organic radicals on ZGNR does not change the magnetic ordering of the ribbon itself. In addition, each edge provided ferromagnetic coupling with respect to the radical-edge-radical coupling along the edge, as expected from the spin alternation rule.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +82-31-299-4560. Fax: +82-31-290-7075. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by National Research Foundation (NRF) grants funded by the Korean government (MEST; 2007-0056343 and 2013R1A1A2062901). The authors would like to acknowledge the support from KISTI Supercomputing Center through the Strategic Support Program for the Supercomputing Application Research [No. KSC-2014-C3018].

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4. CONCLUSIONS We investigated the spin−spin interactions between terminated organic radicals and localized magnetic edge states on ZGNR. According to the spin alternation rule and the classification scheme for radicals and couplers, we compared the magnetic behaviors of pristine 8-ZGNR, TMM-ZGNR-TMM (TZT), OVER-ZGNR-OVER (OZO), and TMM-ZGNR-OVER (TZO). Our investigation on 8-ZGNR reproduced the AFM ground state of ZGNR with an energy gap of 24 meV/supercell. TZT and OZO, ZGNR terminated with same-group radicals (syn−syn and anti−anti combinations) at both edges, had antiferromagnetic (low-spin) ground states, while TZO, ZGNR terminated with syn and anti group radicals at both edges, had a ferromagnetic (high-spin) ground state with a very strong magnetic coupling of 462.68 K (321.57 cm−1). Due to the strong magnetic interaction, newly designed TZO is a potential candidate for room temperature pure organic GNR-based ferromagnetic materials, assuming appropriate experimental fabrication methods. Furthermore, we addressed the usefulness of the spin alternation rule and classification scheme for radicals and couplers in designing ferromagnetically coupled organic magnetic materials.

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FM

−574.9027 −574.9049 −0.00225 (−18.15) 1.9941 0.0001 0.1873 0.2190 0.1905 0.2165

TZO

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ASSOCIATED CONTENT

S Supporting Information *

Calculated electronic energies (eV), energy difference between two lowest magnetic states ΔE = Elow‑spin − Ehigh‑spin (in eV and in cm−1 in the parentheses), net spin moment μs (μB, Bohr magneton), and band gap (eV) for each magnetic state of 8ZGNR, TZT, OZO, and TZO computed with PBE and PBED2 functionals. Calculated band structure with a PBE-vdW-DF E


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