Doping Effect on Edge-Terminated Ferromagnetic Graphene

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Doping Effect on Edge-Terminated Ferromagnetic Graphene Nanoribbons Yeonsig Nam, Daeheum Cho, and Jin Yong Lee* Department of Chemistry, Sungkyunkwan University, Suwon 16419, Korea S Supporting Information *

ABSTRACT: The doping effect on intramolecular magnetic exchange coupling of an edge-terminated zigzag graphene nanoribbon (ZGNR) with organic radicals was studied with density functional theory calculation. We investigated magnetic behaviors of boron (B)- and nitrogen (N)-doped ZGNRs, terminated with trimethylenemethane (TMM) and 6oxoverdazyl (OVER) radicals, that is, TMM-ZGNR-TMM, OVER-ZGNR-OVER, and TMM-ZGNR-OVER. A doping with B or N on the spin-coupling pathway of radical-ZGNRradical changed the spin distribution pattern of each system and hence its magnetic ground configuration, magnetic coupling strength, and magnetic moment. The first doping switched the magnetic ground configuration of a system from antiferromagnetic (AFM) to ferromagnetic (FM) and vice versa. An additional doping switched it back to its original magnetic ground configuration. Moreover, N doping on a radical-terminated edge increased the magnetic coupling strength as compared with the undoped system, while B doping decreased it. Furthermore, B or N doping on a TMM-terminated edge increased the magnetic moment of the system, while the same doping on an OVER-terminated edge decreased it. Our results demonstrate a possibility of reversible spin control of organic magnetic materials from AFM to FM and vice versa by chemical doping and the enhancement of the magnetic coupling strength of edge-terminated ZGNRs.

1. INTRODUCTION Organic magnetic materials have received considerable attention due to their advantages of being lightweight, environmentally friendly, and simple to manufacture compared to inorganic magnetic materials, as well as their potential applications as superconductors1,2 and spintronics materials.3,4 Contrary to inorganic magnetic materials for which magnetic interaction arises from partially filled d or f orbitals, organic magnetic interaction arises from unpaired p electrons of stable organic radicals. Organic magnetic materials have smaller spin− orbit coupling, which indicates a longer spin coherence length compared to conventional inorganic materials. Despite these advantages, practical use of organic magnetic material has been limited by its loss of magnetism even at low temperature due to weak magnetic interaction. Therefore, many efforts have been made to develop ferromagnetic organic magnetic materials that have strong magnetic interaction above room temperature.5−7 As a design strategy, a variety of stable neutral radicals were coupled with different couplers to generate magnetic interaction in organic magnetic molecules.8−11 Generally, magnetic properties of pure organic materials are controlled by intra- and intermolecular magnetic interaction. Intramolecular magnetic interaction arises from magnetic exchange interaction between unpaired electrons in a molecule. Intermolecular magnetic interaction arises when ferromagnetic (FM) or antiferromagnetic (AFM) molecules approach each © 2016 American Chemical Society

other. A number of theoretical and experimental studies have been performed to understand intramolecular and intermolecular interactions.12,13 Most of intramolecular interactions in π-conjugated organic magnetic materials can be explained with a spin polarization mechanism14,15 and spin alternation rule.16,17 These two rules provide qualitative prediction of the magnetic ground configuration of π-conjugated organic molecules. Although a single molecule has FM order, an organic crystal could be paramagnetic, FM, AFM, or ferrimagnetic depending on intermolecular magnetic interactions and the molecular packing patterns. Therefore, it is important to control the orientation of magnetic molecules to obtain high-spin organic magnets. However, controlling the orientation of magnetic molecules remained a challenging task because of the difficulties in predicting the orientation and weak bond strength between organic molecules. It was reported that polymer-type materials that have a vast number of unpaired electrons in a molecule can be used to generate cooperative magnetism while minimizing the chance of disjointed intermolecular stacks,5,18−20 eliminating the need to control the intermolecular magnetic interactions. As a potential polymer backbone to generate a pendant polyradical, Received: February 20, 2016 Revised: April 9, 2016 Published: May 9, 2016 11237

DOI: 10.1021/acs.jpcc.6b01737 J. Phys. Chem. C 2016, 120, 11237−11244

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The Journal of Physical Chemistry C

Scheme 1. (a) Spin Distribution Pattern on Each Edge of the ZGNR and (b) the Radical Classification Scheme on the TMM and OVER Radicals

Figure 1. Optimized geometries of (a) 8ZGNR, (b) TZT, (C) OZO, and (d) TZO. The major spin coupling pathway (red line) and doping position (blue circle) are marked.

degeneracy suppresses the spin density of the substituted edge, which leads to magnetic transition from an AFM to FM configuration.43 Recently, our group proposed a radical classification scheme47,48 and coupler classification scheme32 in order to provide a systematic strategy for designing organic FM molecules. On the basis of these rules and the spin alternation rule, we reported that edge-functionalized ZGNRs with organic stable radicals have total FM spin orderings.49 In this study, we investigated the effect of B and N dopants on the ZGNR basal plane on the magnetic behaviors of radical-terminated ZGNRs.

the graphene nanoribbon (GNR) has received considerable attention due to its extraordinary properties. A GNR is a twodimensional material with an extensive π-conjugated molecular framework that has the advantage of delivering magnetic exchange coupling through an sp2−pz carbon network due to its almost infinite spin coupling pathways.21−29 In addition, the absence of a chemical defect18,30 or heteroatom,31,32 such as S, N, and O, which interrupts effective magnetic exchange, contributes to excellent electronic and transport properties. There are two types of GNRs, depending on the type of nanoribbon edges: the armchair graphene nanoribbon (AGNR) and zigzag graphene nanoribbon (ZGNR). Especially the ZGNR has edges that are ferromagnetically ordered and antiferromagnetically coupled to each other (Scheme 1a). Because the two edges show opposite spin direction, the ZGNR is AFM.33−35 Therefore, many efforts have been made to convert AFM ZGNRs into FM materials via chemical modifications.36−39 Especially doping on a GNR has been reported to change its electronic and magnetic properties significantly.40−46 According to the previous studies, boron (B) or nitrogen (N) doping on a ZGNR breaks the spin degeneracy of the ZGNR. This induces electronic transition from the semiconductor to half metal. Additionally, B or N doping on both edges leads the ZGNR to the metal.45,46 This loss of spin

2. COMPUTATIONAL DETAILS We performed spin-polarized DFT calculations using the Vienna Ab Initio Simulation Package (VASP)50 code with a Perdew−Burke−Ernzerhof generalized gradient approximation (PBE-GGA)51 and the projector-augmented wave (PAW).52 Although the DFT functional provides a somewhat overestimated magnetic coupling constant to some extent due to the approximation to the exchange−correlation term,53,54 GGA functionals provide a qualitatively reliable description on intramolecular magnetic interactions. In this regard, we also performed PBE0,55 which incorporates 25% of Hartree−Fock exact exchange into the PBE functional for a more accurate 11238

DOI: 10.1021/acs.jpcc.6b01737 J. Phys. Chem. C 2016, 120, 11237−11244

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Table 1. Electronic Energy Differences between FM and AFM Configurations (ΔEFM−AFM = EFM − EAFM, in meV), Net Magnetic Moment per Unit Cell (μs, in μB) of Undoped TZT, OZO, TZO, and Their Doped Derivatives Calculated with the PBE-vdWDF Functionala TZT ΔEFM−AFM μs(FM) μs(AFM)

OZO

undoped

B-doped

N-doped

BN-doped

undoped

B-doped

N-doped

BN-doped

1.070 1.998 0

−0.510 3.000 1.000

−1.980 2.999 1.001

0.170 4.000 0

7.370 4.003 0

−3.500 2.999 1.003

−8.840 2.997 1.083

4.970 1.959 0.004

TZO ΔEFM−AFM μs(FM) μs(AFM) a

undoped

B-TMM

B-OVER

N-TMM

N-OVER

B-TMM/N-OVER

N-TMM/B-OVER

−2.280 2.999 0.967

1.480 3.999 0.026

1.490 1.996 0.002

0.900 3.999 0

4.460 1.971 0.007

−0.890 2.866 0.999

−0.410 2.998 1.002

The values for B-TMM/N-OVER and N-TMM/B-OVER systems represent those for B/N and N/B edges, respectively.

calculated electronic energy difference between FM and AFM configurations (ΔEFM−AFM = EFM − EAFM) and the magnetic moment per unit cell of the undoped TZT, OZO, and TZO are shown in Table 1. Here, FM/AFM denotes the case when the two radicals on the opposite edge have the same/opposite spins. Due to the spin ordering in the ZGNR, the total magnetic moment of the AFM configuration is not necessarily zero. The system with negative ΔEFM−AFM indicates the FM ground configuration. The results were qualitatively consistent with our previous study;49 however, ΔEFM−AFM was slightly decreased due to structural differences, such as decreased planarity of the ZGNR coupler, and the size of the vacuum layer. As previously reported, TZT and OZO showed the AFM ground configuration, and TZO showed the FM ground configuration. We introduced B and N dopants on the shortest spin coupling pathway along with the radical-ZGNR-radical to investigate the doping effect on the magnetic ground configuration, magnetic coupling strength, and magnetic moment, as depicted in Figure 1. Here we define the major coupling pathway as the shortest spin coupling pathway in our model because this pathway gives the strongest coupling between radicals. Especially, calculations were performed on the cases where the dopant atoms were introduced on the edge positions (blue circled) because doping on edge of the ZGNR was known to be the most stable among every possible position.46,59−61 3.1. Magnetic Ground Configuration. The spin density patterns of doped and undoped TZT, OZO, and TZO systems are shown in Figure 2. As shown in Figure 2, doping on the major coupling pathway changed the spin distribution pattern of the system. Especially, spin directions of the doped edge and a radical were reversed regardless of B or N doping. As a result, the first B or N doping switched the magnetic ground configuration of TZT and OZO from the AFM to FM configuration. In contrast, the magnetic ground configuration of TZO was switched from the FM to AFM configuration. In the case of the TZO system, we doped either the B or N atom on both TMM- and OVER-radical-terminated edges of the ZGNR to investigate the difference in magnetic behavior, depending on radical types. As a result, all of the B- and N-doped TZO showed the AFM ground configuration regardless of the radical type, as shown in Figure 2c. However, an additional B or N doping on a singly doped system switched the magnetic ground configuration back to the original one. For example, additional B doping on the N-doped TZT and OZO system or N doping on the B-doped TZT and OZO system showed the AFM

description of the electron exchange−correlation potential, and single-point calculation on the TZT system to validate the PBE results. A one-dimensional periodic boundary condition was used along the growth direction to describe the nanoribbon system (Figure 1). Vacuum layers, at least 12 Å, were inserted in the nonperiodic direction to avoid interlayer interaction. Geometry optimization was performed with 25 × 1 × 1 Monkhorst−Pack k-point56 mesh and plane wave basis sets with an energy cutoff of 400 eV. The convergence threshold for energy was set to 10−5 eV. Additionally, ab initio nonlocal van der Waals density functional (PBE-vdW-DF)57,58 single-point calculation was performed to account for the dispersion interaction with 100 × 1 × 1 k-point sampling at optimized geometries at the PBE functional.

3. RESULTS AND DISCUSSION According to the spin alternation rule, one can predict the ground spin distribution pattern on the molecule; adjacent carbon atoms in a π-conjugated system have opposite spins. For example, the ZGNR has an odd number of atoms between edge atoms in each edge, while it has an even number of atoms along the shortest pathway between the two edges. Thus, the ZGNR has localized edge states that are ferromagnetically ordered, and the two edges are antiferromagnetically coupled, as illustrated in Scheme 1a. However, spin the alternation rule cannot fully explain the spin distribution pattern for radicals containing heteroatoms. Therefore, a radical classification scheme was suggested to explain spin distribution patterns of well-known stable organic radicals.47,48 As shown in Scheme 1b, organic radicals can be classified into syn and anti groups depending on the spin direction of the connected atom and radical dot atoms. Syn radicals have parallel spin on the connected atoms and radical dot atoms, while anti radicals have antiparallel spin on those atoms. According to the classification scheme, trimethylenemethane (TMM) and oxoverdazyl (OVER) can be classified as syn and anti radicals, respectively. On the basis of the spin alternation rule and radical, coupler classification scheme, we successfully designed FM ZGNR derivatives by modifying each edge of the ZGNR with TMM and OVER radicals, that is, TMM-8ZGNR-TMM (TZT), OVER-8ZGNR-OVER (OZO), and TMM-8ZGNR-OVER (TZO) in the previous work,49 and their optimized geometries are shown in Figure 1. The lattice constant of optimized 8ZGNR in the growth direction was found to be 9.92 Å. The 11239

DOI: 10.1021/acs.jpcc.6b01737 J. Phys. Chem. C 2016, 120, 11237−11244

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Figure 2. Spin distribution patterns of doped and undoped (a) TZT, (b) OZO, and (c) TZO systems. Yellow and cyan colors represent up and down spins, respectively. The B- or N-doping positions are marked with green or blue circles, respectively. Ground spin configurations are marked in red.

ground configuration, and the TZO system showed its original FM ground configuration. The change in the magnetic ground configuration of the ZGNR derivatives upon B and/or N doping was further validated by PBE0 calculation on the doped TZT system, which shows qualitatively the same results as the PBE result, as shown in Figure S1 and Table S1. The change on the magnetic ground configuration can be explained with the spin alternation rule. The spin polarization patterns for a simplified model of undoped, B-doped, N-doped, and BN-doped systems are described in Figure 3. By the spin alternation rule, adjacent carbon atoms show opposite spin direction from each other. Therefore, both radicals, radical 1 (R1) and radical 2 (R2), have opposite spin direction and show AFM ground configurations, as shown in Figure 3a. In the case of Figure 3b, the boron atom has a vacant p orbital. Now, the π

Figure 3. Spin polarization pattern of simplified (a) undoped, (b) Bdoped (c) N-doped, and (d) BN-doped systems.

electron in C directly interacts with R1 by passing through the vacant p orbital of the boron atom. Therefore, both radicals have parallel spin direction and show FM ground config11240

DOI: 10.1021/acs.jpcc.6b01737 J. Phys. Chem. C 2016, 120, 11237−11244

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Table 2. Atomic Magnetizations (μ(Xi) where X = C, N, and A in 0.0001 μB) on Radical (Cn or Nn) and Edge Atoms (An) Compared to Undoped Systems by Dopinga for TZT and OZO, Selected Bond Lengths (r1, r2, r3, and r4 in Å), Dihedral Angle between the Radical and Ipso Atom against the ZGNR Coupler (θ1−θ4 in deg), and Coupler Length (d, in Å) between Radicalsb

a

Atom magnetizations of undoped system are written in brackets. bThe values for BN-doped systems represent those for the B/N edge.

the dihedral angle and spacer length due to the diminished overlap between spin orbitals. The calculated ΔEFM−AFM values and net spin moments (μs) of each undoped and doped unit cell are listed in Table 1. The atomic magnetizations of radical and edge atoms and the dihedral angle of the radical and ipso atom against the ZGNR in TZT and OZO are also listed in Table 2. Those in TZO are presented in Table S4. As shown in Table 1, ΔEFM−AFM value was changed by B and N doping as compared with the undoped system. The spin density of the TMM radical and doped edge atoms increased by B or N doping, compared to that of the undoped edge, which remained almost unchanged. In contrast, the dihedral angle of the TMM radical against the ZGNR coupler increased as noted in Table 2. The optimized geometry of TZT showed a dihedral angle of 47° due to steric repulsion between hydrogen atoms. B and N doping further increased the dihedral angle to 61 and 65°, respectively. However, the coupler length between two TMM radical sites decreased by N doping, while it increased by B doping due to the difference in atomic radii of atoms. Nitrogen has a smaller atomic radius than carbon, while boron has a larger atomic radius than carbon. Therefore, the coupler length was decreased by N doping, whereas it was increased by B doping. As a result, the ΔEFM−AFM value of the N-doped system increased to 1.98 meV, and that of the B-doped and BN-doped systems decreased to 0.51 and 0.17 meV, respectively. In the case of the OZO system, there was no significant change in the dihedral angle between radicals and ZGNR couplers. Instead, the spin density of the OVER radical and doped edge was decreased by both B and N doping. Same as the TZT case, the coupler length between two OVER

urations. Contrary to the boron atom, the nitrogen atom has a p orbital filled with lone pair electrons. One electron in the lone pair interacts with R1, and the other electron interacts with its paired electron to show the opposite spin direction by Pauli’s exclusion principle. Therefore, R2 in (c) has parallel spin direction with R1 again, which shows the FM ground configuration. By the same principle, (d) shows AFM configurations. This change on then magnetic ground configuration was also observed for all cases when dopant atoms were introduced at the middle of the major coupling pathway as well as for cases of doping at the edges, as shown in Figure S2 and Tables S2 and S3. Therefore, doping on the major spin coupling pathway of the system reverses the spin direction of the radical on one edge and thus switches the magnetic ground configuration of the systems. This result suggests the possibility of reversible spin control by B or N doping. 3.2. Electronic Energy Difference between FM and AFM Configurations: ΔEFM−AFM. The electronic energy difference between FM and AFM configurations (ΔEFM−AFM) is an important factor to evaluate the strength of intramolecular magnetic interaction. A large negative ΔEFM−AFM value indicates a strong FM coupling between radicals. It was reported that intramolecular magnetic coupling between two radical sites is affected by spin polarization induced by radical species, the coupler length, and the dihedral angle between the radical and coupler.31,62−64 For a π-conjugated system, the magnetic coupling strength generally increases with strong spin polarization of the radical and coupler-edge atoms. In contrast, the magnetic coupling strength decreases with an increase in 11241

DOI: 10.1021/acs.jpcc.6b01737 J. Phys. Chem. C 2016, 120, 11237−11244

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connected atom, as shown in Table 2 and Figures S5 and S6. However, the magnetic exchange between edge atoms was considerably interrupted by the heteroatom; thus, atomic magnetization on the OVER-terminated edge was significantly reduced. As shown in Figures S5 and S6, the electron spin density (both up spin and down spin) of edge atoms decreased to almost zero for the B-doped edge and offset each other for the N-doped edge. Therefore, the OVER-terminated edge atoms had almost no spin density when B or N was introduced, as shown in Figure 2b,c. As a result, the net magnetic moment of each magnetic state was changed by doping. The net magnetic moment of FM configuration for undoped TZT was increased from 1.998 μB to 3.000, 2.999, and 4.000 μB by B, N, and BN doping, respectively, due to the increased magnetic moment of the TMM moiety. For the AFM configuration, the net magnetic moment was also increased from 0 to 1.000 and 1.001 μB by B and N doping because the increased magnetic moment of the TMM radical on the doped side exceeded that of the undoped side, thus resulting in a net magnetic moment. For the AFM configuration of BN-doped TZT, the increased magnetic moments of both radicals offset each other and showed 0 μB. Contrary to TZT, both B and N doping reduced the magnetization of edge atoms for OZO. Therefore, the net magnetic moment of the FM configuration of OZO was decreased from 4.003 to 2.999, 2.997, and 1.959 μB by B, N, and BN doping, respectively. Similarly, the net magnetic moment of the AFM configuration showed 1.003, 1.083, and 0.004 μB for B-, N-, and BN-doped OZO. The magnetic moment of the FM configuration of TZO was increased from 2.999 to 3.999 μB by B and N doping on the TMM side edge and was decreased to 1.996 and 1.971 μB by B and N doping on the OVER side edge. For AFM configurations, both B and N doping showed around 0 μB regardless of the doping position. The B and N doping on each edge showed almost the same result as undoped TZO.

radicals was decreased by N doping, while it was increased by B doping. As a result, ΔEFM−AFM was increased to 8.84 meV by N doping, and it was decreased to 3.50 and 4.97 meV by B and BN doping, respectively. The same tendency of ΔEFM−AFM was also observed in the TZO system. The ΔEFM−AFM values were generally decreased by any doping in all of the systems investigated except for N doping on the OVER-terminated edge system, where the ΔEFM−AFM value increased from 2.28 to 4.46 meV. 3.3. Magnetic Moment. Furthermore, the net magnetic moment per unit cell of each system was changed by around 1 μB by each doping. As shown in Table 2, the atomic magnetization of the TMM radical and the edge atoms of the ZGNR were increased by B or N doping as compared with the undoped system, while those of the OVER radical and the edge atoms were decreased. According to previous studies, the existence of a heteroatom on the spin polarization pathway interrupts effective magnetic exchange.31,32 For TZT, the introduced B or N atom on the ipso position, which has an sp3 orbital to make a single bond with the connected atom of the radical, disturbs π-conjugation between coupler and radical atoms. As a result, the bond length r1 in TZT was lengthened from 1.37 to 1.55 and 1.40 Å by B and N doping, while r2 was shortened from 1.49 to 1.44 and 1.42 Å, respectively. Finally, r2, r3, and r4 have similar bond lengths, implying a resonance within each radical moiety through πconjugation, which may result in effective magnetic exchange. The magnetization of the C4 atom considerably increased and contributed to the increase in the total magnetic moment of the TZT system. This change of magnetization was a signature of the density of state (DOS) of the TZT system (Figure S3). For both B- and N-doped systems, there was a significant increase in the electron density of the connected atom near the Fermi level compared with that of the undoped system, which contributed to the increase in the total electron density of the TMM radical. In addition to the bond length, there was a considerable change in the dihedral angle of the radical moiety (θ1) and the ipso atom (θ2) in the coupler, compared to the ZGNR coupler for the TZT system by doping. The TMM radical moiety had a low dihedral angle to maintain magnetic exchange with the coupler despite the steric repulsion between hydrogen atoms. However, the magnetic exchange between the radical and coupler was significantly reduced after the introduction of B and N. Therefore, the dihedral angle of B- and N-doped TZT was increased from 47 to 66 and 65°, respectively. Contrary to the TMM radical moiety, the dihedral angle of the ipso atom was decreased from 9.48 to 0.78 and 1.37° for B- and N-doped TZT systems, respectively, as shown in Table 2. Due to the recovered planarity, the magnetization of the edge atom on the TMM-terminated edge was rather slightly increased, although the heteroatom interrupts the magnetic coupling between edge atoms considerably. To confirm this, we substituted the B/N atom of the optimized B/N-doped system with a carbon atom and performed single-point calculations. As shown in Figure S4, the magnetization of edge atoms was clearly decreased by heteroatoms. Contrary to TZT, there was no significant change in the dihedral angle and bond length except for r1 for OZO. The bond length r1 was increased by B doing and decreased by N doping, which may originate from the difference in the atomic radius of each atom. As a result, there was little change in the magnetization and DOS for OVER radical atoms, including the

4. CONCLUSIONS We have investigated the doping effect on the magnetic ground configuration, the electronic energy difference between FM and AFM configurations, and the net magnetic moment of TZT, OZO, and TZO. Our study indicates the possibility of magnetic ground configuration crossover between FM and AFM by B and N doping. TZT and OZO, which have AFM ground configurations, were switched into the FM ground configuration by B or N doping, while TZO was switched from the FM ground configuration to the AFM ground configuration. An additional doping of B or N on singly doped systems switched the magnetic ground configuration back to their original (undoped) configurations. We also showed that N doping on a radical-terminated edge increased the magnetic coupling strength, while B doping decreased it. Therefore, each Ndoped TZT and OZO had a higher ΔEFM−AFM value compared to that of undoped TZT and OZO. Furthermore, the net magnetic moment of the system was increased by B or N doping on the TMM-terminated edge, whereas it decreased by the same doping on the OVER-terminated edge. Due to the reversible magnetic ground configuration and increase in net magnetic moment, our results demonstrated the possibility of reversible spin control with enhancement of the magnetic coupling strength, which will be helpful in designing future spin-electronic devices. 11242

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b01737. Magnetic behaviors of TZT with the PBE0 functional and changes of the magnetic ground configuration, magnetic moment, and density of states by doping for TZT, OZO, and TZO systems (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +82-31-299-4560. Fax: +8231-290-7075. 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 (2013R1A1A2062901). The authors would like to acknowledge the support from the KISTI supercomputing center through the strategic support program for the supercomputing application research [No. KSC-2014-C3-018].

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DOI: 10.1021/acs.jpcc.6b01737 J. Phys. Chem. C 2016, 120, 11237−11244