Article pubs.acs.org/JPCC
Edge-Modified Graphene Nanoribbons: Appearance of Robust Spiral Magnetism Chengxi Huang,†,‡ Haiping Wu,*,† Kaiming Deng,*,† and Erjun Kan*,† †
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Department of Applied Physics and Key Laboratory of Soft Chemistry and Functional Materials (Ministry of Education), Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, P. R. China ‡ Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284, United States ABSTRACT: Materials with competitive spin interactions can show multiple quantum magnetic states under external manipulation, which is important for spin-related research and applications. Although the magnetism in graphene nanoribbons has been intensively studied, robust spin interactions have not been reported. Here, we explored graphene nanoribbons modified with Ti and V atomic chains that show competitive spin interactions and robust spiral magnetism. On the basis of firstprinciples calculations, we systematically investigate the possibility of inducing robust and competitive magnetic ordering in graphene nanoribbons through transition-metal (TM) atomic chain decoration (denoted as TM-ZGNR, TM = Ti−Co). On the basis of the Heisenberg XY model including nearest-neighbor (NN) and next-nearest-neighbor (NNN) magnetic interactions, Ti-ZGNR and V-ZGNR are predicted to have spiral magnetic order due to spin frustration. By Monte Carlo simulations, the Néel temperatures for Ti-ZGNR and V-ZGNR are estimated to be 45 and 100 K, respectively. Our studies will benefit further spin-control research on graphene nanoribbons.
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INTRODUCTION Graphene nanoribbons (GNRs), which are one-dimensional stripes of graphene, are of great interest because their particular electronic and magnetic properties depend on their sizes and edge structures.1−9 Armchair and zigzag are two typical kinds of edges. While armchair GNRs are nonmagnetic, zigzag GNRs (ZGNRs) have localized edge states10,11 and are theoretically predicted to have ferromagnetic (FM) coupling at each edge and antiferromagnetic (AFM) coupling between the two edges.12 Plenty of investigations have been performed to explore the spin-related properties, such as stable magnetism and catalysis by embedded external atoms,13−17 half-metallic character by an external electric field, edge modification or doping,18−21 defects or external strain,22 spin-transport behaviors,23 and magnetoresistance.24 But the magnetic moment of each edge carbon atom is very small (0.3 μB),25 and the edge magnetic states are highly unstable.26 These make ZGNRs infeasible for practical spintronics. Actually, the predicted magnetic edge states of ZGNRs have still not been experimentally observed. To overcome these problems and give rise to the further development of spintronic applications based on ZGNRs, it remains a challenge to design and synthesize GNR-based materials with robust magnetism. TM atom decoration is feasible in experiments27 and is an effective way to induce strong magnetism.28−31 However, most of the previous studies on the edge magnetism of ZGNRs considered only the nearest-neighbor (NN) interactions and the simple collinear spin models. In general, this approximate © 2016 American Chemical Society
model is reasonable because the long-range interactions are usually rather small compared to the NN interactions. But in some cases, the next-nearest-neighbor (NNN) interactions are comparable to the NN interactions, where strong competitions of spin interactions take place. This could result in some novel and interesting magnetic structures and spin dynamical phenomena such as spiral magnetism32,33 and spin liquids.34,35 In these cases, the simple collinear model is not sufficient to describe the accurate magnetic structures, and a more reliable noncollinear spin model should be used. With this concern, on the basis of first-principles calculations and the Heisenberg spin models, we comprehensively studied the edge magnetism of the ZGNRs terminated by 3d TM atoms (Ti−Co). We found that Ti-, V-, Mn- and Fe-GNR systems all show strong NNN interactions compared to their NN interactions. For Ti- and V-GNR, the NN interactions between edge TM atoms are FM, whereas the NNN interactions are AFM. Such strong spin frustrations will lead to noncollinear spin configurations. The spiral magnetism caused by the competition of spin interactions is clearly explored, which is quite different from the results extracted from the simple collinear models. Moreover, we estimated the propagation constant along the chain direction of the spiral magnetic arrangement and the Néel temperature (TN) by Received: October 31, 2016 Revised: December 28, 2016 Published: December 30, 2016 1371
DOI: 10.1021/acs.jpcc.6b10883 J. Phys. Chem. C 2017, 121, 1371−1376
Article
The Journal of Physical Chemistry C Monte Carlo (MC) simulations based on the Heisenberg XY model. Our results show that such spiral magnetism is robust, which will move the spin-related research forward.
Table 1. Bond Lengths between TM Atoms and Neighboring C Atoms (d1) and between Neighboring TM Atoms (d2), Binding Energies per TM Atom (Eb), Exchange Energies per Unit Cell (Eex), Magnetic Quantum Number on Each TM Atom (S), and Nearest-Neighbor (J1) and Next-Nearest Neighbor (J2) Exchange Parameters for TM-GNR
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METHODS Our calculations are performed on the basis of first-principles density functional theory (DFT) implemented in the Vienna ab initio simulation package (VASP).36 A generalized gradient approximation of Perdew−Wang 91 (GGA-PW91)37 for the exchange correlation potential is chosen for spin-unrestricted computations. A vacuum space of 20 Å along the Y and Z directions was adopted to avoid interactions between neighboring images. The Brillouin zone was sampled using a 15 × 1 × 1 Monkhorst−Pack grid38 for a unit cell, and the energy cutoff was set to 500 eV. The convergence criteria of energy and force for geometry optimizations were 10−5 eV and 0.01 eV/Å, respectively.
d1 (Å) d2 (Å) Eb (eV) Eex (eV) S J1 (meV) J2 (meV)
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Ti
V
Cr
Mn
Fe
Co
2.13 2.76 7.01 −0.232 1/2 −232 84
2.09 2.70 7.42 −0.268 3/2 −30 18
2.09 2.79 6.85 −0.054 2 −3
2.08 2.62 6.56 0.389 2 24 −7
2.02 2.63 6.37 0.052 3/2 6 7
1.96 2.66 6.02 0.009 1
we plot the charge difference in V-GNR as an example (Figure 1b). One can see that when the TM atomic chain adsorbs on the zigzag edge of ZGNR, the charge transfers from the interspace of TM atoms to the edge C atoms, which indicates the weakening of TM−TM bonds and strong chemical bonding between TM atoms and ZGNR. Figure 1c shows that the magnetic moment of the system mainly comes from the TM atoms, and the neighboring C atoms have very small opposite spin moments (
