Edge-Modified Graphene Nanoribbons: Appearance of Robust Spiral

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Edge-Modified Graphene Nanoribbons: Appearance of Robust Spiral Magnetism Chengxi Huang, Haiping Wu, Kaiming Deng, and Erjun Kan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b10883 • Publication Date (Web): 30 Dec 2016 Downloaded from http://pubs.acs.org on January 1, 2017

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The Journal of Physical Chemistry

Edge-modified Graphene Nanoribbons: Appearance of Robust Spiral Magnetism Chengxi Huang†, ‡, Haiping Wu†,*, Kaiming Deng†,*, and Erjun Kan†,*

†

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

Correspondence and requests for materials should be addressed to

E. K. (email: [email protected]), H. W. ([email protected]), or K. D ([email protected])

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ABSTRACT Materials with competitive spin interactions can show multiple quantum magnetic states under external manipulation, which are important for spin-related research and applications. Although the magnetism in graphene nanoribbons has been intensively studied, robust spin interactions are still not reported. Here, we explored that graphene nanoribbons modified with Ti and V atomic chains show the competitive spin interactions and robust spiral magnetism. Based on first-principles calculations, we systematically investigate the possibility of inducing robust and competitive magnetic ordering in graphene nanoribbons through transition-metal (TM) atomic chains decoration (denoted as TM-ZGNR, TM=Ti-Co). Based on the Heisenberg XY model including nearest neighbour (NN) and the next nearest neighbour (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 temperature for Ti-ZGNR and V-ZGNR are estimated to be 45K and 100K, respectively. Our studies will benefit the further spin-control research in graphene nanoribbons. TOC GRAPHICS


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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 which 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 theoretically predicted to be ferromagnetic (FM) coupling at each edges 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 catalytic by embedded external atoms,13-17 half-metallic by external electric field, edge modification or doping18-21, defect or external strain22, spin-transport behaviors23 and magnetoresistance24. But the magnetic moment of each edge carbon atom is too 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 so far. To overcome these problems and give rise to the further development of spintronic applications based on ZGNRs, it remains a challenge to design and synthesis GNR based materials with robust magnetism. TM atoms decoration is feasible in experiment27 and is an effective way to induce strong magnetism.28-31 However, most of the previous studies on the edge magnetism of ZGNRs only considered the nearest-neighbor (NN) interactions and the simple collinear spin models. In general, this approximate model is reasonable, because the long-range interactions are usually rather small compared to the NN interactions. But 4 ACS Paragon Plus Environment

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in some cases, the next-nearest-neighbor (NNN) interactions are comparable with the NN interactions, where strong competitions of spin interactions take place. This could results in some novel and interesting magnetic structures and spin dynamical phenomena such as spiral magnetism32,33 and spin liquid34,35. In these cases, the simple collinear model is not sufficient to describe the accurate magnetic structures and a more reliable non-collinear spin model should be taken. With this concern, here, based on 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 Tiand V-GNR, the NN interactions between edge TM atoms is FM, while the NNN interactions is AFM. Such strong spin frustrations will lead to non-collinear spin configurations. The spiral magnetism caused by competitions 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 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.

Methods Our calculations are performed based on the first-principles density functional theory (DFT) implemented in the Vienna Ab-initio Simulation Package (VASP)36. Generalized gradient approximation of Perdew-Wang 91 (GGA-PW91)37 for 5 ACS Paragon Plus Environment


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exchange correlation potential are chosen for spin-unrestricted computations. A vacuum space of 20 Å along Y and Z directions was adopted to avoid interaction between neighboring images. The Brillouin zone was sampled using a 15×1×1 Monkhorst-Pack gird38 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.

Results and discussion As we know, the interactions between the two edges of ZGNRs are greatly affected by the ribbon width. So as to study the magnetism of TM-terminated edge without the interference of interactions between edges, a 5-ZGNR (11 Å in width) with one edge reconstructed and the other side modified by TM atoms is chosen as our representative TM-GNR. Figure 1a shows the optimal geometry of the TM-GNRs. Since the covalent radiuses of TM atoms are larger than that of C atom, the adsorbed TM atomic chains are not linear but present zigzag shapes. The optimized bond lengths of the TM-TM and TM-C bonds are shown in table 1. The listed binding energies (Eb) for each TM atom to ZGNR are defined as Eb = (EZGNR + 2ETM – ETM-ZGNR) / 2 . One see that all the binding energies of the TM atoms in TM-GNR are larger than their cohesive energies39, indicating that the edge adsorptions are stable against clustering between metal atoms. To investigate the interactions between TM atoms and ZGNR, we plot the charge difference in V-GNR as an example (see figure 1b). One can see that, when the TM atomic chain adsorbs on the zigzag edge of ZGNR, the charge transfers from interspace of TM atoms to the edge C atoms, which 6 ACS Paragon Plus Environment

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means the weakening of TM-TM bonds and strong chemical bondings between TM atoms and ZGNR.

Figure 1. a) Top and side view of 5-ZGNR with one edge reconstructed and the other side modified by TM atoms. Green and gray balls denote carbon and TM atoms, respectively. b) Differential charge density for V-GNR (isovalue of 0.05 e/Å3). Orange represents charge increase, and green represents charge decrease. c) Spin density for the ferromagnetic states of V-GNR (isovalue of 0.05 e/Å3).

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 (< 0.1 µB). The magnetic moment of reconstructed edge is totally quenched, thus we omit the magnetic interactions between the two edges. To study the magnetic coupling between the TM sites at the edge, we first considered the FM and AFM1 configurations (see figure 3) by arranging the same and reverse spin directions of the two TM atoms in a unit cell, respectively. The exchange energy (defined as Eex = EFM – EAFM1) per unit cell and the magnetic quantum number (S) on TM atoms are listed in table 1. A negative exchange energy indicates FM interaction between NN TM atoms, 7 ACS Paragon Plus Environment


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while positive one means AFM interaction. We found that for Ti-GNR, V-GNR and Cr-GNR, the NN interactions are FM, while for Mn-GNR, Fe-GNR and Co-GNR, those are AFM. In other words, from Ti to Co, the NN interactions change from FM to AFM. To understand this, we analyzed the electronic structures of these systems. Figure 2a shows that the large spin polarization around the Fermi energy is mainly contributed by V atoms for V-GNR system, which is consistent with the spin density shown in figure 1c. Similarly for the other systems, TM atoms dominate the spin polarization, for their highly localized 3d orbitals. Figure 2b shows the projected density of states (PDOS) of the 3d orbitals for V-GNR, Cr-GNR and Mn-GNR in their ground states. One find that, from V to Mn, the 3d orbitals become more and more localized, which makes the overlap of between Mn-d orbitals smaller. Besides, for V, the d orbitals are less than half filled, when one d electron hop from one magnetic site to the other, it needn’t to change its spin orientation, which makes the FM exchange interactions more effective. While for Mn, the d orbitals are more than half filled, an antiparallel arrangement of major spins will be favored, thus leading to an AFM coupling.

Table 1. Bond lengths between TM atoms and neighboring C atoms (d1), between neighboring TM atoms (d2), binding energies per TM atoms (Eb), exchange energies per unit cell (Eex), magnetic quantum number on each TM atom (S), the nearest (J1) and next nearest (J2) neighboring exchange parameters for TM-GNR.

Ti

V

Cr

Mn

Fe

Co

d1 (Å)

2.13

2.09

2.09

2.08

2.02

1.96

d2 (Å)

2.76

2.70

2.79

2.62

2.63

2.66

Eb (eV)

7.01

7.42

6.85

6.56

6.37

6.02


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Eex (eV)

-0.232

-0.268

-0.054

0.389

0.052

0.009

S

1/2

3/2

2

2

3/2

1

J1 (meV)

-232

-30

-3

24

6

--

J2 (meV)

84

18

--

-7

7

--

Figure 2.a) Total DOS and PDOS of V and C atoms for V-GNR. b) PDOS of the 3d orbitals on V, Cr and Mn atoms for V-GNR, Cr-GNR and Mn-GNR, respectively. Positive and negative values refer to spin up and spin down states, respectively. The Fermi energy is set to 0.

On the other hand, we found that, to determine the magnetic arrangement of the ground states for these TM-GNR systems, simply considering the NN interaction is not sufficient. We took both the NN (J1) and NNN (J2) interactions into account by constructing three different spin arrangements FM, AFM1 and AFM2 (see figure 3). To extract the values of the exchange parameters J1 and J2, we map the relative energies of the three ordered spin arrangements FM, AFM1 and AFM2 for 2×1×1 supercells. This mapping analysis was carried out as:



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Where S represents the spin quantum number on metal atom. The calculated exchange parameters are specified in table 1, where the negative ones indicate FM couplings and the positive ones indicate AFM couplings. We found that, for Ti-, V-, Mn- and Fe-GNR systems, the intensities of NNN interactions are comparable to that of the NN interactions. Due to the strong competitions of spin interactions in these systems, the optimal spin configurations could be quite complex instead of simple collinear spin orderings.

Figure 3. Schematic diagrams for the FM, AFM1, AFM2 and spiral spin arrangements and the exchange paths J1 and J2. Arrows indicate spin directions.

Next, we discuss the effect of spin frustration on the magnetic structures. Since 10 ACS Paragon Plus Environment

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V-GNR and Ti-GNR system has the strongest FM spin-interaction in the NN spin path, in the following, we focus on these two systems. Comparing the values of J1 to J2, we find that spin frustrations in Ti-GNR and V-GNR systems are quite strong. Previous studies on Heisenberg spin chains have claimed that, depending on the ratio of J2 to J1, a complex phase diagram including FM, AFM, spin spiral and spin liquid phases can be plotted. In this case, the frustrations between FM NN and AFM NNN interactions may lead to spin spiral magnetic states40, which is similar to the LiCu2O241 and LiCuVO442 cases. To verify this, we perform non-collinear calculations for V-GNR system. We define the propagation constant q as the angle between two NN spin moments (Figure 3). One possible spin spiral arrangement with q = π/3 was calculated by constructing a 3×1×1 supercell, in which the six non-collinear spin moments at the TM sites can form periodic spiral ordering. The initial magnetic moment of each spin is 3 µB and the angles between each two NN spins are π/3. After convergence, the spins remain their initial orientations and the lengths of the spin moments are same as that in the FM case. The results show that the spin spiral state (q = π/3) is lower in energy (0.03 eV per unit cell) than the FM state (q = 0). Thus a spin spiral magnetic state is more preferred than a collinear magnetic state in this system. We also have examined the effect of spin-orbit coupling (SOC) on the spiral magnetism. The corresponding energies for the FM and the spin spiral state barely change compared to the results without SOC. The magnetic anisotropic energy (defined as the energy difference between the magnetic states with spin moment along a and c orientations) is also very small (

Edge-Modified Graphene Nanoribbons: Appearance of Robust Spiral

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