Magnetic properties of 3d transition metals and nitrogen functionalized armchair graphene nanoribbon

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http://dx.doi.org/10.1039/c3ra43810d

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1

Magnetic Properties of 3d Transition Metals and Nitrogen Functionalized Armchair

Graphene Nanoribbon

Shyam Kattel*

Department of Mechanical Engineering and Materials Science, University of Pittsburgh,

Pittsburgh, PA 15261, USA.

*Corresponding Author: [email protected]

Table of Contents Entry

Abstract

First-principles density functional theory (DFT) calculations were performed to study the

stability and magnetic properties of 3d transition metal (TM= Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu

and Zn) and nitrogen functionalized armchair graphene nanoribbon (9-AGNR). The results

showed that the edge functionalization of 9-AGNR by TM-N2 defects is energetically more

favorable compared to the edge functionalization by TM-C2 and TM-CN defects. Furthermore,

we found that edge TM-CxNy defects in 9-AGNR support high and localized magnetic moments.

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View Article OnlineDOI: 10.1039/C3RA43810D


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The magnetic moment of TMs in TM-CxNy edge defects increases with an increase in the

number of unpaired electrons in the 3d orbitals, and the calculated magnetic moment is largest

for an edge Mn-N2 defect. The analysis of magnetization of TMs reveals that the magnetic

moment mainly comes from the electrons in the 3d orbitals and the contribution of 4s electrons

to the total magnetic moment is very small. Our calculations also show that the magnetic

moment of TMs in edge TM-N2 defects in AGNR is independent of edge TM-N2 defect

concentrations and AGNR width in the present study. The interedge magnetic coupling between

the edge TM-N2 defects is explored by investigating the competing ferromagnetic and

antiferromagnetic spin structures. We found that the interedge magnetic coupling depends on the

type of TMs in edge TM-N2 defects and TM-N2 edge defect concentrations.

Introduction

Graphene is a two dimensional allotrope of carbon in which sp2 hybridized carbon atoms

are arranged in a honeycomb lattice. Because of its novel physical properties, it has drawn

enormous interest for applications in nanoelectronics,1-3 spintronics,4-6 catalysis,7-11 and

sensors.12, 13 Graphene nanoribbons (GNRs), one dimensional strips of graphene, can be obtained

by cutting graphene along two high symmetry crystallographic directions. Such cutting results in

two distinct types of edges: armchair and zigzag. The electronic structure of GNRs depends on

the type of edge and their width. Based on their electronic structure, armchair GNRs (AGNRs)

can be further categorized into three different types: 3m, 3m+1 and 3m+2 where m is an

integer.14 For AGNRs, the 3m+1 family has the largest electronic band gap, while the electronic

band gap for the 3m+2 family is minimum14, 15 Due to their unique electronic structures, GNRs

and their derivatives have been predicted to be promising materials for applications in

nanoelectronics,2, 16-19 and spintronics.6, 20-23

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Edge C atoms in GNRs have dangling bonds. The presence of these intrinsic C dangling

bonds provides excellent opportunity for the chemical functionalization of GNRs to achieve new

functionalities. Nitrogen (N) doping and transition metals (TMs) termination of GNRs have been

studied for potential application in nanoelectronics.24-27 In addition, it has been previously

reported that zigzag GNR (ZGNR) shows half-metallic properties in the presence of an external

transverse electric field.6 Previous theoretical calculations have demonstrated that ZGNRs are

magnetic where antiferromagnetic (AFM) interedge coupling is energetically favorable over

ferromagnetic (FM) interedge coupling.6, 28, 29 In contrast, armchair GNRs (AGNRs) are

predicted to be non-magnetic.24 Furthermore, theoretical methods have been used to study the

interedge magnetic coupling in GNRs. Such studies have shown that the interedge magnetic

coupling in ZGNR depends on ribbon width.24, 30, 31 The interedge magnetic coupling in TMs

terminated zigzag and armchair GNRs has also been reported in the literature.24 It was found that

Fe terminated ZGNR shows AFM coupling between two edges, whereas the interedge magnetic

coupling in Co terminated ZGNR is FM.24 On the other hand, in the case of AGNRs, it was

found that the interedge magnetic coupling shows oscillatory Ruderman-Kittel-Kasuya-Yosida

(RKKY) type behavior with respect to ribbon width24 similar to graphene with magnetic

dopants.32, 33

Transition metals and combined transition metals-nitrogen (TM-N) doping in carbon

nanostructures (such as graphene and carbon nanotube (CNT)) have gained significant attention

for their applications in nanoelectronics,34 spintronics35, 36 and catalysis.37-41 Graphitic TM-Nx

defects are predicted to be thermodynamically stable in graphene and CNT.35, 38, 39, 42-46 In

particular, a defect in which a TM has largest N coordination (i. e. TM-N4 defects) is predicted to

be energetically most favorable in graphene. Moreover, embedded graphitic TM-N4 defects in a


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monolayer graphene have been shown to simultaneously possess high magnetic moments and

FM spin structures.34-36 At present, the combined effect of TM and N on the magnetism of edge

TM-N functionalized GNRs remains largely unknown.

In the present study, we performed first-principles density functional theory (DFT)

calculations to explore the stability of TM-CxNy (TM=Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn;

x/y=0, 1, 2 and x+y =2) edge defects in 9-AGNR and their magnetic properties. The results show

that TM-N2 edge defects are energetically most favorable to be formed in 9-AGNR among all the

TM-CxNy edge defects in this study. The calculated magnetic moment of a TM in TM-CxNy edge

defects is highest for a TM with highest number of unpaired electrons in its 3d-orbitals.

Furthermore, we found that the interedge magnetic coupling depends on the type of TMs in edge

TM-N2 defects and TM-N2 edge defect concentrations.

Computational Details

Spin polarized density functional theory (DFT)47, 48 calculations were performed using

plane wave basis set Vienna Ab-Initio Simulation Package (VASP) code.49, 50 The electronic

exchange and correlation effects were described with the generalized gradient approximation

(GGA) within the Perdew-Burke-Ernzerhof (PBE) parametrization.51 The interactions between

electrons and nuclei were described within the framework of PAW formalism52, 53 using a kinetic

energy cut-off of 400 eV. The Brillouin-zone integration was performed on a regular 2 × 4 × 1

Monkhorst-Pack54 k-points mesh. Armchair graphene nanoribbon (AGNR) simulated in the

present study has 9 C atoms across the ribbon width (Figure 1a) and is denoted as 9-AGNR,

following the naming convention in literature.55 All the atoms in the simulation cell were

allowed to relax until Hellman-Feynman force on each ion is less than 0.02 eV/Å. The Fermi

level was slightly broadened by using a Fermi-Dirac smearing of σ = 25 meV. AGNRs were


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decoupled from their periodic images along x (ribbon width) and z (perpendicular to GNRs)

directions by introducing large vacuum layers of ~10Å and ~12Å thickness, respectively. The

unit cell parameters for 9-AGNR were: a=19.686 Å, b= 8.524Å and c=12Å.

In a unit cell of 9-AGNR, there are total of 8 edge C atoms (4 from each two edges) with

dangling bonds. These dangling bonds were saturated by H atoms (Figure 1a). Edge-C2, -CN and

-N2 defects in figures 1b, 1c and 1d, respectively, were created by decorating edge C atoms with

appropriate number of N atoms and removing terminating H atoms. On the other hand, transition

metal and nitrogen (TM-CxNy, x/y=0, 1, 2 and x+y=2) functionalized AGNRs were created by

decorating AGNR edge/edges with combined transition metal and nitrogen atoms. In detail, edge

TM-CxNy defects were created by adding a transition metal at the center of two edge C/N atoms

that form a valley at the edge of AGNR. Following the method in previous works,34, 45 the

binding energy (BE) of a transition metal at the edge–CxNy defects and the formation energy

(∆E) of edge TM-CxNy defects were calculated according to:

Binding energy (BE) = E(TM–CxNy) – E(CxNy) – E(TM)

Formation energy (∆E) = E(TM–CxNy) + 2µ(H) + bµ(C) – E(9-AGNR) – aµ(N) – E(TM)

where E(TM–CxNy) is the total energy of TM-CxNy functionalized 9-AGNR, E(CxNy) is the total

energy of 9-AGNR with edge CxNy defects, µ(H) is the chemical potential of H defined as the

half of the binding energy of H2 molecule,25 E(9-AGNR) is the total energy of H-terminated 9-

AGNR, µ(C) is the chemical potential of C defined as the energy per C atom obtained from

infinite graphene sheet,25, 34 µ(N) is the chemical potential of N defined as half of the total energy

of N2 molecule,56-58 and E(TM) is the total energy of isolated transition metal atom.4, 34, 43 a is the

number of N atoms added and b is the number of C atoms removed during the functionalization


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of 9-AGNR. Negative BE/∆E corresponds to the energetically stable configuration unless noted

otherwise.

Results and Discussion

In the present study, combined transition metal (TM) and nitrogen (N) functionalization

of 9-AGNR is achieved by decorating edge/edges of 9-AGNR with TM-CxNy (TM=Sc, Ti, V,

Cr, Mn, Fe, Co, Ni, Cu and Zn; x/y=0, 1, 2 and x+y=2) defects. Firstly, we calculated the

formation energy of TM-CxNy edge defects in 9-AGNR. The results (Figure 2a) show that the

formation energy is lowest for edge TM-N2 defects and highest for edge TM-C2 defects among

all the edge TM-CxNy defects in this study. We further noticed that the variation in formation

energy of edge TM-CxNy defects is similar for all transition metals (TMs). Therefore our DFT

calculations predict that edge TM-N2 defects are energetically most favorable to be formed at the

edges of 9-AGNR among all the edge TM-CxNy defects. Interestingly, this prediction remains

true for all TMs. Moreover, this finding also indicates that increasing N coordination of a TM is

beneficial in stabilizing a TM at the edges of AGNR. In fact this observation agrees well with the

previously reported order of stability of graphitic TM-Nx defects in a monolayer graphene.34 In

an extended monolayer graphene sheet, graphitic TM-N4 defect in which a central TM is only

coordinated to N (i.e. largest in-plane N coordination possible to a TM) is predicted to be

energetically most favorable among the family of in-plane graphitic TM-Nx (x=0, 1, 2, 3, 4)

defects in graphene.34, 35 Consequently, it could be expected that combined TM and N edge

functionalization of AGNRs in experiments might be feasible when AGNRs are functionalized in

the presence of intermittent mixture of TM and N sources. It is also worth mentioning that

energetically most favorable edge TM-N2 defects in GNRs could be of paramount importance as


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catalytic centers for electrochemical reactions (for example oxygen reduction reaction) similar to

the in-plane graphitic TM-Nx defects in graphene.39, 45

We further calculated the binding energy of TMs in edge-CxNy defects in 9-AGNR. The

binding energies in figure 2b show exact opposite trend compared to the formation energies in

figure 2a, however, the trend is identical for all TMs. The magnitude of TMs binding energy is

highest in edge-C2 and lowest in edge-N2 defects. We predict that edge-N2 configuration is 2.94

eV lower in total energy than edge-C2 configuration. Thus N decoration of edge-C2 defect to

form edge-N2 defect is energetically favorable. It is due to the fact that in edge-C2 defect, the

dangling electronic orbitals are only half-filled which destabilize the GNR with edge-C2

configuration. Contrarily, in edge-N2 defect N electronic orbitals are filled which lower the total

energy of GNR with edge-N2 configuration. This stabilization of AGNR edge by N passivation

also facilitates the formation of edge TM-N2 defects as predicted by our DFT calculated

formation energies.

The relaxed geometries of TM-CxNy functionalized 9-AGNR are planar (Figure 1). The

DFT calculated bond lengths for TM-C (dTM-C) and TM-N (dTM-N) are presented in figure 3. As

shown in figure 3, we found that our DFT calculated TM-C and TM-N bond lenghts in 9-AGNR

are shorter than the sum of covalent radii, rTM+C for TM and C, and rTM+N for TM and N59, when

TM=Sc, Ti, V, Mn, Fe, Co, Ni and Cu. For Cr, Cr-N bond length in edge Cr-CN defect is

slightly longer than rCr+N. However for Zn, rZn+C and rZn+N are always shorter than dZn-C and dZn-N

in Zn-CxNy edge defects. This suggests that Zn-CxNy defects are less stabilized at the edge of 9-

AGNR compared to the topologically identical Sc, Ti, V, Cr, Mn, Fe, Co, Ni and Cu

coordinated-CxNy defects. Such prediction is further corroborated by our DFT calculated

formation energies and binding energies. The formation energies of Zn-CxNy edge defects are


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largest (Figure 2a) and the binding energies of Zn in edge -CxNy defects are lowest (Figure 2b)

among all the TMs studied in the present study. These calculated bond lengths also indicate the

formation of covalent bond between TM and C/N in 9-AGNR edges.

The magnetic properties of edge TM-CxNy functionalized 9-AGNR were explored by

spin polarized DFT computations. In figure 4, we plotted our calculated magnetic moments of

TMs in edge TM-CxNy defects in 9-AGNR. Figure 4 shows that Cu embedded all edge defects

(Cu-C2, Cu-CN and Cu-N2) favor non-magnetic ground state. Edge Zn-C2 is non-magnetic while

the magnetic moment of Zn is very small 0.14 µB and 0.20 µB in edge Zn-CN and Zn-N2 defects,

respectively. Similar to edge Zn-C2, we found non-magnetic ground state of edge Ni-C2. In

contrast all other edge TM-CxNy defects favor magnetic ground state (Figure 4).

The magnetic moment of TM-doped graphene mainly comes from TM dopants.4,34

Similar to graphene, spin density plots for Mn-CxNy edge functionalized 9-AGNR in figure 5

demonstrate that the magnetic moment in 9-AGNR is mainly localized on TMs (Mn in this case)

of TM-CxNy edge defects. Thus the primary source of magnetism in TM-CxNy functionalized 9-

AGNR is the embedded TMs. Figure 5 also shows that the magnetic moments of N and C atoms

that are coordinated to TMs are very small and are aligned antiparallel to the magnetic moment

of the TMs. Moreover, our magnetization analysis (Table 1) reveals that the magnetic moment of

TMs mainly arises from the electrons in the 3d-orbitals and the contribution of 4s electrons to the

total magnetic moment is very small.

Our calculated results show significantly large magnetic moments for Ti, V, Cr, Mn, and

Fe derived edge TM-CxNy defects. For example, the calculated magnetic moment of Fe (coming

from its 3d electrons) in Fe-C2, Fe-CN and Fe-N2 defects are 3.1, 2.89 and 2.86 µB, respectively

which are at least ~34% larger than the elemental magnetic moment of Fe in bcc phase.60


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However, we observed that the calculated magnetic moments of TMs in TM-CxNy edge defects

are smaller than the magnetic moments of isolated TM atoms. Electrons from TM 3d orbitals

participate in TM-C/N covalent bonds formation in TM-CxNy edge defects. As a result, TMs in

TM-CxNy edge defects have reduced magnetic moments compared to their magnetic moments in

isolated atomic configuration.

The calculated magnetic moment of TMs in edge TM-CxNy defects in 9-AGNR nearly

shows a volcano shape as shown in figure 4. The magnetic moment increases with the increase in

the number of unpaired electrons in TM 3d orbitals among TM elements (i. e. Sc, Ti, V, Cr, Mn,

Fe, Co, Ni, Cu, Zn) and the calculated magnetic moment is highest (4.32 µB) for an edge Mn-N2

defect. Beyond Mn among TM elements, the magnetic moment of TM in TM-CxNy defects

decreases and Cu-CxNy edge defects are predicted to be non-magnetic. The calculated magnetic

moments per TM in edge TM-CxNy defects can be qualitatively explained by the electron

arrangement in TM 3d orbitals. TMs with highest number of unpaired electrons in their 3d

orbitals show highest magnetic moment and TMs that do not have unpaired electrons in their 3d

orbitals either favor non-magnetic ground state or have very small magnetic moments mainly

coming from 4s electrons. For example, Cu and Zn have filled d-shell (3d10) valence electronic

configurations, consequently, all edge Cu-CxNy defects are non-magnetic and the magnetic

moment of Zn-CxNy edge defects is either zero or very small (Table 1). It can be seen from Table

1 that the magnetic moment of Zn in Zn-CN and Zn-N2 edge defects comes from 4s electrons. 4s

electrons in Cu and Zn form covalent bonds with coordinating C/N atoms in Cu/Zn-CxNy edge

defects and a very small magnetic moment of Zn in Zn-CN and Zn-N2 defects is due to

remaining unsaturated 4s electrons.26


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On the other hand, according to valence electronic configurations of TMs, unpaired

electrons in TM 3d orbitals increase monotonously from Sc to Mn. Due to this, the magnetic

moments of TMs in TM-CxNy defects also increase, as shown in figure 4. Beyond Mn in the TM-

3d series, the number of unpaired electrons decrease, as a result the magnetic moments also

decrease (Figure 4). We note in passing that the magnetic moments observed in fully nitrogen

coordinated edge Fe-, Co-, and Ni-N2 defects in 9-AGNR are larger than those observed in-plane

graphitic Fe-, Co-, and Ni-N4 defects (also fully nitrogen coordinated) in a monolayer

graphene.34, 38

Since we predict that edge TM-N2 defects are energetically most favorable among all the

TM-CxNy edge defects, we further explored the dependence of the magnetic moment of edge

TM-N2 defects with defect concentration. In detail, the magnetic moment of a TM is calculated

for three different concentrations of edge TM-N2 defects: i) one edge TM-N2 defect per

simulation cell (Figure 1g), ii) two edge TM-N2 defects per simulation cell (Figure 6a) and, iii)

four edge TM-N2 defects per simulation cell (Figure 6b). The new configurations with two and

four edge TM-N2 defects per simulation cell not only have increased defect concentrations but

also allow us to study the interedge magnetic coupling. The DFT calculated magnetic moment

per TM for one, two and four edge TM-N2 defects per simulation cell are listed in Table 2. We

noted that the magnetic moment per TM remains fairly unchanged for different levels of edge

TM-N2 defect concentration except for Sc. For edge Sc-N2, we observed decrease in the

magnetic moment of Sc by 0.36 µB for four edge Sc-N2 defect concentration as compared to its

magnetic moment for one Sc-N2 defect per simulation cell configuration. Thus we conclude that

the magnetic moments of TMs in TM-N2 edge functionalized 9-AGNR are fairly independent of

defect concentrations in this study.


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To further examine the robustness of magnetic moments observed in edge TM-N2 defects

in AGNR, we increased AGNR width to include all three types of AGNRs: 3m, 3m+1, and

3m+2.14 Then we calculated the magnetic moment of Cr-, Mn- and Fe-N2 edge defects in 10- and

11-AGNRs. More specifically, we carried out spin polarized computations in 10- and 11-AGNRs

that have one Cr-N2, Mn-N2, and Fe-N2 defect per simulation cell. Cr-N2, Mn-N2, and Fe-N2

defects were chosen because these defects have been predicted to possess high magnetic

moments based on our calculations in 9-AGNR (Table 1, Figure 4). We found that the magnetic

moments calculated for Cr, Mn and Fe in 10- and 11-AGNRs are very much similar to those

calculated in 9-AGNR (Table 2). This observation suggests that the magnetic moment of TMs in

edge TM-N2 defects in AGNR likely remain unchanged and is independent of ribbon width.

The magnetic ground state of GNRs could be ferromagnetic (FM) or antiferromagnetic

(AFM). Here we explored the possible magnetic interaction between the edge TM-N2 defects

(interedge magnetic coupling). To this end, we defined magnetic stabilization energy (∆EMS) as

the energy difference between AFM and FM calculations. Positive ∆EMS here indicates that the

FM spin structure is lower in total energy as compared to the competing AFM spin structure and

hence FM coupling between the edges is energetically favorable over AFM coupling between the

edges and vice versa. The interedge magnetic interactions are calculated in 9-AGNR for two and

four edge TM-N2 defects per simulation cell as shown in figure 6. For both FM and AFM

calculations, the magnetic moments of TMs on the same edge point in the same direction.

Parallel-antiparallel arrangement of TMs spins on the same edge is excluded, as this arrangement

does not necessarily account for interedge magnetic coupling. The calculated ∆EMS are plotted in

figure 7. The plot of ∆EMS in figure 7 shows that the interedge magnetic coupling is

concentration dependent. For lower edge TM-N2 defect concentration (two defects per


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simulation cell), FM coupling between the edges is energetically favorable for V, Cr, Mn, Co

and Ni over competing AFM interedge coupling. Thus V-, Cr-, Mn-, Co- and Ni-N2 edge defects

favor FM ground states. In contrast, the results showed that AFM interedge coupling is

energetically favorable over competing FM spin structure for Sc-, Ti- and Fe-N2 defects.

However, we do not observe the similar trend when the AGNR edges were fully functionalized

with TM-N2 defects (four TM-N2 defects per simulation cell, Figure 6b). For fully functionalized

9-AGNR, Sc, Mn, Fe, Co and Ni favor FM interedge coupling while Ti, V and Cr favor AFM

interedge coupling. We observed that the magnetic coupling observed in Ti, Mn, Co and Ni is

independent of defect concentration (Figure 7). But ∆EMS changes sign when going from two

TM-N2 defects to four TM-N2 defects per simulation cell in the case of Sc, V, Cr and Fe.

The DFT calculated ∆EMS values in figure 7 reveal that the magnetic coupling between

the edge TM-N2 defects is stronger (i. e. large |∆EMS|) in a two TM-N2 edge defects per

simulation cell configuration (Figure 6a) than that in a four TM-N2 edge defects per simulation

cell configuration (Figure 6b) for TM=Ti, V, Cr, Mn, Fe and Co. In contrast, Sc and Ni show

opposite behavior compared to Ti, V, Cr, Mn, Fe and Co. The magnetic interaction between the

magnetic dopants in graphene is of Ruderman-Kittel-Kasuya-Yosida (RKKY) type and is

mediated by conducting electrons in graphene lattice.33, 61 Similar to graphene, Fe and Co

terminated AGNRs also show damped oscillatory RKKY interactions.24 For TM-N2 edge defect

configuration herein, TMs do not occupy either of sublattices A and B. In other words sublattice

position is no longer maintained at the position of magnetic impurity (i. e. position of TMs).

Consequently, we did not notice any systematic interedge magnetic coupling for TM-N2 edge

functionalized AGNRs. Thus the strength and type (FM or AFM) of interedge magnetic coupling

in 9-AGNR functionalized by edge TM-N2 defects are primarily determined by the type


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transition metal elements consistent with previous DFT predictions in TM terminated GNRs.24

The relatively strong magnetic coupling observed here could be due to the narrow width of

AGNRs. The strength of interedge magnetic coupling in TM-N2 functionalized AGNR is

expected to decrease with the increase in AGNR width because of decoupling of the magnetic

edges in AGNR.24, 30, 31, 62

Following previous works,62-64 we estimated the Curie temperature TC by using the

expression TC = 2∆EMS/3kB. Here, ∆EMS is the energy required to change the orientation of spins

from FM state to AFM state, i. e. the energy difference between AFM and FM configurations.62

For fully functionalized 9-AGNR in figure 6b, our calculated ∆EMS are 19.031, 12.944, 2.372,

5.024 and 35.739 meV for transition metals Sc, Mn, Fe, Co and Ni, respectively. The

corresponding TC are ~147, 100, 18, 39 and 276 K for Sc-, Mn-, Fe-, Co-, and Ni-N2

functionalized 9-AGNR, respectively. These calculated transition temperatures are below room

temperature, but are higher than TC (~10 K) calculated in ZGNR.62, 65 Our calculated low

formation energy, high and localized magnetic moment and high TC suggest that 9-AGNRs that

are fully functionalized by Mn, Fe, and Co-N2 edge defects may find applications in

nanomagnetism and spintronics.

The magnetic properties of GNRs depend on the type of their edge. To examine if TM-

CxNy edge defects have unique magnetic properties independent of GNR edges, we calculated

the stability and magnetic properties of edge TM-CxNy (TM=V, Cr, Mn and Fe) defects in zigzag

nanoribbon (5-ZGNR as shown in Figure 8). Our calculated results in Table 3 show that TM-N2

edge defects are energetically most favorable to be formed in 5-ZGNR among all the TM-CxNy

edge defects. Furthermore, we found that our calculated magnetic moments of TMs in TM-CxNy

edge defects in 5-ZGNR are similar to those calculated in 9-AGNR. For a 5-ZGNR that is fully


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functionalized by Mn-N2 edge defects (Figure 8e), 4s and 3d electrons contribute 0.21 and 4.42

µB, respectively to the magnetic moment of Mn in Mn-N2 edge defect. These values are similar

to the values calculated for a single Mn-N2 edge defect per simulation cell (Figure 8d, Table 3).

Different from the energetically favorable FM interedge coupling observed in a 9-AGNR that is

fully functionalized by Mn-N2 edge defects (Figure 6b), our calculations show that AFM

interedge coupling is energetically favorable by 15.34 meV over FM interedge coupling in a 5-

ZGNR that is fully functionalized by Mn-N2 edge defects (Figure 8e). Thus we predict that the

order of stability of TM-CxNy edge defects and the magnetic moment of TMs in TM-CxNy edge

defects remain largely unchanged independent of GNR type. In contrast, the interedge magnetic

coupling in TM-CxNy functionalized GNRs may depend on the GNR type.

Conclusions

In summary, we systematically studied the stability and magnetic properties of 3d

transition metals (TM=Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) and nitrogen edge

functionalized armchair graphene nanoribbon (9-AGNR) by a first-principles density functional

theory (DFT) method. Our calculated results show that edge TM-N2 defects are energetically

most favorable to be formed in 9-AGNR among all the edge TM-CxNy (x/y =0, 1, 2 and x+y =2)

defects studied in the present study. Moreover, we found high and localized magnetic moment in

TM-CxNy functionalized 9-AGNR. Our analysis of magnetization reveals that the magnetic

moment of TM-CxNy edge defects mainly comes from TM 3d electrons and the contribution

from 4s electrons to the total magnetic moment is very small. The calculated magnetic moment

of TMs in TM-CxNy edge defects increases with the increase in the number of unpaired electrons

in the 3d-orbitals and the magnetic moment is found to be largest for an edge Mn-N2 defect. The

magnetic moment is observed to decrease beyond Mn among TM-3d elements and Cu embedded


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edge Cu–CxNy defects are predicted to be non-magnetic. In addition, our calculations also show

that the magnetic moment of TMs in edge TM-N2 defects in AGNR is independent of the edge

TM-N2 defect concentration and AGNR width. The interedge magnetic coupling between the

TM-N2 edge defects is explored by calculating the total energy of the competing ferromagnetic

and antiferromagnetic spin structures. Our calculations show that the interedge magnetic

coupling to a large extent is determined by the type of transition metal elements and the defect

concentrations. We found strong interedge magnetic coupling in TM-N2 functionalized 9-AGNR

and the DFT estimated Curie temperatures for Sc-, Mn-, Fe-, Co-, and Ni-N2 functionalized 9-

AGNR (Figure 6b) are higher than that observed for ZGNR. Furthermore, we calculated the

stability of TM-CxNy edge defects and the magnetic moment of TMs in TM-CxNy (TM=V, Cr,

Mn and Fe) edge defects in zigzag nanoribbon (5-ZGNR). We predict that the order of stability

of TM-CxNy edge defects and the magnetic moment of TMs in TM-CxNy edge defects remain

largely unchanged independent of GNR type. In contrast, the interedge magnetic coupling in

TM-CxNy functionalized GNRs may depend on the GNR type. For fully functionalized 9-AGNR

by TM-N2 edge defects, Mn-N2, Fe-N2, and Co-N2 defects simultaneously show low formation

energy, high Curie temperature, and high and localized magnetic moments. Therefore Mn-, Fe-

and Co-N2 functionalized 9-AGNRs may find applications in nanomagnetism and spintronics.

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Tables

Table 1. Magnetic moment (m in µB) of transition metals (TM) in edge TM-CxNy defects in 9-

AGNRs (one defect per simulation cell). Magnetic contributions from 4s and 3d electrons are

also given.

TM-C2 TM-CN TM-N2

Metal 4s 3d 4s 3d 4s 3d

Sc 0.08 0.34 0.09 0.54 0.11 0.41

Ti 0.11 1.39 0.13 1.72 0.16 1.93

V 0.12 2.55 0.13 2.90 0.15 2.99

Cr 0.11 3.54 0.13 3.83 0.11 4.05

Mn 0.09 4.01 0.10 3.75 0.19 4.32

Fe 0.09 3.10 0.03 2.89 -0.03 2.86

Co 0.05 0.94 0.07 1.73 -0.02 1.69

Ni 0.00 0.00 0.01 0.74 -0.01 0.72

Cu 0.00 0.00 0.00 0.00 0.00 0.00

Zn 0.00 0.00 0.14 0.00 0.20 0.00


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Table 2. Magnetic moment (m in µB) of transition metals (TM) in edge TM-N2 defects in 10-

and 11-AGNRs (one defect per simulation cell), 9-AGNR (two defects per simulation cell), and

9-AGNR (four defects per simulation cell). Magnetic contributions from 4s and 3d electrons are

also given.

TM-N2 TM-(TM-N2)-TM 2TM-(TM-N2)-2TM

10-AGNR 11-AGNR 9-AGNR 9-AGNR

Metal 4s 3d 4s 3d 4s 3d 4s 3d

Sc -- -- -- -- 0.11 0.54 0.04 0.12

Ti -- -- -- --- 0.15 1.83 0.15 1.47

V -- -- -- -- 0.15 2.93 0.15 2.83

Cr 0.11 4.04 0.11 4.04 0.12 4.00 0.11 3.85

Mn 0.17 4.27 0.19 4.36 0.19 4.32 0.12 4.11

Fe -0.03 2.88 -0.02 2.91 -0.02 2.89 -0.02 2.85

Co -- -- -- -- -0.02 1.67 -0.02 1.74

Ni -- -- -- -- -0.01 0.65 -0.01 0.60

Cu -- -- -- -- 0.00 0.00 0.00 0.00

Zn -- -- -- -- 0.20 0.00 0.20 0.00


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Table 3. Formation energy (∆E in eV) of TM-CxNy defects and magnetic moment (m in µB) of

transition metals (TMs) in edge TM-CxNy defects in 5-ZGNRs (one defect per simulation cell as

shown in figure 8). Magnetic contributions from 4s and 3d electrons are also given.

TM-C2 TM-CN TM-N2

∆E m ∆E m ∆E m

Metal 4s 3d 4s 3d 4s 3d

V 1.66 0.10 1.94 0.53 0.12 2.63 -0.43 0.14 3.00

Cr 2.82 0.12 3.24 2.00 0.11 3.54 0.82 0.10 4.07

Mn 2.94 0.09 3.86 1.76 0.10 3.97 0.66 0.19 4.41

Fe 2.64 0.07 2.92 1.62 0.09 3.02 0.59 0.01 2.96


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Figure Captions

Figure 1. 9-AGNRs. a) H terminated perfect GNR, b) Edge C2 (two edge C atoms with dangling

bonds), c) Edge CN (one edge C with dangling bond and one edge N atoms), d) Edge N2 (two

edge N atoms), e) Edge TM-C2, f) Edge TM-CN, and g) Edge TM-N2 defects in 9-AGNR.

TM=3d transition metals=Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn. Rectangle enclosed by

dashed black line shows unit cell used in calculations. In the figure, grey balls represent C atoms,

blue balls represent N atoms, brown balls represent transition metal (TM) atoms, and green balls

represent H atoms.

Figure 2. (a) Formation energy (∆E) of edge TM-CxNy defects, and (b) Binding energy (BE) of

transition metals (TMs) in edge-CxNy defects in 9-AGNR (one defect per simulation cell as

shown in figures 1e, 1f and 1g).

Figure 3. Calculated TM-N and TM-C bond lengths in edge TM-C2, TM-CN and TM-N2 defects

in 9-AGNR (one defect per simulation cell as shown in figures 1e, 1f and 1g). For comparison,

the sum of covalent radii of TM and C (rTM+C) and TM and N (rTM+N) are also shown. The

covalent radii of TM, N and C are taken from ref 59. Covalent radii for Mn, Co and Fe are taken

for their high spin states.

Figure 4. Calculated magnetic moments (contribution from TM-3d orbitals) of transition metals

(TMs) in edge TM-C2, TM-CN and TM-N2 defects in 9-AGNR (one defect per simulation cell as

shown in figures 1e, 1f and 1g).

Figure 5. Spin density plots for a) Mn-C2 b) Mn-CN and c) Mn-N2 edge defects in 9-AGNR.

The isosurface value of 0.007 e Å-3 was chosen following ref 26. Different colors of isosurface


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show different spin directions. In the figure, grey balls represent C atoms, blue balls represent N

atoms, brown balls represent transition metal (Mn) atoms, and green balls represent H atoms.

Figure 6. a) 9-AGNR with two edge TM-N2 defects (one at each edge) and b) 9-AGNR with

four edge TM-N2 defects (two at each edge) per simulation cell. In the figure, grey balls

represent C atoms, blue balls represent N atoms, brown balls represent transition metal (TM)

atoms, and green balls represent H atoms.

Figure 7. Calculated difference in total energies (∆EMS) between antiferromagnetic (AFM) and

ferromagnetic (FM) calculations for two and four edge TM-N2 defects per simulation cell as

shown in figures 6a and 6b, respectively.

Figure 8. 5-ZGNRs a) H terminated perfect 5-ZGNR unit cell, b) TM-C2, c) TM-CN, d) TM-N2

edge defects in 5-ZGNR, and e) 5-ZGNR fully functionalized by TM-N2 edge defects .The unit

cell is periodically repeated along horizontal direction and the width of ZGNR is along vertical

direction. TM=V, Cr, Mn, and Fe. In the figure, grey balls represent C atoms, blue balls

represent N atoms, brown balls represent transition metal (TM) atoms, and green balls represent

H atoms.


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Figure 1.

a)

f) e)

b) c) d)

g)


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Figure 2.

5

4

3

2

1

0

For

mation

Ener

gy (∆∆ ∆∆E in

eV

)

TM-C2

TM-CN TM-N2


-7

-6

-5

-4

-3

-2

-1

0

Bin

din

g Ener

gy o

f TM

(B

E in

eV

)


TM-C2

TM-CN TM-N2

a)

b)


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Figure 3.

2.50

2.40

2.30

2.20

2.10

2.00

1.90

dT

M-N

/C (in

Å)

Sc Ti V Cr Mn Fe Co Ni Cu

dTM-C 2

dTM-CN

dTM-CN

dTM-N 2

rTM+N

rTM+C

Zn


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Figure 4.

5

4

3

2

1

0

TM

Mag

net

ic M

omnet

(in

µµ µµΒΒ ΒΒ)) )) TM-C2

TM-CN TM-N2



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Figure 5.

c)

b) a)


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Figure 6.

a) b)


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Figure 7.

100

80

60

40

20

0

-20

-40

-60

EA

FM-E

FM

(m

eV)


2(TM-N2)

4(TM-N2)


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Figure 8.

b) a) c)

d) e)


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Magnetic properties of 3d transition metals and nitrogen functionalized armchair graphene nanoribbon

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