DSpace at VNU: Graphene-Cr-Graphene Intercalation Nanostructures: Stability and Magnetic Properties from Density Functional Theory Investigations

conducted a theoretical investigation of two graphene layers intercalated by Ca, and the electronic structures and vibrational modes of which were carefully examined.3b Embedding transit

Graphene-Cr-Graphene Intercalation Nanostructures: Stability and Magnetic Properties from Density Functional Theory Investigations Viet Q Bui and Hung M Le*

Faculty of Materials Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam

Yoshiyuki Kawazoe

New Industry Creation Hatchery Centre, Tohoku University, 6-6-4, Aramaki, Aoba, Sendai, 980-8579, Japan

Duc Nguyen-Manh

Theory and Modeling Department, Culham Centre for Fusion Energy, United Kingdom Atomic Energy Authority, Abingdon, OX14 3DB, U.K

ABSTRACT: A theoretical investigation of two-dimensional

graphene-Cr-graphene intercalation nanostructures has been

carried out using density functional theory (DFT) calculations

The intercalation nanostructures of interest are classified based

on the atomic ratio of Cr with respect to C on two graphene

layers, and we accordingly assign nomenclatures to the

intercalation nanostructures as 1-4, 1-12, and 1-16 GMG

Binding energy analysis suggests that the 1-12 and 1-16 GMG

structures are energetically stable, whereas the 1-4 GMG

structure is unstable When examining the 1-4 bilayer

graphene-Cr (GGM) structure, we have found that it is

energetically stable and nonmagnetic On the other hand, all

three GMG intercalation structures are found to be ferromagnetic, and the 1-16 GMG structure exhibits the highest total magnetization (2.00μB/cell), whereas the 1-12 GMG structure exhibits the lowest total magnetization (0.46μB/cell) Interplays between stability and magnetic properties of these three nanostructures are discussed from electronic structure analysis It is found for the two stable nanostructures that the 2pzorbitals of graphene layers are aligned antiferromagnetically with respect to the Cr layer, thus causing negative contributions to total magnetic moments of two stable GMG nanostructures

I INTRODUCTION

Graphene is an infinite honeycomb monolayer of carbons, in

which each atom connects to three surrounding others by sp2

-hybridized bonds Since the discovery of this new material,1

graphene has attracted huge attention of the research

community in the 21st century Besides its interesting physical

strength and superconductivity,2 the coordination chemistry

between graphene and metals has been continuously explored

and well-established during these recent years.3The adsorption

on metallic materials can alter its electronic properties (shift of

the Fermi level) and thus leads to different electronic transport

behaviors.3e

A vast variety of metals interacting with graphene have been

investigated both experimentally as well as theoretically by

first-principles computational methods By employing X-ray

magnetic circular dichroism, Weser and co-workers studied

the induced magnetism of carbons in the graphene/Ni(111)

interacting surface.4 The decoration of Au nanoparticles on

graphene was conducted by Muszynski et al.5using a chemical

reduction of AuCl4−ions Positively charged Au nanoparticles

were deposited on the graphene surface, and it was reported that such a structure had some featured applications in biosensors.6 By employing atomic resolution scanning trans-mission electron microscopy, Zan and co-workers investigated detailed surface interactions between graphene and three

concluded that different metals tended to bond to a specific site

on the graphene sheet While it was discovered that Au and Fe, respectively, bonded to the T and B adsorption sites (the nomenclature of the three binding sites is given in Figure 1), Cr atoms were found to bond more strongly on the H site of the graphene monolayer than the other two metals More information regarding experimental graphene−metal surface interactions is available for consulting in a review paper by Wintterlin and Bocquet.8

Received: November 1, 2012

Revised: January 23, 2013

Published: January 24, 2013

pubs.acs.org/JPCC

Since the advanced development of density functional theory

development of computational packages for condensed-matter physics and nanostructured materials science calculations As a matter of applications, numerous DFT-based approaches of graphene−metal interactions have been vastly performed in order to inspect the physical properties and coordination chemistry In a theoretical work conducted by Nakada and Ishii,3c the decorations of many kinds of metals (including alkali, alkali-earth, and d transition metals) were investigated

(LDA) for the exchange-correlation functional, and it was suggested that, in most cases, a metal atom tends to locate on the hexagonal (H) adsorption site, while few other metals assumed other adsorption positions (bridge (B) and top (T) sites), as defined in Figure 1 The 3d metal of interest in this study, Cr, was reported to most stably interact with graphene when assuming the H site on the graphene sheet In a theoretical work reported by Giovannetti et al.,3e interactions between graphene and several metal substrates (Al, Ag, Cu, Au, and Pt) were inspected, and the resulted data have suggested

caused shifts of approximately 0.5 eV in the Fermi level (with respect to the conical points in graphene) When the

Figure 1 Definitions of three adsorption sites on the graphene

surfaces: hexagonal (H), bridge (B), and top (T).

Figure 2 Two-dimensional periodic structures of three GMG intercalation nanostructures: (a) 1-4, (b) 1-12, and (c) 1-16.

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interactions of graphene−Ni and graphene−Cu were

inves-tigated, the theoretical observations clearly demonstrated that

the adhesive energy of graphene−Ni was much stronger than

that of graphene−Cu.11

A super effort to construct a graphene nanoribbon interfaced with the surfaces of two Ni electrodes

was contributed by Smolyanitsky and Tewary12using atomistic

simulation methods Recently, Jishi et al conducted a

theoretical investigation of two graphene layers intercalated

by Ca, and the electronic structures and vibrational modes of

which were carefully examined.3b Embedding transition-metal

atoms on graphene exhibits interesting magnetic behavior,

which involves the role of the sp2-hybridized orbital from

graphene and spd orbitals from transition metals.13Spintronics

was also of concern, and it was previously investigated by

Maassen et al.14 using first-principles calculations with spin

efficiencies reported as 80% and 60%, respectively

By definition, an intercalation nanostructure consists of two

(or multiple) graphene monolayers embedded by a layer(s) of

metal atoms Interestingly enough, the electronic conductivity

of such structures is surprisingly high, and may consequently

lead to some potential technologies and applications, especially

in electronic transporting devices The modulation of graphene

magnetic behavior, as shown in a previous study,14suggested

potential applications in spintronics as well In this study, we

present a theoretical investigation of structural stability,

electronic structures, and magnetisms of various

graphene-Cr-graphene intercalation nanostructures using a DFT-based

approach (for convenience, we denote GMG as an abbreviation

for graphene-Cr-graphene intercalation nanostructures)

distribution of Cr on graphene surfaces, which consequently

results in various periodic two-dimensional structures We

examine the stabilities of our GMG structures by investigating

binding energies and dissociation energies of Cr−graphene

coordination bonds In addition, we also interpret magnetisms

based on the analysis of spin-polarized electronic structure to

reveal the interesting magnetic properties of these GMG

nanostructures

II INTERCALATION STRUCTURES

The distribution of Cr on the surfaces of two graphene layers

certainly has a significant effect on the structural stability and

hence results in a typical strength of coordination bonds

(binding energy) and magnetic property.13,14 In this study, we

consider three different GMG intercalation nanostructures that

are classified by the distribution ratio of Cr per C atoms on two

graphene sheets

The most Cr-concentrated structure is referred to as “1-4

GMG” In this structure, Cr atoms are distributed in such a way

that they occupy all“honeycomb units” (six-membered carbon

rings like benzene) on the graphene lattice In the

two-dimensional unit cell, there are one Cr and four C atoms (two

C from the upper layer and two C from the lower layer) As

shown in Figure 2a, there are two types of chemical interactions

that involve transition metal−carbon complex interactions and

possible metallic bonding between Cr atoms

In the second intercalation structure of interest, the unit cell

contains 1 Cr and 12 C atoms (6 C from each layer), and it is

consistently named as the“1-12 GMG intercalation

nanostruc-ture” The distribution of Cr in this lattice, as shown in Figure

2b, allows Cr to occupy one centered honeycomb unit and

leave six surrounding honeycomb units unoccupied More

importantly, we believe that the Cr−Cr metal interaction is not found in this structure

In the last intercalation structure investigated in this study (Figure 2c), metal−metal interaction is least likely to be observed among the three investigated cases, since Cr is least concentrated In a unit cell of such a structure, each Cr atom has 16 C atoms with the nearest-neighbor coordination (8 from each graphene layer), and we thereby name this nanostructure

The conventional unit cells of the three intercalation nanostructures have a 2D characteristic in the x and y directions The z direction, on the other hand, is treated within a vacuum by employing a 30 Bohr (15.88 Å) length for the c axis

III COMPUTATIONAL DETAILS The Quantum Espresso package15is employed to execute all

Ernzerhof (PBE) exchange-correlation functional16 with the ultrasoft pseudopotential17for Cr and C The local spin-density approximation18(LSDA) is adopted to deal efficiently with the metal−aromatic interaction of the GMG intercalation elec-tronic structure In addition, we also testify 1-16 GMG and a

generalized gradient approximation16a(GGA) for the purpose

of comparisons with available LSDA results The k-point mesh

is selected as (12 × 12 × 1), which is sufficient to provide convergence satisfaction in total energy calculations A consistent kinetic energy cutoff for plane-wave expansion is selected as 45 Ry for all calculations performed in this study

In numerical optimizations of lattice constants, we employ the Broyden−Fletcher−Goldfarb−Shanno19

(BFGS) algorithm with tight convergence criteria, that is, 10−5eV/cell for energy

Since all investigated structures are two-dimensional lattices, as mentioned earlier in the previous section, the unit cell length of the z direction is set to 30.00 Bohr (15.88 Å) to accommodate vacuum treatment

IV RESULTS AND DISCUSSION

i 1-4 GMG Nanostructure In the most Cr-concentrated nanostructure (1-4 GMG), every aromatic honeycomb unit in the infinite lattice is occupied by a Cr atom As mentioned earlier in this paper, such an occupation of Cr atoms on the two graphene sheets consequently allows them to form an interacting rhombus network, as illustrated in Figure 2a Interestingly enough, this rhombus network has an effect on the bonding interaction of 1-4 GMG and its structural stability

It is observed in the relaxed structure of 1-4 GMG that the Cr−

Cr distance is 2.532 Ǻ For a comparison, the experimental

body-centered cubic (bcc) lattice is 2.503 Ǻ The exact formation angles of such a rhombus are 60° and 120° due to the periodicity of two graphene layers, which certainly have a total effect on constructing the metal network Recall that, in nature, the Cr crystal stably assumes the body-centered cubic (bcc) structure, and on its 110 crystallographic plane, four neighboring Cr atoms constitute a rhombus with two angles being 45° and 135°

resulting length of 1.462 Ǻ, which is longer than the C−C bond

in an isolated graphene sheet given by our DFT calculations

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(1.422 Ǻ) The distance between Cr and one graphene layer is

reported as 1.945 Ǻ, while the Cr−C distance is 2.433 Ǻ When

we compare these resulting atomic distances to those resulting

from the optimized structures of 1-12 and 1-16 GMG, the 1-4

GMG nanostructure is least compressed in the z direction

among the three intercalation structures Although the 1-4

GMG structure provides the longest Cr layer−graphene layer

distance, the Cr−graphene interaction in such a structure is

almost similar to that in 1-12 GMG, as shown in the electron

density analysis (Figure 3a) of Cr−C interactions for these two

interactions in the 1-4 GMG and 1-12 GMG nanostructures

(Figure 3b), it can be seen in both cases that electron density

mostly resides near Cr nuclei; however, the electron density in

the middle of Cr−Cr in 1-4 GMG is slightly higher Therefore,

we can conclude that Cr−Cr interaction is more likely

dominant in the 1-4 GMG structure

To determine the thermodynamic stability of each

intercalation structure, it is necessary to determine the binding

energy of Cr attaching to two graphene surfaces In this work,

we determine the binding energy of a GMG nanostructure as

follows

Ebinding 2Egraphene ECr layer Ecompound (1)

where Egraphenerepresents the total energy of a graphene sheet,

ECr_layer represents the energy of the Cr layer, and Ecompoundis

the total energy of the intercalation structure of interest A

positive binding energy indicates an energetically stable product (which can be exothermically synthesized); on the other hand,

a negative binding energy reveals an unstable structure Adopting eq 1, the binding energy of Cr in the 1-4 GMG intercalation nanostructure is calculated as−0.090 eV/cell (of five atoms) (−2.07 kcal/mol), which reveals the instability of

1-4 GMG This amount of binding energy suggests that the adsorption of Cr on every honeycomb unit of the two graphene units results in an endothermic process If we use the energy of one Cr in the bcc unit cell (instead if using the energy of a Cr layer), the new resulting binding energy is −1.99 eV, which even reveals a more unstable structure However, since there is

no mutual interaction between Cr−Cr in the z direction in 1-4 GMG, we believe that using a Cr layer in binding energy calculations is more sensible For comparison purposes, the bond distances and binding energies for three GMG intercalation structures in this study are summarized in Table 1

The electronic property of 1-4 GMG is explored in our calculations by examining the total density of state (DOS) and partial density of state (PDOS) of Cr 3d and graphene 2p orbitals In Figure 4a, the spin-polarized DOS plot of the 1-4 intercalation nanostructure clearly shows band overlapping at the Fermi level (positioned at 0 eV) and exhibits conducting behavior of the material It is found that the high values of DOS

at the Fermi energy (E = 0) for both up- and down-spin contributions from the Cr layer are the origins of structural instability in this case

We notice spin polarizations from the DOS plot that consequently cause magnetization behavior of the 1-4 GMG intercalation nanostructure Two magnetic quantities for each nanostructure are reported in our study, which are the total magnetization (MT) and absolute magnetization (MA) In the

computed as the integral of magnetization over the unit cell volume, while an absolute magnetization is the integral of absolute value of magnetization over the unit cell volume The mathematical expressions of total and absolute magnetizations are respectively shown in the following equations:

∫

∫

(3)

As we notice in the above equations, a positive orbital polarization contributes ferromagnetism to the total magnetic

Figure 3 (a) Electron density plots of Cr−C interactions in 4 and

1-12 GMG (b) Electron density plots of Cr−Cr interactions in 1-4 and

1-12 GMG.

Distances, and Binding Energies of the 1-4, 1-12, and 1-16 GMG Nanostructures

bonddistance(Å)

GMG intercalation structure C −C Cr −C Cr layerdistance (Å)−graphene layer

binding energy (eV/cell)

1.439 2.266 1.427

a There are three different C−C and two different Cr−C bonds in the 1-16 GMG structure.

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moment On the other hand, a negative orbital polarization

contributes antiferromagnetism, and consequently reduces the

total magnetic moment (in this case, we would have the total

magnetic moment to be lower than the absolute magnetic

moment) As a result, when the total and absolute

magnet-izations are identical, we can conclude that all orbital

polarizations in the system of interest are positive (absolute

ferromagnetism)

Recall that chromium metal in the bcc lattice exhibits

spin-density-wave antiferromagnetism;20however, when a layer of

Cr is introduced in between two graphene monolayers, the

magnetic behavior turns to ferromagnetism, as shown in the

total DOS and PDOS of the Cr 3d orbital (Figure 4a) It is

shown from the plot that the total magnetic moment is

dominated by the contribution of the Cr layer, while the

contribution of two graphene layers (2pz orbitals) is smaller

According to our spin-polarization analysis, the total and

absolute magnetizations of the 1-4 intercalation nanostructure

are 1.36 and 1.58μB/cell, respectively

A critical issue regarding structural stability is raised when such intercalation structures of graphene layers and 3d transition metals are to be experimentally synthesized; therefore, it is of importance to examine the structural stability

of our proposed intercalation nanostructures by computational DFT methods In this study, besides investigating binding energies and electronic and magnetic properties of GMG crystals, we also look forward to examining the dissociation and/or migration energy barriers

As previously mentioned, the bonding scheme between graphene and a transition metal is mostly formed by coordination bonds when the metal (for instance, Cr in this study) has a great tendency to accept electron donation from graphene 2pzorbitals The strength (stability) of such types of bonds may vary depending upon the nature of donating and accepting groups Anyhow, it is revealed in most cases that the coordination interaction is often weak,21and the coordination interaction might be destroyed under the effects of temper-ature/pressure

To examine the bonding stability of graphene-Cr-graphene nanostructures, we attempt at two important aspects: (i) direct dissociation of intercalation structures in the z direction and (ii) migration of Cr from the hexagonal (H) site (most stable) to a less stable position (bridge (B) or top (T))

In a previous study reported by Nakada and Ishii,3cCr was reported to most favorably assume the H site when attaching to

a single graphene sheet (with a positive binding energy reported as 3.99 eV) In our study, when Cr is located at the T (or B) site in the 1-4 GMG intercalation structure, the optimizations of graphene-metal-graphene do not successfully converge; in fact, the two graphene layers are pushed far away from the Cr layer during the optimization processes Therefore,

we conclude that the decorations of Cr on the T and B sites of 1-4 GMG do not result in Cr−graphene interactions, as we see

in the H-site adsorption case Hence, we proceed the stability investigation by only examining the direct dissociation scheme

of 1-4 GMG

After conceiving a negative binding energy (−0.090 eV/cell),

to further testify the instability of 1-4 GMG, we inspect the direct dissociation barrier of such an intercalation nanostructure

by performing relaxations based on total energy calculations

structure is relaxed in the x and y directions, while the z direction isfixed Consequently, we obtain a dissociation barrier

as shown in Figure 5 At the transition state, the Cr−graphene distance is found to be 2.420 Å, and the corresponding energy barrier is 0.217 eV/cell (of 5 atoms) or 5.00 kcal/mol Recall that the 1-4 GMG structure is unstable in terms of binding energy, and the low destruction energy of such a structure is reasonable in terms of coordination interaction between graphene and transition-metal adatoms.21 At the end of the dissociation process, we should be able to obtain a more stable product (two graphene sheets and a Cr layer) than the reactant (by an amount of 0.090 eV/cell, as suggested in previous binding energy calculations) At the transition state, the complex interaction between Cr and graphene starts to decrease, and we notice a significant increase in magnetism magnitude Interestingly, the total and absolute magnetizations become almost similar (3.20 and 3.21 μB/cell, respectively) This fact reveals that all orbital polarizations are ferromagnetic,

as previously stated from the mathematical interpretation of eqs

2 and 3

Figure 4 (a) Total DOS for 1-4 GMG and the corresponding PDOS

for graphene 2p and Cr 3d orbitals (the Fermi level is positioned at 0

and indicated by a vertical line) In this plot, the up and

spin-down states are not perfectly aligned, which demonstrates that 1-4

GMG is ferromagnetic (b) Total DOS and PDOS for the 1-4 G1G2M

structure (the Fermi level is positioned at 0 and indicated by a vertical

line) Note that the second graphene layer (G2) is in direct contact

with the Cr layer The spin-up and spin-down states are perfectly

aligned, which demonstrates that 1-4 GGM is nonmagnetic.

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We further inspect the 1-4 graphene-graphene-Cr (1-4

GGM) nanostructure using DFT calculations In this case,

two graphene layers are not in superposition, as seen in the

GMG structures; in fact, we use a bilayer graphene consisting of

two monolayers stacked as in natural graphite, which was

proved to be stable in a previous experimental study.22At the

optimized equilibrium, the binding energy for 1-4 GGM is

found to be 0.850 eV/cell, suggesting that the new structure is

energetically stable The interlayer distance between the two

graphene monolayers is 3.2 Å, whereas the Cr−G nearest layer

distance is 1.97 Å, which is a bit higher than the Cr−G distance

within the 1-4 GMG structure (1.945 Å) In addition, when the

spin-polarized DOS is analyzed (as shown in Figure 4b), the

spin-up and spin-down states perfectly align Consequently, all

orbital spin polarizations vanish, and we conclude that 1-4

GGM is a nonmagnetic nanostructure

ii 1-12 GMG Nanostructure In the 1-12 GMG

intercalation nanostructure, with the Cr concentration being

reduced, we observe some major changes in the cell structural

stability as well as magnetic property As revealed in Figure 2b,

the chromium atom in the 1-12 GMG structure occupies one

honeycomb unit and six surrounding honeycomb units are

interacting network in the 1-12 GMG intercalation

nanostruc-ture The C−C bond in the graphene sheet is 1.433 Å, which is

Cr−C in the 1-12 intercalation structure is 2.176 Å (15.7%

longer than that in the 1-4 GMG intercalation structure) In

addition, the Cr layer−graphene surface distance is 1.639 Å,

and the distance between two graphene layers is consequently

3.278 Å, which is very close to the distance between two layers

in the graphite lattice (3.361 Å according to our DFT

calculations) From the reported evidence, it is easy to find

out that the 1-12 GMG structure is more compressed than the

previous 1-4 GMG structure In fact, if we compare all three

investigated structures, as we will see later, the 1-12 GMG

nanostructure is most compressed, and the graphene−graphene

interlayer distance is very close to that of graphite Note that

there is a major difference between our intercalation models

and graphite; that is, in our models, carbon atoms from two

graphene sheets are in superposition A charge density analysis

for the C−C interaction from the two graphene layers for 1-4 GMG, 1-12 GMG, and graphite is reported in Figure 6 Despite

having the highest interlayer distance, the 1-4 GMG has the highest electron density in between two carbon atoms (of two distinct graphene layers), whereas we observe less overlapping

of electron density between carbon atoms from two layers in

1-12 GMG and graphite

We again employ eq 1 to determine the binding energy of the Cr atom in the corresponding structure of 1-12 GMG, and the resulting binding energy is 1.010 eV/cell (of 13 atoms), or 23.4 kcal/mol This positive binding energy suggests an exothermic reaction when the 1-12 GMG structure is synthesized Recall that, in the previous case (1-4 GMG intercalation structure), the binding energy is−0.090 eV/cell Hence, a huge difference in thermodynamic properties between the 1-4 and 1-12 GMG structures is observed In the 1-4 GMG case, we conceive an unstable product, but in the 1-12 GMG case, a much more stable product is obtained In a previous theoretical study,3cthe adsorption of a Cr atom on a graphene layer resulted in a binding energy of 3.99 eV, which is higher than the decoration of the Cr layer in between two graphene monolayers in our case

The 1-12 GMG nanostructure is believed to share structural similarities to a metallorganic compound, which is

similar DFT calculations to optimize the equilibrium structure

of bis(benzene)chromium, and the results have revealed significant structural similarities between the 1-12 GMG lattice and bis(benzene)chromium For the metallorganic molecule, the Cr−C bond is 2.140 Å, which is only 1.65% lower than the corresponding bond in 1-12 GMG Moreover, the distance between Cr and a benzene ring in bis(benzene)chromium is 2.26% lower than the interlayer distance between Cr and graphene in 1-12 GMG We believe that the above closely related bond lengths are useful to make a connection between the two structures in terms of stability and magnetism In fact, the binding energy of bis(benzene)chromium is calculated as 2.923 eV/molecule and reveals better stability of this

Figure 5 Direct dissociation of 1-4 GMG At 2.420 Å, we observe a

transition state for dissociation with an activation energy of 0.217 eV/

cell.

Figure 6 Electron density plots for C−C interaction from different layers in 4 GMG, 12 GMG, and graphite Unlike graphite, in our

1-4 and 1-12 GMG models, carbon atoms from the two layers are in superposition.

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metallorganic compound comparing to the 1-12 GMG

nanostructure We note, however, that a nonmagnetism is

found in bis(benzene)chromium, whereas 1-12 GMG is weakly

ferromagnetic

When the direct dissociation barrier of the 1-12 GMG

structure is investigated, the transition state is not observed

during the process Such a structure is very stable when

comparing to the initial reactants in terms of binding energy;

thus, the reaction of 2graphene + Cr to produce 1-12 GMG is

believed to be barrierless (spontaneous), and we should not

observe any transition state for the dissociation

In the next stage, the migrations from the H site to the other

less stable sites (B and T) are inspected using the

handle transition-state locating In the NEB algorithm,

(product) states, one can locate the transition state by

analyzing the gradients (first derivative) of atoms within the

unit cell In this study, we employ the NEB algorithm

transition states for H−T and H−B transitions During an

optimization, the norm of perpendicular force with respect to

the reaction path is used as a numerical convergence criterion

If it is less than 0.05 eV/Å/atom, calculations are terminated

and thefinal result is then reported

At equilibrium, the energies of B and T adsorptions are

found to be higher than the energy of H adsorption by an

amount of 0.342 and 0.382 eV/cell, respectively From the

above relative energies (compared to the energy of H

adsorption), it is shown that the adsorption of Cr in the

adsorption right on top of C With the knowledge of thefinal

products, we perform two NEB optimizations to scan for the

transition structures In each optimization, a series of

intermediate structures (images) are produced, and the two

transition states are found, as presented in Figure 7 For the H−

B migration in 1-12 GMG, the activation energy for such a

transformation is reported as 0.351 eV/cell, whereas an

activation energy of 0.433 eV/cell is required for the H−T migration to occur According to our calculations, it can be concluded that the B adsorption of Cr in the 1-12 GMG structure is quite more energetically favored than the T

migration is more advantageous because of its lower activation

respectively, which is lower than the total and absolute magnetizations of the H−T transition state (4.06 and 4.44

μB/cell, respectively)

For the equilibrium 1-12 GMG intercalation nanostructure, according to our calculations using LSDA treatments, the total

respectively, which are significantly less than the magnetizations

structure analysis indicates ferromagnetism with a nonzero total magnetization value In fact, the ferromagnetic property of the 1-12 GMG nanostructure is much weaker than that of the previous structure (4 GMG) by observing the total DOS of

1-12 GMG and the corresponding PDOS for Cr 3d orbitals (illustrated in Figure 8a) Around the Fermi level (positioned at

0 eV), the spin-polarized DOS distributions of Cr 3d orbitals are slightly different, and a weak ferromagnetism for the 1-12 GMG intercalation structure is observed As shown in Figure 8b, the difference in Cr 3dz2 spin distribution mainly causes a weak ferromagnetism in 1-12 GMG We also see good electron localization in the 1-12 nanostructure when Cr 3dz2, 3dzx, 3dzy orbitals and C 2pzorbitals overlap around the Fermi state The LDOS of C 2px(and similar 2py) orbitals indicate that they do not really participate in the bonding interaction between Cr and graphene According to our spin-polarized DOS analysis, the Cr 3dz2 orbital contributes largely to the total magnetic moment (0.293μB/cell), whereas other orbitals in the Cr 3d shells do not have a large impact on total magnetization The contribution of the C 2pzorbital, however, results in a negative magnetic moment (−0.076 μB/cell) and causes a decrease in total magnetization As for the bis(benzene)chromium case, which has a close chemical configuration to that of 1-12 GMG,

we witness a nonmagnetic case The empty shells in Cr 3d are

effectively filled by electrons from benzene 2pz orbitals; thus, such an electronic interaction results in a nonmagnetism molecule

To validate the ferromagnetism of our GMG models, it is useful to perform LDA calculations for the graphene-Cr-graphene-Cr-graphene (GMGMG) structure (in this case, we have 6 C atoms in one graphene layer, and thereby have 24 C atoms in the unit cell) In this examination, the case of antiferromagnetism is tested by assigning positive and negative initial magnetizations to two Cr atoms in the unit cell Interestingly, it is found that, at equilibrium, all atomic shell polarizations vanish, and we obtain zero total and absolute magnetic moments We also employ GGA calculations for GMGMG optimizations, and the resulting spin polarization is totally consistent with previous LDA calculations In con-clusion, we strongly believe that, even with two Cr atoms in the unit cell, the ground state of the GMGMG model does not exhibit antiferromagnetism Therefore, we believe that the ground states of GMG models are actually ferromagnetic, as shown by the provided theoretical evidence

and C−C bond lengths in the 1-16 GMG nanostructure It has been shown from our DFT calculations that the average Cr−C

Figure 7 Potential energy barriers for H−B and H−T migrations

provided by NEB optimizations H−B migration is more energetically

favored than H−T migration.

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bond distance is 2.263 Å The distance between the Cr layer

and a graphene layer is approximately 1.746 Å From the

reported structural geometries, it is observed that the 1-12

GMG structure is the most-compressed structure in the z

direction among the three cases, although it has an intermediate

Cr concentration compared to the other two GMG structures

To test the structural stability, we again employ eq 1 to

calculate the binding energy, and obtain a resulting amount of

2.093 eV/cell (of 17 atoms) Such a binding energy suggests

that the formation of 1-16 GMG is exothermic and results in a

stable product When this binding energy is compared to that of

the previous cases (1-4 and 1-12 GMG structures), the 1-16

GMG structure is most stable among the three nanostructures

When performing a direct dissociation scan, we observe no

transition states for the dissociation, and therefore, it can be

concluded that the formation process of 2graphene + Cr→

1-16 GMG is barrierless (spontaneous)

In the 1-16 intercalation structure (least Cr-concentrated),

we observe the strongest magnetization magnitude (total and

respectively) Such important magnetic behavior is, however, strongly related to the structural stability of 1-16 GMG (with a binding energy of almost twice the binding energy of 1-12 GMG) The spin-polarized states (up and down) in Cr 3d orbitals are observed to be largely different, as shown in Figure 9a, which suggests a strong ferromagnetism exhibited by the

1-16 GMG structure Further analysis of magnetism and chemical bonding is provided in Figure 9b as we plot the local DOS for

Cr 3dz2, 3dzx, 3dzyand C 2p orbitals Around the Fermi level, we see good overlapping of the Cr 3d and C 2p shells

Figure 8 (a) Total DOS for 1-12 GMG and the corresponding PDOS

for graphene 2p and Cr 3d orbitals (the Fermi level is positioned at 0

and indicated by a vertical line) In this plot, the up and

spin-down states are slightly different in distributions, which indicates a

weak ferromagnetism (b) Partial DOS for C 2pz, 2px, 2pyorbitals of

C, and 3dz2 , 3dzx, 3dzyorbitals of Cr in 1-12 GMG Note that the state

distribution of the Cr 3dzyorbital is exactly similar to that of the Cr

3dzxorbital, and C 2pxis exactly similar to C 2py The Fermi level is

positioned at 0.

Figure 9 (a) Total DOS for 1-16 GMG and the corresponding PDOS for graphene 2p and Cr 3d orbitals given by LSDA calculations (the Fermi level is positioned at 0 and indicated by a vertical line) The spin-up and spin-down states of Cr and graphene are largely different

in distributions, which results in a large total spin difference and indicates the strongest ferromagnetism (among the three investigated GMG structures) (b) Partial DOS for C 2pz, 2px, 2pyorbitals of C and 3dz2, 3dzx, 3dzyorbitals of Cr in 1-16 GMG The state distribution of the Cr 3dzyorbital is exactly similar to that of the Cr 3dzxorbital, and C 2p x is exactly similar to C 2p y The Fermi level is positioned at 0.

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Furthermore, a large difference in distribution between spin-up

and spin-down can be conceived in the Cr 3dz2orbital (with a

contribution of 0.827μB/cell to the total magnetic moment) In

addition, we alsofind significant contributions from the Cr 3dxy

and 3dx2

−y 2 orbitals (0.492μB/cell in both cases), whereas the

3dzxand 3dzyhave less impacts (0.258μB/cell) The C 2pxand

2py orbitals have insignificant impacts on the total magnetic

moment In fact, the LDOS of C 2pxand 2pyorbitals indicate

that they are not involved in the bonding interaction between

Cr and graphene layers Importantly, considering the

contribution to total magnetization, we witness that the C

2pz orbitals result in a strong negative contribution in total

magnetization (by an amount of−0.446 μB/cell)

GMG nanostructure, the generalized-gradient

structure As a result, the total and absolute magnetizations are,

respectively, calculated as 1.98 and 3.05μB/cell When these

results are compared to previous results given by LSDA

calculations, we realize that the numerical differences are

insignificant, and consequently conclude that both LDA and

GGA calculations arrive at consistent results Furthermore, a

comparison of electronic structures resulting from the two

methods is made, and we concur that the electronic structures

from the two different calculations also share good agreement

For convenience, we present the total and absolute

magnetizations of the three GMG nanostructures in this

study in Table 2 Different orbital contributions (of C 2s, 2p

and Cr 3s, 3p, 3d, 4s, 4p shells) to total magnetic moments of

1-12 and 1-16 GMG nanostructures are computed and

presented in Table 3 It is expected from the spin-polarized

orbital analysis that the contributions from C 2px and 2py

should be equal From the summarized results, the most

Cr-concentrated and unstable intercalation structure (1-4 GMG)

has an intermediate magnetization, whereas the 1-12 GMG

structure exhibits the weakest magnetic behavior among the

three cases

V SUMMARY

In this study, we present a theoretical investigation of three

GMG intercalation nanostructures using a DFT approach with

LSDA treatments Three intercalated nanostructures are

classified by the atomic ratio of Cr per C on two graphene

sheets, and we accordingly denote those three structures as the

1-4, 1-12, and 1-16 GMG intercalation nanostructures (as indicated in Figure 2)

The equilibrium periodic molecular structures are optimized using local spin-density approximations (LSDA) as imple-mented in the Quantum Espresso package.15 At equilibrium, the bonding distances, stability, and magnetic properties are inspected, and we have observed some major differences among the nanostructures The 1-4 GMG nanostructure is found to be the least compressed structure in the z direction, and its corresponding binding energy is−0.090 eV/cell Therefore, we believe that this intercalation structure is energetically unstable

In fact, this statement is further implied when the dissociation energy of the coordination bond is investigated As two graphene sheets in 1-4 GMG are pulled away from the equilibrium position, we observe a transition state for dissociation at a distance of 2.420 Å with a calculated activation energy of 0.217 eV/cell When we further examine the 1-4 GGM structure with bilayer graphene stacked as in the natural graphite, a positive binding energy of 0.850 eV/cell is found, and we believe that this structure is more energetically favored than 1-4 GMG during experimental synthesis Furthermore, we find that 1-4 GGM exhibits no magnetism from the spin-polarized DOS analysis

The 1-12 GMG nanostructure is most compressed among the three GMG structures, whereas the 1-16 GMG nanostructure is less compressed than 1-12 GMG The binding energies of the 1-2 and 1-16 GMG nanostructures are 1.010 and 2.093 eV/cell, respectively, and it is suggested that the formations of these two structures are exothermic with stable products Examinations of 1-12 and 1-16 GGM indicate that they are less stable than 1-12 and 1-16 GMG, respectively; therefore, they would be less favorable during experimental synthesis

In the 1-12 GMG structure, Cr is also capable of assuming the B and T sites (B adsorption is quite more stable) The

subsequently investigated From the NEB optimizations,24 it

is suggested that the H−B and H−T migration barriers are 0.351 and 0.433 eV/cell, respectively

In nature, Cr metal is known to have spin-density-wave

behavior completely changes when we embed Cr in between two graphene layers According to the reported results, ferromagnetism behaviors are found for all three GMG structures For the most energetically stable structure (1-16 GMG nanostructure), the total and absolute magnetizations are found to be the highest (as shown in Table 2) From spin-polarized DOS analysis, orbital contributions in total magnetic moments are determined, and we conceive major contributions from the Cr 3dz2 orbitals in the stable 1-12 and 1-16 GMG nanostructures, while the other Cr 3d shells also contribute significantly The C 2pz orbitals, however, result in an antiferromagnetic alignment of graphene layers with respect

to the stronger ferromagnetic behavior of the Cr layer Hence,

Table 2 Total and Absolute Magnetizations of the 1-4, 1-12,

and 1-16 GMG Nanostructures

GMG intercalation

structure

total magnetization ( μ B /cell)

absolute magnetization ( μ B /cell)

Table 3 Main Orbital Contributions to Total Magnetic Moments in 1-12 and 1-16 GMG

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the C 2pz orbitals cause negative effects and reduce total

magnetizations

In 1-16 GMG, the bond strength (from binding energy

calculations) is observed to be higher than that in 1-12 GMG

At the same time, from our DFT calculations, we also conceive

a greater Cr−graphene interlayer distance (as well as Cr−C

bond distance) in 1-16 GMG In addition, from the PDOS

analysis of polarized spin states in 1-16 GMG, we observe that

the Cr 3d shells receive more electron donation from graphene

2pz, which causes greater different distributions of spin-up and

spin-down in the partially filled 3d orbitals (i.e., 3dz2, 3dxy,

3dx2

−y 2) As a result, higher ferromagnetism is observed in 1-16

coordination bond Therefore, we conclude that there is a

strong relationship between structural stability (interpreted in

terms of binding energies), partiallyfilled states, and total (and

absolute) magnetic moments in the two stable nanostructures

(1-12 and 1-16 GMG)

Corresponding Author

*E-mail: hung.m.le@hotmail.com

Notes

The authors declare no competingfinancial interest

The authors thank the Vietnam Ministry of Science and

Technology (MOST) and Vietnam National University, Ho

Chi Minh City (VNU-HCM), for their support in this project

We acknowledge supercomputing assistance from the Institute

for Materials Research at Tohoku University, Japan We also

thank Prof Thoa T P Nguyen for her helpful discussions

during the initial stage of this research

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