Graphene-Cr-Graphene Intercalation Nanostructures: Stability and

Article pubs.acs.org/JPCC

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 (2.00 μB/cell), whereas the 1-12 GMG structure exhibits the lowest total magnetization (0.46 μB/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 2pz orbitals 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 sp2hybridized 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.3 The 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 firstprinciples 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.5 using a chemical reduction of AuCl4− ions. Positively charged Au nanoparticles © 2013 American Chemical Society

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 transmission electron microscopy, Zan and co-workers investigated detailed surface interactions between graphene and three metals, which were Au, Fe, and Cr.7 Consequently, it was 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 3605

dx.doi.org/10.1021/jp310806a | J. Phys. Chem. C 2013, 117, 3605−3614

The Journal of Physical Chemistry C

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Since the advanced development of density functional theory (DFT),9 significant efforts have been devoted toward the 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 using a DFT method within local density approximation10 (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 that weak bonding graphene−metal substrate interactions 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. 3606



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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 as “1-16 GMG”. 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.

interactions of graphene−Ni and graphene−Cu were investigated, 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 Tewary12 using 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.13 Spintronics of graphene−ferromagnet interfaces (Co(111) and Ni(111)) 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,14 suggested potential applications in spintronics as well. In this study, we present a theoretical investigation of structural stability, electronic structures, and magnetisms of various graphene-Crgraphene intercalation nanostructures using a DFT-based approach (for convenience, we denote GMG as an abbreviation for graphene-Cr-graphene intercalation nanostructures). Various GMG nanostructures are classified by the atomic 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.

III. COMPUTATIONAL DETAILS The Quantum Espresso package15 is employed to execute all DFT calculations in this study using the Perdew−Burke− Ernzerhof (PBE) exchange-correlation functional16 with the ultrasoft pseudopotential17 for Cr and C. The local spin-density approximation18 (LSDA) is adopted to deal efficiently with the metal−aromatic interaction of the GMG intercalation electronic structure. In addition, we also testify 1-16 GMG and a GMGMG structure (defined in a latter section) using 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, 10−5 eV/cell for energy convergence and 10−4 eV/Å/cell for gradient convergence. 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.

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 twodimensional 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 nanostructure”. 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

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 bond length between first nearest-neighbor Cr atoms in the 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°. The C−C bond in a graphene sheet in 1-4 GMG has a resulting length of 1.462 Ǻ , which is longer than the C−C bond in an isolated graphene sheet given by our DFT calculations 3607



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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

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 14 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. Table 1. Cr−C and C−C Bond Distances, Cr−Graphene Distances, and Binding Energies of the 1-4, 1-12, and 1-16 GMG Nanostructures bonddistance(Å) GMG intercalation structure 1-4 1-12 1-16a

C−C

Cr−C

1.462 1.433 1.442 1.439 1.427

2.433 2.176 2.263 2.266

Cr layer−graphene layer distance (Å)

binding energy (eV/cell)

1.945 1.639 1.746

−0.090 1.010 2.093

a

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

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 Quantum Espresso package,15 a total magnetization is 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:

Figure 3. (a) Electron density plots of Cr−C interactions in 1-4 and 112 GMG. (b) Electron density plots of Cr−Cr interactions in 1-4 and 1-12 GMG.

GMG structures. Similarly, when we investigate the Cr−Cr 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 E binding = 2Egraphene + ECr_layer − Ecompound

(1)

where Egraphene represents the total energy of a graphene sheet, ECr_layer represents the energy of the Cr layer, and Ecompound is the total energy of the intercalation structure of interest. A

MT =

∫ (nup − ndown)d3r

(2)

MA =

∫ |nup − ndown|d3r

(3)

As we notice in the above equations, a positive orbital polarization contributes ferromagnetism to the total magnetic 3608



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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 2pz orbitals. 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,21 and the coordination interaction might be destroyed under the effects of temperature/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,3c Cr 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 with various Cr−graphene distances. At each point, the structure is relaxed in the x and y directions, while the z direction is fixed. 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 spin-up and spindown 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.

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 magnetizations 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 spindensity-wave antiferromagnetism;20 however, 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 1.58 μB/cell, respectively. 3609



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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

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 1-4 GMG, 1-12 GMG, and graphite. Unlike graphite, in our 14 and 1-12 GMG models, carbon atoms from the two layers are in superposition.

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.22 At 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 unoccupied; therefore, we do not observe a direct Cr−Cr interacting network in the 1-12 GMG intercalation nanostructure. The C−C bond in the graphene sheet is 1.433 Å, which is shorter than the C−C bond in the 1-4 GMG structure. The 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

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 112 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,3c the 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 bis(benzene)chromium.23 For comparison purposes, we employ 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 3610



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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 adsorption with an amount of 0.040 eV/cell, and the H−B migration is more advantageous because of its lower activation energy. The total and absolute magnetizations of the H−B transition state are computed as 2.69 and 3.02 μB/cell, 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 and absolute magnetizations are 0.46 and 0.60 μB/cell, respectively, which are significantly less than the magnetizations of the H−B and H−T transition states. Again, electronic 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 (1-4 GMG) by observing the total DOS of 112 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 2pz orbitals 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 (0.293 μB/cell), whereas other orbitals in the Cr 3d shells do not have a large impact on total magnetization. The contribution of the C 2pz orbital, 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-Crgraphene-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 conclusion, 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. iii. 1-16 GMG Nanostructure. There are various Cr−C and C−C bond lengths in the 1-16 GMG nanostructure. It has been shown from our DFT calculations that the average Cr−C

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 nudgedelastic-band (NEB) method,24 which has been developed to handle transition-state locating. In the NEB algorithm, providing the knowledge of initial (reactant) and final (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 implemented in the Quantum Espresso package15 to locate 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 the final 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 middle of a C−C bond is quite more stable than the Cr adsorption right on top of C. With the knowledge of the final 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

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. 3611



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In the 1-16 intercalation structure (least Cr-concentrated), we observe the strongest magnetization magnitude (total and absolute magnetizations being 2.00 and 3.07 μ B /cell, 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 116 GMG structure. Further analysis of magnetism and chemical bonding is provided in Figure 9b as we plot the local DOS for Cr 3dz2, 3dzx, 3dzy and 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 spin-up and spindown states are slightly different in distributions, which indicates a weak ferromagnetism. (b) Partial DOS for C 2pz, 2px, 2py orbitals of C, and 3dz2, 3dzx, 3dzy orbitals of Cr in 1-12 GMG. Note that the state distribution of the Cr 3dzy orbital is exactly similar to that of the Cr 3dzx orbital, and C 2px is exactly similar to C 2py. The Fermi level is positioned at 0.

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 → 116 GMG is barrierless (spontaneous).

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, 2py orbitals of C and 3dz2, 3dzx, 3dzy orbitals of Cr in 1-16 GMG. The state distribution of the Cr 3dzy orbital is exactly similar to that of the Cr 3dzx orbital, and C 2px is exactly similar to C 2py. The Fermi level is positioned at 0. 3612



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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 implemented 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 spinpolarized 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 migration energies of H−B and H−T transitions are 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 antiferromagnetism.20 Interestingly enough, the magnetic 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 spinpolarized 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,

Furthermore, a large difference in distribution between spin-up and spin-down can be conceived in the Cr 3dz2 orbital (with a contribution of 0.827 μB/cell to the total magnetic moment). In addition, we also find significant contributions from the Cr 3dxy and 3dx2−y2 orbitals (0.492 μB/cell in both cases), whereas the 3dzx and 3dzy have less impacts (0.258 μB/cell). The C 2px and 2py orbitals have insignificant impacts on the total magnetic moment. In fact, the LDOS of C 2px and 2py orbitals 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). To reaffirm the interesting magnetism found in the 1-16 GMG nanostructure, the generalized-gradient approximations16a (GGA) are employed to reinvestigate the 1-16 GMG structure. As a result, the total and absolute magnetizations are, respectively, calculated as 1.98 and 3.05 μB/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 Table 2. Total and Absolute Magnetizations of the 1-4, 1-12, and 1-16 GMG Nanostructures GMG intercalation structure

total magnetization (μB/cell)

absolute magnetization (μB/cell)

1-4 1-12 1-16

1.36 0.46 2.00

1.58 0.60 3.07

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 Crconcentrated 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

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

Cr

GMG structure

2pz

2px (2py)

4s

4p

3dz2

3dzx (3dzy)

3dx2−y2

3dxy

1-12 1-16

−0.076 −0.446

0.003 0.034

0.012 0.034

0.023 0.019

0.293 0.827

0.035 0.258

0.077 0.492

0.077 0.492

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(7) Zan, R.; Bangert, U.; Ramasse, Q.; Novoselov, K. S. Metal− Graphene Interaction Studied via Atomic Resolution Scanning Transmission Electron Microscopy. Nano Lett. 2011, 11 (3), 1087− 1092. (8) Wintterlin, J.; Bocquet, M. L. Graphene on Metal Surfaces. Surf. Sci. 2009, 603 (10−12), 1841−1852. (9) (a) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136 (3B), B864−B871. (b) Kohn, W.; Sham, L. J. SelfConsistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140 (4A), A1133−A1138. (10) Sahni, V.; Bohnen, K. P.; Harbola, M. K. Analysis of the LocalDensity Approximation of Density-Functional Theory. Phys. Rev. A 1988, 37 (6), 1895−1907. (11) Xu, Z.; Buehler, M. J. Interface Structure and Mechanics between Graphene and Metal Substrates: A First-Principles Study. J. Phys.: Condens. Matter 2010, 22 (48), 485301. (12) Smolyanitsky, A.; Tewary, V. K. Atomistic Simulation of a Graphene-Nanoribbon−Metal Interconnect. J. Phys.: Condens. Matter 2011, 23 (35), 355006. (13) Krasheninnikov, A. V.; Lehtinen, P. O.; Foster, A. S.; Pyykkö, P.; Nieminen, R. M. Embedding Transition-Metal Atoms in Graphene: Structure, Bonding, and Magnetism. Phys. Rev. Lett. 2009, 102 (12), 126807. (14) Maassen, J.; Ji, W.; Guo, H. Graphene Spintronics: The Role of Ferromagnetic Electrodes. Nano Lett. 2010, 11 (1), 151−155. (15) Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; Corso, A. D.; de Gironcoli, S.; Fabris, S.; Fratesi, G.; Gebauer, R.; Gerstmann, U.; Gougoussis, C.; Kokalj, A.; Lazzeri, M.; Martin-Samos, L.; Marzari, N.; Mauri, F.; Mazzarello, R.; Paolini, S.; Pasquarello, A.; Paulatto, L.; Sbraccia, C.; Scandolo, S.; Sclauzero, G.; Seitsonen, A. P.; Smogunov, A.; Umari, P.; Wentzcovitch, R. M. QUANTUM ESPRESSO: A Modular and Open-Source Software Project for Quantum Simulations of Materials. J. Phys.: Condens. Matter 2009, 21 (39), 395502. (16) (a) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865− 3868. (b) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865;(c) Phys. Rev. Lett. 1997, 78 (7), 1396−1396. (17) (a) Vanderbilt, D. Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism. Phys. Rev. B 1990, 41 (11), 7892− 7895. (b) Dal Corso, A. Density-Functional Perturbation Theory with Ultrasoft Pseudopotentials. Phys. Rev. B 2001, 64 (23), 235118. (18) Perdew, J. P.; Ruzsinszky, A.; Tao, J.; Staroverov, V. N.; Scuseria, G. E.; Csonka, G. I. Prescription for the Design and Selection of Density Functional Approximations: More Constraint Satisfaction with Fewer Fits. J. Chem. Phys. 2005, 123 (6), 062201. (19) Shanno, D. F. An Example of Numerical Nonconvergence of a Variable-Metric Method. J. Optim. Theory Appl. 1985, 46 (1), 87−94. (20) Fawcett, E. Spin-Density-Wave Antiferromagnetism in Chromium. Rev. Mod. Phys. 1988, 60 (1), 209−283. (21) Banhart, F.; Kotakoski, J.; Krasheninnikov, A. V. Structural Defects in Graphene. ACS Nano 2010, 5 (1), 26−41. (22) Oostinga, J. B.; Heersche, H. B.; Liu, X.; Morpurgo, A. F.; Vandersypen, L. M. K. Gate-Induced Insulating State in Bilayer Graphene Devices. Nat. Mater. 2008, 7 (2), 151−157. (23) Seyferth, D. Bis(benzene)chromium. 1. Franz Hein at the University of Leipzig and Harold Zeiss and Minoru Tsutsui at Yale. Organometallics 2002, 21 (8), 1520−1530. (24) (a) Henkelman, G.; Jonsson, H. Improved Tangent Estimate in the Nudged Elastic Band Method for Finding Minimum Energy Paths and Saddle Points. J. Chem. Phys. 2000, 113 (22), 9978−9985. (b) Sheppard, D.; Terrell, R.; Henkelman, G. Optimization Methods for Finding Minimum Energy Paths. J. Chem. Phys. 2008, 128 (13), 134106.

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−y2). As a result, higher ferromagnetism is observed in 1-16 GMG, the nanostructure with the stronger Cr−graphene coordination bond. Therefore, we conclude that there is a strong relationship between structural stability (interpreted in terms of binding energies), partially filled states, and total (and absolute) magnetic moments in the two stable nanostructures (1-12 and 1-16 GMG).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS 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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REFERENCES

(1) Geim, A. K.; Novoselov, K. S. The Rise of Graphene. Nat. Mater. 2007, 6 (3), 183−191. (2) Ghaemi, P.; Wilczek, F. Near-Zero Modes in Superconducting Graphene. Phys. Scr. 2012, 2012 (T146), 014019. (3) (a) Sargolzaei, M.; Gudarzi, F. Magnetic Properties of Single 3d Transition Metals Adsorbed on Graphene and Benzene: A Density Functional Theory Study. J. Appl. Phys. 2011, 110 (6), 064303. (b) Jishi, R. A.; Guzman, D. M.; Alyahyaei, H. M. Theoretical Investigation of Two-Dimensional Superconductivity in Intercalated Graphene Layers. Adv. Stud. Theor. Phys. 2011, 5 (13-16), 703−716. (c) Nakada, K.; Ishii, A. Migration of Adatom Adsorption on Graphene Using DFT Calculation. Solid State Commun. 2011, 151 (1), 13−16. (d) Avdoshenko, S. M.; Ioffe, I. N.; Cuniberti, G.; Dunsch, L.; Popov, A. A. Organometallic Complexes of Graphene: Toward Atomic Spintronics Using a Graphene Web. ACS Nano 2011, 5 (12), 9939− 9949. (e) Giovannetti, G.; Khomyakov, P. A.; Brocks, G.; Karpan, V. M.; van den Brink, J.; Kelly, P. J. Doping Graphene with Metal Contacts. Phys. Rev. Lett. 2008, 101 (2), 026803. (4) Weser, M.; Rehder, Y.; Horn, K.; Sicot, M.; Fonin, M.; Preobrajenski, A. B.; Voloshina, E. N.; Goering, E.; Dedkov, Y. S. Induced Magnetism of Carbon Atoms at the Graphene/Ni(111) Interface. Appl. Phys. Lett. 2010, 96 (1), 012504. (5) Muszynski, R.; Seger, B.; Kamat, P. V. Decorating Graphene Sheets with Gold Nanoparticles. J. Phys. Chem. C 2008, 112 (14), 5263−5266. (6) Hong, W.; Bai, H.; Xu, Y.; Yao, Z.; Gu, Z.; Shi, G. Preparation of Gold Nanoparticle/Graphene Composites with Controlled Weight Contents and Their Application in Biosensors. J. Phys. Chem. C 2010, 114 (4), 1822−1826. 3614


Graphene-Cr-Graphene Intercalation Nanostructures: Stability and

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