Transition Metal (Fe and Cr) Adsorptions on Buckled and Planar

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Transition Metal (Fe and Cr) Adsorptions on Buckled and Planar Silicene Monolayers: A Density Functional Theory Investigation Viet Quoc Bui, Tan-Tien Pham, Hoai-Vu Si Nguyen, and Hung Minh Le J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp407601d • Publication Date (Web): 10 Oct 2013 Downloaded from http://pubs.acs.org on October 11, 2013

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The Journal of Physical Chemistry

Transition Metal (Fe and Cr) Adsorptions on Buckled and Planar Silicene Monolayers: A Density Functional Theory Investigation Viet Q. Bui, Tan-Tien Pham, Hoai-Vu S. Nguyen, Hung M. Le* Faculty of Materials Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam AUTHOR EMAIL ADDRESS [email protected]

RECEIVED DATE

TITLE RUNNING HEAD Transition Metal (Fe and Cr) Adsorptions on Buckled and Planar Silicene Monolayers

CORRESPONDING AUTHOR FOOTNOTE Corresponding

author:

correspondence

should

be

addressed

[email protected].

1 ACS Paragon Plus Environment

to

Hung

M.

Le

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ABSTRACT The adsorption of metals on silicene monolayer may potentially offer advantageous applications in electronic and spintronic devices. In this study, by employing first-principles calculations, we investigate the attachment of two 3d transition metals (Fe and Cr) on buckled and planar silicene surfaces. Besides examining structural stability, we also explore interesting ferromagnetic as well as half-metallic features of the material. All Fe adsorption cases are found to be more stable (with the lowest binding energy being 3.39 eV) than Cr adsorption cases. When the metal adsorption rate is high, Fe tends to penetrate into both buckled and planar silicene layers. This insertion behavior allows the 3d shells of Fe to enhance bonding interactions with all 3px, 3py, and 3pz orbitals of Si, thus produce more stable structures. The adsorptions of Cr with high distribution ratio are found to be more stable than the low-Cr-distribution structures. It is observed that Cr does not penetrate into the silicene layer like Fe. Overall, ferromagnetism is dominant with five nanostructures, while two Cr adsorption cases on planar silicene preferentially behave as anti-ferromagnets, and one Fe adsorption case is non-magnetic. From our observation, there is an inversed interplay between structural stability and magnetic moments, i.e. FeSix nanostructures (more stable) tend to exhibit lower ferromagnetic moments. The half-metallic characteristic is found in four nanostructures, which can be potentially applied in spin-electronic devices. The gaps derived from spin-down states for those half-metallic nanostructures vary from 0.28 to 0.57 eV. Keywords: silicene, DFT, metal-silicene interaction, magnetism, half-metallic, metal adsorption.


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I. INTRODUCTION Advanced two-dimensional (2D) materials have highly attracted attention of the research community for years. Silicene,1 one of such interesting materials, is an infinite monolayer of silicon, whose structure is very similar to that of graphene.2 Purely consisting of silicon atoms, silicene can be integrated into electronic components, and is expected to have a great deal of potential applications in electronic transporting devices. In the most stable form, each silicon atom in silicene connects to three surrounding others by sp2-sp3-hybridized bonds, which consequently results in a “low-buckled” honeycomb structure.1,

3-5

The electronic structure of

silicene has been proved to establish a zero band gap when the bonding (π) and anti-bonding orbitals (π*) are shown to contact at the Dirac point, which consequently results in very high electron mobility.1 Besides the low-buckled structure, first-principles calculations also suggests the existence of planar derivative of silicene, whose structural configuration is even more similar to the conformation of graphene.6,

7

In this study, we investigate the bonding interactions

between two different silicene conformations (both low-buckled (B, more stable) and planar (PL, less stable) forms) and two transition metal atoms (Cr and Fe). There have been successful efforts in synthesizing silicene on metal and semiconductor surface for electronic applications. Lalmi et al.8 showed an experimental evidence in which silicene had epitaxial development on Ag(111) by condensing a silicon flux on the surface in vacuum condition. Nevertheless, those results highly relied on scanning tunneling microscopy (STM) observations, which approximately resulted in a Si-Si distance of 1.9 Å. This bond distance was, however, much smaller than the theoretically-predicted value varying in the range of 2.22 to 2.24 Å.1, 9, 10 By employing tunneling microscopy and angular-resolved photoemission spectroscopy in conjunction with first-principles simulations, Vogt et al.11 provided an 3 ACS Paragon Plus Environment


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experimental evidence of epitaxial silicene sheets on Ag(111). The distance between Si-Si was then determined as 2.22 Å in such a study, which established consistency with the previous theoretical results.1 In term of metal contact investigations, Feng et al.12 also presented an experimental investigation showing a procedure for synthesizing silicene on Ag(111). Since the early initialization of silicene investigations, computational efforts dedicating to study metal-attached silicene have attained remarkable achievements thanks to the rigorous development of Density Functional Theory (DFT)13, 14 and noticeable efforts in improvement of computational packages for condensed matter calculations. There have been several DFT-based investigations conducted to study silicene-metal interactions, especially their coordination chemistry and physical properties. In a theoretical work conducted by Sahin and Peeters,15 the attachments of alkali, alkaline-earth, and 3d transition metal atoms were investigated using DFT methods, and several possible absorption positions (hexagonal, bridge, valley, and top sites, as shown in Fig. 1) of a metal atom on silicene were suggested. It was reported by Dzade et al.16 that many transition metals (such as Ti, Nb, Ta, Cr, Mo, and W) tended to preferably locate on the H site of silicene when they occupied all honeycomb units on the silicene monolayer (with empirical formulas of MSi2). They witnessed that the electronic and magnetic properties of silicene changed significantly due to metal adsorptions. Particularly, CrSi2 became a twodimensional magnet and exhibited a strong piezomagnetic property with a magnetic moment in the range of 3.08 and 3.33 µB. When inspecting the electronic and magnetic properties as well as interactions of silicene with H and Br, Zheng and Zhang17 reported that the investigated structures displayed either ferromagnetic semiconducting or half-metallic behaviors. In this study, we concentrate on two 3d transition metals, Cr and Fe, which are wellknown for their interesting magnetic behaviors. Particularly, Fe is known as a ferromagnet, while 4 ACS Paragon Plus Environment

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Cr exhibits spin-density-wave antiferromagnetism.18 In addition, such transition metals are believed to establish stable coordination bonds with two-dimensional structures, such as graphene.19, 20 Being motivated by the recent experimental results of silicene,8, 11, 12, 21-23 in this study, we attempt to conduct a theoretical investigation of structural stability, electronic structure, and magnetic property of two-dimensional metal-silicene nanostructures (MSix, M = Fe, Cr) using a DFT-based approach. II. METAL-SILICENE ADSORPTION STRUCTURES (MSix) The distribution rates of Cr/Fe on silicene and the silicene conformation itself (B or PL) have a significant impact on the stability of the investigated structures, which can be evaluated by estimating strength of coordination bonds (via binding energy). In this investigation, we study different metal absorption ratios on two silicene conformations (B/PL), which include MSi2(B), MSi2(PL), MSi6(B), and MSi6(PL) as clearly shown in Fig. 2. Indeed, the H site is most favored when M adsorbs on either buckled or planar silicene,15 which accordingly produces a twodimensional lattice that has a 2D hexagonal unit cell. We first consider metal adsorptions with high M concentration (MSi2(B) and MSi2(PL)). In those structures, M atoms occupy all available honeycomb units of the surface. As a result, there are two Si atoms and one M atom in a two-dimensional unit cell. In Fig. 2(a) and 2(c) respectively representing FeSi2(B) and CrSi2(B), M atoms absorb all honeycomb rings in the low-buckled silicene sheet. The nanostructures of FeSi2(PL) and CrSi2(PL) (Fig. 2(b) and 2(d), respectively) has one M atom located at the center of every planar honeycomb silicon ring. In the case of MSi6(PL) and MSi6(B), there are six Si atoms and one M atom in a primitive hexagonal unit cell. The metal atom in these structures tends to occupy a center 5 ACS Paragon Plus Environment


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honeycomb unit and leave six adjacent (surrounding) units empty (unoccupied). In Fig. 2(e) and 2(g), Fe and Cr atoms are respectively located on a low-buckled silicene sheet, while in Fig. 2(f) and Fig. 2(h), Fe and Cr are located on planar silicene (denoted as FeSi6(PL) and CrSi6(PL), respectively). There are two types of bonding in those structures: coordination bonds between MSi (under the hybridization effect of 3d orbitals of M and 3p orbitals of Si), and Si-Si interactions. In the hexagonal unit cell of each investigated nanostructure (with lattice parameter a listed in Table 1), the two-dimensional characteristic orientation is established in the x and y directions. The vacuum assumption is constituted in the z direction by employing large lattice parameter c (30 Bohr or 15.87 Å) in all cases. III. COMPUTATIONAL DETAIL In this study, we employ the Perdew-Burke-Ernzerhof (PBE)24,

25

exchange-correlation

functional within generalized gradient approximations and the ultrasoft pseudopotentials26, 27 for Cr, Fe, and Si to perform first-principles calculations. All calculations are executed using the Quantum ESPRESSO package.28 In addition, we utilize spin polarization implementation to inspect the electronic and magnetic properties. The nanostructures are optimized by relaxing atomic positions and unit-cell vectors simultaneously using the Broyden-Fletcher-Goldfarb-Shanno (BFGS)29 algorithm with the energy and gradient convergence criteria being 10-5 eV and 10-4 eV/Bohr, respectively. The kpoint mesh for all hexagonal lattices (with lattice parameter a given in Table I) is selected as (12 × 12 × 1) in all calculations to ensure consistency in total energy calculations, and the kinetic

energy cut-off of 45 Rydberg (612 eV) is chosen for plane-wave expansions. 6 ACS Paragon Plus Environment

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For each optimized structure, we employ the following formula to analyze the binding energy of M atoms attached on silicene: Ebinding = Esilicene + EM – Estructure

(1)

where Esilicene, EM, and Estructure are the total energies of silicene, M layer, and the investigated Msilicene adsorption nanostructure given by DFT calculations, respectively. IV. RESULTS AND DISCUSSION 1. FeSi2(B) and FeSi2(PL) nanostructures In the FeSi2 (as well as CrSi2) structures, the metal atoms occupy all available honeycomb units on buckled/planar silicene. Particularly, in FeSi2(B), Fe atoms have a tendency to penetrate into the silicene layer, and interact with both upper and lower Si atoms (as shown in Fig. 2(a)). Fe, therefore, forms bonding interactions with the surrounding Si atoms and heavily alters the buckled silicene structure by stretching the Si-Si interaction. The Si-Si and Fe-Si distances in FeSi2(B) are 2.60 and 2.27 Å, respectively. Recall that in an isolated buckled silicene monolayer, the Si-Si bond is only 2.29 Å, which is much shorter than the Si-Si bond in FeSi2(B). The Fe-Si bond is, however, almost equal to the Si-Si bond in isolated buckled silicene according to our DFT calculations. In addition, the buckled gap between the upper and lower Si layers is much distorted (estimated as 1.45 Å), while the original buckled gap in silicene is only 0.45 Å. Hence, we believe that such Fe penetration with a high distribution ratio would cause a significant change in structural configuration to the buckled silicene structure. Equation (1) is then employed to derive the binding energy, and FeSi2(B) is found to be highly stable with a binding energy of 3.67 eV/cell.



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Subsequently, spin polarizations are inspected to predict the magnetic property of FeSi2(B). By observing the total density of state (DOS) and the corresponding partial density of state (PDOS) of Fe 3d and Si 3p subshells (as illustrated in Fig. 3(a)), we are able to address a non-magnetic behavior (polarization is not found in the DOS). In addition, this nanostructure is believed to be metallic because of electronic state distribution around the Fermi level (positioned at 0 in the plot). We also conceive that the 3d shells of Fe and 3p shells of Si highly overlap, which consequently results in a strong bonding interaction. Especially, it can be seen that the electron distribution in 3d z 2 gives a strong peak near the Fermi level, which indicates a high electron accepting behavior of Fe. The 3pz subshell of Si, unsurprisingly, overlaps much with 3d orbitals of Fe. As mentioned earlier, the penetration of Fe into the silicene layer also allows the metal 3d orbitals to have more interactions with 3px and 3py of Si, and consequently results in high binding stability. Furthermore, such geometric configuration in general allows spin-up and spin-down states to form exactly similar interactions and therefore align identically (no spin polarization). This is a unique behavior when Fe is attached on the surface of buckled silicene, and we do not observe such similarities in other cases. In the FeSi2(PL) structure, Fe is located at the centers of all honeycomb rings in the infinite planar (PL) silicene sheet. The occupancy of such metal atoms results in an interwoven network with an infinite planar structure as illustrated in Fig. 2(b). At equilibrium, we have found in the relaxed FeSi2(PL) structure that Fe atoms again penetrate into the surface of planar silicene; hence, the resulted structure is perfectly planar and can be considered as the most compressed structure in this investigation. We observe that the Si-Si and Fe-Si bond distances are identical (2.33 Å). The Si-Si bond in this case is slightly longer than the Si-Si bonds in an isolated planar silicene sheet (given by our DFT calculations as 2.25 Å). Consequently, the 8 ACS Paragon Plus Environment

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silicene network is slightly loosened under the effect of Fe penetration by 3.4%. For comparison purposes, we summarize bonding distances and binding energies of FeSi2(B) and FeSi2(PL) (as well as the other investigated nanostructures) in Table 1. To evaluate structural stability, we subsequently calculate the binding energy of FeSi2(PL) using equation (1). Indeed, its binding energy is 3.76 eV, which is the highest among eight investigated nanostructures. In spin-polarized DOS analysis, it can be seen that there is a difference in distributions of the spin-up and spin-down states. Unlike the previous structure (FeSi2(B)), we observe ferromagnetism and electron conductivity in FeSi2(PL). In the bonding aspect, when bonding orbitals (3d subshells of Fe and 3p subshells of Si) are analyzed, the overlapping behavior is similar to the previous case study of FeSi2(B). More specifically, the 3d orbitals of Fe strongly hybridize with not only Si 3pz but 3px and 3py orbitals as well. However, we do not observe equal distributions in spin-up and spin-down states, which adequately produces a small ferromagnetic moment. There are two types of magnetic terms reported in this study, i.e. the total (MT) and absolute magnetizations (MA) which are derived in the following equations:

M T = ∫ (nup − ndown )d 3r

(2)

M A = ∫ nup − ndown d 3r

(3)

The total magnetization of FeSi2(PL) indicates ferromagnetism with a magnitude of 1.20 µB/cell, while the absolute magnetization is 1.48 µB/cell. For convenience, all total and absolute magnetizations of the investigated nanostructure are summarized and reported in Table 2. A calculation of a 2 × 1 supercell is performed to validate ferromagnetism of this structure. In fact,



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the ferromagnetic configuration is proved to be more energetically stable, which provide a valid evidence to conclude ferromagnetism. All 3d orbitals tend to align ferromagnetically, especially Fe 3d z 2 , which produces a ferromagnetic moment of 0.77 µB. Moreover, 3dzx and 3dzy exhibit similar magnetic contributions of 0.17 µB, while 3d x 2 − y 2 and 3dxy are observed to contribute small magnetic moments of 0.08 µB. In the other hand, all Si 3p orbitals give negative magnetic terms (anti-ferromagnetic); especially, the largest anti-ferromagnetic contribution comes from Si 3pz (-0.09 µB). The orbital contributions to magnetism can be consulted in Table 3. We perform additional calculations for double adsorption cases in order to validate the ferromagnetic properties of FeSi2(B) and FeSi2(PL). In such calculations, Fe atoms are considered to adsorb on both sides of a silicene monolayer. In the case of buckled silicene, we observe that the condensed Fe adsorption on both sides does not result in a stable structure. In the later case, we are able to obtain an equilibrium structure where Fe atoms adsorb on both sides of planar silicene (with the empirical formula of Fe2Si2(PL)). This structure is found to exhibit a total ferromagnetic moment of 4.50 µB/cell, which is almost three times the ferromagnetic moment given by FeSi2(PL) (1.20 µB/cell). 2. CrSi2(B) and CrSi2(PL) nanostructures The interacting configurations of CrSi2 structures (in both buckled and planar forms) are very different from that of FeSi2. In fact, it can be seen from Fig. 2(c) and 2(d) that in both cases, the Cr atoms do not penetrate into the silicene monolayer like the previous cases. Therefore, we consider CrSi2 as real adsorption cases. This observation is contradicting to a previous study, in


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which Cr atoms were shown to penetrate into the silicene layer.16 Unfortunately, no experimental evidences are available to validate the contradicting theoretical results. In CrSi2(B), Cr atoms adsorb on the H site of a buckled silicene honeycomb ring. The SiSi distance is calculated as 2.38 Å, while two Cr-Si bonds are 2.52 and 3.11 Å. The condensed adsorption of Cr on a buckled silicene surface significantly pushes the lower Si atoms away; consequently, the buckled gap between the upper and lower Si layers increases to 0.95 Å. Compared to that in the FeSi2(B) case, this buckled gap is smaller but it should be noticed in this case that Cr does not penetrate into silicene. The stability of this structure is, however, relatively low (1.77 eV) compared to FeSi2 nanostructures owning to its lower binding energy. Ferromagnetism is found to be more energetically favored than anti-ferromagnetism in the case of CrSi2(B) when we perform total energy calculations for a (2 × 1) supercell. The total ferromagnetic moment is estimated as 4.00 µB/cell from spin-polarized calculations. In the total DOS of CrSi2(B) and PDOS of Cr 3d and Si 3p orbitals (illustrated in Fig. 4(a)), there is a large distinction in distribution of spin-up and spin-down states of Cr 3d and Si 3p. Besides, we also observe a very important characteristic when the schematic spin-up state indicates conducting, while the spin-down state ends up as a semi-conducting material with a band gap estimated as 0.28 eV. In terminology, the nanostructure of this type is often referred to as “half-metallic” material, which may offer great potential applications in spin-electronic devices. The spin polarization effect can be employed to evaluate the conducting behavior, which is empirically defined as following:30

P=

ρ ↑ (EF ) − ρ ↓ (EF ) ρ ↑ (EF ) + ρ ↓ (EF )

(4)



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In this equation, ρ ↑ ( E F ) and ρ ↓ ( E F ) represent the spin-up and spin-down densities of states at the Fermi level, respectively. For a half-metallic material (CrSi2(B) in this case), we expect that the calculated value of P to approach unity. Otherwise, a conducting material would have a lower-than-1 P value. As expected, in the FeSi2(B) and FeSi2(PL) cases, the P values are less than 1. For convenience, such spin polarization values for all investigated nanostructures are provided in Table 3. The PDOS of Cr 3d z 2 is highly polarized as we clearly see a dominant peak of the spinup states in the valence band (prior to the Fermi level positioned at 0 in the plot). 3dzx and 3dzy also contribute strong ferromagnetic moments while 3d x 2 − y 2 and 3dxy are observed to contribute much smaller ferromagnetic terms. In the contrary, the 3pz (as well as 3px and 3py) subshells of Si provide insignificant anti-ferromagnetic moments. Overall, this nanostructure is reported to be ferromagnetic with estimated total and absolute magnetizations being 4.00 and 4.60 µB/cell, respectively. Similarly to CrSi2(B), the relaxed structure of CrSi2(PL) (Fig. 2(d)) demonstrates a metal adsorption case. The Si-Si bond (2.31 Å) is more slightly compressed than that in CrSi2(B), while the Cr-Si distance is estimated as 2.56 Å. The distance between Cr and planar silicene layer is observed as 1.11 Å. When comparing the interlayer distance (between metal and silicene layers), CrSi2(PL) is most compressed in the z direction (excluding the penetration cases, i.e. FeSi2(B) and FeSi2(PL)). Compared to CrSi2(B), the nanostructure of CrSi2(PL) is more stable with a binding energy of 1.94 eV. When decorating highly concentrated Cr on the buckled/planar silicene surface, we conceive less stable nanostructures compared to FeSi2. Deliberately, we believe that this fact is 12 ACS Paragon Plus Environment

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well associated with the bonding behavior. While we suggest the involvement of Si 3px and 3py in forming coordination bonds in FeSi2, a similar behavior is less likely to be observed in CrSi2 as we conceive less overlapping in the PDOS distribution (Fig. 4). It should be noticed that the ability to accept more electrons (electronegativity) of Fe is higher than that of Cr.31 From DOS plots, CrSi2(PL) is also found to behave as a metallic material, which exhibits electron conductivity at the Fermi level. Unlike CrSi2(B), total energy calculations of a (2 × 1) supercell indicate that CrSi2(PL) favors anti-ferromagnetism with a magnitude of 4.15 µB/cell (absolute magnetization). According to the PDOS distribution in Fig. 4(b), the electronic states of two Cr atoms are opposing to one another. All 3d subshells of each Cr atom are polarized indistinctively (shown in Table 3), which all contribute to anti-ferromagnetic terms. Overall, we observe that CrSi2(B) and CrSi2(PL) are close in bonding stability, but have different magnetic behaviors (ferromagnetic versus anti-ferromagnetic). Even though planar silicene is less stable than low-buckled silicene, the high-concentrated Cr attachment on the planar structure helps to stabilize planar silicene and results in a higher binding energy. We also consider introducing Cr atoms to both sides of silicene to produce Cr2Si2(B) and Cr2Si2(PL). In both cases, the resulted structures favor anti-ferromagnetism. As illustrated in Fig. 5, the PDOS distributions of two Cr atoms in these two structures are opposing to each other and thereby produce anti-ferromagnetism. The absolute magnetizations of Cr2Si2(B) and Cr2Si2(PL) are reported as 7.00 and 7.39 µB/cell, respectively. 3. FeSi6(B) and FeSi6(PL) nanostructures In FeSi6(B) (Fig. 2(e)), we no longer observe a penetration behavior in the optimized structure like in the FeSi2 case. In fact, Fe actually adsorbs on the buckled silicene surface and 13 ACS Paragon Plus Environment


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coordinatively bonds to six Si atoms. As mentioned earlier, in FeSi6(B) (and other MSi6 nanostructures), the metal atom tends to occupy one center honeycomb unit while leaving six surrounding units empty (unoccupied). In this buckled structure, there are two different Fe-Si bonds with the distances reported to be 2.38 and 2.64 Å. The original Si-Si bond in buckled silicene is 2.28 Å; however, under the effect of coordination bonds with Fe, the Si-Si bond distance is 2.29 Å, which indicate a very slight stretching. Unlike the previous FeSi2(PL) case, the buckled gap between the upper and lower Si layers is only 0.66 Å. In FeSi2(PL), due to the lack of electron donation from Si (because of high distribution rate of Fe), the metal atom (Fe) has a tendency to approach closer and penetrate into the silicene layer to get more electron density from Si 3p orbitals. As a result, both upper and lower Si atoms are stretched due to the insertion of Fe. The metal distribution rate in MSi6 is, however, much lower than in the case of MSi2, and we believe that the Si 3pz orbitals sufficiently provide electron donation toward the 3d shell in metal atoms. Therefore, in MSi6, the metal atom is less likely to form bonding hybridization with 3px and 3py orbitals. Using equation (1), we again evaluate the stability based on binding energy analysis. With a binding energy of 3.49 eV, the nanostructure of interest is believed to be highly stable. The FeSi6(PL) nanostructure (Fig. 2(f)) has been optimized using a similar calculation method, and the Fe atoms do not penetrate into planar silicene as in the case of FeSi2(PL). Instead, Fe forms a separated layer, and the interlayer distance between Fe and silicene is 1.10 Å. The Fe-Si distance is found to be 2.49 Å, while the nearest-neighbor Si-Si distance is 2.24 Å. According to equation (1), the FeSi6(PL) nanostructure is proved to be stable with a reported binding energy of 3.39 eV. Compared to the previous structure (FeSi6(PL)), we obtain a slightly


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lower binding energy. Considerably, this energy is relatively high when it is compared to the binding energies of Cr adsorption cases. Interestingly, the overlapping of Fe 3d and Si 3p in FeSi6(B) and FeSi6(PL) are very similar as illustrated in Fig. 6. In both cases, we conceive a good overlap between 3dzx (3dzy) of Fe and 3pz of Si. By examining PDOS distributions at the Fermi level, FeSi6(B) and FeSi6(PL) are both found to be half-metallic because there are gaps in the spin-up states (0.51 and 0.49 eV, respectively). The spin polarization effects are then calculated using equation (4), and we obtain P to be almost unity as expected for half-metallic materials. The total magnetizations of FeSi6(B) and FeSi6(PL) are calculated as 2.10 and 2.05 µB/cell, respectively. There are, however, some particular distinctions in the 3d orbital contributions to total magnetization. More specifically, the 3d z 2 contribution (0.78 µB) is dominant in FeSi6(PL), while in FeSi6(B), the polarizations of 3dzx and 3dzy give the highest contributions. The 3d x 2 − y 2 and 3dxy orbitals in both cases contribute minor ferromagnetic moments to the total. Again, our theoretical evidences show that buckled/planar silicene plays the role as an anti-ferromagnet (with a negative magnetic moment causing opposing effects to the ferromagnetic moment caused by Fe). At this point, it is seen that all FeSix nanostructures are highly stable and exhibit small or intermediate ferromagnetic moments. Especially, in the FeSi2(PL) case, we even observe a nonmagnetic case. Because of having higher electronegativity, Fe tends to approach closer to Si (considering Fe-Si bonds and metal-silicene interlayer distances) in order to receive more electron donation not only from 3pz, but also from 3px and 3py orbitals of Si.



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FeSi6 nanostructures exhibit higher magnetic moments than FeSi2 even though the concentration of Fe in FeSi6 is lower. Hence, there is an inversed interplay between bonding stability (bond strength) and magnetism. In FeSi6, we observe smaller 3d-3p orbital overlap (because Si 3px and 3py do not seem to involve in the hybridization) but higher spin polarization (causing higher ferromagnetism). When Fe atoms are distributed on both sides of silicene (Fe2Si6(B) and Fe2Si6(PL)), we have found that Fe atoms can stably bind to both sides of a silicene monolayer. The equilibrium Fe2Si6(B) and Fe2Si6(PL) lattices exhibit total ferromagnetic moments of 4.26 and 4.27 µB/cell, respectively, which strongly imply ferromagnetism of Fe in the nanostructures. 4. CrSi6(B) and CrSi6(PL) nanostructures The CrSi6(B) and CrSi6(PL) nanostructures are considered less stable since their binding energies are relatively lower than the previous FeSix cases. Both nanostructures are reported to have somewhat similar binding energies (above 2.6 eV). Compared to CrSi2, both CrSi6 nanostructures are more stable. Observationally, two Cr-Si bonds in CrSi6(B) are 2.50 and 2.74 Å, and the Cr-Si bond in CrSi6(PL) is 2.55 and 2.82. The Si-Si bond in CrSi6(B) is 2.32 Å, longer than the Si-Si bond in CrSi6(PL) (2.27-2.29 Å). We also find in CrSi6(B) a short buckled gap between Si atoms (0.62 Å). As shown in Table I, the buckled gap in FeSi6(B) (0.66 Å) is higher than in CrSi6(B). We suggest there is a clear correlation between binding strength and buckled gap distance. Comparing CrSi6(B) to FeSi6(B), the compound with Fe adsorption is much more stable (with 29% difference between two binding energies). Similarly, when comparing CrSi2(B) to FeSi2(B), we observe that the Fe compound has higher binding stability while its buckled gap


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is shorter. We are convinced at this point that the strong binding behavior of metal-Si would then weaken the Si-Si bond and thereby extend the silicene buckled gap. Interestingly, the adsorption of Cr on planar silicene with low concentration pushes two Si atoms out of the plane (Fig. 2(h)), thus produces another buckled structure (for consistency in naming, this structure is still referred to as CrSi6(PL)). Two different Cr-Si distances are reported as 2.55 and 2.82 Å. Because of the distortion of the planar structure, there is a silicene buckled gap in this case, which is 0.21 Å. By performing DFT calculations for (2 × 1) supercells and comparing total energies, CrSi6(B) is found to favor ferromagnetic. The ferromagnetic spin polarizations of 3d z 2 in CrSi6(B) is 0.88 µB, which is equal to 3dzx and 3dzy polarizations, while 3d x 2 − y 2 and 3dxy magnetic contributions, as shown in Table 3, are somewhat indistinctive (0.67 µB). The PDOS distributions of Cr 3d and Si 3p subshells in CrSi6(B) are illustrated in Fig. 7(a). Buckled silicene has insignificant effects on the total magnetic moments by contributing small negative amounts. Overall, the total magnetization of CrSi6(B) is found to be 4.00 µB/cell. Again, it is interestingly observed that the CrSi6(B) nanostructure has a half-metallic characteristic when we conceive discontinuity in the spin-up electron density (with a gap of 0.57 eV estimated from the PDOS plot). CrSi6(PL), in the other hand, tends to be an anti-ferromagnet (with 0.03 eV lower in total energy than the ferromagnetic configuration). As shown in Fig. 7(b), the electronic states of two Cr atoms are found to be opposing like the earlier case (CrSi2(PL)). The 3d subshell contributions of each Cr atom to anti-ferromagnetism are found to be large, and the antiferromagnetic contribution from six Si atoms (especially from the 3pz orbitals) in the unit cell is



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significant. Overall, a high absolute magnetization representing anti-ferromagnetism is estimated as 4.57 µB/cell. Low concentrated Cr adsorptions on both sides of buckled and planar silicene are then considered. Two equilibrium structures, namely Cr2Si6(B) and Cr2Si6(PL), are optimized using DFT calculations. A similar opposing effect in DOS can be observed between Cr atoms like the previous Cr2Si2 cases, which consequently results in anti-ferromagnetic behaviors. As a result, the total magnetic moments in both cases are found to vanish, while large absolute magnetizations of Cr2Si6(B) and Cr2Si6(PL) are estimated as 5.56 and 6.34 µB/cell, respectively. V. SUMMARY By employing DFT calculations, we have carefully examined and characterized the adsorption behaviors of two 3d transition metals (Fe and Cr) on both buckled and planar silicene surfaces. The distribution rate of metal atoms on silicene is taken into account when we consider MSi2 and MSi6 lattice models. Overall, eight metal-silicene nanostructures with two-dimensional characteristic are investigated in this study. The coordination bonds between silicene and transition-metal atoms are constituted from the hybridization effect of metal 3d and Si 3pz orbitals with/without possible involvements of Si 3px and 3py subshells. Fe has a tendency to penetrate into both buckled and planar silicene monolayers when the iron distribution rate is high (FeSi2). Such an insertion allows Fe to have more interactions with the 3px and 3py orbitals. Therefore, in the FeSi2(B) and FeSi2(PL) nanostructures, we believe that Si 3px and 3py orbitals jointly involve in bonding hybridization and contribute to strengthen the coordination chemistry between Fe and silicene. In general, all


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FeSi2 and FeSi6 nanostructures are found to be more stable than CrSi2 and CrSi6. Particularly, the lowest binding energy among four FeSix nanostructures is found to be 3.39 eV. An inversed interplay between binding energies and magnetic moments is suggested, i.e. the stronger binding energy is observed, the ferromagnetic (or anti-ferromagnetic) moment tends to be lower (excluding two anti-ferromagnetic case). In the most stable nanostructure (FeSi2(B)), due to metal penetration into buckled silicene, the spin-up and spin-down states are observed to hybridize in a similar manner, which causes a non-polarized electronic structure. Excluding FeSi2(B), the remaining seven nanostructures of interest are found to be either ferromagnetic or anti-ferromagnetic. In FeSi2(PL), FeSi6(B), and FeSi6(PL), we observe low total magnetic moments in the range of 1.20 to 2.10 µB/cell. The total ferromagnetic moments in the CrSi2(B) and CrSi6(B) cases are found to be high, while two Cr adsorption cases on planar silicene exhibit anti-ferromagnetism. Further validations to magnetism are made when we consider metal adsorptions on both sides of buckled/planar silicene. In the Fe adsorption cases, we conceive rigorous increases in ferromagnetism, while in the Cr adsorption cases, the spin-polarized electronic states of Cr atoms align adversely, which strongly indicates anti-ferromagnetism behaviors. Another important characteristic is observed in this study, which is the half-metallic property of four ferromagnetic nanostructures (FeSi6(B), FeSi6(PL), CrSi2(B), CrSi6(B)). When deriving the band gaps from DOS, we conceive that they vary in the range of 0.28 to 0.57 eV with the polarization effects (P) being almost unity. Such half-metallic characteristic and interesting ferromagnetism may potentially offer good applications in fine-tuning spin-electronic transistors and devices.



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VI. ACKNOWLEDGEMENTS The authors thank the Faculty of Materials Science, University of Science, Vietnam National University in Ho Chi Minh City for their computing support in this project. We also thank Nam H. Vu for his helpful discussions during the initial stage of this research.


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Figure 1. Three possible metal adsorption sites on buckled/planar silicene: hexagonal (H), bridge (B), and top (T). When considering a buckled silicene sheet, there are actually two different T sites, which correspond to the upper and lower Si atoms in the buckled form.



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Figure 2. Top views and side views of Fe/Cr adsorptions on silicene. There are eight investigated nanostructures in this study: (a) FeSi2(B), (b) FeSi2(PL), (c) CrSi2(B), (d) CrSi2(PL), (e) FeSi6(B), (f) FeSi6(PL), (g) CrSi6(B), and (h) CrSi6(PL). The top views are provided to illustrate the distribution ratio of metal on silicene.


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Figure 3. (a) Total DOS and PDOS of the Fe 3d and Si 3p subshells in FeSi2(B), where spin polarization is not observed, (b) Total DOS and PDOS of the Fe 3d and Si 3p subshells in FeSi2(PL).



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Figure 4. (a) Total DOS and PDOS of the Cr 3d and Si 3p subshells in CrSi2(B), (b) PDOS of each Cr and all Si atoms CrSi2(PL). In CrSi2(B), we can derive a small band gap of 0.28 eV from the spin-down state. CrSi2(PL) is anti-ferromagnetic according to the opposing behavior of electronic states of two Cr atoms (in the supercell).


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Figure 5. Total DOS and PDOS of Cr and Si atoms when Cr atoms are attached on both sides of (a) buckled and (b) planar silicene. In both cases, Cr atoms occupy all honey comb unit of silicene (high distribution rate). The electronic states of two Cr atoms are opposing to each other, which implies anti-ferromagnetism.



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Figure 6. (a) Total DOS and PDOS of Fe 3d and Si 3p subshells in FeSi6(B), (b) Total DOS and PDOS of Fe 3d and Si 3p subshells in FeSi6(PL). Both nanostructures are shown to be halfmetallic (with band gaps in the spin-down states derived as 0.51 and 0.49 eV, respectively).


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Figure 7. (a) Total DOS and PDOS of the Cr 3d and Si 3p subshells in CrSi6(B), (b) PDOS of each Cr and Si atoms in a (2 × 1) supercell of CrSi6(PL). CrSi6(PL) can be seen as an antiferromagnet from this plot.



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Table 1. Lattice parameter a, M-Si, Si-Si bonds, M-silicene interlayer distances, and binding energies of the MSi2(B), MSi2(PL), MSi6(B), and MSi6(PL) nanostructures (with M = Fe, Cr) a (Å) FeSi2(B)

Bond distance (Å) Si-Si M-Si

M-silicene interlayer distance (Å)

Silicene buckled gap (Å)

Binding energy (eV/cell)

3.73

2.60

2.27

--

1.45

3.67

FeSi2(PL) 4.03 CrSi2(B) 3.74

2.33

0.00

--

3.76

--

0.95

1.77

CrSi2(PL) 4.01 FeSi6(B) 6.65

2.31

1.11

--

1.94

--

0.66

3.49

FeSi6(PL) 6.79

2.24

1.10

--

3.39

CrSi6(B)

6.71

2.32

--

0.62

2.61

CrSi6(PL) 6.79

2.27 2.29

2.33 2.52 3.11 2.56 2.38 2.64 2.49 2.50 2.74 2.55 2.82

1.23

0.26

2.64

2.38

2.29


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Table 2. Total magnetizations, absolute magnetizations, and estimated band gaps of the investigated nanostructures (*anti-ferromagnetic nanostructure)

FeSi2(B) FeSi2(PL) CrSi2(B) CrSi2(PL)* FeSi6(B) FeSi6(PL) CrSi6(B) CrSi6(PL)*

Total magnetization (µB/cell) 0.00 1.20 4.00 0.00 2.10 2.05 4.00 0.00

Absolute magnetization (µB/cell) 0.00 1.48 4.60 4.15 3.04 2.91 4.69 4.57

Electron conductivity

Estimated P

metallic metallic half-metallic metallic half-metallic half-metallic half-metallic metallic

0.00 0.56 1.00 0.00 1.00 1.00 1.00 0.00


Band gap (eV)

0.28 0.51 0.49 0.57


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Table 3. Main orbital contributions to ferromagnetic/anti-ferromagnetic moments in MSi2(B), MSi2(PL), MSi6(B), MSi6(PL) (M = Fe, Cr) Si

3pz FeSi2(B) FeSi2(PL) CrSi2(B) CrSi2(PL)* FeSi6(B) FeSi6(PL) CrSi6(B) CrSi6(PL)*

0.00 -0.09 -0.30 0.14 -0.31 -0.21 -0.32 0.32

3px (3py)

4s

0.00 -0.01 0.00 0.05 0.02 -0.03 0.06 0.09

0.00 0.04 0.10 0.12 0.05 0.04 0.08 0.09

4p 0.00 0.05 0.13 0.07 0.06 0.04 0.08 0.07

M (Fe, Cr) 3dzx 3d z 2 (3dzy) 0.00 0.77 0.90 0.89 0.54 0.78 0.88 0.87

*

Anti-ferromagnetic cases: absolute magnetic contributions are reported.


0.00 0.17 0.84 0.78 0.65 0.54 0.88 0.88

3d x 2 − y 2 (3dxy) 0.00 0.08 0.75 0.63 0.27 0.25 0.67 0.56 (0.72)

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SYNOPSIS TOC


Transition Metal (Fe and Cr) Adsorptions on Buckled and Planar

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