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The Novel Graphene-Like Co2VAl (111): Case Study on Magnetoelectronic and Optical Properties by First Principles Calculations Arash Boochani, Bromand Nowrozi, Jabbar Khodadadi, Shahram Solaymani, and Saeid Jalali-Asadabadi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b10572 • Publication Date (Web): 27 Jan 2017 Downloaded from http://pubs.acs.org on January 28, 2017

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The Journal of Physical Chemistry

The Novel Graphene-Like Co2VAl (111): Case Study on Magnetoelectronic and Optical Properties by First Principles Calculations Arash Boochani 1,*, Bromand Nowrozi 1, Jabbar Khodadadi 2, Shahram Solaymani 3, Saeid Jalali-Asadabadi 4 1

2

Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran. 3

4

*

Department of physics, Islamic Azad University, Kermanshah Branch, Kermanshah, Iran.

Department of physics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

Department of Physics, Faculty of Sciences, University of Isfahan (UI), Hezar Gerib Avenue, Isfahan 81746-73441, Iran.

Corresponding author: [email protected]

Abstract The electronic, magnetic and optical properties of Co2VAl(111) graphene-like (GL) mono-layer as well as the (101) and (011) terminations have been calculated based on the density functional theory (DFT) and FP-LAPW+lo method. The GL (111) Co2VAl has been grown in (111)crystallographic direction, leading to various and interesting physical properties than those of ther considered directions. The films grown in (101) and (011) directions have shown metallic behavior with low spin-polarization at the Fermi level, while the GL case has shown a perfect half-metallic behavior with an integer amount of magnetic moment (1.00 ) and 0.5 spin flip gap. Thus, it can be a good candidate for spintronic applications. Although all these thin films behave similarly at the UV region, the GL case appears to be different in the infrared (IR) and visible regions. The main plasmonic energies occur in the 12-13.8 eV energy range in the parallel (xx) and perpendicular (zz) directions. Our results show that the incident light cannot propagate in the visible region for all the considered monolayers. 1. Introduction The unusual electronic properties of the graphene, which is originated from its planar honeycomb structure, lead to charge carriers resembling massless Dirac fermions.1 In the typical Dirac cone graphenes, several electronic and spintronic behaviors2-5 such as ballistic charge transport6, high carrier mobility7 and quantum Hall effect 8 are observed. The honeycomb structures with complete hexagonal symmetry play an important role in the Dirac cones. Many 2D Dirac materials such as hexagonal carbon9, Silicone, Germanium10, Pmmn boron 11 and TiB2 12 are promising materials in high performance electronic and spintronic devices. For better electronic, optical and spintronic conditions, it is needed to search the new 2D materials. The GLs of the form MB2 or MB4 (M=Al, Mg, Ti, Mo; B=Boron) 13, 14 with high structural stability due to their ionic bonds are good candidates for superconductor applications. Furthermore, based 1 ACS Paragon Plus Environment


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on the theoretical and experimental efforts, many 2D honeycomb materials have been considered15-17, and it has been reported that these materials have different physical functions compared to their bulk shapes, including electronic, magnetic, thermal, optical and transport properties which could be controlled by thickness and the number of layers.18 Seeking for 2D materials with non-zero bandgap and massless charge carries has led to the discovery of 2D substances from Silicone and Germanium. But, it is necessary to find new classes by magnetic behavior and integer amount of magnetic moment to use in spintronic devices. So, we focus on the full-Heusler compounds that belong to half-metals (HMs). Based on the faced centered cubic crystals and magnetic properties of full-Heuslers, these materials are good candidates for 2D honeycomb materials by magnetic nature. One of the serious problems for theoretical prediction of new materials is their feasibility in nature. The cohesive energy has been frequently considered as a pivotal criterion for theoretically showing the feasibility of the new materials, as it can be used to evaluate the stability of the predicted materials. For instance, one can refer to the reports of computations carried on the FeB2 mono-layer19, carbon allotropes20 and GL Mg3N2. 21 Half-Metals (HMs) are a class of materials which exhibit metallic behavior for electrons of one spin orientation but semiconducting property for those of opposite spin orientation. They are generally divided into two main classes, i.e., binary22-25 and Heusler 26, 27 compounds. The Heusler compounds are in turn classified into two main groups as half-Heuslers and fullHeuslers.28, 29, 30 The second group contains the X2YZ compounds with (Clb or L21) crystalline structure where X and Y denote transition metals while Z is a sp element of the periodic table. Galanakis and de Groot are pioneers in predicting HM properties of the Husler compounds by the first-principles DFT calculations.26, 27 Recently, Co-based full-Heuslers have been of more interest owing to their high magnetic moment and Curie temperature as well as good metallic and semiconducting behavior at majority and minority spins, respectively.31-35 Among these, the thin films of multilayer Co-based full-Heusler alloys are potentially the most promising candidate for spintronic devices, but a fundamental issue is that HM behavior is destroyed or decreased at the film surface or interfaces.36 In this respect one would refer to the Galanaki’s efforts on the (001), (111) and Co2CrAl (001) and also the (001) & (111) films of the NiMnSb, Co2MnGe and Co2MnSi.37, 38 However, some studies on the Co2FeSi (001) and Co2VGa(111) films have revealed HM property on their surfaces.39 Co2VAl is one of the Co-based Full-Heusler compounds, which has been reported in various experimental and theoretical reports by different lattice constants (5.7798 A°, 5.766 A°, 5.742 A°), magnetic moments (1.86µB, 2.0µB and 1.92µB), and Curie temperatures (342.7K, 384.81K).40-43 By now, some efforts have been devoted to the (011) and (111) Co2VAl films resulting that the Al- and V-terminations have a 100% spin polarization (full HM).40, 41, 44 Recently, the Co2VAl/PbS interface has been under consideration45, although none of the mentioned mono-layer films of the Co2VAl have been synthesized or simulated so far.

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Furthermore, regarding the interesting behaviors of the nano-scale materials, the Heusler nanotube and nanowires have been studied.46, 47 In this report, a new GL monolayer of the Co2VAl is introduced, which is expected to represent unique properties due to the nano-structures of the same family compared to the bulk form. To evaluate its physical properties, the (101) and (110) mono-layers, as auxiliary samples, are also considered and their thermodynamic stability, electronic and magnetic, as well as optical properties are calculated and compared with the GL monolayer. The rest of this article is composed of two sections, Sec. 2 and Sec. 3. In Sec.2, computational methods and in Sec. 3, which is divided into two subsections, results and discussions are presented. In the first subsection, stability, electronic and magnetic properties and in the second subsection optical properties are discussed.

2. Computational details The calculations are carried out using DFT, and full potential linear augmented plane waves plus local orbital (FP-LAPW+lo) method, as well as the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA) as implemented in the WIEN2k code.48-50 The RKmax, Gmax and K-points parameters are optimized to be 8.0, 12 and 5000, respectively. To achieve the optimum atomic positions, the atoms are fully relaxed and the atomic forces are minimized to 1.0 /ℎ. The optimized mono-layer structures are shown in Figure 1. Moreover, in the selfconsistent field (SCF) calculations, the electron charge density ( /ℎ ) is selected and let be converged by the accurately of 0.00001 for the charge density distance between last two iterations of the SCF cycles. Optical calculations have been done by Random Phase Approximation (RPA).51 Figure 1 is plotted by XCrysDen package52, but all of the other figures in this article are plotted by SigmaPlot software.



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(a)-(011)

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(b)-(101)

(c)- (111)

(d)-(111)

Figure 1: The layers of Co2VAl along (a) (011), (b) (101) crystallographic directions. The (c) side and (d) top views of the GL (111) Co2VAl.


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3. Results and discussions 3.1. Stability of the system and its electronic and magnetic properties The feasibility of a system is a crucial problem for any theoretical prediction. There are several quantities to make sure about the feasibility of a predicted system theoretically. One of the important physical quantities to judge about the thermodynamic stability of materials is the cohesive energy ( ): =

!""

− $% + % % + % + % &'()"

&'()"

+ %

&'()"

+

, (1)

where is the total energy of any sheet, . and %. (X=Co, V, Al) are the energy and number of the single X atoms, respectively. Our results show that the cohesive energies are negative for the three films, see Table 1. Thus, the films are all predicted to be thermodynamically stable. Another important physical quantity to ensure about the feasibility of the thin films is enthalpy. Therefore, for the systems under question we have also calculated the change in enthalpy (∆0), as defined below:

!""

∆0 =

!""

− $% + % % + % + % 12

12

&'()"

+ %

12

+

, (2)

is the crystallization energy of a typical X atom. Our results, as presented in where . Table 1, show that ∆0 is negative for all of the considered cases. The negative sign of ∆0 can be taken as another evidence of the stability and as a result feasibility of the systems. Moreover, to make more sure about the feasibility of the system, the total energy are calculated as a function of volume of for the GL Co2VAl(111) and the data are fitted with the Brich-Mornaghan equation of state. The obtained energy versus volume (E-V) curve, as shown in Figure 2, clearly shows a minimum which can be considered as another theoretical verification for the mechanical stability and thereby the feasibility of the system. 12

Let us now turn our attention to the electronic structure of the systems. To this end, the total densities of states (DOSs (states/eV)) for the auxiliary (011), (101) and the (111) monolayers of the Co2VAl, as shown in Figures 3(a)-(c), and the partial DOS (PDOS (states/eV)) for the Co2VAl (111) monolayer, as shown in Figures 3(d)-(f), are calculated. In both up and down spins, the auxiliary cases have the same metallic behavior. Thus, their magnetic moments, unlike the bulk state, are nearly zero (see Table 1) with a small spin polarization at the Fermi level. Hence, our magnetic moment calculations predict that the auxiliary cases may not be suitable for the spintronic applications. However, a 100% spin polarization is observed at the Fermi level of the GL film which makes it a good candidate for the HM-based devices. As shown in Figure 1, in the auxiliary cases, arrangements of the surface atoms of the films, apart from very small deviations, are very similar. Thus, it is reasonable to observe the same physical behaviors for



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them. Existence of the superficial dangling bonds causes an increase in the electrostatic potential on the surfaces which destroys spin polarization at the Fermi level. Principally, hexagonal arrangement of the atoms may provide the GL case with very important changes in the electronic functions compared to the two other films. In the light of the PBEGGA functional, it can be observed a perfect HM behavior at its Fermi level as well as more values of PDOS for surface atoms than for the middle atoms. This behavior can be related to the presence of the dangling bonds and the destruction of the crystal symmetry. The DOSs presented in Figure 3 show that the main contributions of Al electronic states lie in the [-6, 6 eV] energy range. Below the Fermi level, where the electronic states are filled the Al- and V-electronic states for both up and down spins are smaller than those of Co states. The spin dependence of the (111) sheet is related to the electronic states around the Fermi level in which the Co and V atoms due to their half field d-orbitals have main role. Besides, comparing with the other two mono-layers, it is concluded that atomic symmetry is of significant importance. Spin flip gap, defined as separation of the Fermi level from the minimum of the conduction band in minority spin, is an important parameter for the electron injection in HMs. It is worth mentioning that the spin flip gap is obtained from the calculated DOS shown in Figure 3(f) to be about 0.5 eV for the film which is greater than that of reported in the literature for its bulk shape. 9 Low magnetizations are predicted for the two auxiliary sheets, while a larger integer value of 1.000 is predicted for the Co2VAl(111) monolayer, which can be compared with the values of 1.999 , 2.002 reported for the bulk form. 24 The magnetic moments, as presented in Table 1, shows that the atomic magnetic moments of the surface Al and V atoms in the auxiliary mono-layers are bigger than those of the middle layers, whereas the Co atoms exhibit quite a reversed behavior. The two auxiliary planes include all three atomic types (Al, V, and Co) with lower crystalline symmetry, whose dangling bonds lead to increment in the surface electronic density and reduction of magnetic moments. Because of the V and Co atoms and high hexagonal symmetry, magnetic moment attains the integer amount of 1.000 and thus the GL Co2VAl film would be considered as a promising material for the spintronic applications.


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Figure 2: The Energy-Volume (E-V) curve of GL Co2VAl in its magnetic state.



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Figure 3: Total DOS(states/eV) contribution of the up and down spins to the (a) Co2VAl(011), (b) Co2VAl(101) and (c) Co2VAl(111). PDOS(states/eV) of (d) Al, (e) V, and (f) Co atoms in the middle and surface layers of the Co2VAl(111).


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Table.1: The atomic magnetic moments (AMMs) of the middle and superficial atoms, together with the total magnetic moment (TMM) and cohesive energy (EC) of the (011), (101) and (111) Co2VAl monolayers.

Co2VAl film AMM- Co-middle (µB)

(011) 0.4144

(101) 0.3530

(111) 0.6739

AMM-Co-surface (µB)

-0.1245

-0.1077

-0.1041

AMM-V-middle (µB)

-0.0054

0.0198

0.2861

AMM-V-surface (µB)

-0.01381

-0.0205

0.0935

AMM -Al-middle (µB)

-0.0008

0.0002

-0.0039

AMM -Al-surface (µB)

-0.0012

0.0014

-0.0092

TMM (µB)

0.2260

0.2144

1.000

EC(eV)

-5.34

-5.28

-5.12

H(eV)

-0.43

-0.36

-0.63

3.2.Optical Properties Optical response of the mentioned monolayers to the incident light has been calculated and the results are shown in Figures 4 to 7. The symbols xx and zz are used to denote the in-plane (or parallel) and normal (or perpendicular) directions with respect to the planes, respectively. The real parts of the dielectric functions, Re[ε(ω)], in both directions are shown in Figures 4(a) and (b). The curves of the two auxiliary films almost coincide with each other and thus they show similar behaviors in both directions. The large values of the static points in the real part of the dielectric functions, i.e., Re[ε(0)], for both of the auxiliary films show high metallic property for these structures in both parallel and perpendicular directions. In contrast to the auxiliary cases, the GL case exhibits a quite different behavior taking Re[ε(0)] into account for both directions. The values of the static points are finite for the GL case in both xx- and zz-directions, see Figures 4(a) and (b). The value of Re[ε(0)] in the normal direction is almost one third of the corresponding value in parallel direction for the GL case. However, right after the visible region, the Re[ε(ω)] curves of the three monolayers, including axillary and GL cases, get coincident with each other. If Re[ε(ω)]=0 in an energy interval, the charge carriers oscillate by the incident light and form standing waves (named plasmonic oscillations). In this case, the materials will not respond to the 9 ACS Paragon Plus Environment


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light. It can be clearly seen from Figure 4 that the Re[ε(ω)] has two roots for the auxiliary films in the visible region, while it has only one root for the GL (111) case. Moreover, another root lies at the ultraviolent (UV) range with 12.8 eV, 13.8 eV and 12 eV for the parallel component of the mentioned films, respectively. Negative sign of Re[ε(ω)] in an energy interval implies that the light cannot propagate with the corresponding frequencies. The parallel Re[ε(ω)] spectra of the three films are negative in a wide energy interval in the visible region. Although the perpendicular Re[ε(ω)] spectra are also negative in a wide energy window and have four roots from visible to UV range, the absolute values of the negative Re[ε(ω)] are very small and almost negligible. Consequently, the Co2VAl monolayer films are optically active and responsible to the incident lights in the infrared and visible regions, while they are inactive in the higher energies (after the plasmonic energy) as the parallel and perpendicular Re[ε(ω)] spectra approach to small and ignorable values.

Figure 4: (a-b) Re[ε(ω)], (c-d) Im[ε(ω)] for the three monolayers of (011), (101) and (111) Co2VAl in the parallel (denoted by xx) and perpendicular (denoted by zz) directions versus the incident photon energy.


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The imaginary parts of the dielectric functions of the three cases are shown for parallel direction in Figure 4(c) and for perpendicular direction in Figure 4(d). These figures show that the bandgap of the thin films under question are all zero, since the Im[ε(ω)] spectra start to rise up immediately from zero energy. 53 This, consistent with the DOSs shown in Figure 3 and the Re[ε(ω)] spectra shown in Figures 4(a) and (b), reconfirms that these thin films are all metal. The peaks of the imaginary part of dielectric function, Im[ε(ω)], can give the inter- or intra-band optical transitions from an occupied level to an unoccupied one. Analogous to the real part of the dielectric function behaviors, the results presented in Figures 4(c) and (d) clearly show, apart from some deviations in the infrared region and low energies, that the Im[ε(ω)] spectra of the two auxiliary films also behave similarly and approximately coincide with each other, while these of the GL case again exhibit different behaviors compared to the axillary spectra. These figures also show that the Im[ε(ω)] spectra of the three cases completely coincide with each other after the visible area. The discussed similarities between the behaviors of Re[ε(ω)] and Im[ε(ω)] of the three cases may not be surprising because they are connected to each other via the kramres-Kronig formula. The intra-band transitions play a key role in optical properties of all mentioned films, because higher peaks of the Im[ε(ω)] appear in the interval [0-4eV]. The metallicity of the auxiliary monolayers are higher compared to the Co2VAl(111), since the Im[ε(0)] values of the two auxiliary sheets are larger than that of the third case. Another important optical parameter is the energy loss function (ELF). The ELF can be used to show the lost energy of the incident beam after coming out of the considered thin films. The ELF is maximized at the plasma energy (4 ) where Re[ε(ω)] becomes zero. Thus, the roots of Re[ε(ω)] spectrum yield the 4 . The components of the ELF tensor (5'6 ) are calculated for the cases under study by the following formula: 5'6 (7) = 8 9

8[:'6 (7)] −1 ;= @ @ . (3) :'6 (7) > [:'6 (7)]? + >8$:'6 (7)+?

Figure 5 illustrates an almost isotropic behavior for the ELF in both parallel and perpendicular directions. As aforementioned above, the peaks of ELF spectrum can be corresponded to the roots of Re[ε(ω)] spectrum (see Eq. 3), and by using this correspondence the plasma energies can be determined. By taking this technical point into account, the main plasma energies are double checked and practically calculated and the results are tabulated in Table 2.



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Figure 5: ELF of the three Co2VAl films versus the incident photon energy in (top) parallel (xx) and (bottom) perpendicular (zz) directions.

Table 2: The plasmonic energies for (101), (011), and (111) monolayers of the GL Co2VAl in both parallel (xx) and perpendicular (zz) directions. The mono-layers (111)

Plasmonic energy-xx 12.0

Plasmonic energy-zz 12.5

(101)

12.8

12.7

(011)

13.8

13.2


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The absorption spectra of the monolayers versus photon energy are calculated and the results are shown in Figures 6(a) & (b) for both in-plane and perpendicular directions. It is clear that by increasing the intensity of the incident light the absorption spectra remarkably rise up in both directions which are in complete accord with Im[ε(ω)] diagrams, but they fall down or almost remain constant in the energies for which Re[ε(ω)]=0 due to reduction of the matter absorption in the plasmonic frequencies. Furthermore, absorption spectra reveal a relatively isotropic behavior over the visible area up to 8 eV (UV region) in the two directions, and after that they all show the same behavior. The drastic increment of the absorption spectrum in [0, ~3.8eV], especially in parallel direction, show the high metallic nature of the considered films. This can be reconfirmed by calculating the optical conductivity (B). Thus, the components of the optical conductivity tensor, B'6 (7), are calculated using the following formula: B'6 (7) =

7'6 8$:'6 (7)+. (4) 4D

The results are represented in Figures 6(c) & (d). For the in-plane waves, the optical conductivities of the auxiliary films are very high at the static point (7 = 0), but for the perpendicular waves they show a different trend with very low values at low energies. Hence, we conclude that the main metallic properties are mostly originated from the parallel components. The (111) case conductivity behaves differently in analogy with the auxiliary cases, especially for parallel direction at the [0, 4eV] energy range where it rapidly increases by the photon energy. In the perpendicular direction, the optical conductivity of the (111) case also rises up but from 0.5 eV up to 4 eV, as well. Optical conductivity is considerable at the visible edge for the parallel direction but at the range of [2, 8eV] for the normal component. In high energies (after the plasmonic points given in Table 2) the optical conductivity reduces and approaches to a saturated value.



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Figure 6: The (a & b) absorption peaks, and (c & d) optical conductivity of the three (011), (101) and (111) monolayers of Co2VAl for parallel (xx) and normal (zz) incident lights.

F = E(7) + GH(7) can be obtained by calculating its real part The complex refraction index E(7) known as index of refraction, E(7), and its imaginary part known as extinction coefficient, H(7), using the following formulas: E'6 (7) = I

J:'6 (7)J + $:'6 (7)+ , (5) 2

J:'6 (7)J − $:'6 (7)+ H'6 (7) = I , (6) 2

where J:'6 (7)J = L> $:'6 (7)+? + >8$:'6 (7)+? . @

@


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The E(7) spectra, as shown in Figure 7, show that the auxiliary films behave similarly which but different from the spectra of the GL (111) case, especially in the infrared region. The comparison of the parallel and normal components of the E(7) spectra shows that the values of the parallel spectra are larger than those of the perpendicular spectra at the static point, E(7 = 0). However, all of the spectra asymptotically approach to the unity at higher energies (above the plasmonic points) for all cases and directions, viz E(7) ≅ 1. The latter asymptotical limit can be taken as an indication to the fact that the thin films behave like vacuum space when they are subjected to high energy electromagnetic waves. Remarkably, the static value of E(0) = 3.4 for the GL case makes it somehow comparable with the semiconductors such as Si. In contrast to E(7), H(7) is different for all three films, especially in the infrared region and visible edge. It is obvious that most dissipation occurs in the mentioned optical ranges, confirming the intra-band transitions and metallic properties of the layers. The N(7) of the (111) case drops at the energies that Re[ε(ω)]=0 and appears with static amounts of 3.2 and 1.0 for the parallel and normal directions respectively, approving its metallic behavior (Figure 7 (c & d)).



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Figure 7: The (a & b) refraction, (c & d) extinction, and (e & f) reflectivity indices of the (011), (101) and (111) monolayers of Co2VAl for parallel (xx) and normal (zz) directions of the incident light.

Reflection index, (7), shows the light percentage which is reflected from the material’s surface, so metal-shaved shiny surfaces show high amounts of reflectivity obtained from below: (7) = O

> :(7) +

> :(7) +

P G 8:(7)?@ P G 8:(7)?@

@

−1 O (7) +1 16

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Figures 7(e) and (f) indicate the reflection indices of the mentioned monolayers in both directions. It is obvious that auxiliary monolayer films have a 98% static reflection for parallel waves, while it decreases nearly to 50% for the normal waves. Besides, by increasing the photon energy, reflections get reduced and thus, the optical transitions will go up. Also, reflection of the GL case differs from the two others in both directions, especially by its lower values at the static point. Noticeably, reflection of all films approach to zero at high energies, inferring to a full optical transmission in this limit.

4. Conclusion We have predicted half-metallic (HM) properties of the (011), (101) and GL (111) Co2VAl monolayers, using DFT and FP-LAPW+lo method with GGA approximation. In the (111) direction growth, Co2VAl monolayer is formed in the GL structure and interestingly the results show that all the physical properties of this structure such as HM and optical characteristics differ from the two other sheets. The electronic and magnetic calculations show that (011) and (101) monolayers are metals with a very low spin polarization at the Fermi level and magnetic moments of 0.226 μS and 0.2144 μS , respectively. However, the GL case is a full HM with 100% spin polarization at the Fermi level and the integer magnetic moment of 1.00 μS as well as a suitable spin flip gap of about 0.5 eV. In addition, it is found that its optical properties differ from the two other discussed monolayers, especially in the infrared and visible edge regions, however, increasing the photon energy leads to a gradual adaption between them. Furthermore, the real parts of the static dielectric functions of (011) and (101) cases confirm their metallic nature, whereas the GL sheet has a different behavior. The imaginary part of the dielectric function shows the intra-band transitions, because its peaks mainly reside at the range [0, 2.5 eV], which by comparison with Re[ε(ω)] roots and the energy loss function, it turns out that the main plasmonic frequencies occur in the UV area. Finally, our calculations indicate that Co2VAl acts as dark matter in the UV region only.

Acknowledgments This work is resulted from a scientific research in the Kermanshah Branch, Islamic Azad University.



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