Defect induced magnetism in planar silicene: a first principles study

Abstract

We study here the magnetic properties of two dimensional silicene using spin polarized density functional theory. The magnetic properties were studied by introducing monovacancy and di-vacancy, as well as by doping phosphorous and aluminium into the pristine silicene. It is observed that there is no magnetism in the monovacancy system, while there is large significant magnetic moment present for the di-vacancy system. Besides, the numerical computation reveals that the magnitude of the magnetic moment is more when the system is doped with aluminium than phosphorous. All these theoretical predictions in this two dimensional system may shed light to open a new route to design silicon based nano-structures in spintronics.

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1 Introduction

2D materials are always fascinating in their own right from a basic physics point of view, as well as in technology. The hottest material in the world of materials is two dimensional graphene. Since its discovery, it has led to many new research ideas due to its unusual properties and it has been found to have great potential for use in future nanoelectronic devices.^1–6 Note that the low energy physics of graphene can be described by 2D massless Dirac fermions. Because of its semi-metallic nature, it is not suitable for nano-electronic devices. For practical applications in nano electronics devices, it is always desirable to have a finite band gap. A band gap opening in graphene is possible by applying uniaxial strain,⁷ B–N doping⁸ and chemical functionalization.⁹ The choice of B–N in the hexagonal unit cell is because of their similar radii and it has been observed that B–N doping can significantly alter the electronic, optical and electrochemical properties of carbon nanotubes (CNT).^10–12 Recently, Nath et al.¹³ have demonstrated the anisotropic signature in the optical properties of graphene by BN doping through first principles calculations. Opening of the band gap is observed by doping in an uncontrollable manner, which makes it incompatible for use in building practical devices. In this situation, researchers have found a replacement for graphene in the form of silicene, a monolayer of silicon atoms forming a two dimensional honey-comb lattice like graphene. Note that silicon to date is the most semiconducting element used in nanotechnology. In contrast to the advantage obtained from graphene, silicene thus may be easily interfaced/integrated with existing micro or nano-electronic devices. This new two dimensional material has been found to be compatible with the present Si based nano electronics industry, both experimentally and theoretically.^14–30 A graphene-like band structure has been reported for the case of planar silicene.¹⁷ Silicene has been epitaxially grown on a silver surface Ag (111).¹⁶

The similar properties of silicene and graphene have been observed both experimentally²³ and theoretically.³¹ The striking similarity between graphene and silicene originates from the basic fact that both carbon (C) and silicon (Si) belong to the same group in the periodic table of elements. Besides, along the row of the periodic table (C → Si → Ge → Sn), the atomic weight increases from 12 to 119. This implies a strong relativistic effect as the velocity of electrons is proportional to atomic number. This has a two fold effect. Firstly, the low energy physics can be described by a Dirac type energy–momentum relation similar to graphene. Secondly, there is a significant increase in spin–orbit splitting in comparison to graphene. Thus, like massless Dirac fermions in graphene, silicene has massive Dirac fermions due to the large spin–orbit gap (1.55 eV). Moreover, unlike graphene, silicene is a topological insulator characterized by a full insulating gap in bulk with a helical gapless edge.³² Again, Si has a larger ionic radius than C, so sp³ hybridization is favorable to Si in contrast to common sp² hybridization in C. Therefore, the mixing of sp² and sp³ hybridization in Si results in buckling.¹⁷ This buckling structure in silicene,³³ due to the pseudo Jahn–Teller effect in contrast to graphene, is significantly promising in the sense that the bandgap in such a structure can be easily tuned by application of an external electric field, without the need for any chemical functionalization. In recent work carried out by Jose and Datta,³⁴ the characteristic chemical and structural properties of silicene have been compared with graphene. In fact, the band gap opening has been observed in silicene by applying an external transverse static electric field^35–38 compatible with experimental conditions. Recently, first-principles DFT calculations have revealed an opening of the band gap³⁹ at the Dirac point in pristine and Ti adatoms adsorbed in single layer silicene and germanene when subjected to a perpendicular electric field. In such a situation, it has been pointed out³⁹ that the symmetry between the two sides of the honey-comb structure (existing in buckled atoms in their plane) is broken. As a consequence, the linearly crossing bands split, giving rise to a bandgap, which varies linearly with the value of the electric field. Note that this opening of bandgaps does not occur in graphene because of the planar geometry of the constituent C atoms or the equivalency between the two sublattice structures. First principles calculations have been employed to study the magnetic properties of functionalized silicene.^42–44 Hydrogenation in silicene is comparatively easy, as silicene prefers sp³ hybridization to sp², and this process can also open up a band gap. In particular, the chemical functionalization with Br and H in silicene has been shown to be quite effective in tuning the electronic and magnetic properties of functionalized silicene. Besides, the anti-ferromagnetic (AFM) state with a zero magnetic moment of silicene with a Ti adsorbed atom at a 1 V Å⁻¹ perpendicular electric field can be modified³⁹ to ferromagnetic (FM) with a non-zero magnetic moment by reversing the field or by charging. Although graphene and silicene have perfect honeycomb structures, thermodynamic arguments indicate that defects can always exist at a finite non-zero temperature. Defects present in any material can strongly influence⁴⁵ the structural, electrical, optical and magnetic properties and hence a proper understanding is desirable for a better tuning of the properties of the material. In fact, it has recently been observed that topological defects like Stone–Wales⁴⁶ can significantly alter the electronic density of states near the Fermi energy.⁴⁷ It has been observed that with suitable control of the C-vacancies (V_C) in graphene, one can tailor the magnetic moment from 1.12 μ_B to 1.53 μ_B.⁴⁰ First principles calculations have indicated that the non-magnetic character of armchair silicene nanoribbons (ASiNRs) is unchanged⁴¹ by a monovacancy or a di-vacancy. However, the presence of a monovacancy or parallel oriented di-vacancy can change the original direct semiconducting nature of ASiNR to an indirect one.⁴¹ Motivated by the new structure of silicene and its advantages over graphene and the defect/doping studies on 2d and 3d systems, it is highly desirable from the view point of practical applications that significant magnetization or a sizeable bandgap or both may be established in non-magnetic silicene. In this article we have explored the magnetic properties of silicene due to vacancies (mono and di) and doping by aluminium (Al) and phosphorous (P). The choice of Al and P in silicene is almost the same as given in B and N for graphene. The magnetism obtained in silicene in the case of vacancies is also compared with the case of doping by Al and P.

2 Computational details

We study the magnetic properties of doped and co-doped silicene using ab initio calculations^48–50 within the domain of spin-polarized Density Functional Theory (DFT) by solving the standard Kohn–Sham equations as embedded in the SIESTA^51–53 software. The norm-conserving Troullier-Martins pseudopotentials⁵⁴ are used here for numerical computation. We apply Generalized Gradient Approximation (GGA) for the exchange-correlation functional given by Perdew–Burke–Ernzerhof (PBE).⁵⁵ The GGA results have also been compared with those obtained from the local density approximation (LDA).⁵⁶ The double ζ plus polarized basis set is employed throughout the whole range of models. An energy cutoff of 300 Ry is used for grid integration and for sampling the Brillouin zone (BZ) a (20 × 20 × 1) Monkhorst Pack (MP)⁵⁷ grid is used. It is to be noted that spin–orbit coupling is neglected and the simulations are run using the diagonalization method. The structures are optimized by minimizing the forces on individual atoms below 10⁻² eV Å⁻¹. The convergence criterion for energy of the SCF cycle is chosen to be 10⁻⁴ eV. The unit cell has two Si atoms (A and B) and the space group is P3m1. The bond length and bond angles between the silicon atoms are 2.22 Å and 119.98°, respectively, with lattice constant 3.84 Å. Since the value of the bond angle in silicene is close to 120°, we have not considered the buckling in our geometrical structure for numerical computation. All the 2D systems are simulated within a supercell (for pristine (4 × 4 × 1) and for other structures (2 × 2 × 1)) approach with 30 Å of vacuum in the direction perpendicular to the 2D crystal surface, in order to avoid the artificial interaction between the artificial images of the 2D sheet. The electronic band structures obtained from LDA have been compared with those from GGA, to point out the ineffectiveness over GGA in the geometrically optimized structures for the calculation of magnetism.

3 Results and discussion

Before computing the electronic band structure of the doped and vacancy induced silicene, we have studied the defect/vacancy formation energy of all the structures. The typical defect formation energy of a single vacancy and the surrounding temperature determines the equilibrium vacancy concentration in silicene. There are various approaches to compute this energy and a comparison of these approaches has been beautifully demonstrated in the work by Özcelik et al.⁵⁸ The defect formation energy per dopant is defined as
where n_dope is the number of dopants, E_df, E_d, E_Si, E_pris and E_dope represent defect formation energy per dopant, total energy of the doped system, energy of a single silicon atom, energy of the pristine silicene system and energy of a single dopant atom, respectively. The vacancy formation energy per vacancy is defined as
where n_Si is the number of silicon atoms of the pristine system and E_vac is the vacancy formation energy per vacancy. For a single vacancy n_Si is 32. The energy difference between the pristine system and the 32 individual silicon atoms divided by 32 gives the single vacancy formation energy. For the double vacancy case we take the silicon atoms in pairs, hence n_Si is equal to 16. So when forming a double vacancy silicon atoms are taken out in pairs. The results are summarized in Table 1. These calculations reveal the stability of the structure and thus the structures are ready for spin-polarized density calculations. It is noticed from Table 1 that the defect formation energy is lower in single vacancy scenario, with 1 Al atom and 1 P atom, compared to the double vacancy with 2 Al atoms and 2 P atoms.

Table 1 Defect formation energy for all 2-dimensional structures

Systems	Defect formation energy (eV/defect or vacancy)
1 Al atom	5.42 (4)
2 Al atom	5.61 (4)
1 P atom	1.83 (2)
2 P atom	2.70 (0)
Single vacancy	8.11 (0)
Double vacancy	8.87 (3)

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In this communication we are interested in studying the magnetic properties of silicene with seven different configurations (Al and P doped as well as with vacancies) as shown in Fig. 1. Before we show the electronic DOS of the above systems, we compare the Fermi energy following the LDA and GGA schemes in Fig. 2. It is interesting to note that for all the systems, the computed values in GGA are slightly higher than those computed in LDA. This implies numerical consistencies, as required in our computation.

Fig. 1 Different structures of defected silicene. The blue, green and red balls respectively indicate the silicon, aluminium and phosphorous atoms. (Left column) corresponding unit cells of all the structures. (Right column) (a) 4 × 4 × 1 super cell of pristine silicene, (b) 2 × 2 × 1 super cell of silicene with monovacancy, (c–e) 2 × 2 × 1 super cells of silicene with di-vacancies with three different configurations, (f) 2 × 2 × 1 super cell of silicene doped with one P atom per hexagonal unit cell, (g) 2 × 2 × 1 super cell of silicene doped with two P atoms per hexagonal unit cell, (h) 2 × 2 × 1 super cell of silicene doped with one Al atom per hexagonal unit cell, (i) 2 × 2 × 1 super cell of silicene doped with two Al atom per hexagonal unit cell.

Fig. 2 Comparison of values of the Fermi energy of the various systems using LDA and GGA schemes in DFT.

We show schematically in Fig. 3 the spin-polarized electronic DOS of one configuration of doped and two vacancy mediated silicene systems as a function of energy measured from the Fermi energy (E_F). In the inset, the difference between spin-up states and spin-down states is indicated. The effective electronic DOS values at the Fermi energy are also compared in Fig. 4. It is observed that the effective electronic DOS at the respective Fermi energy is highest for double vacancy systems and lowest for the single vacancy one. This large electronic DOS at the Fermi energy may act as a key parameter to control the magnetic states. This is important from the point of view of quantum information devices in some magnetic nano-structures. As a further consistency check on our numerical results, we have performed the spin polarized electronic DOS of pristine silicene by both LDA as well as GGA. It is observed that both the schemes give us a zero magnetic moment for the monovacancy system, consistent with the previous observation of the diamagnetic signature of the system.³⁸ This observation can be compared with the fact that although SiC is diamagnetic in nature, Si + C di-vacancies can induce room temperature ferromagnetism.^59,60 In other words, as evident from the inset of Fig. 3(a), like the pristine monovacancy case, the spin-up electronic DOS and spin-down electronic DOS exactly cancel each other out for all values of energy measured from the Fermi energy. The non-magnetic nature of the monovacancy in silicene has been physically explained by the geometrical symmetry arising due to the single vacancy.⁵⁸ In the process of reconstruction of this single vacancy,⁵⁸ the resulting structure becomes symmetrical around this vacancy. This resultant geometrical symmetry leads to a singlet ground state. In a singlet state, since the magnetic moments cancel each other out, we get a zero magnetic moment for the single vacancy in silicene, consistent with earlier observations.^61,62 It is to be noted that this situation is completely different from the magnetic ground state of graphene with a single vacancy. However, this situation never arises in other doped systems or in the double vacancy case. In fact, for silicene with two vacancies per hexagonal unit cell, as seen in Fig. 3(b), the difference between spin-up electronic DOS and spin-down electronic DOS is the highest, and the relevant magnetic moment is 2.26 μ_B, where μ_B is the Bohr magneton. The other two variant double vacancy configurations Fig. 1(d) and (e) do possess magnetic moments 1.98 μ_B and 1.66 μ_B, respectively. This in fact points out the importance of the interaction between the monovacancies and double vacancies of silicene. Besides, it is also evident that with the increase in separation between the two vacancies, the magnitude of the magnetic moment decreases. In fact, the effects of di-vacancies on the structural and electronic properties of 2D silicene depend critically on the orientation⁵⁸ of the two removed Si atoms. Due to this specific reason of the orientation of the removed Si atoms or the presence of four dangling sp² bonds in the reconstructed structure, one gets a finite non-zero magnetic moment. It is interesting to note that graphene with a double vacancy does not show any finite non-zero magnetic moment,⁵⁸ due to the absence of any dangling bonds in the reconstructed configuration. In fact, the buckled structure of silicene is responsible for the formation of dangling bonds, as opposed to graphene for this observation of non-zero magnetic moments in the di-vacancy system. Besides, this magnetic moment turns out to be highest among all the above configurations. It has been observed by Liu⁵⁹ and his collaborators that defects created by neutron irradiation in a single crystal of 6H–SiC can induce significant magnetism by di-vacancies (V_SiV_C). The experimental results were further supported by the first principles calculation⁵⁹ regarding the role played by the extended tail of the defect states. In the same spirit, it may be possible to understand the presence of a large significant magnetic moment in di-vacancies as the development of long range couplings between the local moments. The important key role played by the interaction between V_Si and V_C in zigzag SiC nanoribbons (Z-SiCNR) in inducing ferromagnetism has been demonstrated by an ab initio study.⁶³ It is also worth mentioning that in the BN sheet, it is possible to induce a magnetism of 0.29 μ_B via the B-vacancy, while a single N vacancy (V_N) has a much lower significance for the magnetic properties.⁴⁰ It will be interesting to explore the variation in magnetic moments with systems having more than double vacancies. In fact, triple vacancies in a single layer of MoS₂ can give rise to a net non-zero significant magnetic moment.⁶⁴ Besides, as observed from Fig. 3(c), the exact cancellation of spin-up and spin-down states does not occur for the 1 Al atom silicene structure through GGA schemes resulting in a non-zero magnetic moment. This non-zero magnetic moment is also supported by the LDA scheme.

Fig. 3 Spin polarized electronic DOS of silicene for different systems.

Fig. 4 Numerical values of the electronic DOS at the respective Fermi energies of the various systems using GGA schemes in DFT.

With a single phosphorus atom as the dopant, it is observed that the spin polarized magnetism is zero according to LDA but non-zero (0.13 μ_B) in the GGA computation. However, for two P atoms in a hexagonal unit cell, both LDA and GGA give exactly a zero magnetic moment. A non-zero magnetic moment is obtained for silicene doped with a single Al atom both by LDA and GGA. A significant magnitude of 0.21 μ_B is noticed when doped with 2 Al atoms. All the above results are summarized with the help of a bar diagram in Fig. 5. These results indicate that a significant amount of magnetic moment can be achieved by introducing a double vacancy and by doping with two Al atoms in the hexagonal unit cell of silicene. It is worth mentioning that systems having a double vacancy and 2 Al atoms possess a significant electronic DOS at their respective Fermi energies. Like other various approximations adopted in DFT, it is noticed that GGA may be used in the computation of spin-polarized electronic DOS or in general magnetism over LDA, although the computed numerical values of Fermi energy are almost the same.

Fig. 5 Comparison of values of the magnetic moment of the materials using LDA and GGA schemes in DFT.

4 Conclusions

In summary, the magnetic properties of two dimensional silicene have been explored using spin polarized density functional theory, by incorporating monovacancies and di-vacancies, as well as by doping with phosphorous and aluminium atoms in the hexagonal network of pristine silicene. The numerical studies have revealed that there is no magnetism in the system for the monovacancy case, and 2 P atoms in a unit cell are supported by LDA as well as GGA, while GGA yields a large substantial magnetic moment present for the di-vacancy, as well as by doping with 2 Al atoms. Furthermore, comparison of the results from LDA with those from GGA strongly indicates that the magnetic studies in vacancy mediated silicene or doped silicene should be performed with GGA rather than LDA. Besides, the numerical computation indicates a substantial amount of magnetic moment for doping with Al in comparison with P atoms. Thus, the magnetic properties can be engineered by vacancies as well as by doping with Al and P atoms in silicene. All these theoretical predictions in this emerging two dimensional system are expected to shed light in designing silicon based nano-structures in spintronics.

Acknowledgements

This work is financially supported by DST-FIST, Government of India. One of the authors (SC) would like to thank Department of Science and Technology (DST) for the award of DST-INSPIRE fellowship. One of the authors (PN) gratefully acknowledges Council of Scientific and Industrial Research (CSIR), Government of India for providing financial assistance. The authors would also like to thank two anonymous reviewers for their critical comments and suggestions to improve the quality of this paper.

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