Spin-polarised DFT modeling of electronic, magnetic, thermal and optical properties of silicene doped with transition metals
Nzar Rauf Abdullah, Mohammad T. Kareem, Hunar Omar Rashid, Andrei Manolescu, Vidar Gudmundsson
aa r X i v : . [ c ond - m a t . m e s - h a ll ] S e p Spin-polarised DFT modeling of electronic, magnetic, thermal and optical propertiesof silicene doped with transition metals
Nzar Rauf Abdullah a,b , Mohammad T. Kareem c , Hunar Omar Rashid a , Andrei Manolescu d , Vidar Gudmundsson e a Division of Computational Nanoscience, Physics Department, College of Science, University of Sulaimani, Sulaimani 46001, KurdistanRegion, Iraq b Computer Engineering Department, College of Engineering, Komar University of Science and Technology, Sulaimani 46001, KurdistanRegion, Iraq c Chemistry Department, College of Science, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq d Reykjavik University, School of Science and Engineering, Menntavegur 1, IS-101 Reykjavik, Iceland e Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik, Iceland
Abstract
The geometric, electronic, magnetic, thermal, and optical properties of transition metal (TM) doped silicene aresystematically explored using spin-dependent density functional computation. We find that the TM atoms decrease thebuckling degree of the silicene structure caused by the interaction between the dopant TM atoms and the Si atoms inthe silicene layer plane which is quite strong. In some TM-silicenes, parallel bands and the corresponding van Hovesingularities are observed in the electronic band structure without and with spin-polarization. These parallel bands arethe origin of most of the transitions in the visible and the UV regions. A high Seebeck coefficient is found in some TM-silicene without spin-polarization. In the presence of emergent spin-polarization, a reduction or a magnification of theSeebeck coefficient is seen due to a spin-dependent phase transition. We find that the preferred state is a ferromagneticstate with a very high Curie temperature. We observe a strong interaction and large orbital hybridization between theTM atoms and the silicene. As a result, a high magnetic moment emerges in TM-silicene. Our results are potentiallybeneficial for thermospin, and optoelectronic nanodevices.
Keywords:
Magnetization, Thermal transport, Silicene, DFT, Electronic structure, Optical properties
1. Introduction
A two-dimensional allotrope of silicon is silicene, whichwas first reported in 1994 [1]. Silicene has a periodicallybuckled topology leading to different properties comparedto some other 2D materials [2, 3], and it is composed of sil-icon (Si) atoms with some benefits compared to graphene[4, 5] as it is compatible with the present silicon-basedtechnology. Therefore, silicene has been extensively in-vestigated in electronics [6], optical [7], thermoelectric [8],and magnetic [9] devices. Silicenes with Transition met-als (TM) have also several applications in chemistry suchas hydrogenation evolution reaction [10], designing oxy-gen reduction reaction electro-catalysts [11], and silicenesuperlattice for Na-ion [12] Li-O [13] batteries.Despite its unique properties, silicene is not a very goodmaterial for some applications such as thermoelectric de-vices due to the zero bandgap. However, the zero-gap dis-advantage can be overcome [14]. Transition metals (TM)doped silicene (TM-silicene) are candidates in which thebandgap can be tuned [15]. It has been shown that in TMthe semi-metal characteristics of silicene are changed to be Email address: [email protected] (Nzar RaufAbdullah) semiconducting or metallic depending on the type of theTM dopant atoms. Among the ten types of TM-siliceneinvestigated, Ti-, Ni-, and Zn-doped silicene have shownsemiconducting properties, whereas Co- and Cu- dopedsilicene present a half-metallic material [16].In addition to the advantage found in the aforemen-tioned studies, another point speaking for TM-silicene isthat it is a strong candidate for the quantum spin Hall ef-fect. This is again attributed to the enhanced bandgap ofTM-silicene [17, 18]. Therefore, the investigations of themagnetic properties of TM-silicene are of potential impor-tance in diverse fields such as quantum electronics, spin-tronics, and optoelectronics [17, 19]. It has been shownthat the magnetic behavior of silicene can also be tunedby different TM dopant atoms [20]. The magnetic modifi-cations mainly come from the 3d orbitals of the TM dopantatoms along with a partial contribution from the adjacentSi atoms.The optical properties of silicene is another importantaspect of research because it also has many applicationsin the optoelectronic industries [20, 21]. It has been re-ported that optical response of silicene is in the IR andvisible regions [22]. The absorption spectra of P and Al-doped silicenes show higher absorption compared to pris-tine silicene, and no important changes in the electrical
Preprint submitted to Elsevier October 1, 2020 onductivity are found with the doping concentration forin-plane light polarization [23]. The optical properties ofTM-doped silicene have shown that the intensity of theabsorption peaks decreases for out of the plane light po-larization [24].The thermoelectric characteristics of pristine silicenecan also be improved by doping. For example, the presenceof defects may decrease the phononic thermal conductance.This enhances the thermoelectric efficiency or the figure ofmerit ZT [25]. A substitutional B/N doping [26] and di-hydrogenation [27] of silicene have been regarded as aneffective way to enhance the thermoelectric efficiency. Allthe methods used to increase the thermoelectric efficiencyfocus on tuning the bandgap of the silicene structure.In this work, we consider the effects of TM doping onthe physical properties of silicene. We first study the elec-tronic, thermal and optical characteristics of TM-silicene.We then use a TM dopant as a prototype magnetic impu-rity to show that it is possible to achieve magnetic prop-erties such as ferro- or antiferromagnetism. We will showhow magnetically active phases in TM-silicene can enhancethe thermoelectric properties such as the Seebeck coeffi-cient. It will be shown that TM-doped silicene monolayerscould be prominent candidates for spintronic devices.In Sec. 2 the structure of TM-silicene is briefly over-viewed. In Sec. 3 the main achieved results are analyzed.In Sec. 4 the conclusions of the modeling results are pre-sented.
2. Computational Tools
All the calculations of the pure and the TM-siliceneproperties are performed with the Quantum espresso (QE)simulation package [28, 29]. For visualization of the sam-ples, the crystalline and molecular structure the visual-ization program (XCrySDen) is used [30]. In QE, thegeneral gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) potential is employed with a cut-off energy of 1088 .
45 eV. In our samples consisting of a2 × . × − eV/˚A, and the total energy changes less than1 . × − eV. The Brillouin zone (BZ) is sampled by aMonkhorst-Pack k -mesh of 15 × ×
1. The same k -meshpoints are used for the SCF calculations. In the densityof state (Dos) calculations, a 100 × × .
3. Results
Our results are divided into two groups: First, the re-sults of the spin-independent model, the electronic, the thermal and optical properties for TM-silicene. Second,we show the results of the spin-dependent model, the elec-tronic band structure, the density of states of TM-silicene,and the thermal properties. In addition the magneticproperties including the magnetic moments of TM-siliceneare presented.
In this section, we show the results of the spin-independent model. The structures under investigationare shown in Fig. 1. The left panel of Fig. 1 is the pris-tine buckled silicene, b-Si (top panel), and the TM-dopedsilicene (bottom panel). In addition, the right panel is theside view of the b-Si and TM-silicene for five selected TMdopants including Ti, V, Mn, Fe, and Co atoms. The TMatoms are doped at the para-positions of the 2 × (purple), VSi (red), MnSi (lightblue), FeSi (blue), and CoSi (black). In b-Si, the Si-Sibond length is found to be 2 .
27 ˚A, which agrees well witha previous study [36]. This larger Si-Si bond length weak-ens the π - π overlaps, resulting in a low-buckled structure.The buckling parameter of b-Si is 0 .
45 ˚A which is in a goodagreement with previous studies [37].
Figure 1: Left panel: the pure silicene, b-Si, (top panel) and theTM-doped silicene (bottom panel). Right panel: side view of b-Si(golden), TiSi (purple), VSi (red), MnSi (light blue), FeSi (blue),and CoSi (black).Table 1: The buckling parameter of the structures. Structure δ (˚A)b-Si 0.45TiSi δ ) for all structures under investigationare presented in Tab. 1.It can be seen that the TM atoms leave the siliceneplane in the fully relaxed structures [38]. Consequently,the buckling degree of TM-silicene is decreased comparedto b-Si. The outward movement of the TM atoms fromthe silicene layer and the occupation of almost perfectlysymmetric 3-fold positions have been reported previously[39]. This reveals that in contrast to graphene the in-teraction between the TM atoms and the silicene layeris quite strong due to its highly reactive buckled hexago-nal structure [40]. The lowest buckling degree occurringfor TiSi reveals a maximum distortion, and the highestbuckling degree of CoSi among TM-silicene indicates aminimum distortion in the silicene structure. These dis-tortions emerge here because the bonding energy of the Tiatoms, 4 .
89 eV, to silicene occurs with a significant buck-ling and lattice a distortion [40]. In addition, the atomicradii of the Ti atoms are much larger than these of the Coatoms which may influence the distortion and the bucklingdegree.The DFT calculations of the formation energy indicatethat TiSi has the lowest, and CoSi has the highest for-mation energy among all the investigated structures. TheTiSi is thus the most structurally stable system.The electronic band structures of b-Si (a) and the TM-silicenes (b-f) are presented in Fig. 2. The electronic eigen-values along high symmetry directions (Γ M K Γ) in thefirst Brillouin zone are calculated self-consistently. Our re-sults for the band structure show that the TiSi (b) andVSi (c) are semiconducting materials due to the presenceof a finite bandgap around Fermi energy, while MnSi (c),FeSi (e), and CoSi (f) are metals because the Fermi en-ergy crosses valence or conduction bands. The bandgapof TiSi and VSi are 0 .
51 and 0 .
59 eV, respectively. Itshould be noticed that the Dirac cone in the TM silicenevanishes. This is caused by the orbitals of the TM atomwhich make a considerable contribution to the energy lev-els through the hybridization between the TM atom andthe silicene as is seen in Fig. 2(g). It can be clearly seenthe density of states of the TM atom around the Fermienergy has a high contribution. The semiconductor prop-erties of some TM-silicenes with Ti dopant atoms haverecently been studied [24].The bandgap tuning directly influences the thermoelec-tric properties of a system. The Seebeck coefficient, S , ofa pristine b-Si and TM-silicenes are displayed in Fig. 3 attemperature T = 100 K. We focus on this low temperaturerange from 20 to 160 K, where the electrons and phononsare decoupled. At this temperature range the electronsdeliver the main contribution to the thermal behavior[41, 42, 43]. The gapless b-Si exhibits poorer thermoelec-tric performance, than the gapped TM-silicenes. The lowSeebeck coefficient and the thermoelectric performance ofb-Si is caused by the cancellation of the electron-hole con-tributions to the transport quantities. As we stated before,an effective way to enhance the thermoelectric properties Figure 2: The electronic band structure of b-Si (a), TiSi (b), VSi (c), MnSi (d), FeSi (e), and CoSi (f). The density of state (Dos)of the Si and TM atoms in TM-silicene, FeSi , (g). The Fermi energyis set at zero. of a system is to open up a bandgap, and thus lifting thiscancellation effect [44].We therefore see the maximum Seebeck coefficient forTiSi (purple) and VSi (red) as they have a bandgaparound the Fermi energy behaving as semiconductor ma-terials.The optical response of a 2D structure is also directlyrelated to the electronic band structure [45]. For instancethe imaginary part of the dielectric function denotes theabsorbed energy by the structure. The imaginary dielec-tric functions, ε , in the case of an in-plane or a parallel,E in , (a) and an out-plane or a perpendicular, E out , (b)electric fields are shown in Fig. 4 for b-Si and TM-silicene.It is well known that the two main peaks in the imaginarydielectric function of b-Si are at 1 .
68 eV corresponding tothe π to π ∗ states, and at 3 .
85 eV revealing the transitionbetween the σ to the σ ∗ states in the parallel electric field.Similar to graphene, inter-band transitions for perpendic-ular polarized light are observed for pristine b-Si except3 S ( m V / K ) E-E F (eV) b-SiTiSi VSi MnSi FeSi CoSi Figure 3: Seebeck coefficient of the b-Si (golden) and the TM-siliceneat temperature T = 100 K. including TiSi (purple), VSi (red),MnSi (light blue), FeSi (blue), and CoSi (black). the transitions here occur below 10 eV.It is interesting to see that the optical response for TM-silicene is strong at low energy (in the visible and the UVregions) for both the parallel and the perpendicular polar-izations of the electromagnetic fields. This is attributed tothe following facts related to the band structure of TM-silicene. First, the gap at the Γ point in the band structurefor all TM-silicene decreases with a increasing atomic ra-dius of the dopant atoms. The higher the atomic radiusthe smaller gap at Γ point is. Second, parallel bands areformed in all directions between bonding and antibondingorbitals of the TM-silicene. These parallel bands lead tomost of the transitions in the visible and the UV regions.Third, optical transitions occur around van Hove singu-larities. A van Hove singularity is caused by a flat bandformed along the M to K as is seen in the band structureof MnSi and CoSi . The effects of a van Hove singularityon the optical response have been reported for 2D materi-als [22]. In this section, we show the results of a spin-dependentmodel for the pristine b-Si and the TM-silicenes. First, wepreform both ferromagnetic (FM) and antiferromagnetic(AFM) calculations where the strength of the magnetiza-tion is assumed to be 0 . E = E AFM − E FM .The ∆ E of TiSi is zero indicating a nonmagnetic struc-ture, and for VSi , MnSi , FeSi , and CoSi the differ-ences are 85 .
05, 50 .
05, 13 .
6, and − . , MnSi , and FeSi favor FM, butCoSi favors AFM.Based on ∆ E , one can further estimate the Curie tem-perature, T MFA C , via a mean field approximation using32 k B T MFA C = ∆ EN imp , (1)with N imp the number of TM atoms in the structure. TheCurie temperature of TiSi , VSi , MnSi , FeSi , and CoSi Figure 4: The imaginary dielectric function of pristine b-Si (golden)and TM-silicene including TiSi (purple), VSi (red), MnSi (lightblue), FeSi (blue), and CoSi (black) for in-plane, E in , or parallel(a) and out-plane or perpendicular, E out , (b) electric fields. is found to be 0, 657, 386, 105, and 609 K. The resultsfor the Curie temperatures in our calculations agree wellwith a previous study [39], and they are candidates forthermospin devices at 100 K as our study shows.It is known that the TM atoms have a strong cou-pling with silicene giving a strong modification of the spin-dependent band structures, density of states, and spintransport properties [39]. Figure 5 and 6 show the elec-tronic band structure and the Dos of b-Si and TM-silicenefor both spin-up (solid lines) and spin-down (dotted lines),respectively. The band structure and the Dos for b-Si re- -2-1012 E - E F ( e V ) (a) (b) (c) (d) -2-1012 E - E F ( e V ) (e) (f) (g) (h) -2-1012 Γ M K Γ E - E F ( e V ) (i) Γ M K Γ (j) Γ M K Γ (k) Γ M K Γ (l) Figure 5: Spin-dependent electronic band structure of b-Si (golden)and TM-silicene including TiSi (purple), VSi (red), MnSi (lightblue), FeSi (blue), and CoSi (black). The sold lines are spin-upand dotted lines are spin-down. The Fermi energy is at 0. igure 6: Spin-dependent Dos of b-Si (golden) and TM-silicene in-cluding TiSi (purple), VSi (red), MnSi (light blue), FeSi (blue),and CoSi (black). The sold lines are spin-up and dotted lines arespin-down. The Fermi energy is at 0. veals that the spin-up and the spin-down band structuresand Dos are symmetric indicating no magnetic properties.In addition, a spin splitting does not occur between thespin-up and the spin-down close to the Fermi energy show-ing the pristine b-Si is non-magnetic.In the TM-silicene, the band structures and the Dosmanifest different trends such as nonmagnetic semicon-ductors, magnetic metals, and half-metals. Namely, TiSi (purple) has nonmagnetic or spin unpolarized semicon-ducting property with bandgap 0 .
51 eV for both spin chan-nels. The bandgap here is exactly equal to the bandgapof the structure predicted by the spin-independent modelmentioned before. Spin unpolarized semiconducting is asemiconductors having a bandgap but there is no spinsplitting between the spin-up and spin-down, and bothspin channels have the same structure. These struc-tures are called nonmagnetic semiconductors. Further-more, VSi (red) and FeSi (blue) indicate a magnetic orspin polarized metallic behavior with a spin splitting be-tween the spin-up and the spin-down states around theFermi energy, and the Fermi energy crosses the valenceor the conduction bands. In the two TM-silicene, MnSi (light blue) and CoSi (black), we notice a spin polarizedhalf-metallic feature with the states of one spin directionshowing a semiconducting behavior, while the other dis-plays a metallic behavior. Such property is a basis forspintronic applications. The indirect bandgap of the spin-down channel of MnSi is 0 .
64 eV, and CoSi it is 0 .
21 eV.It is interesting to see that VSi has a semiconductor prop-erty, when the spin is ignored as is shown in Fig. 2c, butin the spin-dependent model VSi becomes metallic. Thesame applies to MnSi and CoSi , which are metallic ac-cording to the spin-independent model, but they becomehalf metallic when spin is accounted for. These spin phasetransitions have been observed for silicene materials andsuperlattices [46]. The spin-phase transition process leadsto an increase in thermal efficiency. For instance, the spin-independent Seebeck coefficient of MnSi and CoSi weresmall shown in Fig. 3, but the spin-polarized Seebeck coef- Figure 7: Seebeck coefficient of b-Si and TM-silicene at T = 100 Kfor both spin-up (a) and spin-down (b) channels. ficient of MnSi and CoSi is enhanced for the spin-downchannel as is shown in Fig. 7. This is attributed to theopening of bandgaps for the spin-down channel makingthem half-metals. It should be mentioned that the See-beck coefficient of TiSi is the same for both spin-up anddown because TiSi is nonmagnetic material. In contrast,the spin-independent Seebeck coefficient of VSi was highbut it is suppressed for spin-up and totally vanished forspin-down channel. This spin-dependent phase transitionis an important property, through which a bandgap canbe induced by means of magnetic dopants. The systemswith such a bandgap can be applicable to practical areas,such as field-effect transistors (FETs) [2], single-spin elec-tron sources [47], and nonvolatile magnetic random accessmemory [48]. This is also important for thermospin filter-ing in spintronic devices.The spin-dependent phase transition can mainly be re-ferred to the spin-dependent orbitals of the TM atoms,which contribute to the energy level through the hybridiza-tion between the TM atom and the silicene layer as is pre-sented in Fig. 8. We clearly see that the density of stateof the TM atom for both spin-up and spin-down aroundthe Fermi energy has high contributions. Especially, thespin-down density of states of TM atoms is much strongeraround the Fermi energy compared to the spin-up states.Another magnetic property of the TM-silicene is themagnetic moment. The 3 d -orbitals of the TM atoms givesrise to the magnetism of TM-silicene, and its partial den-sity of state difference for both spin-up and spin-downstates shown in Fig. 9, which is responsible for the netmagnetic moment. In particular, one can observe that thePDos (partial Dos) peaks of the d-orbitals of the transitionmetal, d-TM, can align with the peaks of the p-orbitals ofthe Si atoms of silicene, p-Si, very well. This implies thatthere are the strong interaction and large orbital hybridiza-5 igure 8: The spin-dependent density of state of the Si and TMatoms in TM-silicene, FeSi , for spin-up (a) and spin-down (b). tion between the TM atoms and the silicene. As a result,high magnetic moments are found in TM-silicene. Figure 9: The partial density of state, PDos, of the d-orbital of TM-atom, d-TM, and p-orbital of Si atoms of silicene, p-Si, for bothspin-up (a), and spin-down (b).
Figure 10 shows the magnetic moments of the b-Si andthe TM-silicene systems for the p-orbital contribution ofthe Si atoms ( µ p ), 3d orbitals of the TM atoms ( µ ), andthe total magnetization of the TM-silicene ( µ Total ). Onecan clearly see that the magnetization is mainly caused bythe TM atoms. In addition, we should remember that ourresults for the magnetic moment is underestimated by theGGA-PBE calculations. If GGA+U or HSE calculationsare used, the obtained magnetic moments will be higher.For instance, the magnetic moment of MnSi is 3 µ B usingthe GGA-PBE approach, but it is increased to 4 µ B if theGGA+U or HSE are used. This smaller value of magneticmoment of MnSi here can be attributed to the fact that,the semilocal GGA functional tends to delocalize the d electrons and increase the d - p overlapping, consequentlyleading to the underestimation of the magnetic moment ofthe Mn dopant [39].In order to give a more clear picture of the magneticdistribution, we plot the spin polarized density (∆ ρ = ρ up − ρ down ) in Fig. 11 for b-Si and TM-silicene. Thespin polarized distribution of b-Si and TiSi is very small.It is neglectable even on the finer scale used on these twosubfigures (see the scale of the z-axis). Remarkably, Thespin polarized distribution of other TM-silicenes is almost -0.5 0 0.5 1 1.5 2 2.5 3 3.5b-Si TiSi VSi MnSi FeSi CoSi M agne t i c M o m e m n t ( µ B ) µ p µ µ Total
Figure 10: Magnetic moments of b-Si and TM-silicene for the p-orbital contribution of Si atoms ( µ p ), 3d orbitals of TM atoms ( µ ),and total magnetization of TM-silicene ( µ Total ). entirely located on the dopant atoms, showing highly lo-calized magnetic features. Especially, the spin polarizationof the Mn atom in MnSi is highest, revealing the highestmagnetic moment as was mentioned before. Figure 11: The spin polarized density of b-Si and TM-silicene struc-tures.
4. Summary and Conclusions
We have studied TM-silicene with density functionalcomputation models neglecting, or accounting for spin-polarization. In the absence of spin-polarization in TM-silicene, we observe both metallic and semiconductor be-havior depending on the TM dopant atoms. As a resulta thermoelectric property such as the Seebeck coefficientis enhanced, and TM-silicenes show a large optical re-sponse at low energy. In the presence of spin-polarizationin TM-silicene, a spin phase transitions occurs leading tohalf metallic, metallic, and semiconductor properties ofthe TM-silicene. The spin phase transitions induce spinfiltering or the possibility to access a thermospin trans-port via spin-up and down channels depending on thespin-dependent band structure. In addition, strong or-bital interactions between the Silicon and the TM atomsare observed. These interactions control the magnetiza-tion of the system, in which a high magnetic moment ofTM-silicene is generated.6 . Acknowledgment
This work was financially supported by the Universityof Sulaimani and the Research center of Komar Univer-sity of Science and Technology. The computations wereperformed on resources provided by the Division of Com-putational Nanoscience at the University of Sulaimani.
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