Versatile electronic and magnetic properties of chemically doped 2D platinum diselenide monolayers: A first-principles study Muhammad Zulfiqar, Geng Li, Yinchang Zhao, Safdar Nazir, and Jun Ni
Citation: AIP Advances 7, 125126 (2017); View online: https://doi.org/10.1063/1.5011054 View Table of Contents: http://aip.scitation.org/toc/adv/7/12 Published by the American Institute of Physics
AIP ADVANCES 7, 125126 (2017)
Versatile electronic and magnetic properties of chemically doped 2D platinum diselenide monolayers: A first-principles study Muhammad Zulfiqar,1,2 Geng Li,1,2 Yinchang Zhao,3 Safdar Nazir,4 and Jun Ni1,2,a 1 State
Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People’s Republic of China 2 Collaborative Innovation Center of Quantum Matter, Beijing 100084, People’s Republic of China 3 Department of Physics, Yantai University, Yantai 264005, People’s Republic of China 4 Department of Physics, University of Sargodha, 40100 Sargodha, Pakistan (Received 29 October 2017; accepted 19 December 2017; published online 29 December 2017)
First-principles calculations have been performed to study the chemically doped platinum diselenide (PtSe2 ) monolayers. We examine the stability of different doping sites by calculating the formation energy. The different electronic and magnetic characters originate from hybridization between the dopants and nearest local atoms. Exceptional electronic and magnetic characters are observed in the B-, P-, Li-, and Ca-doped cases because of doping site independence. The magnetic behavior of the dopant atoms is found to be complex because of interplay between strong structural relaxation, spin lattice coupling, and crystal field splitting. More interestingly, the ferromagnetic half metallic character obtained in B- and N-doped cases, expected to be very useful because of large half metallic energy bandgap. The interaction between dopants is analyzed as a function of their separation, showing that substitution typically counteracts spin polarization. The long range ferromagnetic behavior can be established with improved stability which suggest the high magnetic transition temperatures, found for the B-, F-, N-, P-, and Li-doped at Pt sites which make them potential candidate for applications in electronic devices as well as in spintronics. © 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5011054
I. INTRODUCTION
Graphene has fascinated the immense research interests over the last decade1 due to its unique properties such as high mobility, good conductivity, and massless Dirac fermion feature.2–7 However, the presence of zero-bandgap limits the practical implementation of graphene in optoelectronic nanodevices. It led to extensive experimental and theoretical efforts, which devoted in search of new low-dimensional structures with finite band gaps. The sequential rise of silicene,8–10 h-BN,11–15 transition metal dichalcogenides (TMDC),16,17 black phosphorene18,19 are the results of these efforts. Generally, 2D transition metal dichalcogenides are represented by the formula MX 2 , where M and X denote transition metals and chalcogen atoms, respectively. Due to variety available for the combinations of transition metals and chalcogen atoms, bulk TMDC possess various properties ranging from insulators (HfS 2 ), semiconductors (MoS 2 ,WS 2 ), semimetals (WTe2 , TiSe2 ), metals (NbS 2 , V Se2 ) to superconductors (NbSe2 , TaS 2 )20 etc. The counterparts of bulk MX 2 at Low-dimensions, not only preserve certain bulk properties but also some new characteristic appear due to quantum effects.21–23 For instant, TMDC at low dimension offers various new research prospective in different fields like catalysis, energy storage, sensing and electronic devices. a
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In contrast to the conventional fabrication techniques such as exfoliation11,24 or chemical vapor deposition (CVD).25,26 The PtSe2 monolayer is synthesized via single step, i.e. selenization of platinum substrate. The results obtained from angle-resolved photoemission spectroscopy and band structure calculations suggest that it exhibits semiconducting nature in contrast to semi-metallic character of its corresponding bulk counterpart. The results obtained from photo-degradation experiment clearly indicates that it can be utilize as visible light-driven photocatalyst.27 The PtSe2 monolayer is also expected to be a good candidate for valleytronics as predicted by circular polarization calculations.27 Moreover, at room temperature, the PtSe2 monolayer possesses the highest mobility (3000 cm2 /V /s) among the large family of 14 kinds of atomically thin TMD,28 which is even larger than the black phosphorus (1000 cm2 /V/s).18,29 Hence, in view of the simplicity of fabrication, the ultra-high electron mobility, the sizable bandgap, and good photocatalytic performance, the PtSe2 monolayer is viewed as one of the most promising candidate as far as practical applications are concerned. Since most of the members of 2D TMDC are intrinsically diamagnetic, so a natural desire grows up for the investigation of the magnetism in 2D TMDC.30–32 As compare to extensively studied functionalized MoS 2 monolayer, the effect of these substitutional dopants on the electronic and magnetic properties of the PtSe2 monolayer have not been investigated yet. Whereas, the doping has been considered as a well-known, effective, and appealing methodology to induce magnetic behavior in other 2D non-magnetic materials.33–36 Thus, in this work, we study the electronic and magnetic properties of non-metals (B, C, N, O, S, P, and F), alkali metals (Li and Na) and alkaline earth metals (Mg and Ca) doped PtSe2 monolayer using first-principles investigations. The results of our calculations exhibits that enriched electronic and magnetic properties like semiconductor, metal, spin semiconductor, and half metal can be developed effectively by substituting these dopants either at Pt or Se site in the PtSe2 monolayers. Interestingly, half metallicity obtained in the B-and N-doped systems with large fascinating half metallic bandgap, which is very useful in spintronics as far as its practical realization is concerned. Moreover, the formation energy calculations are used to find the favorable doping sites and the spatial arrangement of the dopant atoms is studied to clarify the effect of chemical functionalization. II. COMPUTATIONAL METHODS
We have calculated our doped systems by Vienna ab initio simulation package (VASP),37,38 using plane wave basis set, based on spin-polarized density-functional theory. The ion cores and valence electrons interactions are dealt by projector augmented-wave (PAW)39 potentials by using 500 eV energy cutoff. Generalized gradient approximation along the Perdew-Burke-Ernzerhof (PBE) functional40 is utilized to deal with valence electron exchange and correlation potentials. A 4 × 4 PtSe2 monolayer supercell comprising of Pt, Se and only one substituted dopant is employed for the calculations. A vacuum space of 15 Å along perpendicular direction is used to restrict the interlayer interactions. For electronic iterations, the energy convergence threshold is set to be 10 5 eV. Conjugate gradient algorithm are used to fully optimize all the geometries until the Hellmann Feynman forces become less than 0.02 eV/Å for each atom. For a 4 × 4 supercell of doped PtSe2 monolayer, the Brillouin zone (BZ) for structure optimizations is tested by a Monkhorst Pack 41 k-grid of 5 × 5 × 1 but in case of static and electronic density of state (DOS) calculations a k-mesh of 9 × 9 × 1 is utilized. The formation energies for the doped systems can be calculated according to the following formula:42 EF = Etot,X − Etot,perfect − µX + µPt(Se)
(1)
Where, µPt (Se) represents Pt(Se) atom’s chemical potential. E tot ,perfect and E tot ,X denote the ground state energies of a perfect 4 × 4 supercell and a 4 × 4 supercell containing one dopant atom X, respectively. The µX denotes the chemical potential of substituted atoms which is considered equivalent to the energy of atoms in isolated form. µPt (Se) is related to the growth condition. In the Se rich condition, µSe is subject to an upper bound, it is given by the energy of Se atom while it is in bulk phase. For hexagonal Se: µSe = 1/3 E Se ,hex , gives the lower bound on the µPt i.e. µPt = E tot,f.u 2µSe . Whereas, in the Pt rich condition, µPt is subject to an upper bound given by the Pt atom’s
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energy when it is in bulk phase, for fcc Pt, µPt = 1/4 E Pt ,fcc . Correspondingly, the upper bound on Pt gives a lower bound on Se: µSe = 1/2 (E tot,f.u µPt ). E tot,f.u is equivalent to the ground state energy of the pristine PtSe2 unit cell. III. RESULTS AND DISCUSSION A. Structural properties and defect formation energies
Before revealing the influence of substitutional dopants on the electronic and magnetic characteristics of the doped PtSe2 monolayers, we have first focused on the structural changes caused by these dopants. The typical structure studied in this paper is presented in Fig. 1(a). The relaxed lattice constant, bond length of Pt Se and Se Pt Se bond angle are 3.75 Å, 2.528 Å and 95.630 , respectively. These are consistent with other experimental and theoretical works.27,43 The spin polarized electronic band structure is presented in Fig. 1(c), which clearly shows that the pristine PtSe2 monolayer exhibits an indirect bandgap of 1.22 eV. We have calculated the total DOS and orbital resolved density of states as presented in Fig. 1(d), in order to clarify the contributions made by different orbitals. The electronic states lying near the Fermi level are mainly comprise of both p and d orbitals of Se and Pt atoms, as shown in Fig. 1(d). However, it is worthy to mention that the contributions made by the p orbitals of Se atoms are dominant on the valance band while on the conduction band edge contributions mainly come from the d orbitals of Pt atoms in the total DOS. Partial charge densities corresponding to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for the pristine PtSe2 monolayer are presented in Fig. 1(b), respectively.
FIG. 1. (a) Top and side view of the pristine PtSe2 monolayer. (b) Partial charge densities of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), (c) the electronic band structure, and (d) the total and partial electronic density of states (DOS) for unit cell. The Fermi level is set to be zero for all DOS and band structures.
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TABLE I. The calculated spin polarization energy (∆E sp ), Bader charge transferred (ρdopant ), total magnetic moment (µtot ), energy bandgap (E gap ) and the formation energy (E F ) of the (4 × 4) doped PtSe2 systems, when Se site is chosen for doping. In the energy bandgap (E gap ) column ‘M’ and ‘HM’ denote metal and half-metal, respectively. E F (eV) Elements B C N O F P S Li Na Mg Ca
∆E sp (meV)
ρdopant
µ tot (µ B )
E gap (eV )
Se-rich
Se-poor
-20.4 0.00 -272 0.00 0.00 -516 0.00 -5.72 -0.36 19.8 -34.2
-0.29 0.28 0.66 0.72 0.74 -0.002 -0.29 -0.50 -0.48 -1.23 -0.98
1.0 0.0 1.0 0.0 0.0 1.0 0.0 0.9 1.0 2.0 2.0
HM 1.00 0.96 1.30 M 0.40 1.40 M M HM 0.06
-8.90 -8.93 -6.79 -7.72 -5.87 -7.52 -7.86 -5.63 -5.20 -5.02 -6.66
-8.55 -8.58 -6.44 -7.37 -5.52 -7.17 -7.51 -5.28 -4.58 -4.67 -6.31
The calculated results for all doped systems when substitutions made at cation and anion sites are tabulated in Table I and Table II, respectively. In case of substitution made at anion (Pt) site, shrinkage in the X Se bond lengths is being observed for the B-, C-, N- and O-doped systems after the structure relaxation, while the F, P, S, Li, Na, Mg and Ca substituted atoms force the neighboring Se atoms to move outward from their initial positions, which enlarges the X Se bond lengths. In case of substitution made at cation (Se) site, the shrinkage in the Pt X bond length is being observed for the B, C, N, O, P, and S atoms as compared to the original Pt Se bond length of 2.528 Å, while bond lengths get enlarged for the Li, Na, Mg and Ca atoms. The difference in the atomic radii and electronegativities for all the dopants in comparison to Pt or Se plays a vital role in the shrinkage or stretching of the bonds. Meanwhile, formation energy determines the experimental growth possibility and stability of these doped PtSe2 monolayers. It is important to mention here that for all the doped systems, the formation energies under Pt or Se enrich growth conditions are sensitive to cation or anion doping site. The order of the formation energies when cation (Se) site is chosen for doping either under Se rich or poor conditions are as follows: E f (Na) > E f (Mg) > E f (Li) > E f (F) > E f (Ca) > E f (N) > E f (P) > E f (O) > E f (S) > E f (B) > E f (C). In the same manner, the order of the formation energies when anion (Pt) site is chosen for doping either under Pt rich or poor conditions are as follows: E f (F) > E f (N) > E f (Na) > E f (O) > E f (Li) > E f (S) > E f (Mg) > E f (C) > E f (P) > E f (Ca) > E f (B).
TABLE II. The calculated spin polarization energy (∆E sp ), Bader charge transferred (ρdopant ), total magnetic moment (µtot ), energy bandgap (E gap ) and the formation energy (E F ) of the (4 × 4) doped PtSe2 systems, when Pt site is chosen for doping. In the energy bandgap (E gap ) column ‘M’ and ‘HM’ denote metal and half-metal, respectively. E F (eV) Elements B C N O F P S Li Na Mg Ca
∆E sp (meV)
ρdopant
µ tot (µB )
E gap (eV )
Pt-rich
Pt-poor
-38.7 0.00 -50.1 0.00 -26.0 -38.7 0.00 -23.8 -6.36 -17.7 -48.4
-0.50 0.19 0.19 0.43 0.68 -0.97 -0.89 -2.56 -6.66 -1.33 -1.24
1.0 0.0 1.0 0.0 1.0 1.0 0.0 3.0 1.0 2.0 2.0
HM 1.00 HM 0.75 M 0.20 1.00 M HM 0.04 0.10
-5.08 -3.89 -1.12 -1.45 0.56 -4.09 -2.76 -1.77 -1.16 -2.78 -4.62
-5.43 -4.24 -1.47 -1.80 0.19 -4.45 -3.11 -2.12 -1.51 -3.13 -4.97
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In addition, it can be noted from Tables I and II that for all the doped PtSe2 systems except for that of F substituted at Pt site, the formation energies are negative, which confirms the stability of these doped monolayers. Furthermore, it also indicates the possibility of an exothermic reaction during their practical realization in experiments under equilibrium conditions. Although the formation energies of the F-doped at Pt site in PtSe2 monolayer is positive but the value is not high at all, which indicates that this doping may be realized under non-equilibrium conditions during their experimental realization. Next, we address to the question whether these dopants in the PtSe2 monolayer either doped at anion or cation site could induce magnetic moment in PtSe2 monolayer. Our calculations show that when Se site is chosen for doping, the total magnetic moment are 0.9, 1, 1, 1, 2, 1 and 2µB for the Li-, B-, N-, Na-, Mg-, P-, and Ca-doped PtSe2 monolayers, respectively, while the C-, O-, F-, and S-doped monolayers have non-magnetic ground state. If Pt site is chosen, the Li-, B-, N-, F-, Na-, Mg-, P-, and Ca-doped PtSe2 systems attain the net magnetic moment of 3, 1, 1, 1, 1, 2, 1 and 2µB , respectively, while the C-, O-, and S-doped monolayers alike the former cases are non-magnetic. It is further confirmed by the calculations of polarization energy (∆E sp ) which is the energy difference between spin-polarized (E spin ) and non spin-polarized (E nspin ) states of these doped systems. For all the doped systems exhibiting the nonmagnetic state, the energy difference (∆E sp ) becomes zero as shown in the Table I and Table II. B. Non-metal doped systems 1. Substitution at Se site
Origin of magnetism can be understood qualitatively by analyzing the Bader charge for all the doped systems. The results indicate that for the B-, C-, N-, O-, F-, P-, and S-doped cases, there are -0.29, 0.28, 0.66 , 0.72, 0.74, -0.002 and -0.29 charge transfer among p-orbitals of dopants and neighboring atoms, respectively. However, in the C-, O-, F-, and S-doped cases, the unavailability of unpaired electrons leads to zero magnetic moment. Moreover, the electron transfers in the B-, N- and P-doped systems induce unpaired electrons, which induces a net magnetic moment. To get better understanding of the mechanism behind the magnetic properties of the B-, N-, and P-doped monolayers, we plot the total and orbital resolved DOS for impurity atoms along nearest Se and Pt atoms in Fig. 2(a–d). For the C-, O-, F-, and S-doped cases, the majority and minority spin states of total DOS are symmetric, which indicates that these substituting atoms cannot induce magnetic moments in the PtSe2 monolayer. In contrast, the B-, N-, and P doped cases exhibit net magnetic moments because their majority and minority spin states in the total DOS and orbital resolved DOS are not symmetric, which is further confirmed by the results of charge density difference (CDD) isosurfaces in the FIG. 1S(a,b,d) (see supplementary material). Additionally, Fig. 2(a) indicates that B-doped PtSe2 monolayer, the half-metallic behavior can be observed with the minority spin metallic and majority spin semiconducting, which suggests that the B-doped PtSe2 monolayer can be practically utilized for injecting the spin-polarized species into the non-magnetic PtSe2 monolayer. Moreover, the N- and P-doped systems exhibit the spin semiconducting characteristics. Furthermore, Fig. 2(a–d) shows that hybridized p-orbitals dopants and 4p- and 5d-orbitals of the nearest atoms mainly contribute to the induced impurity states. This hybridization causes the energy levels exiting near the Fermi energy to split. Therefore, this p-d hybridization serves as the main reason behind the mechanism of the induced magnetism in these doped systems. One can also see from Fig. 2(a,b,d) that for spin-polarized cases, the p-orbitals of non-metal dopants mainly contribute in the spin polarizations. Such as, for B-, N-, and P-doped systems, the 2px , 2py -orbitals and 3px -orbitals, respectively contribute significantly to induce net magnetic moment. 2. Substitution at Pt site
Bader charge transfer between the p orbitals of corresponding atoms and neighboring Se atoms are presented in the form of CDD isosurfaces in the FIG. 1S(e–h) (see supplementary material). Alike the above mentioned cases except for the F-doped case, the C-, O-, and S-doped systems show zero magnetic moment due to the lack of unpaired electrons. Whereas, the B-, N-, F-, and P-doped atoms result into the unpaired electrons, which developed net magnetic moments in these doped systems.
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FIG. 2. The total and orbital resolved DOS for (a) B, (b) N, (c) F, and (d) P doped systems when atoms are doped at Se site and (e) B, (f) N, (g) F, and (h) P doped systems when atoms are doped at Pt site, respectively. All the PDOSs are magnified by 15 times.
Figure 2(e–h) shows the total DOS for the B-, N-, F-, and P-doped cases, orbital resolved DOS of dopants and the nearest Se atom around dopants. It can be seen that the impurity atoms N and F which carry a Bader charge of 0.18e and 0.67e respectively, form acceptor impurity states at the top of valence band, so causing p-type doping in PtSe2 monolayer. However, the B and P atoms with Bader charge of -0.5e and -0.97e, respectively, donor impurity states produce close to Fermi level like the other active non-metal dopants. In spite of that Fig. 2(e,h) also shows that the B- and P-doped case do not differ much from the former cases, with similar overall characteristics such as half-metallic and spin semiconducting features. For the B- and N-doped monolayers, minority spin is metallic while
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majority spin is semiconducting. However, the P-doped case exhibits spin semiconducting, while the F-doped system shows the metallic characteristics with magnetic ground state because impurity states are asymmetric. Such impurity states develop from the hybridization of the p-orbitals of these dopants and the 4p-orbitals of the surrounded Se atoms because every dopant substituted at Pt site is surrounded by six Se atoms only, which differ from the former case. This hybridization causes the splitting of energy levels existing close to Fermi level. Hence, the origin of the induced magnetism in these cases is the p-p hybridization indeed. In addition, for spin-polarized systems shown in Fig. 2(e–h), similar to the above mention cases, the major source of spin polarization for different non-metal atoms originates from different p-orbitals. For instance, in the B-, N-, F-, and P-doped cases, major contribution to the magnetic moment stems from the 2pz , 2px , 2py and 3py orbitals, respectively. Interestingly, impurity atoms especially the B and P show exceptional magnetic properties because of their doping site independence. Hence, we proposed that B- and P- doped PtSe2 monolayers have potential applications in spintronics as well as nanoelectronic devices. To further elaborate, we have drawn the band structures of the non-metal doped PtSe2 monolayers, with the substitution at Se and Pt site are shown in Fig. 5(b–h) and Fig. 6(b–h), respectively. For all the doped systems, band structures are highly affected by the specific impurity atom. From Fig. 5(c,e,f,h), it can be seen that the C-, O- and S-doped at Se site possess non-magnetic ground states with indirect bandgaps of 1, 1.3 and 1.4 eV, respectively. The F-doped case shows the metallic characteristics by retaining its non-magnetic ground state. Interestingly, spin polarize energy bandgap is originated for N- and P-doped PtSe2 monolayers, which justify their dilute magnetic semiconducting behavior. Furthermore, B-doped PtSe2 monolayer, the only minority spin band crosses Fermi level and the majority spin band keep semiconducting behavior. So, the B-doped monolayer PtSe2 system possesses the half-metallic characteristics. In a similar way, from Fig. 6(c,e,h), with Pt substituted site, the C-, O- and S-doped monolayers exhibit non-magnetic ground states with direct reduced bandgaps of 1, 0.75 and 1 eV, respectively. Remarkably, spin polarized energy gap is found for the P-doped system, which exhibit the properties of narrow band spin magnetic semiconductor. Whereas, for B-and N-doped systems, only the minority spin band crosses the Fermi level. Thus, the B- and N-doped PtSe2 systems possess the half-metallic behaviors with the large fascinating half metallic band gap. It is obvious that the large half-metallic gap is crucial for half metal regarding it practical implementation in spintronics because a significant half-metallic gap effectively controls the spin flip of charge carriers caused from thermal excitations. So, half metallicity can be preserved even at high temperatures. These all results are in good agreement with the analysis of the DOS of non-metals doped PtSe2 monolayers as shown in Fig. 2. C. Alkali metal doped systems 1. Substitution at Se site
The calculated spin polarized total and orbital resolved DOSs for the Li- and Na-doped systems are shown in Fig. 3(a–b) when the substitution is made at Se site. It can be seen that the DOSs are very sensitive to dopants because of charge transfer. Alkali atoms have small electron affinities because of this charge get transfer to PtSe2 monolayer. Thus according to Bader charge analysis, 0.50e and 0.48e are transfered from Li and Na atoms, respectively. As a result, these doped systems switched to metals due to shifting of E F . For an isolated alkali atom, s orbital is always half filled due this alkali atoms carry a net magnetic moment of 1.0µB . Thus, in Li- and Na-doped systems the s states are nearly empty, so the bonding between an alkali atom and neighboring atoms is mainly ionic in nature. Therefore, the net effect of Li- and Na-doped cases can be regarded as electron doping only. The Liand Na-doped systems are spin polarized with the net magnetic moment of 1µB in each case. The impurity states present at Fermi level are non-symmetric for both cases. It means that the most part of electrons transfer to the surrounding atoms and only small amount of charge accumulate around Li(Na) which causes a small magnetic moment. Figure 3(a–b) shows the total density of states (DOS) of the ground state for the Li- and Na-doped PtSe2 monolayers and the partial DOS of dopants, the nearest Se and Pt atoms around dopants. It can be seen that the transfer of electrons to surrounding atoms creates donor defect states at the Fermi level due to which both doped systems switch to metallic state. The s orbitals of the Li and Na atoms
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FIG. 3. The total and orbital resolved DOS for (a) Li and (b) Na doped PtSe2 monolayers when atoms are doped at Se site and (c) Li and (d) Na doped systems with dopants substituted at Pt site, respectively. All the PDOSs are magnified by 15 times.
are hybridized with the 5d orbitals of the nearest Pt atom around the dopants. These impurity states originate due to this hybridization, which further causes these energy levels to split close to Fermi level. Hence, the s-d hybridization explain the mechanism of magnetism developed in these doped systems. Moreover, it is more obvious that major contribution to the magnetism evolved in these cases come from the 5d orbitals of the nearest Pt atom, while a minor contribution come from the s-orbitals of alkali metals as expected, which is further confirmed by the charge redistribution of the doped system, shown as the CDD isosurfaces in the FIG. 2S(a–b) (see supplementary material). 2. Substitution at Pt site
Similar to the substitution at the Se site, substitution of Li and Na atoms at the Pt site significantly varies the electronic properties of PtSe2 monolayer as presented in Fig. 3(c–d). Since Li(Na) atom transfers -0.26e(-0.67e) to surrounding Se atoms so doping of Li and Na can also be considered as electron doping. This charge transfer causes the E F to shift, which forces the Li-doped system into metallic states while Na-doped system attains the properties of half metal. The s states in the Li- and Na-doped systems are nearly unoccupied, which results into the ionic bonding between alkali atoms and neighboring Se atoms. This is further clarified by CDD isosurfaces in the FIG. 2S(c–d) (see supplementary material). However, due to the unpaired electrons present in the Li- and Na-doped systems, the net magnetic moment of 3µB and 1µB , is developed. Figure 3(c–d) shows the calculated spin polarized total and orbital resolved DOS of the ground state for the Li- and Na-doped PtSe2 monolayers. Even though the Li and Na atoms have less valence electron than Pt due to the transfer of electrons to surrounding Se atoms, donor defect states are created above the top of the valence bands. It is also found that the s orbitals of the Li and Na atoms are hybridized with the 4p orbitals of the nearest Se atom around the dopants. Impurity states originates due to this hybridization, which further causes these energy levels to split near the Fermi level. Hence, the s-p hybridization is responsible for this kind of magnetism in these doped systems. Moreover, it is also noticeable that 4p-orbitals of the nearest Se atom mainly serve as a source for the spin polarization in these doped systems, while a minor contribution comes from the s-orbitals of alkali metals. For instance, for the Li- and Na-doped cases, the 4pz - and 4px -orbitals, respectively
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plays a vital role in developing a net magnetic moment. Interestingly, the Li-doped system sustains its metallic properties with magnetic ground state either it is doped at Se or Pt site. Figures 5(i–j) and 6(i–j) show the spin polarized band structure of the 4 × 4 supercell of the Liand Na-doped PtSe2 monolayers. Owning to Li and Na atoms substitutions at either site, the doped bands close to Fermi level appear. Additionally, the charge transfer from dopants to surrounding atoms, the Fermi level of the Li and Na-doped PtSe2 monolayers are shifted and the numbers of the valence bands are increased as compared to the pristine PtSe2 monolayer. If substitution is made at the Se site, the Li- and Na-doped PtSe2 systems both show metallic character because the impurity bands crossing the Fermi level. For the Pt site substitution, Li-doped system continues to exhibit metallic nature with spin-up and spin-down bands crossing the Fermi level, resulting into the net magnetic moment. Whereas, for Na substituted at the Pt site, only spin-up band crosses the Fermi level and corresponding system switches to a half-metal state. D. Alkali earth metal doped systems 1. Substitution at Se site
The calculated spin polarized total and orbital resolved DOS near E F for Mg- and Ca-doped systems are shown in Fig. 4(a–b). Similar to former cases, the overall DOS is modulated due to the presence of Mg and Ca dopants as a result the impurity bands appeared. The Mg- and Ca-doped systems are also exhibiting the net magnetic moment of 2µB in each case. The isolated Mg(Ca) atom has two electrons in the 3s(4s) shell. When Mg(Ca) is substituted at the Se site, the two electrons migrate to the PtSe2 monolayer, due to this an ionic bond forms among Mg(Ca) atom and surrounding Pt and Se atoms. The charge transfer from the Mg(Ca) to surrounding atoms is 0.12(0.98)e, revealing the ionic nature of bonds. Moreover, the CDD isosurfaces in the FIG. 3S(a–b) (see supplementary material) also shows the ionic nature. As a result, E F is get shifted, which makes the Mg-doped system to attain the characteristics of half metal and the Ca-doped system begins to exhibit the characteristics of narrow band spin semiconductor. Hence, the effect of the Mg- and Ca-dopings is alike that of the Li- and Na-doped cases, which can also be consider as electron doping.
FIG. 4. The total and orbital resolved DOS for (a) Mg and (b) Ca doped PtSe2 monolayer when Se site is chosen for doping and (c) Mg and (d) Ca doped systems with substituted at Pt site, respectively. All the PDOSs are magnified by 15 times.
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2. Substitution at Pt site
According to the Bader charge analysis, the Mg(Ca) atom transfer -0.13e(-0.14e) to the surrounding Se atoms, so again the dopings of the Mg and Ca are electron dopings, which effectively shift the Fermi levels. As a result, both Mg- and Ca-doped systems show the characteristics of spin semiconductors. Hence, the Mg and Ca-doped PtSe2 monolayers retain the spin semiconductor characteristics irrespective of their anion or cation doping site. Therefore, the Mg- and Ca-doped PtSe2 monolayers have the potential applications in nano-electronics and spintronics. Also, the CDD isosurfaces of these atoms are provided in the FIG. 3S(c–d) (see supplementary material) clarify the ionic bonds between the Mg(Ca) and the Se atoms lying in the surrounding regime. However, the Mg- and Ca-doped PtSe2 monolayers are fully spin polarized, developing net magnetic moments of 3µB and 1µB , respectively. Also, Figure 4(c–d) illustrates the total density of states (DOS) for the Mg- and Ca-doped systems along the partial DOS of dopants and the nearest Se atom. In a similar way, the Mg and Ca dopants donate electrons to the surrounding Se atoms. Thus impurity states form at the top of the valence band. These impurity states close to Fermi level originate because of s-p hybridization. Additionally, it can also be noticed that the spin polarized 4p orbitals of the nearest Se atom mainly contribute to develop magnetism in these systems whereas the contribution from the s-orbitals of alkali metals is negligible. Hence, the 4px orbitals of Se atoms play the major role in making the system spin polarized in order to develop net magnetic moment in both cases. The calculated spin polarized band structures of the Mg- and Ca-doped PtSe2 monolayers are shown in Figs. 5(k–l) and 6(k–l), respectively. The substitutions of the Mg and Ca atoms at both Pt and Se sites, successfully developed the doped bands close to E F because of electron transfer. By choosing either Pt or Se site for doping, the Ca-doped systems behave as spin semiconductors.
FIG. 5. Band structures of the 4 × 4 pristine and B-, C-, N-, O-, F-, P-, S-, Li-, Na-, Mg-, Ca-doped PtSe2 monolayers when dopants substituted at Se site. The black and red solid lines represent the spin-up and spin-down states, respectively.
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FIG. 6. Band structures of the 4 × 4 pristine and B-, C-, N-, O-, F-, P-, S-, Li-, Na-, Mg-, Ca-doped PtSe2 monolayers when dopants substituted at Pt site. The black and red solid lines represent the spin-up and spin-down states, respectively.
But the substitution of Mg at the Se site, only the spin up doped band crosses the Fermi level, which turns it into half metal. If the substitution is made at the Pt site, it behaves as a spin semiconductor. These results of spin polarized band structures for the Mg and Ca doped systems are consistent with the DOS calculations. To illustrate the spin distributions of the doped systems with magnetic ground states, the spin density distributions are plotted in Fig. 7. We have excluded those doped systems which possess the non-magnetic ground state. With Se doping site, it can be seen from Fig. 7(a–g) that the net magnetic moment is evolved from the polarized charges of the non-metal doped PtSe2 monolayers due to the p-d hybridization of non-metal dopants and the surrounding Se atoms, while the nearby Pt atom’s contribution is small. In a similar way, for the doping with alkali metals (Li and Na) and alkaline earth metals (Mg and Ca) the contributions to net magnetic moment mainly come from the s-p hybridization of spin polarization charges. In this s-p hybridization, the major contribution is made by the p orbitals of Se atoms in both cases. If the Pt site is chosen for doping, it is demonstrated in Fig. 7(h–o) that the spin polarization of such non-metal doped PtSe2 systems is mainly achieved due to p-p hybridization of non-metal dopants and the surrounding Se atoms, whereas in this p-p hybridization the contributions to the net magnetic moment are made by the nearby Se atoms. For alkali metals (Li and Na) and alkaline earth metals (Mg and Ca), the s-p hybridization of spin polarization charges is responsible for the developed net magnetic moments in both cases but it important to mention here that in these s-p hybridizations, the contributions from the p orbitals of nearby Se atoms dominate. Finally, we have investigated the magnetic coupling between dopants substituted at both sites in PtSe2 monolayer. It is common practice to establish long range magnetic interaction in 2D monolayers with low dopant concentration. Therefore, two Se or Pt atoms are replaced by two dopants in a 5 × 5 supercell. Additionally, we have considered the interaction of two dopants at three different separations (3.5Å, 7.7Å and 12.9Å; for all dopants substituted at Se sites) and (6.5Å, 7.7Å and 12.9Å;
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FIG. 7. Spin charge density distributions for all doped systems with magnetic ground state. For (a g), the Se site is chosen for substitution of corresponding atoms while for (h o), the Pt site is chosen for substitution of corresponding atoms. Green and blue regions correspond to the surplus spin-up and spin-down electrons, respectively. The isosurface value is taken at 0.001e/Å3 .
for all dopants substituted at Pt sites) in the 5 × 5 supercell. Usually, the strength of exchange coupling is likely to be determined from the energy difference (∆E = E FM E AFM ) between the ferromagnetic (FM) and antiferromagnetic (AFM) states. For dopants substituted at the Se and Pt sites, the energy differences between the FM and AFM states for all doped systems have been shown in Fig. 8. Figure 8 also, clarifies the change in the strength of magnetic interaction with respect to separation between dopants. Moreover, the strength of magnetic interactions for the dopants substituted at Se sites can be categorized as short range ferromagnetic interaction as mentioned in Fig. 8(a) while the strength of magnetic interactions regarding the dopants substituted at Pt sites can be considered as long range ferromagnetic interactions as mentioned in Fig. 8(b). To analyze the range of ferromagnetic interactions, we have also calculated the ferromagnetic interactions between these dopants at much
FIG. 8. Energy differences (∆E) between the FM and AFM states for (a) the dopants substituted at Se sites and (b) for the dopants substituted at Pt sites calculated at different separations (d 1 , d 2 and d 3 ) in the 5 × 5 supercell, respectively.
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larger separations by keeping the dopant concentrations same. The interaction of two dopants at the separation of 13Å is considered in the (5 × 5) supercell. For all the substitutions made at Se sites, the energy differences between the FM and AFM states are almost zero for B, N, P, Li, Ca, and Mg doped systems, suggesting paramagnetic ground states while non-magnetic state for Na doped system only. This fact indicates that there is essentially no ferromagnetic interactions exist between the dopant atoms, which is expected at a distance 13Å. Strikingly, some of the dopants like B, N, P, F, and Li substituted at Pt sites even sustain their ferromagnetic ground state at such a longer distance other than Ca and Mg doped systems which attain the paramagnetic and the nonmagnetic states respectively. The s-p and p-d hybridizations in case of dopants substituted at Se and Pt site of PtSe2 monolayer systems is characterized by their long range ferromagnetic couplings and exchange interactions between host atoms and dopants. In other words, for the dopants substituted at Se sites exchange interaction aligns the spin parallel only for short distances as presented in Fig. 8(a). But for the dopants substituted at Pt sites the behavior of the exchange interactions sustain the ferromagnetic orders at short distances as well as longer distances (other than Ca and Mg doped systems), with improved stability due to lower energy obtained as shown in Fig. 8(b). In other words, for such dopants substituted at Pt sites, these interactions have positive exchange coupling with the increasing distances, leading to ferromagnetic orders while antiferromagnetic orders are not favorable in both cases studied. These long range ferromagnetic features with large energy difference suggesting the high magnetic transition temperatures, found in the B-, F-, N-, P-, and Li-doped at Pt sites can find their potential applications in electronic devices as well as spintronics. Such FM coupling stem from double-exchange interactions, which requires the availability of delocalized carriers which jump to localized spins as a result of that the system’s kinetic energy get lower due to ferromagnetic alignment of localized spins.44 IV. CONCLUSION
In summary, we have carried out first-principles calculations to investigate the electronic and magnetic properties of chemically doped platinum diselenide (PtSe2 ) monolayers. Taking the experimental growth conditions into account i.e. Se(Pt) rich or poor conditions, all the doped systems exhibit the negative formation energies except for the F doped at Pt site, which suggests the possibility of these doped systems to be realized experimentally. When these atoms are chemically doped in the PtSe2 monolayers, it results into the formation of impurity states close to Fermi level. Because impurity states lying close to Fermi level are quite sensitive to the nature of the dopants, the doped PtSe2 monolayers exhibit various desired electronic and magnetic properties including semiconducting, metallic, half-metallic, and spin-semiconducting. Especially, the unusual behavior is found for the B-, P-, Li-, and Ca-doped cases, because the substitutions of these atoms at Pt or Se sites are quite independent as far as their obtained electronic and magnetic properties are considered. Interestingly, the ferromagnetic half-metallic character in the B- and N-doped cases may find practical applications for future spintronics because of large half metallic energy bandgap. The interaction between dopant atoms is analyzed as a function of their separation, showing that substitution typically counteracts spin polarization. The long range ferromagnetic features can be established with improved stability, suggesting the high magnetic transition temperatures, found for the B-, F-, N-, P-, and Li-doped at Pt sites. These rich electronic and magnetic properties of chemically functionalized PtSe2 monolayer, make them promising candidates in the future spintronics applications. SUPPLEMENTARY MATERIAL
See supplementary material for Charge density difference for doped PtSe2 monolayers. ACKNOWLEDGMENTS
This research was supported by the National Natural Science Foundation of China under Grant Nos. 11774195 and 11374175, and the National Key Research and Development Program of China under Grant No. 2016YFB0700102.
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S. Novoselov, A. K. Geim, S. V. Morozov, D. Z. Y. Jiang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666–669 (2004). 2 M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Nat. Phys. 2, 620–625 (2006). 3 Z. Liu, K. H. Suenaga, J. Peter, and S. Iijima, Phys. Rev. Lett. 102, 015501 (2009). 4 C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov et al., Science 312, 1191–1196 (2006). 5 Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Nature 438, 201–204 (2005). 6 A. K. Geim and K. S. Novoselov, Nat. Mater. 6, 183–191 (2007). 7 A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009). 8 P. De Padova, C. Quaresima, P. Perfetti, B. Olivieri, C. Leandri, B. Aufray, S. Vizzini, and G. Le Lay, Nano Lett. 8, 271–275 (2008). 9 P. Vogt, P. De Padova, C. Quaresima, J. Avila, E. Frantzeskakis, M. C. Asensio, A. Resta, B. Ealet, and G. Le Lay, Phys. Rev. Lett. 108, 155501 (2012). 10 L. Tao, E. Cinquanta, D. Chiappe, C. Grazianetti, M. Fanciulli, M. Dubey, A. Molle, and D. Akinwande, Nat. Nanotechnol. 10, 227–231 (2015). 11 K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, Proc. Natl. Acad. Sci. USA. 102, 10451–10453 (2005). 12 C. Jin, F. Lin, K. Suenaga, and S. Iijima, Phys. Rev. Lett. 102, 195505 (2009). 13 L. Ci, L. Song, C. Jin, D. Jariwala, D. Wu, Y. Li, A. Srivastava, Z. F. Wang, K. Storr, L. Balicas et al., Nat. Mater. 9, 430–435 (2010). 14 Q. Tang and Z. Zhou, Prog. Mater. Sci. 58, 1244–1315 (2013). 15 Q. Tang, Z. Zhou, and Z.-F. Chen, Wiley Interdiscip. Rev. Comput. Mol. Sci. 5, 360–379 (2015). 16 F. K. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Phys. Rev. Lett. 105, 136805 (2010). 17 Q. H. Wang, Z. K. Kalantar, A. Kis, J. N. Coleman, and M. S. Strano, Nat. Nanotechnol. 7, 699–712 (2012). 18 L. Li, Y. Yu, J. Ye Guo, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, Nat. Nanotechnol. 9, 372–377 (2014). 19 Y. Z. X. Jing and Z. Zhou, Wiley Interdiscip. Rev. Comput. Mol. Sci. 6, 5–19 (2016). 20 M. Chhowalla, H. S. Shin, G. Eda, L.-J. Li, K. P. Loh, and H. Zhang, Nat. Chem. 5, 263–275 (2013). 21 T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, B. Liu et al., Nat. Commun. 3, 887 (2012). 22 H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, Nat. Nanotechnol. 7, 490–493 (2012). 23 K. F. Mak, K. He, J. Shan, and T. F. Heinz, Nat. Nanotechnol. 7, 494–498 (2012). 24 B. Radisavljevic, A. Radenovic, J. Brivio, I. V. Giacometti, and A. Kis, Nat. Nanotechnol. 6, 147–150 (2011). 25 A. M. Van der Zande, P. Y. Huang, D. A. Chenet, T. C. Berkelbach, Y. You, G. H. Lee, T. F. Heinz, D. R. Reichman, D. A. Muller, and J. C. Hone, Nat. Mater. 12, 554–561 (2013). 26 A. L. Elias, N. Perea-L´ opez, A. Castro-Beltr´an, A. Berkdemir, R. Lv, S. Feng, A. D. Long, T. Hayashi, Y. A. Kim, M. Endo et al., ACS Nano 7, 5235–5242 (2013). 27 Y. Wang, L. Li, W. Yao, S. Song, J. T. Sun, J. Pan, X. Ren, C. Li, E. Okunishi, Y. Wang et al., Nano Lett. 15, 4013–4018 (2015). 28 W. Zhang, Z. Huang, W. Zhang, and Y. Li, Nano Res. 7, 1731–1737 (2014). 29 H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tom´ anek, and D. Ye Peide, ACS Nano 8, 4033–4041 (2014). 30 A. Kuc, N. Zibouche, and T. Heine, Phys. Rev. B 83, 245213 (2011). 31 Z. Y. Zhu, Y. C. Cheng, and U. Schwingenschl¨ ogl, Phys. Rev. B 84, 153402 (2011). 32 C. Ataca, H. Sahin, and S. Ciraci, J. Phys. Chem. C 116, 8983–8999 (2012). 33 A. Hashmi and J. Hong, J. Phys. Chem. C 119, 9198–9204 (2015). 34 W. Yu, Z. Zhu, C. Niu, C. Li, J.-H. Cho, and Y. Jia, Nanoscale Res. Lett. 11, 1–9 (2016). 35 Y. G. Zhou, J. Xiao-Dong, Z. G. Wang, H. Y. Xiao, F. Gao, and X. T. Zu, Phys. Chem. Chem. Phys. 12, 7588–7592 (2010). 36 Y. C. Cheng, Z. Y. Zhu, W. B. Mi, Z. B. Guo, and U. Schwingenschl¨ ogl, Phys. Rev. B 87, 100401 (2013). 37 G. Kresse and J. Furthm¨ uller, Comput. Mater. Sci. 6, 15–50 (1996). 38 G. Kresse and J. Furthm¨ uller, Phys. Rev. B 54, 11169 (1996). 39 G. Kresse and D. Joubert, “From ˙ ultrasoft pseudopotentials to the projector augmented-wave method,” Phys. Rev. B 59, 1758 (1999). 40 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). 41 H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976). 42 C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, and C. G. Van de Walle, Rev. Mod. Phys. 86, 253 (2014). 43 M. Zulfiqar, Y. Zhao, G. Li, S. Nazir, and J. Ni, J. Phys. Chem. C (2016). 44 C. Zener, Phys. Rev. 82, 403–405 (1951).
