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Extended Moment Formation in Monolayer WS2 Doped with 3d Transition-Metals Nirpendra Singh and Udo Schwingenschlögl* King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering Division (PSE), Thuwal 23955-6900, Saudi Arabia ABSTRACT: First-principles calculations with onsite Coulomb interaction and spin−orbit coupling are used to investigate the electronic structure of monolayer WS2 doped substitutionally with 3d transition-metals. While neither W vacancies nor strain induce spin polarization, we demonstrate an unprecedented tendency to extended moment formation under doping. The extended magnetic moments are characterized by dopant-specific spin density patterns with rich structural features involving the nearest neighbor W and S atoms.
KEYWORDS: transition-metal dichalcogenide, monolayer, doping, magnetism, extended moment
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INTRODUCTION Layered transition-metal dichalcogenides are emerging materials for a wide range of applications, including optoelectronics and transistor technology.1−3 Monolayer MoS2 and WS2, for example, are semiconductors with direct band gaps of 1.9 and 2.1 eV, respectively, whereas the corresponding bulk compounds have indirect band gaps of 1.2 and 1.4 eV.4,5 A combined experimental and theoretical study on bulk and monolayer WS2 has been reported in ref 6. MoS2 is already in use in logic circuits,7 phototransistors,8 ambipolar transistors,9 bilayer transistors,10 and nonvolatile memories.11 Related systems, including monolayer MoTe212 and WS2,13 currently are subject of intensive studies. Surface functionalized nanosheets of WS2, for example, have been used as anode material in Li-ion batteries.14 Being key for the quickly developing field of spintronics, more and more attention is being paid nowadays to material design based on monolayer transition-metal dichalcogenides.15−17 While pristine monolayer transition-metal dichalcogenides show no spin polarization, spin-polarized states have been reported for the edges of MoS2 nanosheets,18 similar to grain boundaries in bulk MoS2.19 Doping is a well-established method for controlling the electronic properties of a material and therefore offers a promising approach to induce spin polarization in monolayer transition-metal dichalcogenides, which has been studied theoretically in ref 20 but without taking into account the spin−orbit coupling. Co-doped monolayers of MoS2 and WS2 previously have been studied in ref 21, and Mn-doping has been addressed in ref 22 by different theoretical methods, demonstrating that the Mn atoms substitute Mo atoms and couple ferromagnetically by double exchange. The effects of nonmetal atoms (H, B, C, N, O, and © XXXX American Chemical Society
F) adsorbed on monolayer MoS2 have been investigated by first-principles calculations in ref 23.
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METHODOLOGY
In the present work we present a comparative study of transition-metal doping from Ti to Ni at the W site in monolayer WS2 and demonstrate much richer magnetic properties than reported for other dichalcogenides, which are attributed to the interplay of the localized 3d states of the transition-metal dopants with the more delocalized W 5d and S 3p states of the host. Because the properties of Mn-doped MoS2 have been found to depend critically on the level of theory employed,22 we use full-potential density functional theory,24 relaxing the atomic positions until the residual forces have converged to 0.5 mRy/bohr. Because transition-metal 3d orbitals require an appropriate treatment of electronic correlations, we complement the spin-polarized generalized gradient approximation by an onsite Coulomb interaction of U = 4 eV for the dopant atoms. We have checked that our results do not depend on the chosen value of U within a range of ±1 eV. Spin− orbit coupling can play an important role in two-dimensional materials3,25,26 and thus is taken into account in our calculations.27 The size of the plane wave basis is determined by RmtKmax = 7, with lmax = 12 and Gmax = 24, and a 6 × 6 × 1 k-mesh with 10 points in the irreducible wedge of the Brillouin zone is employed. Self-consistency is assumed to be achieved at a total energy convergence of 10−5 Ry. Starting from the experimental lattice parameter (3.16 Å) of monolayer WS2,28 our structural optimization gives a value of 3.19 Å, which is in good agreement with previous findings in ref 29. Monolayer WS2 has a sandwich structure with one W layer between two S layers, see Figure 1a. We construct a 4 × 4 × 1 supercell in order to obtain a doping concentration of 6.25% and use a 15 Å vacuum Received: May 12, 2016 Accepted: August 23, 2016
A
DOI: 10.1021/acsami.6b05670 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Research Article
ACS Applied Materials & Interfaces
checked that neither compressive nor tensile strain (2% and 4%) results in spin polarization in the defective case. We substitute transition-metal atoms (Ti, V, Cr, Mn, Fe, Co, and Ni) at the W site, because the localized 3d states may promote spin polarization, and study first the energetics of the doping by means of the binding energy E b = E V + E TM − E
(1)
where EV refers to the host with W vacancy, ETM to an atom of the elemental solid, and E to the doped system. The values reported in Table 1 show that substitutional doping of WS2 is Figure 1. Monolayer WS2: (a) side view and (b, c) top views with W vacancy and doped transition-metal atom, respectively.
Table 1. Binding Energy, Magnetic Moments, and Orbital Occupations Obtained for Monolayer WS2 Doped with Different Transition-Metals
layer to prevent artificial interaction by the periodic boundary conditions perpendicular to the monolayer. Mn doping has been demonstrated to be substitutional on the W sites,15 which can be safely expected to apply also to other 3d transition-metal dopants and therefore is presumed in this study. For illustration, the employed 4 × 4 × 1 supercell is shown in panels b and c of Figure 1 with a W vacancy and a substituted transition-metal atom at the W site, respectively.
Eb (eV) moment, total (μB) moment, dopant (μB) moment, 6 W (μB) moment, 6 S (μB) moment, interstitial (μB) occupation, dopant d↑3z2−r2 occupation, dopant d↓3z2−r2 occupation, dopant dx↑2−y2,xy occupation, dopant dx↓2−y2,xy occupation, dopant d↑yz,xz occupation, dopant d↓yz,xz occupation, dopant d↑total occupation, dopant d↓total
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RESULTS AND DISCUSSION The total density of states (DOS) shown in Figure 2a demonstrates that monolayer WS2 is a nonmagnetic semi-
Figure 2. Total density of states of monolayer WS2: (a) pristine and (b) with W vacancy. The energy zero is set to the valence band maximum.
Ti
V
Cr
Fe
Co
Ni
12.6 0.0
11.9 1.0
10.4 0.0
8.6 1.0
Mn
8.5 2.0
8.2 3.0
6.7 4.0
0.0
1.3
2.2
2.9
3.5
2.2
1.4
0.0
−0.1
−1.0
−0.6
−1.1
0.1
0.8
0.0
−0.2
−0.5
−0.5
0.1
0.4
0.9
0.0
−0.0
−0.5
−0.5
−0.4
0.2
0.7
0.07
0.64
0.74
0.88
0.88
0.83
0.93
0.07
0.05
0.13
0.19
0.24
0.79
0.83
0.36
0.77
1.30
1.63
1.75
1.75
1.78
0.36
0.32
0.30
0.33
0.47
0.94
1.50
0.44
0.50
0.78
1.19
1.75
1.67
1.83
0.44
0.40
0.43
0.50
0.41
0.69
0.82
0.87
1.91
2.82
3.70
4.38
4.25
4.54
0.87
0.77
0.86
1.02
1.12
2.42
3.15
indeed realistic. In addition, the binding energy decreases monotonously from Ti to Ni doping, which is similar to the trend reported for substitutional 3d transition-metal doping in monolayer MoS2.31 The 2-fold degenerate defect states mentioned above become occupied for Ti doping, while the 1-fold degenerate defect states remain empty, see Figure 3, i.e., the material is in a p-type state. However, close inspection of the DOS just below the Fermi energy shows that the spin degeneracy is lifted slightly, which is a first indication of an inherent instability of WS2, though no magnetic moment develops. On the other hand, for V doping there is an additional electron in the system and we obtain accordingly a finite magnetic moment, which we will discuss below in more detail. In addition, new empty in-gap states appear in the spin up channel, which again follow the trigonal prismatic symmetry. For Cr doping the system is isoelectronic to pristine WS2 so that the p-type defect states created by removing the W atom are filled again. On the other hand, the in-gap states that have split off the conduction band shift toward the Fermi energy to eventually become occupied for Mn, Fe, Co, and Ni doping. Starting from Co doping, Figure 3 also shows in-gap states in the spin down channel,
conductor, as reported previously.3,29 Without considering the spin−orbit coupling, we obtain a direct band gap of 1.9 eV, close to the value predicted in ref 28 and the experimental value of 2.1 eV.30 With spin−orbit coupling included the direct band gap, however, is reduced to 1.6 eV, which is a typical underestimation within the generalized gradient approximation and does not affect the validity of our results. On the other hand, neglecting the spin−orbit coupling would not be justified for W. Because strain can induce significant magnetism in twodimensional materials, we have studied both compressive and tensile strain (2% and 4%) but find no lifting of the spin degeneracy in monolayer WS2. Introduction of a W vacancy (charge +4) does not break the C3v symmetry, see Figure 1b, which is reflected by the DOS in Figure 2b by 2-fold and 1-fold degenerate defect states above the Fermi energy (trigonal prismatic symmetry). The occupied defect states are located close to the valence band, reflecting the expected p-type states. The spin degeneracy is not lifted by the presence of a W vacancy (the four electrons released into the system are split equally into the spin up and down channels), and we also have B
DOI: 10.1021/acsami.6b05670 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Research Article
ACS Applied Materials & Interfaces
Figure 3. Densities of states of the dopant atom (left) and of the nearest neighbor W and S atoms (average; right) for different transition-metal dopants.
which, however, stay empty in the systems under investigation. For both spin channels and all dopants the in-gap states are not mainly due to the 3d orbitals, as one may expect, but reveal strong hybridization with W 5d and S 3p orbitals of atoms adjacent to the dopant (compare the right-hand column of Figure 3). While in the case of Ti doping the spin up and down channels are equally occupied, the d3z2−r2 and dx2−y2,xy orbitals together carry the finite magnetic moment created by V doping (see the orbital occupations summarized in Table 1). In agreement with the naive expectation, we find zero total magnetic moment for Cr doping. However, surprisingly, the Cr atom shows a substantial local magnetic moment of 2.2 μB. In addition, the surrounding W and S atoms (6 W and 6 S nearest neighbors) jointly account for induced magnetic moments of −1.0 μB and −0.5 μB, respectively, and the interstitial space between the atomic spheres for a magnetic moment of −0.5 μB. The minus sign indicates an antiparallel orientation with respect to the Cr atom. Interestingly, the host thus exactly compensates the magnetic moment of the dopant so that we obtain zero total magnetic moment, as expected from simple electron counting. However, the system is still strongly spinpolarized with a characteristic spatial spin density distribution, which is shown in Figure 4. It is obvious that the strong hybridization of the Cr 3d states with the W 5d and S 3p states of the host material plays a key role for the extension of the spin polarization beyond the dopant atom. Indications of an extended moment formation in
Figure 4. Spin densities (ρ↑ − ρ↓) of monolayer WS2 doped with different transition-metals (isovalue ±0.002 electrons/bohr3).
transition-metal oxides have been observed previously,32,33 but the distinct structural pattern shown in Figure 4 as well as the C
DOI: 10.1021/acsami.6b05670 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Research Article
ACS Applied Materials & Interfaces
It is helpful to see Table 1 in connection with Figure 4, which shows the spatial distribution of the spin density for the different dopants, more precisely, the difference of the charge densities of the two spin channels, ρ↑ − ρ↓. The |0,0,0⟩ state of Ti is reflected by the absence of any spin density in the top left plot of Figure 4. For all other cases a distinct localized spin density is found on the dopant atom (green) and different patterns of induced spin density on the nearest neighbor W and S atoms. For V doping, we find essentially one spin up electron on the V atom (slightly more, because the host exhibits a finite antiferromagnetic polarization) so that we have a |↑,0,0⟩ state, see the top right plot of Figure 4. For Cr doping the dopant magnetic moment of 2.2 μB is fully compensated by the host, roughly half by W and half by S, which corresponds to a |↑↑,↓ ,↓⟩ state. The specific spatial shape of the extended moment is shown in Figure 4 in the second row, left plot. It is worth noting that particularly in the case of Cr doping the effects of electronic correlations are strong, because test calculations without onsite Coulomb interaction result in zero spin polarization and not only in a modification of the internal structure of the extended moment as found for the other dopants. For Mn doping we obtain a |↑↑↑,↓,↓⟩ state, for which the spatial form of the extended moment is shown in Figure 4 in the second row, right plot. We note that the obtained local magnetic moment of the Mn dopant agrees with previous results from hybrid functional calculations.22 We also have performed test calculations using the hybrid functional approach and find only minor differences that cannot affect our conclusions. In the case of Fe doping, we obtain a |↑↑↑↑,↓↓ ,0⟩ state (Figure 4 third row, left plot). Interestingly, for Co doping (|↑↑,0,↑⟩ state, Figure 4 third row, right plot) and Ni doping (|↑,↑↑,↑⟩ state, Figure 4 bottom left) the dopant and host magnetic moments have the same orientation, which enhances the total magnetic moment of the systems.
compensation of the local magnetic moments to the naively expected total are characteristic features of WS2. Seemingly, the impurity and host states interact in such a way that the total spin is conserved while a rich structure of spatial spin polarization is created in order to lower the total energy. Looking back to V doping, Table 1 indicates a similar behavior also in this case with a V local magnetic moment of 1.3 μB compensated by the host to the expected total of 1.0 μB. Again a characteristic spatial distribution of the spin density is observed, see Figure 4, involving the dopant atom and its 6 W and 6 S nearest neighbors. Proceeding from Cr to n-type Mn doping, Table 1 indicates that the additional electron occupies the spin up channel, mostly hosted by the dx2−y2,xy orbitals but with substantial contributions of the other 3d orbitals. We note that the DOS in Figure 3 contradicts qualitatively the findings for Mn-doped WS2 in ref 15, in which the authors have not taken into account the effects of spin−orbit coupling and electronic correlations. For this reason we have cross-checked our calculations by repeating them without onsite Coulomb interaction but including spin−orbit coupling and reproduce the reported results of ref 15. Hence, we can conclude that the differences arise from the insufficient treatment of correlation effects. Indeed, it turns out that neglecting the onsite Coulomb interaction for most dopants results in an incorrect description of the material, both with respect to the magnitude of the magnetic moments and the spatial distribution of the spin density. For Fe doping, mainly the occupation of the spin up dxz,yz states increases with respect to the Mn case, see Table 1. The total magnetic moment thus increases from 1.0 μB to 2.0 μB. On the other hand, when turning to Co doping, the next electron added enters the spin down channel, mainly the d3z2−r2 and dx2−y2,xy orbitals, so that the local magnetic moment of the dopant is reduced. Nevertheless, the total magnetic moment increases to 3.0 μB because the host switches from antiparallel to parallel orientation with respect to the Co atom; see below for further details. Finally, for Ni doping, this effect is enhanced, as the local magnetic moment of the dopant is further reduced, while the total magnetic moment grows to 4.0 μB. We note that we obtain for WS2 similar total magnetic moments as previously reported for substitutional doping of 3d transitionmetals in monolayer MoS2.31,34 We next aim at developing a comprehensive picture of the magnetic moments realized in the systems under investigation, as summarized in Table 1. The spin polarization is carried to different amounts by the dopant, W, and S atoms as well as states in the interstitial region between them. We describe this extended moment state in a formal way by the vector |dopant, W, S⟩ of up and down spins contributed by the dopant atom and the 6 W and 6 S nearest neighbor atoms. This representation constitutes, of course, an idealization of the real situation, in particular because we are dealing with strongly hybridized states. The interstitial contribution is neglected, but it will turn out that our model can explain the physics on a qualitative level. As mentioned before, Ti doping does not result in spin polarization because the two induced holes have opposite spin, which corresponds to a |0,0,0⟩ state. We note that the finite occupaction of the Ti d orbitals given in Table 1 is an artifact of our calculations, which overestimate covalency and thus assign charge to the metal atoms that in principle belongs to the S atoms. However, with the problem in mind, the further interpretation of the data does not suffer from this limitation.
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CONCLUSIONS We have demonstrated that W vacancies in monolayer WS2 (ptype defects; trigonal prismatic symmetry) do not result in spin polarization and that neither compressive nor tensile strain can change this situation. Calculated binding energies show that substitutional doping of 3d transition-metal atoms (Ti, V, Cr, Mn, Fe, Co, and Ni) at the W site is likely to be possible. Constituting the main finding of our study, we predict a very rich magnetic behavior for doped monolayer WS2. We observe an unprecedented tendency to extended moment formation, where the magnitude and orientation of the dopant and host magnetic moments always ensure that the sum follows the expectations from basic ionic considerations.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: +966(0) 544700080. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST). We thank B. Amin for fruitful discussions. D
DOI: 10.1021/acsami.6b05670 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Research Article
ACS Applied Materials & Interfaces
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DOI: 10.1021/acsami.6b05670 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
