Structures and Magnetic Properties of MoS2 Grain Boundaries with

Article pubs.acs.org/JPCC

Structures and Magnetic Properties of MoS2 Grain Boundaries with Antisite Defects Nan Gao, Yu Guo, Si Zhou,* Yizhen Bai, and Jijun Zhao Key Laboratory of Materials Modification by Laser, Ion and Electron Beams, Dalian University of Technology, Ministry of Education, Dalian 116024, China S Supporting Information *

ABSTRACT: Monolayer molybdenum disulfide (MoS2), a two-dimensional semiconductor, possesses extraordinary physical properties and holds great promise for electronics, optoelectronics, and optics. However, the synthetic MoS2 samples usually comprise substantial structural defects, which greatly affect the device performance. Herein we comprehensively explore the atomic structures, energetic stability, and electronic and magnetic properties of grain boundaries (GBs) in monolayer MoS2 as well as the GBs decorated by antisite defects by firstprinciples calculations. Eighteen types of GBs each carrying five kinds of antisite defects (a total of 108 defective systems) are constructed. The stability and magnetic properties of these defective monolayers are closely related to the type and number of homoelemental bonds. The GBs dominated by one type of homoelemental bond are ferromagnetic and have intrinsic magnetic moments up to 1.10 μB/nm. The GBs with equal number of defect rings that involve Mo−Mo and S−S bonds can exhibit antiferromagnetic behavior. Formation of antisite defects on the MoS2 GBs is much more favored than that in perfect monolayer, and the antisite defects do not severely affect the magnetic properties of the GB systems. Our theoretical results provide vital guidance for modulating the magnetic properties of monolayer transition metal dichalcogenides by defect engineering.

1. INTRODUCTION Monolayer molybdenum disulfide (MoS2), a two-dimensional (2D) semiconductor with direct band gap of 1.8 eV,1 has drawn tremendous attentions for its intriguing electronic, optic, and catalytic properties.2−5 It is composed of three hexagonally arranged S−Mo−S planes with polar covalent bonding between Mo and S atoms. Complementary to the semimetal nature of graphene, monolayer MoS2 has a proper band gap and theoretical carrier mobility up to 3850 cm2 V−1 s−1,6 rendering it a promising channel material for field-effect transistors (FETs).7−10 However, synthetic MoS2 sheets usually have mobility below ∼200 cm2 V−1 s−1,2,11−13 mainly due to the structural defects formed during the fabrication process.6,14 On the other hand, defects in MoS2 can induce appreciable modulation of band gap,15 anisotropy of electronic transport,16 magnetism,17−19 strong photoluminescence,3,20 and nonlinear optical effects,21 creating new functionalities for the material for a wide range of applications.22 The structural defects in monolayer MoS2 have been intensively explored by experiment. Vacancies and antisite defects are the most abundant point defects present in the MoS2 sheets.6,14,23−28 Hong et al. showed that single and double S vacancies are predominant in monolayer MoS2 prepared by either mechanical exfoliation or chemical vapor deposition with densities up to 0.12 nm−2. The samples by physical vapor deposition growth comprise a large amount of antisite defects with a Mo atom replacing one or two S atoms reaching 0.28 nm−2.6 Other types of point defects were © XXXX American Chemical Society

observed in MoS2 monolayers as well, such as vacancy complexes of a Mo atom and nearby three or six S atoms,14 antisite defects of two S atoms substituting a Mo atom, etc.26 The single S vacancies were found to be mobile under electron beams and can aggregate into extended line defects.27 Moreover, dislocations and defect rings are widely present in the MoS2 sheets constituting various grain boundaries (GBs), such as the ones made of 4|4, 4|6, 4|8, 5|7, or 6|8 ring pairs.14,29−32 The GBs can be mirror symmetric or titled connecting two MoS2 regions with different orientations.30 These structural defects have significant impact on the physical properties of monolayer MoS2.33−35 For instance, point defects were shown to result in hopping transport in the MoS2 sheets and reduce the carrier mobility;36 GBs can induce large variations of band gap15 and electrical conductivity,30 ferromagnetism,37 and photoluminescence enhancement or quenching20,30 depending on the type of defect rings and misorientation angle of the GBs. On the theoretical aspect, extensive efforts have been devoted to uncovering the physical and chemical properties of various defects in monolayer MoS2, from thermodynamic stability,38 formation mechanism,39 and chemical reactivity40 to electronic and magnetic properties and the effects of stains and heteroatom doping, etc.41−43 Most of the point and line defects Received: April 1, 2017 Revised: May 17, 2017 Published: May 18, 2017 A

DOI: 10.1021/acs.jpcc.7b03106 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. Model structures of perfect MoS2 monolayer and 18 MoS2 GBs classified into five categories. The Mo and S atoms are shown in the turquoise and yellow colors, respectively. Quadrilateral, pentagonal, heptagonal, and octagonal rings are filled by sky blue, purple, yellow, and orange colors, respectively. The translation vectors (nL,mL) and (nR,mR) are labeled on top of each model (symmetric GBs are highlighted in blue), and misorientation angles, formation energies (ΔH), and magnetic moments are given below each model.

questions, herein we perform a comprehensive investigation of the structure, stability, and magnetic properties of a variety of GBs with antisite defects in monolayer MoS2 by first-principles calculations. Our calculations show that formation of antisite defects on the GBs is much more favored than that in perfect MoS2 sheet. The stability and magnetic properties of these defective monolayers are closely related to the number and type of homoelemental bonds in the system. These defective sheets can be ferromagnetic with magnetic moments up to 1.10 μB/ nm and can also exhibit antiferromagnetic order. These theoretical results help experimental tuning of the magnetic properties of monolayer MoS2 via defect engineering toward the development of novel 2D magnetic semiconductors and spintronics.

were found to induce localized electronic states in the gap, and the material can exhibit either semiconducting or metallic behaviors.36 More interestingly, structural defects can give rise to magnetism in monolayer MoS2, distinct from that of the other 2D materials.44−46 For instance, the antisite defect of a Mo atom replacing a S atom has a local magnetic moment of 2 μB.6 A single Mo or two S vacancies show magnetic moments above 2 μB per vacancy under some biaxial strains.42 The GBs with 5|7 ring pairs are ferromagnetic, and the magnetic moment increases with the misorientation angle of the GBs up to 1.75 μB/nm. Formation of GBs with 4|8 ring pairs is energetically favored at misorientation angles above 47°, and they show antiferromagnetic behaviors.37 Despite the aforementioned successes, a few critical issues remain unsolved: Are there any other types of GBs possibly present in monolayer MoS2? What are the relative stabilities of various GBs? How about their magnetic properties? Since the defective regions of MoS2 sheets are chemically reactive,47 would antisite defects easily form on the GBs, and how do they affect the magnetic properties of the material? To answer these

2. COMPUTATIONAL METHODS Spin-polarized density functional theory (DFT) calculations48 were performed by the Vienna ab initio simulation package (VASP),49 using the planewave basis set with energy cutoff of 500 eV, the projector augmented wave (PAW) potentials,50,51 B


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Table 1. Misorientation Angles (θ), Period Lengths of GB (L), Formation Energies (ΔH), Linear Densities of Homoelemental Bonds (ρ), and Magnetic Moments Per Unit Length (M) of 18 MoS2 GBsa type I

II

III

IV

V a

GB

θ (deg)

L (nm)

ρ (1/nm)

ΔH (eV/nm)

M (μB/nm)

order

(4,1)|(2,3) (2,1)|(2,1) (2,2)|(1,3) (3,1)|(4,0) (5,1)|(5,1)i2 (4,1)|(4,1)i2 (4,0)|(3,2) (3,2)|(4,1) (5,2)|(5,2) (3,1)|(3,1)i2 (4,1)|(4,1) (5,1)|(5,1) (3,1)|(3,1) (5,0)|(3,3) (2,0)|(1,1) (2,2)|(3,0) (1,1)|(1,1) (3,0)|(3,0)

12.50 21.80 16.10 13.90 17.90 21.80 36.60 25.70 27.80 32.20 38.20 42.10 32.20 30.00 30.00 30.00 0.00 0.00

1.43 0.84 1.13 1.22 1.90 1.47 1.34 1.43 2.01 1.15 1.46 1.79 1.15 1.62 0.60 1.04 0.55 0.94

2.09 3.56 2.66 2.47 3.17 4.10 4.48 4.20 4.49 5.23 6.17 6.70 5.22 5.57 4.97 5.80 0.00 0.00

4.83 4.86 4.94 6.03 5.32 5.67 6.93 7.56 6.48 7.25 8.12 9.12 6.07 6.93 9.97 10.04 3.44 5.28

0.63 0.55 0.58 0.72 0.02 0.00 0.10 0.40 0.63 0.60 1.03 0.38 0.79 0.48 1.10 0.32 0.00 0.06

FM FM FM FM AFM NM NM FM FM FM FM FM FM FM FM FM NM AFM

FM and AFM stand for ferromagnetic and antiferromagnetic order, respectively.

constituting the entire GB. All the MoS2 GBs show planar structures without noticeable vertical buckling or wrinkle. The Mo−S bond length in the vicinity of GBs ranges from 2.35 to 2.51 Å, close to that of perfect MoS2 sheet (2.41 Å). The pentagons and heptagons present homoelemental Mo−Mo or S−S bonds with bond lengths of about 2.31 and 2.11 Å, respectively. To characterize the energetic stability of the MoS2 GBs, we define the formation energy ΔH as

and the generalized gradient approximation (GGA) parametrized by Perdew, Burke, and Ernzerhof (PBE) for the exchange-correlation functional.52 Although the PBE functional is known to underestimate the band gap of materials, in our studies we are interested in the energies and magnetic properties of MoS2 GBs, which are less affected by the functional used for the calculations. To construct the GB models, we used rectangular supercells of MoS2 with a lateral distance of 18 Å between the GB and its replica. The detailed procedures for generating the GBs can be found in Figure S1 of Supporting Information. A vacuum region of 18 Å was applied for the vertical direction to eliminate the interactions between the neighboring layers. The Brillouin zone of the supercell was sampled by a uniform k-point mesh with spacing of 0.03/Å. The model structures were fully optimized for both cell and ionic degrees of freedom with thresholds for the total energy of 10−7 eV and the forces on each atom of 0.01 eV/Å.

ΔH =

(2)

where EGB is the energy of the GB model, Euc is the energy of the unit cell of perfect MoS2 monolayer, N is the number of MoS2 unit cells included in the GB model, L is the periodic length of the GB, and the factor 2 accounts for the GB and its replica in the supercell. The linear density of homoelemental bonds ρ equals the number of homoelemental Mo−Mo or S−S bonds per unit length in the GB model. The structural and energetic information on the 18 MoS2 GBs are summarized in Table 1. The relation of ΔH vs ρ is plotted in Figure 2. Generally speaking, the MoS2 GBs have formation energies ranging from 3.4 to 10.0 eV/nm, close to

3. RESULTS AND DISCUSSION 3.1. Structures and Formation Energies of MoS2 GBs. We construct GBs in monolayer MoS2 consisting of quadrilateral, pentagonal, heptagonal, or octagonal rings using the methodology described by Guo et al.53 The GBs exhibit different misorientation angles defined as θ = θR + θL with θR/L = tan−1[√3mR/L /(mR/L + 2nR/L)]

EGB − NEuc 2L

(1)

where (nL, mL) and (nR, mR) are translation vectors of the domains on the left and right side of the GB, respectively.54 The GBs with the same translation vectors but different arrangement of defect rings are represented by (nL, mL)|(nR, mR)iN (N = 2, 3, ...), as shown in Figure 1. We consider a total of 18 MoS2 GB models classified into five types: (I) pentagon− heptagon (5|7 ring) pairs periodically separated by one or more hexagon rings; (II) two adjacent pentagon−heptagon pairs separated by one or more hexagon rings; (III) pentagons and heptagons adjacent to each other or separated by hexagon rings; (IV) repeated pentagon−heptagon ring pairs filling the entire GB; (V) repeated quadrangle−octagon (4|8 ring) pairs

Figure 2. Formation energy (ΔH) as a function of linear density of homoelemental bonds (ρ) for the five types of MoS2 GBs shown in Figure 1. The black dashed line is a linear fitting of ΔH vs ρ. C


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Figure 3. Spin densities of representative MoS2 GBs comprising (a) Mo−Mo bonds, (b) two 5|7 ring pairs involving S−S bonds and one involving Mo−Mo bond, (c) one 5|7 ring pair involving S−S bonds and one involving Mo−Mo bond, and (d) no homoelemental bonds. The Mo and S atoms are shown in the turquoise and yellow colors, respectively. The red and green surfaces represent charge densities of spin-up and spin-down states, respectively, with isosurface of 2 × 10−3 e/Å3. (e) Ranges of magnetic moments of the MoS2 GBs including only one type of homoelemental bonds (purple), different (yellow) and equal (orange) numbers of defect rings that involve Mo−Mo and S−S bonds, and no homoelemental bonds (sky blue). (f) Electronic band structure and density of states (DOS) of the type-I (3,1)|(4,0) GB. The spin-up and spin-down states are shown in red and black, respectively. The Fermi energy is shifted to zero. The DOS by solid lines is taken from the atoms in the GB region, and the gray-shaded area is the DOS from the atoms in perfect MoS2 region away from the GB.

those of graphene GBs (2.8−8.0 eV/nm) 55 and higher than the values of phosphorene GBs (0.9−2.4 eV/nm).53 The formation energies of MoS2 GBs show a linear correlation with the linear density of homoelemental bonds of the system, which can be understood as that unsaturation of outermost valence shells of Mo and S atoms is detrimental to the thermodynamic stability of monolayer MoS2. In particular, the type-V GBs comprising 4| 8 ring pairs without any homoelemental bonds have lower formation energies of 3.44−5.28 eV/nm. The type-I GBs with 5|7 ring pair separated by one or more hexagon rings are also energetically favorable with formation energies of 4.83−6.03 eV/nm. On the contrary, the type-IV systems with the whole GB filled by 5|7 ring pairs include a large number of Mo−Mo or S−S bonds (ρ = 5−5.8/nm), and accordingly they have formation energies up to 10.04 eV/nm. These results are consistent with previous work by Wang et al.56 showing that the MoS2 GBs composed of isolated 5|7 pair have lower formation energies (0.30−0.40 eV) than those having multiple adjacent 5|7 pairs (0.57−0.73 eV). Moreover, the symmetric GBs (θR = θL) are energetically more stable than the asymmetric ones under the same value of ρ. For instance, the type-I (2,1)|(2,1), type-II (4,1)|(4,1)i2 and (5,1)|(5,1)i2, and type-IV (3,1)|(3,1) systems have symmetric structures about the GBs, and their formation energies are below the fitted linear curve, while the asymmetric GBs such as the type-IV (2,0)|(1,1) and (2,2)|(3,0) are above the fitted curve. These results reveal that formation of GBs with less homoelemental bonds and having symmetric structures is more thermodynamically favorable in monolayer MoS2.

3.2. Magnetic Moments of MoS2 GBs. To explore the electronic and magnetic properties of MoS2 GBs, we calculate their spin-resolved electronic band structures and density of states (DOS). For all the GBs, the defect rings induce mid-gap states as demonstrated by Figure 3f. According to the partial charge densities (see Figure S2 of Supporting Information), these states are localized on the defect rings and the surrounding atoms. The band structure and DOS show the splitting of spin-up and spin-down states near the Fermi level, signifying local magnetic moments for the MoS2 GBs. Parts a− d of Figure 3display the spin density distributions of some representative GB systems. The spin densities are localized on the homoelemental Mo−Mo bonds and the Mo atoms nearby (Figure 3a), as well as the Mo atoms surrounding the S−S bonds (Figure 3b). For the GBs including both Mo−Mo and S−S bonds, the spin densities can exhibit different polarizations on the regions close to Mo−Mo and S−S bonds, respectively (Figure 3c); their band structures present less splitting of spinup and spin-down states (Figure S3 of Supporting Information). Therefore, the GB systems dominated by one type of homoelemental bond may have large net magnetic moments, while the GBs with equal number of defect rings involving Mo−Mo and S−S bonds may show antiferromagnetic behavior. To validate our hypothesis, we calculate the local magnetic moment of our MoS2 GB models defined as the difference of the sum of spin-up and spin-down densities around the GB. The initial spin magnetic moments were set to be ferromagnetic. As expected, the magnetic moment is closely related to the number and type of homoelemental bonds in the D


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Figure 4. (a) Upper panels: optimized structures of five types of antisite defects in perfect MoS2 monolayer including the top and side views. The Mo and S atoms are shown in the turquoise and yellow colors, respectively, and the Mo (S) atoms replacing S (Mo) atoms are highlighted in blue (red). Bottom panels: formation energy (ΔH′) vs linear density of homoelemental bonds (ρ) for the five types of antisite defects in the 18 MoS2 GB systems shown in Figure 1. The black dash lines and the numbers above indicate the formation energies of antisite defects in perfect MoS2 monolayer. The shadow area indicates the regime of negative formation energies. (b−d) Local area of some representative MoS2 GBs (left panel) and antisite defects on the GBs (right panel). The arrows on the left panel indicate the Mo (S) atom to be substituted to form the antisite defect. The formation energies (ΔH′) of antisite defects are given below each model.

Figure 5. Spin densities of (a) type-I (3,1)|(4,0) MoS2 GB and (b−f) five kinds of antisite defects on the GB. The Mo and S atoms are shown in the turquoise and yellow colors, respectively, and the Mo (S) atoms replacing S (Mo) atoms are highlighted in blue (red). The arrow in (a) indicates the S atoms to be substituted. The red and green surfaces represent charge densities of spin-up and spin-down states, respectively, with isosurface of 2 × 10−3 e/Å3. The formation energies (ΔH′) and magnetic moments (M) are given below each model.

The energies of the magnetic states are substantially lower than those of the nonmagnetic states by 110−190 meV, indicating the relatively high stability of magnetic states. Therefore, the MoS2 GBs dominated by one type of homoelemental bond carry intrinsic magnetic moments. On the contrary, the GB systems with equal number of defect rings that include Mo− Mo and S−S bonds or those without homoelemental bonds are either antiferromagnetic or nonmagnetic. Specifically, the typeII (5,1)|(5,1)i2 and type-V (3,0)|(3,0) GBs favor antiferromagnetic over ferromagnetic order between adjacent defect

GB systems (see Table 1 and Figure 3e). In particular, ferromagnetism is achieved in the GBs that include only one type of homoelemental bond, such as the type-I, type-II (3,2)| (4,1), type-III, type-IV (3,1)|(3,1) and (2,0)|(1,1) GBs. The type-IV (5,0)|(3,3) GB, in which the number of defect rings involving Mo−Mo bond is unequal to that having S−S bonds, also shows ferromagnetic order. The magnetic moments of these systems range from 0.38 to 1.10 μB/nm, comparable to those reported by Yakobson et al.37 for the MoS2 GBs with 5|7 ring pairs in various misorientation angles (0.5−1.7 μB/nm). E


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Table 2. Formation Energies (ΔH′) and Magnetic Moments of Five Types of Antisite Defects in Four Representative MoS2 GB Systemsa formation energy (eV)

a

magnetic moment (μB/nm)

type

GB

MoS2

MoS

Mo2S2

S2Mo

SMo

GB only

MoS2

MoS

Mo2S2

S2Mo

SMo

I II III IV

(3,1)|(4,0) (4,1)|(3,2) (3,1)|(3,1)i2 (3,1)|(3,1)

0.77 0.93 6.27 6.74

2.84 3.29 4.32 3.8

6.28 3.35 8.11 7.67

6.54 5.71 5.90 6.23

4.11 4.25 1.64 5.56

0.66 0.33 0.44 0.69

0.50 0.33 0.56 0.58

0.50 0.36 0.55 0.65

0.80 0.42 0.63 1.83

0.48 0.44 0.26 0.69

0.60 0.46 0.14 0.61

The magnetic moments of MoS2 GBs without antisite defect (“GB only”) are also listed for comparison.

compared to 2.31 and 2.11 Å for the MoS2 GBs without antisite defects. To characterize the energetic stability of the MoS 2 monolayers with both GBs and antisite defects, we define another formation energy ΔH′ as6

rings with energies lowered by 62 and 32 meV, respectively (see Figure 3c,d for spin densities); the remaining systems are nonmagnetic without spin density distributions. The MoS2 GBs owe their local magnetic moments to the unsaturated outermost valence electrons of the Mo and S atoms close to the defect rings. Figure 3f displays the local DOS of the type-I (3,1)|(4,0) GB, a typical ferromagnetic system with only one Mo−Mo bond in the supercell. Both Mo and S atoms show asymmetric spin-up and spin-down states near the Fermi level. The split states are attributed to the atoms in the vicinity of the homoelemental bonds, dominated by the 4d orbital of Mo atoms (predominantly dz2, dx2−y2, and dyz orbitals) and less contributed by the 2p orbital of S atoms, in good accord with the spin density and partial charge density distributions (Figures S2 and S4 of Supporting Information). For the GBs with equal number of defect rings that have Mo−Mo and S−S bonds, the spin densities in the regions close to Mo−Mo and S−S bonds can have the same or different polarizations with relatively weak spin coupling strength; hence these systems may not show magnetic order at room temperature. 3.3. Structures and Formation Energies of MoS2 GBs with Antisite Defects. In addition to the ubiquitous line defects, antisite defects are commonly observed in the experimentally fabricated MoS2 samples.6,14,26 As the defective regions of 2D materials are vulnerable to chemical modification,57 it raises an interesting question of whether antisite defects can form more easily on the GBs of monolayer MoS2 than in perfect MoS2 sheet. To clarify this issue, we consider five kinds of antisite defects, including a Mo atom replacing one or two S atoms (denoted as MoS and MoS2, respectively), two Mo atoms replacing two S atoms (denoted as Mo2S2), and one or two S atoms replacing a Mo atom (denoted as SMo and S2Mo, respectively), as illustrated by Figure 4a. These antisite defects are incorporated into the 18 MoS2 GBs (a total of 90 models) as well as perfect monolayer. For the GB systems, the atom in the homoelemental bonds or the one on the joint of defect ring pairs is substituted to form an antisite defect (see Figure 4b−d and Figure 5). Incorporation of antisite defects into the MoS2 GB systems induces appreciable local structural reconstruction. For instance, a MoS defect on the 5|6|7 ring complexes eliminates the original S−S bond, and the neighboring S atoms are relaxed and form three Mo−S bonds, resulting in 4|4 ring pairs on the GB (see Figure 4c). A Mo2S2 defect on the 5|7 ring pairs extinguishes the original two S−S bonds by forming four Mo− Mo bonds (Figure 4b), while a SMo defect removes the original Mo−Mo bond and gives four S−S bonds (Figure 4d). The center atom of the antisite defect is protrusive by up to 0.65 Å above top sublayer of S atoms. The regions away from the GBs remain planar without evident vertical buckling or inflection (see Figure 4a). The newly formed Mo−Mo and S−S bonds have elongated lengths of about 2.74 and 2.28 Å, respectively,

ΔH′ = Etot − NSES_ML − NMoEMo_ML

(3)

with ES_ML = ES0 + E bond

(4)

EMo_ML = EMo 0 + 2E bond

(5)

E bond = [Euc − EMo 0 − 2ES0]/4

(6)

0

EMo0

where ES and are the energies of a S and a Mo atom in their solid phase (the orthorhombic and cubic phases), respectively, and Euc is the energy of the unit cell of perfect MoS2 monolayer. Thus, Ebond given by eq 6 represents the bond energy of a Mo−S bond, and ES_ML and EMo_ML correspond to the energies of a Mo and S atom in perfect MoS2 monolayer, respectively. Figure 4a presents the formation energies ΔH′ of MoS2 GBs with antisite defects. The values of antisite defects in perfect MoS2 sheet are also calculated for comparison, which agree well with the reported DFT results (see Table S1 of Supporting Information).6 Overall speaking, the antisite defects formed on the MoS2 GBs have much lower formation energies than those in perfect MoS2 monolayer. In particular, compared to those in perfect MoS2 sheet, the formation energies are reduced on average by 3.60, 4.58, 6.75, 1.88, and 1.78 eV for the MoS, MoS2, Mo2S2, SMo, and S2Mo antisite defects on the MoS2 GBs, respectively. The GBs with MoS and MoS2 defects have the lowest formation energies (3.64 and 1.40 eV), suggesting that these antisite defects may form easily in the synthetic MoS2 monolayer that inevitably comprises GBs. More interestingly, the MoS antisite defect in the type-III (5,2)|(5,2), (4,1)|(4,1) and (5,1)|(5,1) GBs have negative formation energies of −0.96 to −0.43 eV, indicating the possibility of its spontaneous formation on those GBs. These results are consistent with the experimental observations that the MoS2 and MoS antisite defects are most abundant in monolayer MoS2 with densities up to 0.28 and 0.07 nm−2, respectively.6 The increased stability of antisite defects on the MoS2 GBs is due to the fact that the original homoelemental bonds on the GBs are counteracted by the antisite defect. As a result, the number of homoelemental bonds induced by the antisite defect in the GB systems is less than that in perfect monolayer. For instance, incorporation of the MoS defect into the type-III (5,2)|(5,2) GB eliminates the original S−S bonds without forming additional homoelemental bonds (see Figure 4c). Thus, it has negative formation energy of ΔH′ = −0.43 eV, well F


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particular, we consider two representative GBs models including the type-I symmetric (2,1)|(2,1) and asymmetric (3,1)|(4,0) GBs in monolayer WS2, MoSe2, and WSe2, respectively. Selected chalcogen atoms on the defect rings are substituted by transition metal atoms to form either MX or MX2 antisite defects (M = Mo, W; X = S, Se). The perfect sheets with antisite defects exhibit large formation energies above 10 eV, indicating the less favorable formation of antisite defects in the WS2, MoSe2, and WSe2 sheets than that in perfect MoS2 monolayer (see Table S2 of Supporting Information). In contrast, incorporation of antisite defects into the GB systems gives much lowered formation energies of 4.74−9.13 and −0.75 to 2.54 eV for the system comprising the type-I (2,1)|(2,1) and (3,1)|(4,0) GBs, respectively. The MX2 defect on the (3,1)|(4,0) GB of WS2, MoSe2, and WSe2 monolayers all have negative formation energies of −0.75 to −0.40 eV due to the formation of stable 4|4 ring pairs as that in Figure 4c. These TMD monolayers with GBs show spin density distributions very similar to those of the MoS2 GBs. They exhibit ferromagnetic behaviors with magnetic moments of 0.47−0.74 μB/nm (Figure S7 of Supporting Information). Not only antisite defects but also vacancies can form easily on the MoS2 GBs, as both defects reduce the homoelemental bonds compared to those formed on perfect MoS2 sheet (see Figure S9 of Supporting Information). Therefore, TMD monolayers with GBs are chemically reactive and may present defect complexes giving rise to diverse electronic and magnetic properties to the materials.

accorded with the experimental observation of line defects constitutive of 4|4 ring pairs in monolayer MoS2.29 Similarly, for the type-I (2,1)|(2,1) GB with the Mo2S2 defect and the type-II (4,1)|(4,1)i2 GB with the SMo defect, only four homoelemental bonds are introduced compared to six for those in perfect MoS2 sheet. Thus, the formation energies are significantly lowered from 11.59 to 5.73 eV and from 5.72 to 1.83 eV, respectively (see Figure 4b,d). 3.4. Magnetic Moments of MoS2 GBs with Antisite Defects. To examine the impact of antisite defects on the electronic and magnetic properties of MoS2 GBs, we calculate their electronic band structure, DOS, and magnetic moments. These defective monolayers show similar features in the band structures as those of the GBs without antisite defect; that is, mid-gap states are evident, and the spin-up and spin-down states split near the Fermi level (Figure S5 of Supporting Information). Table 2 lists the local magnetic moments of some representative GB systems including five kinds of antisite defects. Generally speaking, the antisite defects on the MoS2 GBs do not severally affect the magnetic properties of the system. For the GBs that are originally ferromagnetic, substantial magnetic moments are retained upon the incorporation of antisite defects; for those favoring the antiferromagnetic order, introducing antisite defects does not give rise to net magnetic moment. This is different from the situation of perfect MoS2 monolayer: the MoS and Mo2S2 defects induce local magnetic moments of 2 and 4 μB, respectively, and the other three antisite defects in the monolayer are nonmagnetic (see Table S1 of Supporting Information). Further insights into the magnetic behavior can be gained from the structural features and spin density distributions of the MoS2 GBs with antisite defects. Taking the type-I (3,1)|(4,0) GB as a representative, the supercell has one S−S bond showing ferromagnetic order with local magnetic moment of 0.66 μB/nm (see Figure 5a). Upon incorporation of antisite defects, the type and number of homoelemental bonds in the system are changed: two Mo−Mo bonds for MoS, two Mo−Mo and one S−S bonds for MoS2, four Mo−Mo bonds for Mo2S2, four S−S bonds for SMo, and six S−S bonds for S2Mo defect on the GB, respectively (see Figure 5b−f). Nevertheless, these defective monolayers are still dominated by one type of homoelemental bond. The spin densities remain on the Mo atoms surrounding the defect rings, giving net magnetic moments of 0.48−0.80 μB/nm, close to the value of the GB system without antisite defect. The magnetic states are energetically more favored than the nonmagnetic ones by about 90 meV, indicating the reasonable stability of the ferromagnetic order of these defective sheets. Noticeably, the Mo2S2 defect enhances the magnetic moments for all the ferromagnetic GB systems, as two introduced Mo atoms act as the centers for spin density distributions and hence yield prominently larger magnetic moments. On the other hand, for the antiferromagnetic or nonmagnetic GBs, the antisite defects can create homoelemental bonds. However, the defective systems either show antiferromagnetic behavior with weak spin coupling strength below ∼50 meV or remain nonmagnetic (Figure S6 of Supporting Information). Therefore, these MoS2 GBs with or without antisite defects would not present magnetic order at room temperature. According to our calculations, antisite defects can form easily on the MoS2 GBs. Similar behaviors are also found for other transition metal dichalcogenides (TMD) monolayers. In

4. CONCLUSION In summary, the structures, energetic stabilities, and electronic and magnetic properties of GBs in monolayer MoS2 with and without antisite defects are comprehensively investigated by first-principles calculations. A total of 18 GB models categorized into five types are constructed. Their energetic stability increases as the linear density of homoelemental bonds decreases. The GBs dominated by one type of homoelemental bond are ferromagnetic with magnetic moments of 0.32−1.10 μB/nm mainly attributed to the unpaired 4d electrons of the Mo in the vicinity of defect rings. Introducing antisite defects into the GBs results in much lowered formation energies compared with those in perfect MoS2 monolayer. The antisite defects do not severely affect the magnetic properties of the GB systems. Our theoretical results provide vital insights into the physical and chemical properties of synthetic MoS2 monolayers with ubiquitous point and line defects and also guide the rational design of TMD-based novel 2D devices by defect engineering.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b03106. Formation energies and magnetic moments of antisite defects in perfect MoS2 monolayer (Table S1), formation energies, magnetic moments, and spin densities of antisite defects in MoSe2, WS2, and WSe2 monolayers with GBs (Table S2 and Figure S7), structural model, electronic band structures, partial charge densities, density of states, and spin densities of selected MoS2 GBs with and without antisite defect (Figures S1−S6), correlation between M and ρ (or θ) (Figure S8), and G


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stability of vacancy defect on MoS2 GBs (Figure S9) (PDF)

AUTHOR INFORMATION

Corresponding Author

*S.Z.: email, [email protected]. ORCID

Si Zhou: 0000-0002-0842-1075 Jijun Zhao: 0000-0002-3263-7159 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grants 11504041, 11574040), the China Postdoctoral Science Foundation (Grants 2015M570243, 2016T90216), the Fundamental Research Funds for the Central Universities of China (Grant DUT16-LAB01), and the Supercomputing Center of Dalian University of Technology.

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Structures and Magnetic Properties of MoS2 Grain Boundaries with

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