Strain-Induced Magnetism in Single-Layer MoS2 - American Chemical

Article pubs.acs.org/JPCC

Strain-Induced Magnetism in Single-Layer MoS2: Origin and Manipulation Won Seok Yun and J. D. Lee* Department of Emerging Materials Science, DGIST, Daegu 711-873, Republic of Korea

ABSTRACT: We investigate the strain-induced electronic and magnetic properties of single-layer (1L) MoS2 with vacancy defects using the density functional theory calculation. When the tensile strain is applied, 1L-MoS2 with vacancy becomes ferromagnetic and metallic. We elucidate that, from the electronic band structure of vacancy-defect-doped 1L-MoS2, the impurity bands inside the gap play a role of seed to drive novel magnetic and electronic properties as the strain increases. In particular, we also find that 1L-MoS2 with two-sulfur vacancy (V2S) shows the largest magnetic moment at ∼14% strain among various vacancy types and undergoes a spin reorientation transition from out-of-plane to in-plane magnetization at ∼13% strain. This implies that the strain-manipulated 1L-MoS2 with V2S can be a promising candidate for new spintronic applications.

■

edges.22−27 For instance, Ataca et al.15 confirmed that vacancy defects of S, 2S, Mo, and Mo+S introduced in 1L-MoS2 do not induce any magnetism; however, that of Mo+2S results in a sizable magnetic moment in the system. Nanoribbon with zigzag edges exhibit FM metallic phase regardless of its width.22,26 Such FM behavior is attributed to unpaired electrons that are mainly localized on the edge Mo atoms. Moreover, the magnetic property in those systems is made controllable through an application of the tensile strain, i.e., the strain engineering. Recently, the strain-induced magnetism in 1L-MoS2 with atomic vacancies has been proposed by Tao et al.28 and Zheng et al.29 They have been concerned about 1L-MoS2 with single atomic vacancies under the tensile strain. In the present work, we have performed the first-principles calculations to investigate extensively the electronic and magnetic properties of 1L-MoS2 with several types of vacancy defects under the equibiaxial or uniaxial strain. Excavating the unfolded band structures of the supercell calculation for the vacancy-defective 1L-MoS2, we have clarified that the strain-induced magnetism and the accompanying metallic nature are driven by the impurity bands inside the gap. Further, we have found that 1LMoS2 with two-sulfur vacancy (V2S) shows an unexpectedly

INTRODUCTION Tremendous research efforts have been focused on the layered transition-metal dichalcogenides (TMDCs) due to their potential applications in areas such as electronic, optoelectronic, and photovoltaic devices.1−3 Among those, interestingly, MoS2 shows a strong dependence on the layer thickness in its electronic properties. A single-layer (1L) MoS2, which is obtained by employing the micromechanical exfoliation, chemical exfoliation, liquid exfoliation, and chemical vapor deposition (CVD) methods,3−6 is a direct-gap semiconductor with a energy gap of ∼1.8 eV, whereas the bulk MoS2 is an indirect-gap semiconductor with a energy gap of ∼1.3 eV.7,8 Furthermore, tuning the band gap of MoS2 through the strain effect is one of the most feasible approaches to achieve a widerange controllability of their electronic properties.9 Previous theoretical studies have shown that the single- and few-layer MoS2 undergo not only the direct-to-indirect band gap transition but also a change of semiconducting to metallic phases under tensile strains.10,11 Subsequently, the straininduced modulation of band gap was experimentally confirmed.12−14 Great attention has been paid to the exploration of the magnetic properties of MoS2 for the nanoscale spintronic applications. Manifestation of the ferromagnetic (FM) phase has been done in terms of various treatments: vacancy-defect formation,15−17 adsorption or substitution of transition metal or nonmetal elements,15,17−21 and nanoribbon with zigzag © 2015 American Chemical Society

Received: October 13, 2014 Revised: December 16, 2014 Published: January 12, 2015 2822

DOI: 10.1021/jp510308a J. Phys. Chem. C 2015, 119, 2822−2827

Article

The Journal of Physical Chemistry C

Figure 1. (a) and (b) Top views of the supercell models of the pristine and defective (with five different vacancy defects of V1Mo, V1S, V2S, V1Mo+1S, and V1Mo+2S) 1L-MoS2’s. In (a), the biaxial (hexagonal 4 × 4) strain is described. In (b), the uniaxial (rectangular 4 × 2√3) strain is described, where x and y denote armchair and zigzag directions. Green, gray, and white balls stand for Mo, upper S, and lower S atoms, respectively. (c) Straindependent total magnetization mtotal. A zero strain means the equilibrium state. Two arrows in each panel indicate the magnetic transition and maximum magnetization for the biaxial strain, respectively.

large spin magnetic moment up to 7.45 μB per supercell at ∼14% tensile strain and it also shows a spin reorientation transition from out-of-plane to in-plane magnetization at ∼13% strain from a change of the magnetocrystalline anisotropy (MCA). This finding indicates an immediate significance of 1LMoS2 with V2S for new spintronic applications.

2.14 eV at the K-point was recently reported with the hybrid Heyd−Scuseria−Ernzerhof (HSE06) functional.34,35 In DFT, the calculated electronic band structure is important for an interpretation of the experimental measurement like the angle-resolved photoemission spectroscopy (ARPES). Meanwhile, the supercell calculation results in the folded band structure due to a shrinkage of the Brillouin zone, which makes an immediate interpretation of APRES unavailable. Hence, we try to overcome this difficulty using the effective band unfolding technique36,37 to recover a primitive cell picture. In this approach, it is important to construct a spectral function ⃗ ⃗ A(k,E), which is given by A(k,E) = ∑mPK⃗ m(k)⃗ δ(Em−E) with the continuous variable energy E and the spectral weight ⃗ and |K⃗ m⟩ (n and m PK⃗ m(k)⃗ = ∑n|⟨K⃗ m |kn⃗ ⟩|2, where the |kn⟩ indicate band indices) are the eigenvectors in the primitive cell and the supercell, respectively. The spectral weight can be obtained by projecting |K⃗ m⟩ on all primitive cell eigenstates | ⃗ can be obtained, which is ki⃗ n⟩ of a fixed ki. From this, A(k,E) regarded as an effective primitive cell projection of the supercell band structure. The detailed description about the effective band unfolding method can be found elsewhere.36−39 Further, the MCA calculation was also performed in the noncollinear mode with the spin−orbit coupling (SOC) term.40 We have considered two models for applying the tensile strain, i.e., the biaxial and uniaxial strain models. First, the biaxial strain model consists of a hexagonal 4 × 4 supercell of 1L-MoS2 with 16 Mo and 32 S atoms. Subsequently, five

■

COMPUTATIONAL DETAILS First-principles calculations based on the density functional theory (DFT) are performed using the Vienna ab initio simulation package (VASP).30 The generalized gradient approximation (GGA) formulated by the Perdew−Burke− Ernzerhof (PBE) functional31 and the projector augmented wave (PAW) potentials are used.32,33 An energy cutoff of 450 eV was adopted for the plane-wave expansion of the electronic wave function and a 6 × 6 × 1 Monkhorst−Pack k-point grid used for an integration over the 2D Brillouin zone. The unit cell is optimized to obtain the equilibrium lattice parameter at the lowest total energy and atomic positions were fully relaxed until the force on each atom is less than 10−4 eV Å−1. The vacuum space along the z direction was taken to be more than 15 Å for all the considered systems and the convergence criterion in the self-consistency process set to 10−4 eV. The direct band gap at the K-point for the pristine 1L-MoS2 is estimated to be Eg = 1.7 eV, which is moderately consistent with the experimental optical band gap in the range 1.75−1.9 eV.7,8 On the contrary, 2823

DOI: 10.1021/jp510308a J. Phys. Chem. C 2015, 119, 2822−2827

Article

The Journal of Physical Chemistry C

clear in the figure that the biaxial strain induces larger magnetic moment than the uniaxial strain. For this reason, we hereafter focus on the magnetic properties by the biaxial strain for 1LMoS2. It was in fact demonstrated that these 2D nanostructures can endure the strain to the intrinsic limit of ∼25%.42,43 Moreover, according to the previous first-principles calculations, about 20% was also reported as the critical biaxial strain limit.44 Regarding an experimental realization of the strain-induced magnetism in this system, we would suggest another highly stretchable material as a substrate. A very recent work has reported that alginate−polyacrylamide hydrogels can be elongated over 20 times its initial length.45 Therefore, using such a materials with high flexibility and stretchability as a substrate, it would be available to achieve the necessary strain in 1L-MoS2. Except for the V1Mo+2S case, the induced magnetic moments of all the considered systems are negligible for small (and zero) strains. In contrast, the V1Mo+2S defect leads to the magnetism (∼2 μB) even in the equilibrium (unstrained) state, in good agreement with previous theoretical investigations.15,17 A change from the nonmagnetic (NM) to FM state in 1L-MoS2 with V1Mo, V1S, V2S, and V1Mo+1S defects occurs at approximately 6.5%, 8%, 9.5%, and 5.5% strains, respectively. It is noted that the magnetic phase transition for the molybdenum-vacancydoped systems occurs earlier than the sulfur-vacancy-doped systems. Beyond the transition, the induced magnetic moments tend to increase gradually with respect to the applied tensile strain. Incidentally, the calculated magnetic moments for 1L-MoS2 with V1Mo, V1S, V2S, and V1Mo+1S defects have maximum values of 2.02, 4.07, 7.45,46 and 4.04 μB at roughly 14.5%, 14.5%, 13.5%, and 13% strains, respectively. The total energy difference between FM and NM states has been also calculated. In the calculation, the FM state is found to be favored by 101, 350, 1129, and 288 meV over the NM states for the case with V1Mo, V1S, V2S, and V1Mo+1S defects, respectively. From the magnetic moments and total energy difference, we note that the V2S-doped 1L-MoS2 is found to have the largest magnetic moment and, at the same time, be energetically most stable. Let us discuss the electronic and magnetic driving force originated by the vacancy defects in view of the electronic band structure. The zone folding of the electronic bands due to the supercell calculation has been a long-standing difficulty. In the present study, we have tried to overcome the difficulty for the immediate supercell calculation using the effective unfolding technique.36,37 Figure 2 illustrates the results of unfolded band structure for the pristine and five cases of defective 1L-MoS2’s at their equilibrium lattice constants. For the pristine 1L-MoS2 4 × 4 supercell, the direct band gap at the K-point is estimated to be Eg = 1.70 eV, which is very consistent with that of the primitive cell calculation.8,10 Compared with the pristine case, all defective cases introduce the flat impurity bands inside the band gap due to the atomic vacancies. In particular, it is worth noting that the impurity bands for 1L-MoS2 with V1S and V2S defects (i.e., only sulfur vacancy) are found near below the conduction band minimum (CBM). It is known that MoS2 on the bare SiO2 substrate has an unipolar n-type behavior.1 Moreover, sulfur-deficient and sulfur-rich MoS2 are anticipated to result in the n- and p-type, respectively.47 In contrast, the impurity bands of V1Mo, V1Mo+1S, and V1Mo+2S defects (i.e., including molybdenum vacancy) are located near above the valence band maximum (VBM). Further, it is revealed that the

possible vacancy-defect types by removing Mo and/or S atoms in 1L-MoS2 (denoted by V1Mo, V1S, V2S, V1Mo+1S, and V1Mo+2S; e.g., V1Mo implies 1L-MoS2 with 1 Mo atom removed) are considered in the present study, which are displayed in Figure 1a. Note that the chemical compositions correspond to Mo0.9375 S2, MoS1.9375, MoS1.875, Mo0.9375 S1.9375, and Mo0.9375 S1.875 for defect types of V1Mo, V1S, V2S, V1Mo+1S, and V1Mo+2S, respectively. Next, for the uniaxial strain model, we have used a rectangular 4 × 2√3 supercell of 1L-MoS2 containing totally the same number of atoms as in the hexagonal 4 × 4 supercell. Again, five types of vacancy defects in the rectangular supercell are shown in Figure 1b.

■

RESULTS AND DISCUSSION We have optimized the lattice parameter as a0 = 3.184 Å for the pristine 1L-MoS2, which agrees with previous studies.11,28 In the same way, the optimized lattice constants of 1L-MoS2’s with V1Mo, V1S, V2S, V1Mo+1S, and V1Mo+2S defects are determined to be 3.191, 3.166, 3.146, 3.183, and 3.152 Å, respectively, as listed in Table 1. The lattice constant in 1L-MoS2 with V1Mo defect is Table 1. Optimized Lattice Constant a0 (Å) and Defect Formation Energy Ef (eV) for the Pristine and Various Vacancy-Defective 1L-MoS2’s at Their Equilibrium States system

magnetic state

pristine V1Mo V1S V2S V1Mo+1S V1Mo+2S

NM NM NM NM NM FM

a0 3.184 3.191 3.166 3.146 3.183 3.152

(0.22%) (−0.57%) (−1.19%) (−0.03%) (−1.01%)

Ef 7.223 2.772 5.441 7.998 10.364

slightly increased compared to the pristine case, whereas those in 1L-MoS2’s with other types of defects are a bit decreased. Except for 1L-MoS2 with the V1Mo+2S defect, there are not observed the magnetism at their equilibrium lattice constants. To understand the defect-forming stability, we have carried out the calculation of the vacancy-defect formation energy Ef using the following equation, Ef = −Epristine + Edefect + nEMo + mES

(1)

where Epristine and Edefect are total energies of the 4 × 4 supercell of the pristine and defective 1L-MoS2,respectively. EMo and ES are the total energy per atom of the bcc Mo and orthorhombic α-S, respectively, and n and m are the numbers of removed Mo and S atoms, respectively. The results are listed in Table 1. The defect formation energy for the V1S-doped 1L-MoS2 is lowest among the considered systems. The sulfur (and even the twosulfur) vacancy-defect formation is easier than the Mo-vacancy defect, which is consistent with previous reports.6,28 Point defects have been usually observed in the CVD grown MoS2 and can be easily made by the electron or proton irradiation method.17,41 We now examine the magnetic properties of the pristine and vacancy-doped 1L-MoS2’s under the tensile strain, which is more effective than the compressive strain for the present purpose.14,26,29 Figure 1c presents the calculation of total magnetic moment mtotal for the pristine and vacancy-defectdoped 1L-MoS2’s as a function of the tensile strain with a range from 0% to 20%. Here, the strain ε can be defined as ε = (a − a0)/a0 = Δa/a0, where a0 and a are the lattice constants of the unstrained (optimized) and strained systems, respectively. It is 2824

DOI: 10.1021/jp510308a J. Phys. Chem. C 2015, 119, 2822−2827

Article

The Journal of Physical Chemistry C

Figure 2. Unfolded band structures of the pristine and defective 1LMoS2’s at their equilibrium lattice constants. The color bar scale in the bottom represents the number of the primitive cell bands crossing the energy interval at a given primitive wave vector.

Figure 3. Total density of states (DOS) of the pristine and defective 1L-MoS2’s. The positive (negative) values represent the majority (minority) spin bands. Cyan shading, black dotted lines, and red solid lines denote the total DOS at the strain for the equilibrium (i.e., zero strain), magnetic transition, and maximum magnetization, respectively.

impurity bands of V2S and V1Mo defects are derived by Mo d and S p characters near the vacancy sites. To gain more insight into the emergent electronic and magnetic properties of defective 1L-MoS2’s under the tensile strain, the total density of states (DOS) are illustrated in Figure 3. Comparing the equilibrium DOS (shaded cyan lines of Figure 3) among the defective 1L-MoS2’s with respect to the pristine, one can find clearly that the defect levels of the molybdenum vacancy lie close to the VBM, whereas those of the sulfur vacancy are close to the CBM. This is confirmed from the midgap impurity bands found in the corresponding unfolded band structures of Figure 2. In addition, in Figure 3, the systematic band narrowing of defective 1L-MoS2’s occurs as the applied strain increases. In particular, after the magnetic transition, all the considered systems are shown to be metallic (see black dotted lines of Figure 3); i.e., the band gap collapses. As the strain increases more, the DOS of 1L-MoS2 with V1Mo, V1S, V2S, and V1Mo+1S defects apparently exhibit an unbalance between spin majority and minority bands (see red solid lines of Figure 3) and the systems are evidently magnetic. 1L-MoS2 with V2S defect is especially interesting in that its magnetic phase is energetically most stable among other defective 1L-MoS2’s and simultaneously shows the largest magnetic moment at ∼14% strain. To visualize the distribution of net magnetic moments of the 1L-MoS2 with V2S defect, we plot the spin-density isosurfaces in the inset of Figure 4a. It is clearly seen that the distribution of spin density is predominantly localized at the Mo atoms in the vicinity of vacancy defects. Therefore, we naturally attribute the Mo d

states near vacancy defects to the created magnetization under the strain. In particular, as shown in Figure 4a, out-of-plane states (dz2 and dxz/yz orbitals) of the Mo atoms near the defect sites show appreciable unbalanced spin populations in spin-split impurity bands near the Fermi level. Quantitatively, the local spin magnetic moment of the Mo atom is calculated to be 2.09 μB per atom. We have now calculated the bond lengths between Mo and S atoms (dMo−S) in the vicinity of the defect site of the V2Sdefective 1L-MoS2, which are indicated in the inset of Figure 4a. It should be noted that the induced magnetism in this system is mainly localized in Mo atoms near the defect site. Consequently, the bond lengths between Mo and S atoms are calculated to be 2.392, 2.428, and 2.480 Å at the strain for the equilibrium (zero strain), magnetic transition (∼10% strain), and maximum magnetization (∼14% strain), respectively. Simultaneously, the bond lengths between Mo and Mo atoms (dMo−Mo) near the defect site are calculated to be 2.829, 3.452, and 5.079 Å at the strain for the equilibrium, magnetic transition, and maximum magnetization, respectively. Further, we have tried the unrelaxed calculation for the V2S-defective 1LMoS2 at ∼14% strain (i.e., fixing the atomic distances as stretched ones by ∼14% strain from the pristine 1L-MoS2 with two S atoms just removed). In this calculation, dMo−S and dMo−Mo are found to be 2.594 and 3.575 Å, respectively, and the 2825

DOI: 10.1021/jp510308a J. Phys. Chem. C 2015, 119, 2822−2827

The Journal of Physical Chemistry C

Article

■

SUMMARY We have explored the strain-induced magnetism in 1L-MoS2’s with various vacancy defects. When the tensile strain is applied, 1L-MoS2’s with vacancies result in magnetic and metallic phases. From the point of view of the electronic structure, we have found that the resultant impurity bands inside the band gap play a role of seed to drive novel magnetic and electronic properties as the strain increases. In particular, we have also found that the two-sulfur-vacancy-defective 1L-MoS2 has the largest magnetization at ∼14% strain among various defective 1L-MoS2’s and undergoes a switching of the magnetization direction at ∼13% strain. Our finding indicates that the vacancy-defective 1L-MoS2’s promote the application of 2D transition metal dichalcogenides for the nanoscale devices and especially, the two-sulfur-vacancy-defective 1L-MoS2 can be a promising candidate for the nanoscale spintronic application.

■

AUTHOR INFORMATION

Corresponding Author

*J. D. Lee. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Leading Foreign Research Institute Recruitment Program (Grant No. 2012K1A4A3053565) and the Basic Science Research Program (Grant No. 2013R1A1A2007388) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (MEST).

Figure 4. (a) Partial DOS of the Mo atom near vacancy-defect sites for the V2S-defective 1L-MoS2 at ∼14% strain. The inset illustrates the spin-density isosurfaces. The isosurface value is taken as 5 × 10−3 e Å−3 and the blue (red) distribution represents the net spin up (spin down) density. Orange and cyan two-headed arrows (↔) represent the bond lengths between Mo and S atoms (dMo−S) and between Mo and Mo atoms (dMo−Mo), respectively. (b) Magnetocrystalline anisotropy (MCA) energy EMCA as a function of the tensile strain for the V2Sdefective 1L-MoS2. The blue arrow indicates the magnetization direction with respect to the surface.

■

REFERENCES

(1) Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Two-Dimensional Atomic Crystals. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 10451−10453. (2) Lee, C.; Li, Q.; Kalb, W.; Liu, X.-Z.; Berger, H.; Carpick, R. W.; Hone, J. Frictional Characteristics of Atomically Thin Sheets. Science 2010, 328, 76−80. (3) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Single-Layer MoS2 Transistors. Nat. Nanotechnol. 2011, 6, 147−150. (4) Coleman, J. N.; Lotya, M.; O’Neill, A.; Bergin, S. D.; King, P. J.; Khan, U.; Young, K.; Gaucher, A.; De, S.; Smith, R. J.; et al. TwoDimensional Nanosheets Produced by Liquid Exfoliation of Layered Materials. Science 2011, 331, 568−571. (5) Lee, Y.-H.; Zhang, X.-Q.; Zhang, W.; Chang, M.-T.; Lin, C.-T.; Chang, K.-D.; Yu, Y.-C.; Wang, J. T.-W.; Chang, C.-S.; Li, L.-J.; et al. Synthesis of Large-Area MoS2 Atomic Layers with Chemical Vapor Deposition. Adv. Mater. 2012, 24, 2320−2325. (6) Zhou, W.; Zou, X.; Najmaei, S.; Liu, Z.; Shi, Y.; Kong, J.; Lou, J.; Ajayan, P. M.; Yakobson, B. I.; Idrobo, J.-C. Intrinsic Structural Defects in Monolayer Molybdenum Disulfide. Nano Lett. 2013, 13, 2615− 2622. (7) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Atomically Thin MoS2: A New Direct-Gap Semiconductor. Phys. Rev. Lett. 2010, 105, 136805. (8) Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C.-Y.; Galli, G.; Wang, F. Emerging Photoluminescence in Monolayer MoS2. Nano Lett. 2010, 10, 1271−1275. (9) Ma, Y.; Dai, Y.; Guo, M.; Niu, C.; Huang, B. Graphene Adhesion on MoS2 Monolayer: An Ab Initio Study. Nanoscale 2011, 3, 3883− 3887. (10) Yun, W. S.; Han, S. W.; Hong, S. C.; Kim, I. G.; Lee, J. D. Thickness and Strain Effects on Electronic Structures of Transition Metal Dichalcogenides: 2H-MX2 Semiconductors (M = Mo, W; X = S, Se, Te). Phys. Rev. B 2012, 85, 033305.

net magnetic moment is 3.01 μB, which is smaller than that for the relaxed (atomic relaxation allowed) system (7.45 μB). This implies that the atomic relaxation and the bond length change could be a driving force of the strain-induced magnetism.29,48 MCA that originates from the spin−orbit interaction would be an interesting quantity to answer the question how the strain effect have an impact on the spin orientation of the V2Sdefective 1L-MoS2. In Figure 4b, we provide the MCA energy (EMCA) of the system in a range of 10−20% of the tensile strain, where ∼10% strain is the threshold of the magnetic transition. We note a sign change in EMCA. The positive sign of EMCA means the out-of-plane magnetization, whereas the negative sign the in-plane magnetization. As a result, the V2S-defective 1L-MoS2 shows the spin reorientation transition (SRT) from out-of-plane to in-plane order at ∼13% strain. This concludes that the tensile strain can be used as a new control tip not only for inducing the magnetization but also for switching the magnetization direction. Finally, we remark that another important merit of our strategy is to prepare the intriguing nanostructure (i.e., the V2Sdefective 1L-MoS2) rather easily. As mentioned before, various point defects are naturally found in the CVD grown 1L-MoS2. Most easily, one can always choose a piece of 1L-MoS2 with defects of two-sulfur vacancies. Or, more elaborately, one may create two-sulfur vacancies using the scanning tunneling microscope (STM) regularly in 1L-MoS2. 2826

DOI: 10.1021/jp510308a J. Phys. Chem. C 2015, 119, 2822−2827

Article

The Journal of Physical Chemistry C (11) Johari, P.; Shenoy, V. B. Tuning the Electronic Properties of Semiconducting Transition Metal Dichalcogenides by Applying Mechanical Strains. ACS Nano 2012, 6, 5449−5456. (12) He, K.; Poole, C.; Mak, K. F.; Shan, J. Experimental Demonstration of Continuous Electronic Structure Tuning via Strain in Atomically Thin MoS2. Nano Lett. 2013, 13, 2931−2936. (13) Castellanos-Gomez, A.; Roldán, R.; Cappelluti, E.; Buscema, M.; Guinea, F.; van der Zant, H. S. J.; Steele, G. A. Local Strain Engineering in Atomically Thin MoS2. Nano Lett. 2013, 13, 5361− 5366. (14) Zhu, C. R.; Wang, G.; Liu, B. L.; Marie, X.; Qiao, X. F.; Zhang, X.; Wu, X. X.; Fan, H.; Tan, P. H.; Amand, T.; et al. Strain Tuning of Optical Emission Energy and Polarization in Monolayer and Bilayer MoS2. Phys. Rev. B 2013, 88, 121301. (15) Ataca, C.; Ciraci, S. Functionalization of Single-Layer MoS2 Honeycomb Structures. J. Phys. Chem. C 2011, 115, 13303−13311. (16) Zhou, Y.; Yang, P.; Zu, H.; Gao, F.; Zu, X. Electronic Structures and Magnetic Properties of MoS2 Nanostructures: Atomic Defects, Nanoholes, Nanodots and Antidots. Phys. Chem. Chem. Phys. 2013, 15, 10385−10394. (17) Han, S. W.; Hwang, Y. H.; Kim, S.-H.; Yun, W. S.; Lee, J. D.; Park, M. G.; Ryu, S.; Park, J. S.; Yoo, D.-H.; Yoon, S.-P.; et al. Controlling Ferromagnetic Easy Axis in a Layered MoS2 Single Crystal. Phys. Rev. Lett. 2013, 110, 247201. (18) He, J.; Wu, K.; Sa, R.; Li, Q.; Wei, Y. Magnetic Properties of Nonmetal Atoms Absorbed Monolayers. Appl. Phys. Lett. 2010, 96, 082504. (19) Ramasubramaniam, A.; Naveh, D. Mn-Doped Monolayer MoS2: An Atomically Thin Dilute Magnetic Semiconductor. Phys. Rev. B 2013, 87, 195201. (20) Cheng, Y. C.; Zhu, Z. Y.; Mi, W. B.; Guo, Z. B.; Schwingenschlö gl, U. Prediction of Two-Dimensional Diluted Magnetic Semiconductors: Doped Monolayer MoS2 Systems. Phys. Rev. B 2013, 87, 100401(R). (21) Yun, W. S.; Lee, J. D. Unexpected Strong Magnetism of Cu Doped Single-Layer MoS2 and Its Origin. Phys. Chem. Chem. Phys. 2014, 16, 8990−8996. (22) Li, Y.; Zhou, Z.; Zhang, S.; Chen, Z. J. MoS2 Nanoribbons: High Stability and Unusual Electronic and Magnetic Properties. J. Am. Chem. Soc. 2008, 130, 16739−16744. (23) Botello-Méndez, A. R.; López-Uras, F.; Terrones, M.; Terrones, H. Metallic and Ferromagnetic Edges in Molybdenum Disulfide Nanoribbons. Nanotechnol. 2009, 20, 325703. (24) Ma, Y.; Dai, Y.; Guo, M.; Niu, C.; Lu, J.; Huang, B. Electronic and Magnetic Properties of Perfect, Vacancy-Doped, and Nonmetal Adsorbed MoSe2, MoTe2 and WS2 Monolayers. Phys. Chem. Chem. Phys. 2011, 13, 15546−15553. (25) Tongay, S.; Varnoosfaderani, S. S.; Appleton, B. R.; Wu, J.; Hebardet, A. F. Magnetic Properties of MoS2: Existence of Ferromagnetism. Appl. Phys. Lett. 2012, 101, 123105. (26) Kou, L.; Tang, C.; Zhang, Y.; Heine, T.; Chen, C.; Frauenheim, T. Tuning Magnetism and Electronic Phase Transitions by Strain and Electric Field in Zigzag MoS2 Nanoribbons. J. Phys. Chem. Lett. 2012, 3, 2934−2941. (27) Lu, P.; Wu, X.; Guo, W.; Zeng, X. C. Strain-Dependent Electronic and Magnetic Properties of MoS2 Monolayer, Bilayer, Nanoribbons and Nanotubes. Phys. Chem. Chem. Phys. 2012, 14, 13035−13040. (28) Tao, P.; Guo, H.; Yang, T.; Zhang, Z. Strain-Induced Magnetism in MoS2 Monolayer with Defects. J. Appl. Phys. 2014, 115, 054305. (29) Zheng, H.; Yang, B.; Wang, D.; Han, R.; Du, X.; Yan, Y. Tuning Magnetism of Monolayer MoS2 by Doping Vacancy and Applying Strain. Appl. Phys. Lett. 2014, 104, 132403. (30) Kresse, G.; Hafner, J. Ab initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47, 558−561(R). (31) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (32) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953−17979.

(33) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to The Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758− 1775. (34) Niu, M.; Cheng, D.; Cao, D. Understanding the Mechanism of Photocatalysis Enhancements in the Graphene-like Semiconductor Sheet/TiO2 Composites. J. Phys. Chem. C 2014, 118, 5954−5960. (35) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207−8215. (36) Medeiros, P. V. C.; Stafström, S.; Björk, J. Effects of Extrinsic and Intrinsic Perturbations on The Electronic Structure of Graphene: Retaining an Effective Primitive Cell Band Structure by Band Unfolding. Phys. Rev. B 2014, 89, 041407(R). (37) Popescu, V.; Zunger, A. Extracting E Versus k⃗ Effective Band Structure from Supercell Calculations on Alloys and Impurities. Phys. Rev. B 2012, 85, 085201. (38) Rubel, O.; Bokhanchuk, A.; Ahmed, S. J.; Assmann, E. Unfolding the Band Structure of Disordered Solids: From Bound States to High-Mobility Kane Fermions. Phys. Rev. B 2014, 90, 115202. (39) Brommer, P.; Quigley, D. Automated Effective Band Structure for Defective and Mismatched Supercells. J. Phys.: Condens. Matter 2014, 26, 485501. (40) Hobbs, D.; Kresse, G.; Hafner, J. Fully Unconstrained Noncollinear Magnetism within the Projector Augmented-Wave Method. Phys. Rev. B 2000, 62, 11556−11570. (41) Komsa, H.-P.; Kotakoski, J.; Kurasch, S.; Lehtinen, O.; Kaiser, U.; Krasheninnikov, A. V. Two-Dimensional Transition Metal Dichalcogenides under Electron Irradiation: Defect Production and Doping. Phys. Rev. Lett. 2012, 109, 035503. (42) Bertolazzi, S.; Brivio, J.; Kis, A. Stretching and Breaking of Ultrathin MoS2. ACS Nano 2011, 5, 9703−9709. (43) Cooper, R. C.; Lee, C.; Marianetti, C. A.; Wei, X.; Hone, J.; Kysar, J. W. Nonlinear Elastic Behavior of Two-Dimensional Molybdenum Disulfide. Phys. Rev. B 2013, 87, 035423. (44) Li, T. Ideal Strength and Phonon Instability in Single-Layer MoS2. Phys. Rev. B 2012, 85, 235407. (45) Sun, J. Y.; Zhao, X. H.; Illeperuma, W. R. K.; Chaudhuri, O.; Oh, K. H.; Mooney, D. J.; Vlassak, J. J.; Suo, Z. G. Highly Stretchable and Tough Hydrogels. Nature 2012, 489, 133−136. (46) We have checked that the spin-polarized calculation for the V2Sdefective 1L-MoS2 at ∼14% strain using the hybrid HSE06 functional resulted in 7.99 μB per supercell, being very close to the present GGA result (7.45 μB per supercell). (47) McDonnell, S.; Addou, R.; Buie, C.; Wallace, R. M.; Hinkle, C. L. Defect-Dominated Doping and Contact Resistance in MoS2. ACS Nano 2014, 8, 2880−2888. (48) Ma, Y.; Dai, Y.; Guo, M.; Niu, C.; Zhu, Y.; Huang, B. Evidence of the Existence of Magnetism in Pristine VX2 Monolayers (X = S, Se) and Their Strain-Induced Tunable Magnetic Properties. ACS Nano 2012, 6, 1695−1701.

2827

DOI: 10.1021/jp510308a J. Phys. Chem. C 2015, 119, 2822−2827