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Cite this:Phys.Chem.Chem.Phys.,

2018, 20, 553

Structural stability and magnetic-exchangecoupling in Mn-doped monolayer/bilayer MoS2†

Qinglong Fang, a Xumei Zhao,b Yuhong Huang,c Kewei Xu,ad Tai Min, a

Paul K. Chu*e and Fei Ma*ae

Ferromagnetic (FM) two-dimensional (2D) transition metal dichalcogenides (TMDs) have potential applications

in modern electronics and spintronics and doping of TMDs with transition metals can enhance the magnetic

characteristics. In this work, the structural stability, electronic states, and magnetic properties of Mn-doped

monolayer/bilayer MoS2 are studied systematically by first-principles calculations. Substitutional Mn dopants at

the Mo sites are energetically favorable in both monolayer and bilayer MoS2 under the S-rich condition which

is common in the synthesis of MoS2 nanosheets. Two Mn dopants participate in the FM interaction

in monolayer MoS2 and magnetic coupling of two Mn dopants via the double-exchange mechanism

can be mediated by the nearest neighboring S. Magnetic coupling can be ascribed to the competition

between the double-exchange, direct-exchange, and super-exchange interactions, which take place

between two Mn dopants in bilayer MoS2 with the MniMnMo, MniMnS and MnMo–MnMo configurations. Our

results reveal the geometrical dependence of magnetic-exchange coupling suggesting that Mn-doped

monolayer/bilayer MoS2 has large potential in spintronic devices.

1. Introduction

The discovery of graphene and its unique properties have stimu-lated extensive research in two-dimensional (2D) materials1–4 andefforts have been made to fabricate high-quality 2D sheets tostudy the novel physical properties and design new devices.5–9

However, the gapless feature of pristine graphene limits itsintegration into microelectronic and nanoelectronic devices.1

On the other hand, many transition metal dichalcogenides(TMDs) possessing interesting semiconducting, metallic, super-conducting, and magnetic properties have potential applicationsin photovoltaics,10,11 optical detection,12–14 photocatalysis,15,16

field-effect transistors,17,18 as well as lithium-ion batteries.19–22

These compounds are composed of MX2 (M = Mo, W, Nb, Re, Ta;X = S, Se, Te) layers with covalent bonding within the layers andweak van der Waals (vdW) bonding between layers enabling

easy exfoliation. Semiconducting TMDs such as MoS2 arepotential candidates in next-generation electronic and opto-electronic devices.23,24 Recently, a spin lifetime of 1 ns or longerexceeding that of graphene has been observed by polarization-resolved photoluminescence measurements.25 The spin–orbitcoupling and absence of inversion symmetry induce spin splittingat the valence band maximum thus suppressing spin relaxationand enhancing the spin lifetime.26–28

In spintronics, attention has been paid to strategies that induceand manipulate the magnetic properties in semiconductorsand stable magnetism in semiconducting 2D materials. Dopingis a simple technique to produce stable magnetic propertiesin 2D materials.29,30 Theoretical and experimental studies havebeen conducted to explore magnetism in MoS2 nanosheets dopedwith transition metals.31–34 For example, substitutional replace-ment of Mo with TM atoms (V, Mn, Fe, Co, Cu, Ni, Zn, Cd and Hg)can induce significant magnetism in monolayer MoS2

35–38 if thedopants are separated from each other at a certain distance.39

Substitutional replacement of Mo with Mn can even produceFM properties via the double-exchange mechanism.37,38 Sincethis interaction is short-ranged, percolation is a key factor incontrolling the long-range magnetic order.37 Shu et al.40 haveobserved FM coupling in Fe-doped monolayer MoS2 throughmagnetic double-exchange coupling but antiferromagnetic (AFM)coupling in bilayer and multilayer samples by magnetic super-exchange coupling. The electronic states and magnetic propertiescan be manipulated by the ‘pizza’ and ‘sandwich’ configurationsof Mn clusters in MoS2 nanosheets41 thereby suggesting that the

a State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong

University, Xi’an 710049, Shaanxi, China. E-mail: mafei@mail.xjtu.edu.cnb College of Materials Science and Engineering, Shaanxi Normal University,

Xi’an 710062, Shaanxi, Chinac College of Physics and Information Technology, Shaanxi Normal University,

Xi’an 710062, Shaanxi, Chinad Department of Physics and Optoelectronic Engineering, Xi’an University of Arts

and Science, Xi’an 710065, Shaanxi, Chinae Department of Physics and Department of Materials Science and Engineering,

City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China.

E-mail: paul.chu@cityu.edu.hk

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp05988d

Received 2nd September 2017,Accepted 30th November 2017

DOI: 10.1039/c7cp05988d

rsc.li/pccp

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magnetism as well as magnetic-exchange coupling among dopantscan be manipulated by altering the doping configuration anddistribution, which are sensitive to the growth conditions andparameters such as the S/Mo ratio and temperature. Hence, themagnetic coupling behavior and effects of different doping con-figurations are interesting from the perspective of fundamentalunderstanding and spintronic applications. In this work, based onfirst-principles calculations, the structural stability and magneticexchange interactions in Mn-doped MoS2 nanosheets are system-atically studied and applications to spintronic devices are dis-cussed thermodynamically and kinetically.

2. Computational method and model

The calculation is performed using the Vienna ab initio simulationpackage based on density functional theory.42,43 The electron–ioncore interaction is described by the projector augmented wavepotentials44 which are more accurate than the ultra-soft pseudo-potentials. The Perdew–Burke–Ernzerhof45 formulation of thegeneralized gradient approximation is chosen to describe theexchange–correlation interaction. The DFT-D2 approach withinthe Grimme scheme is adopted to correct the contribution of thevdW interactions between different layers46 and the cutoff energyfor the plane waves is 400 eV. To avoid the interactions betweendopants in neighboring unit cells, a 4 � 4 � 1 supercell of theMoS2 primitive cell in which the separation between dopants islarger than 12 Å is adopted. A 15 Å vacuum layer is added in theout-of-plane direction to inhibit the interactions of neighboringlayers. The Brillouin–zone integration is performed by using an11 � 11 � 1 k-mesh according to the Monkhorst–Pack schemeand a Gaussian smearing broadening of 0.2 eV is introduced. Aconjugate-gradient algorithm is implemented to relax the ions tothe ground states with an energy convergence of 1.0 � 10�5 eVand force convergence of 0.02 eV Å�1 on each ion, respectively.The supercells and magnetic moment distribution are visualizedby the VESTA software.47

In addition, the GGA functional fails to describe partiallyoccupied 3d orbitals of transition metal elements. Thereforeusing a model of GGA with the correction of a Hubbard U term(GGA+U) to describe the 3d orbitals of impurity transition metalelements seems to be necessary.36,40 However, several on siteHubbard U parameters have been tested for Mo (4d) orbitals,which yield almost the same results as the GGA calcula-tions.31,48 Similarly, Cheng et al. studied the magnetism ofmonolayer MoS2 doped with Mn by using GGA+U, which agreeswith that of the theoretical results within GGA. In order toobtain a reasonable U parameter, the role of U parameter in therange of 3–5 eV (U = 3, 3.5, 4, 4.5, and 5 eV) is investigated.Taking two Mn dopants substitutionally inserted into mono-layer MoS2 as a test example, we find that adjusting the U valuedoes not change the magnetic moment (total and local mag-netic moments) and FM characteristic upon comparing theresult calculated with the GGA method (Fig. S1 in the ESI†).Thus, the GGA+U method is not considered to describe the Mndopant in MoS2 nanosheets in this work.

The thermodynamic stability of the Mn dopant in MoS2

nanosheets is evaluated by calculating the formation energy (Ef)as shown in the following equation:

Ef = ET � EP � DnMomMo � DnSmS � DnMnmMn, (1)

where ET and EP are the energies of the Mn-doped and perfectMoS2 sheets, respectively, and mi and Dni are the chemicalpotential and difference of atomic species i (i = Mo, S, and Mn)in the Mn-doped and perfect MoS2 sheets. mMnmMn and mMo arethe respective chemical potentials of a single Mn and Mo atom.The energy per atom of a-Mn is taken as mMn.38 mMo is definedwithin a range of values corresponding to Mo-rich or S-richgrowth conditions. For the Mo-rich condition, mMo is taken asthe energy of a Mo atom within its stable fcc lattice. mMo is deter-mined from the difference in the energy between a diatomic S2

molecule and one formula unit of MoS2, corresponding to theS-rich condition. In order to maintain thermodynamic equili-brium of the crystalline phase (mMo + 2mS = mMoS2

), the value of mS

should satisfy the requirement of mS(bulk) � DHf o mS o mS(bulk),in which the upper (lower) limit corresponds to the S-rich(Mo-rich) condition and DHf is the formation heat of MoS2. Thecomputed formation heat is 1.44 eV which is in good agreementwith reported results.40,49

3. Results and discussion3.1 Mn dopant in monolayer MoS2

The structural stability and magnetic properties of the isolatedMn dopant in monolayer MoS2 are first investigated. Five dopingconfigurations are considered, that is, Mn adsorbed on top of theMo, S or hollow sites (AMo, AS, and AH) and Mn replacing Mo or S(MnMo and MnS) as schematically illustrated in Fig. 1a. Metal-doped MoS2 has been synthesized50,51 and Au on top of the S, Mo,and hollow sites of MoS2 has been observed.52 Furthermore,Cr/V/Nb dopants directly substitute Mo atoms,53,54 and Ptatoms are localized at S vacancies exhibiting dynamic hoppingto the nearby surface layers.55 Up to now, the position of Mndopants in MoS2 has been ambiguous. The formation energiesof the five possible doping configurations as a function of thechemical potential difference for different S concentrations(DmS = mS � mbulk) are calculated and shown in Fig. 1b. Theformation energy of the MnMo doping configuration is the lowestone and negative in most cases. In particular, under the S-richgrowth condition, the formation energy of MnMo doping in

Fig. 1 (a) Atomic model and (b) formation energy of a single Mn dopant inmonolayer MoS2.

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monolayer MoS2 is �1.702 eV which is in good agreement withthe reported value of �1.8 eV.42 Therefore, Mn dopants tend toreplace Mo atoms in monolayer MoS2 and it has been observedexperimentally.54,56

To understand the spin splitting, the electronic states ofmonolayer MoS2 with the MnMo doping configurations arecalculated. The trigonal prismatic coordination of Mo atomsleads to degeneracy of the Mo 4d levels. The lowest energy bandof the Mo dz2 orbital is fully occupied, the degenerate energybands of the Mo dxy and Mo dx2�y2 orbitals are unoccupied, andthose of Mo d and Mo dyz bands are the highest ones. Hybridiza-tion among the Mo dz2, Mo dxy, Mo dx2�y2, and S 3p orbitalsdominates the conduction and valence band edges of MoS2.23–27

As shown in Fig. 2, spin polarization occurs in monolayer MoS2

with the MnMo doping configuration leading to highly localizedstates in the band gap. The partial density of states (PDOS)suggests that the mid-gap states mainly arise from the d statesof the Mn dopant and its neighboring spin-polarized 3d states ofMo atoms and 3p states of S atoms. Strong hybridization betweenthe 3d states of Mn and 3p states of adjacent S atoms producesmid-gap states in the spin-up channel (Fig. 3b and c). Moreover,no band gap is observed from the spin-up channel, although aconsiderable band gap is kept in the spin-down channel, indicat-ing the half-metallic feature of the Mn-doped monolayer MoS2.Thus, it is expected to provide 100% spin polarization currentand favorable spintronic applications. Some valence electrons(3d64s1) of the Mn dopant transfer to the nearest-neighboringS atoms and the residual valence electrons produce spin polar-ization and a magnetic moment of 1.035 mB (Table S1, ESI†). Thisis in good agreement with the previously reported value ofB1 mB.32 The Mn 3d orbitals undergo crystal-field splitting(Dcf) and interatomic Hund’s exchange splitting (Dex). The fiveMn 3d states are split into three groups, anti-bonding states, e1

(dxy and dx2�y2), e2 (dxz and dyz), and a1 (dz2) due to the trigonalprismatic coordination of S atoms. As schematically shown inFig. 3d, the energies of the spin-down states a1 and e1 are lowerthan those of the spin-up states e2, suggesting Dcf 4 Dex.

The long-range ferromagnetism is mediated by the AFMcoupling between the localized Mn 3d states and delocalized

S 3p states in monolayer MoS2.37,38 It has been predicted thatthe Curie temperature of Mn-doped monolayer MoS2 can reachroom temperature if the Mn dopant concentration is 10–15%.38

It has been demonstrated by experiments that an inert substrate(i.e., graphene) allows only 2 at% doping of Mn in MoS2, otherwiseit is difficult to retain the 2D morphology.57,58 To further studythe effects of the dopant concentration on magnetic-exchangecoupling, two Mn dopants are substitutionally inserted intomonolayer MoS2 and the magnetic-exchange coupling is evalu-ated by comparing the energies of the FM and AFM states:

DE = EFM � EAFM, (2)

where EFM and EAFM are the energies of the Mn-doped MoS2 inthe FM and AFM states, respectively. The energy of the FM state isless than that of the AFM state when two Mn dopants are closeto each other. That is, the FM state is preferred. The magneticcoupling interactions in Mn-doped monolayer MoS2 are furtherexamined by the spin density distribution (Fig. 4). When twoMnMo dopants are separated by a distance less than 16.53 Å(Fig. S2, ESI†), the Mn dopants are highly spin-polarized with thesame spin-polarization direction and the nearest neighboringS atoms between two Mn dopants are AFM coupled with theS atoms (Fig. 4a–c). But it is different if the separation betweentwo Mn dopants is increased to 22.05 Å and the energy of the FMstate is equal to that of the AFM state (Fig. 4d). The results indi-cate long-range FM coupling of two Mn dopants in monolayerMoS2.38 The results are different from those of Co-doped mono-layer MoS2 that is nonmagnetic when the dopants are close to eachother.59 However, the system becomes magnetic with a magneticmoment of 6.00 mB if the two dopants are separated by 5.50 Å.Based on the mean-field approximation (MFA), the Curie tempera-ture (TC) is estimated from the energy difference between the FMand AFM states with the following equation:

3

2kBTC ¼ �

DEn; (3)

where kB is the Boltzmann constant and n is the number ofdopants in a supercell. The estimated TC is 224 K and lower thanroom temperature and it is in good agreement with the reportedvalue of B200 K obtained by Monte Carlo simulation.37

3.2 Single Mn dopant in bilayer MoS2

In 2D materials, surface doping is commonly implemented tomanipulate the physical properties, but oxidization and migra-tion may take place on these exposed atoms producing structuraland functional instability. It may be overcome if the dopants canbe fixed in the interlayer of bilayer MoS2. The two stackingsequences, AA and AB, exist in bilayer MoS2. In AA (AB) stacking,the Mo atoms in one layer are on top of the Mo (S) atoms in theother layer (Fig. S3, ESI†). The AB stacking configuration is morestable than the AA one, but both AA and AB stacking configura-tions are obtained by CVD.60 Here, both are considered and twotypical interlayer doping sites are considered: (1) dopant justabove the hollow site of the hexagonal rings in bilayer MoS2 (H)and (2) dopant directly under the S atom in the upper layer (S).As shown in Fig. 5a and c, for the Mn dopant at the H site in

Fig. 2 Total and partial density of states of Mn substituting Mo (MnMo) inmonolayer MoS2. The black and red lines represent the spin-up and spin-down channels, respectively, and the Fermi level which is set at zero isindicated by the green line.

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bilayer MoS2 with the AA and AB stacking configurations (AA-Hand AB-H), the Mn dopant is bonded to three S atoms in eachsublayer. For the Mn dopant directly under the S atom in theupper layer of the AA stacking configuration (AA-S), the Mndopant is bonded to one S atom in the upper sublayer and one Satom in the lower sublayer (Fig. 5b). For the Mn dopant directlyunder the S atom in the upper layer in the AB configuration(AB-S), the Mn dopant is bonded to one S atom in the upper

sublayer and three S atoms in the lower sublayer (Fig. 5d).As shown in Table S2 (ESI†), for the Mn dopant in the AA-H(AA-S) stacking configuration, the interlayer distance decreases(increases) to 3.665 Å (3.872 Å) from the original value of 3.720 Å,whereas the interlayer distance in the AB stacking configurationis between 3.112 Å and 3.121 Å, which is close to the idealinterlayer distance of bilayer MoS2 (3.110 Å). In the AA-S and AB-Sconfigurations, the bond lengths between the Mn dopant and

Fig. 3 Orbital decomposed density of states of Mn substituting Mo (MnMo) in monolayer MoS2: (a) Mo 4d states, (b) S 3s and 3p states, and (c) Mn 3dstates. The Mo and S atoms are the nearest to the Mn dopant. The black and red lines represent the spin-up and spin-down channels, respectively. TheFermi level is set at zero and indicated by the green line. (d) Schematic plot of the splitting of Mn d orbitals due to crystal-field splitting (Dcf) andinteratomic Hund’s exchange (Dex).

Fig. 4 Spin-density isosurface distributions for FM and AFM configurations of Mn-doped monolayer MoS2 with the 2MnMo configuration in (a) 4 � 4,(b) 5 � 5, (c) 6 � 6, and (d) 7 � 7 supercells. The red and green isosurfaces represent the positive and negative spin densities, respectively. The isosurfacevalue is 0.003 e �3.

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S atoms are between 2.113 Å and 2.220 Å, which is shorter thanthat of the covalent Mn–S bond (B2.37 Å). However, in theAA-H and AB-H configurations, the bond lengths between theMn dopant and S atoms increase to the range of 2.421–2.563 Å.The interlayer Mn dopant and S atoms of bilayer MoS2 in all theconfigurations are covalent bonded. Fig. 6 shows the chargedensity difference of the Mn-doped bilayer MoS2 with the AA andAB configurations. The electron density accumulates betweenthe Mn dopants and adjacent S atoms characteristic of covalentbonding.

Owing to the different doping environments, the AA-H, AA-S,AB-H, and AB-S doping configurations exhibit completely dis-tinct magnetic moments of 5.07 mB, 3.03 mB, 3.87 mB, and 3.00 mB,respectively. The overall magnetic moments can be ascribed tospin polarization of excess d electrons on the Mn dopant. EachMn atom possesses 5 electrons in the 3d orbital. When Mn isdoped at the H site in bilayer MoS2 with both the AA and ABstacking configurations, the interaction between the Mn dopant

and S is weak because of the larger bond length. Strong inter-actions between Mn and S are induced, accompanied by sub-stantial electron transfer from the 4s to 3d states of the Mndopant if Mn is doped at the S site in bilayer MoS2 with theAA and AB stacking configurations. This reduces the unpairedelectrons and magnetic moment.40,61

To again investigate magnetic coupling of a single Mn dopantin bilayer MoS2, the orbital decomposed density of states andsplitting of Mn 3d orbitals are presented in Fig. 7. The magneticmoment is sensitive to the doping environment. In the AA-Hdoping configuration, the trigonal prismatic coordination of Satoms around the Mn dopant is similar to that of the MnMo

dopant in monolayer MoS2, but the bond length between Mnand S atoms is larger and as a result, crystal-field splitting isreduced and Dcf o Dex (Fig. 7b). The magnetism is mainly dueto spin polarization around the Mn atom (Fig. 7a and Table S2,ESI†). In spite of some differences in the electronic states,similar results are observed from the AA-S doping configuration(Fig. 7c and d). The octahedral and tetrahedral coordinationof S atoms around the Mn dopant exist in the AB-H and AB-Sdoping configurations. The bond length between Mn and S atomsis equal and the antibonding states e1 and e2 have the sameenergy, so that crystal-field splitting disappears (Fig. 7e–h). Similarto the Mn doped bilayer MoS2, the doping environment depen-dent electronic states of Cr, Fe, and Co in bilayer MoS2 are alsoobserved (Fig. S4–S6, ESI†).61

3.3 Double Mn dopants in bilayer MoS2

The structural and magnetic properties of the 4 � 4 supercell inbilayer MoS2 are investigated by considering six doping configu-rations (Fig. 8a): (i) an intercalated Mn atom (Mni) and MnMo

dopant (MniMnMo), (ii) an intercalated Mn atom (Mni) and MnS

dopant (MniMnS), (iii) two intercalated Mn atoms (MniMni),(iv) two MnMo dopants in different sublayers (MnMo–MnMo),(v) two MnS dopants in different sublayers (MnS–MnS), and(vi) MnMo and MnS dopants in different sublayers (MnMo–MnS).Fig. 8b shows the formation energies of the six doping configu-rations as a function of chemical potentials. It can be seen thatMniMnS is the most stable doping configuration under the

Fig. 5 Atomic models of a single Mn dopant in bilayer MoS2 with the (a and b) AA and (c and d) AB stacking configurations.

Fig. 6 Charge density difference of a single Mn dopant in bilayer MoS2

with the (a and b) AA and (c and d) AB stacking configurations. The red andturquoise isosurfaces represent the gain and depletion of charge density,respectively. The isosurface value is 0.005 e �3.

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Mo-rich condition (DmS o �1.024 eV), but MnMo–MnMo becomesthe most stable one in the S-rich regime (DmS 4 �0.75 eV) andMniMnMo and MnMo–MnS are stable if DmS is in the rangebetween �1.024 and �0.812 eV. The doping configurations ofMniMni, and MnS–MnS are energetically unfavorable. Althoughexperimental results demonstrate that S vacancies are energe-tically favorable in most cases,49,62,63 Mn dopants prefer to sub-stitutionally replace Mo under the S-rich condition and theMnMo–MnMo doping configurations can be obtained more easily.

The results are different from the recently reported results inwhich the FeMoFei doping configuration is observed to be stableunder the S-rich condition.40

The magnetic ground states of the stable doping configura-tions are evaluated according to eqn (2). The calculated DE valuesare �823, 42, �241 and 5 meV for the MniMnMo, MniMnS,MnMo–MnMo, and MnMo–MnS doping configurations, respectively.Consequently, the MniMnMo and MnMo–MnMo doping configura-tions should exhibit the FM state, whereas the MniMnS and

Fig. 7 Orbital decomposed density of states and splitting of 3d orbitals in a single Mn dopant in bilayer MoS2 with the (a, b and c, d) AA and (e, f and g, h)AB stacking configurations.

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MnMo–MnS doping configurations should have the AFM state.However, it is hard to obtain the MniMnMo and MnMoMnS dopingconfigurations in bilayer MoS2 due to the small stable region of thechemical potential. Fig. 9 shows the spin density (rm–rk) distribu-tion in the bilayer MoS2 with the MniMnMo, MniMnS, MnMo–MnMo,and MnMo–MnS doping configurations. In bilayer MoS2 with theMniMnMo doping configuration, the two Mn dopants exhibitdouble-exchange coupling and the same spin polarization direc-tion. Moreover, the Mn dopants are AFM coupled with the nearestneighboring S atoms (Fig. 9a), which is similar to the case ofmonolayer MoS2 with FM coupling. In bilayer MoS2 with theMniMnS doping configuration, direct chemical bonding andexchange coupling take place between the two Mn dopants withopposite spin polarization resulting in the AFM state. Although twoMn dopants in bilayer MoS2 with the MnMo–MnS doping configu-ration also have the opposite polarization direction, the magneticexchange coupling is different from that in bilayer MoS2 with theMniMnS doping configuration, and super-exchange coupling takes

place between the two Mn atoms with opposite spin polarization(Fig. 9d). Owing to AFM coupling between the Mn dopants, bilayerMoS2 with the MniMnS and MnS–MnS doping configurationspossesses negligible magnetism. Meanwhile, the opposite polariza-tion of the Mn dopant and nearest neighboring Mo atoms or Satoms leads to AFM coupling. In bilayer MoS2 with the MnMo–MnMo doping configuration, the distance between two Mn dopantsis 6.788 Å which is so large that the interaction between them isweak and they are independent. Hence, the result is the same asthat of the Mn-doped monolayer MoS2. The estimated TC of bilayerMoS2 with the MnMo–MnMo doping configuration is 931 K and wellabove room temperature. Therefore, room-temperature ferromag-netism is expected from bilayer MoS2 with different Mn dopingconfigurations spurring potential application in spintronic devices.

The results indicate that the MnMo doping configuration isenergetically stable in the S-rich regime of the MoS2 nanosheet,while the MniMnS doping configuration is more favorable in theS-deficient environment. The S-rich environment is generallyadopted to synthesize MoS2 nanosheets. Thus, the MnMo dopingconfiguration is energetically favorable in Mn-doped MoS2 andsimilar behaviors occur in Fe-, Cr-, V-, and Nb-doped MoS2

nanosheets.52,53 For instance, in the Fe-doped MoS2 layeredcrystals prepared by the chemical vapor transport method, thereplacement of Mo by Fe takes place in the S-rich regime, whilethe replacement of S by Fe takes place under the Mo-richcondition.40 However, Pt atoms are preferentially localized at Svacancies and usually hop to the nearby surface layers,54 and Auatoms are preferentially on the top of S, Mo, and hollow sites ofMoS2.51 Additionally, Co adsorption on the Mo site was evidencedfrom the high angle annular dark field image, which is confirmedas the energetically favourable geometry by density functionaltheory calculations.

So far, a large number of theoretical studies have been done toexplore the stable magnetism in TM-doped MoS2 nanosheets.However, they mainly focused on studying the influences of a singledopant on the magnetic properties of MoS2 nanosheets and themagnetic-exchange coupling among dopants is commonly ignored.In fact, the magnetic properties are sensitive to magnetic-exchangecoupling among dopants in the host materials. Shu et al.40 showedthat the layer number is crucial in controlling the magneticproperties of Fe-doped MoS2, that is, FM coupling occurs inFe-doped monolayer MoS2, but AFM coupling in Fe-doped bi- and

Fig. 8 (a) Atomic models and (b) formation energy of two Mn dopants in bilayer MoS2.

Fig. 9 Spin-density isosurface distributions of two Mn dopants in bilayerMoS2 with different doping configurations: (a) MniMnMo, (b) MniMnS,(c) MnMo–MnMo, and (d) MnMo–MnS. The red and green isosurfaces repre-sent the positive and negative spin densities, respectively, and the isosurfacevalue is 0.02 e Å�3.

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trilayer MoS2. The direct and mediated bonding interactionsbetween the intercalated and substitutional Fe dopants followthe superexchange mechanism. As for Mn-doped MoS2 nanosheetsin this work, it is found that the doping sites are crucial incontrolling the magnetic properties. Particularly, AFM couplingtakes place in monolayer MoS2 with MnMo–MnS or MniMnS dopingconfigurations, and otherwise, FM coupling occurs in the MnMo–MnMo or MniMnMo doping configurations. Since the doping sitesdepend on the synthesis conditions, the precise control of dopingsites is required to generate ferromagnetism.

4. Conclusion

The structural stability, electronic states, and magnetic propertiesof Mn-doped monolayer/bilayer MoS2 are studied by first-principlescalculations. The structural stability of Mn-doped MoS2 depends onthe chemical potential and layer number. In the S-rich environ-ment, Mn replacement of Mo in monolayer MoS2 (MnMo) is stablebut in the S-deficient environment, the MniMnS doping configu-ration is more favorable in bilayer MoS2. Mn dopants lead to FMcoupling in monolayer MoS2 and magnetic coupling of Mn dopantsvia the double-exchange mechanism can be mediated by thenearest neighboring S. In bilayer MoS2, the magnetic-exchangecoupling is related to the competition between the double-exchange, direct-exchange, and super-exchange interactions. Speci-fically, in the MniMnMo doping configuration, double-exchangecoupling takes place between the two Mn dopants and it is thesame as that of the Mn-doped monolayer MoS2 with FM coupling.Although the two Mn dopants have opposite spin polarization, themagnetic-exchange mechanisms of the MniMnS and MnMo–MnS

doping configurations are different. The findings provide insightsinto the development of intrinsic diluted magnetic semiconductorsbased on 2D MoS2 nanosheets.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was jointly supported by the National Natural ScienceFoundation of China (Grant No. 51471130, 51771144, 51501012), theNatural Science Foundation of Shaanxi Province (No. 2017JZ015),Fund of the State Key Laboratory of Solidification Processing inNWPU (SKLSP201708), Fundamental Research Funds for the CentralUniversities, City University of Hong Kong Applied Research Grant(ARG) No. 9667122, as well as City University of Hong Kong StrategicResearch Grant (SRG) No. 7004644. This work was carried out at theHPCC Platform in Xian Jiaotong University.

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