Introduction

Since a pioneering (re)discovery of the monolayer graphene1,2, enormous researches have been focused on layered crystals during the past decades3. Benefiting from covalence bonds in layers and van der Waals forces among layers, complex structures are easily manipulated in order to reach different application purposes. In contrast to the semimetallic pristine graphene, most of the inorganic layered crystals (ILCs) have non-zero bandgaps. Such semiconducting properties are essential in semiconductor industry. Various species from the nitrides and group VI metal compounds4 enrich the library of the ILCs. Among them, the MoS2 is a conventional lubricant5 and catalyst for hydrogen evolution6,7. When lowering the MoS2 dimensions, a transition of indirect to direct band occurs, leading to the boosting of photoluminescence8,9. Recent investigations of the materials in low dimensions showed that it is advanced in high efficient transistors10, photoelectronic devices11 and electrocatalysis12. To improve the performances of the MoS2-based devices, molecular modulation and engineering are proposed and many of works are in progresses13,14. Ideally speaking, the ILC materials can be piled up to 3D forms, with each 2D layer consisting of enough functional units such as doped atoms or clusters4. So is the few-layer MoS2, which has potentials in various applications and was reported as a key material in high mobility and low power transistors10,15.

Pursuing semiconductors with high performances has always been within the focuses of materials sciences. Due to possible manipulations of electron spins and carrier intensities16, dilute magnetic semiconductors (DMSs) have been one of the key targets within such an issue. Similar to the hosting merits from the transition metal (TM) oxides (say the ZnO)17, the structural uniqueness of ILCs makes such layered groups as new candidate matrixes in the magnetic semiconductors. The 2D DMS systems have been explored in monolayer MoS2 e.g., by substituting Mo ions with 3d TMs18,19 or 4d TMs20. The doping routes in the ILCs are, nevertheless, not an easy task in experiments21. Alternatives were suggested to replace both Mo and neighboring S atoms with the FeX6 (X = S, C, N, O, F) clusters22, or a wetting deposition of the Co layer onto monolayer MoS223. Brewing magnetism into double- or few-layered MoS2 are rather scarcely reported, despite of the magnification of efficiencies in the 3D piled-up electronics4. In a latest work, the Fe doped double layered MoS2 was predicted to enhance the host stabilities as well as to magnetically exchange coupling between the host and dopants24. However, doping or growing dynamics of such hetero functional units normally debuts from a fast nucleation of the metallic ions25,26, resulting in rather small clusters or nanoparticles on the layered crystal surfaces or possibly among the layers27,28,29. Indeed, in addition to clusters’ inimitable properties30,31, combining clusters with the monolayer graphene was predicted to increase the magnetic moment of the cluster32,33,34. Furthermore, the intercalated water molecules between graphene interlayers were observed experimentally and very unique properties have been revealed recently35. Thus, in an analogy to routes of clusters anchoring on the graphene, using the clusters as dopants onto or among the ILCs may offer another effective route to tailor the ILCs properties.

In this article, we reported on a first-principles prediction of magnetic monolayer MoS2 ‘pizzas’ with Mnn (n = 1–4) ‘toppings’ and bilayer MoS2 ‘sandwiches’ with Mnn (n = 1–4) clusters ‘fillings’. The manganese clusters were selected as the start clusters due to their magnetic robustness36, size-dependent magnetism37, as well as easier adsorptions on layered structures38. Hosts of the clusters were extended from monolayer MoS2 ‘crust’ to the bilayer ‘bread slices’. To keep the intrinsic layered structures and prevent introducing defects, the clusters were placed and adsorbed on the top or between the layers. We investigated magnetic properties and electronic structures of the cluster adsorbed mono- and bi-layers. Bonding mechanisms within Mn clusters and between clusters and ILC hosts were studied. In addition to possible variations of magnetic moments by changing the cluster sizes, we also found that introductions of the clusters into the ILC systems will facilitate system stabilities and operate band types.

Results

Geometric structures of the complexes

Investigations of the doped system’s properties debut from the geometric structures. The free Mnn clusters were firstly studied to give basic knowledge of the ‘toppings’ or ‘fillings’ onto or into the crusts or bread slices. More than 60 initial Mnn structures were collected for further DFT optimization. Optimized clusters geometries were depicted in Fig. 1a. Detailed structural parameters for other low-lying isomers are provided in the Supplementary Information (SI). The Mnn clusters evolved from 0D to 2D forms when n was tuned from 1 to 3. However, in the case of n = 4, the 3D tetrahedron cluster was found as the most stable isomer, followed by a rhombus with a relative energy of 0.17 eV higher. Our results of free Mn clusters are in agreement with the previous DFT calculations39,40,41.

Figure 1
figure 1

Optimized geometric structures.

(a) The Mnn (n = 1–4) clusters, (b) the Mnn clusters adsorbed on monolayer and (c) bilayer MoS2 from the top view (up) and the side view (below). The blue, yellow and purple spheres represent the Mo, S and Mn atoms, respectively. Possible adsorption sites are labelled in numbers in (b,c). The dash-dot ball and line refer to metastable positional alignments of the Mnn clusters adsorbed on the MoS2 host upon geometry optimization.

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From the hosts’ side, the 5 × 5 supercells of single- and two-layer MoS2 were firstly relaxed and the optimized results were shown on the left row in Fig. 1b,c. The lattice constants are 3.21 and 3.20 Å for the monolayer and bilayer MoS2, respectively, in good agreements with other density functional theory (DFT) calculations42. In general, the energy and magnetic properties of the Mnn@MoS2 systems are sensitive to coordination and contact positions of the Mnn clusters with respect to the ILC hosts. In what follows, we name the systems of Mnn@MoS2(M) for the Mnn cluster doped Monolayer complexes and Mnn@MoS2(B) for the Bilayer ones. After a full optimization of all possible motifs including magnetic order effects, it is found that the Mnn@MoS2(M) prefer pizza structures. Manganese clusters maintain their initial geometries after being adsorbed on the MoS2 monolayer. However, the Mn clusters evolve to a parallel layer motif when intercalated in the bilayers. The Mnn@MoS2(B) have sandwich structures with the maximal coordination numbers to expand the interactions between the Mnn clusters and two layers of the MoS2.

Geometric arrangements of the Mnn clusters and their hosts were studied in details. For the Mnn@MoS2(M), the most stable adsorption sites of the Mn atoms are right above the Mo atom (numbered 1 in Fig. 1b) from the top view. Other possible adsorption sites on-top S atom, bridge and face as labelled 2, 3 and 4 in Fig. 1b are energetically unfavorable. Our optimizations show that each Mn adatom is bonded to three S atoms at the monolayer MoS2 site. For the Mn4@MoS2(M), the most stable structure is constructed by the tetrahedron Mn4 cluster whose triangular face lays on the MoS2 host. The rhombic structure with four Mn atoms tiled above the Mo site is less stable with higher energy as shown in Fig. 1b. On the contrary, the structure of the three-dimensional tetrahedron Mn4 cluster sandwiched between two layers of the MoS2 is unstable according to our calculation. In the figures, the dash-dot balls and lines refer to metastable positions of the Mnn clusters on the monolayer MoS2. However, in the case of inserting Mnn to bilayer MoS2 systems, the lowest energy structures exhibit odd-even alternations with the number of the Mn atoms. One Mn atom laying under the Mo atom (labelled 1 in Fig. 1c) is the lowest energy structures of odd number n with each adatom Mn bonding six S atoms in the bilayer MoS2, while the Mn atoms preferring to be under the S atom (featured 2 in Fig. 1c) and forming the most stable Mnn@MoS2(B) (n = 2,4) complexes. In this case of evenly numbered n, each Mn atom is bonded to four host S atoms and one Mo atom as Fig. 1c shows.

Bonding scheme and stability

Table 1 gives bond lengths of the Mnn clusters adsorbed on the monolayer and bilayer MoS2 at the most stable adsorption sites. Two kinds of hosting atoms are classified: participators with whom dopants are bonded and spectators where no additional bonding are formed. The MoS2 honey comb structures remain unchanged after absorptions of the Mnn clusters. Very slight lattice distortions are found at the participator area near the Mnn clusters. From Table 1, it can be seen that the distances of the dS–Mo between the participator atoms of the MoS2 became larger than those of the pristine MoS2 in both the ‘pizza’ and ‘sandwich’ cases. These participator S atoms interact with the impurity Mnn clusters, weakening bonding between the S and Mo atoms. On the contrary, the bond length of spectator atoms is the same as the one of the pristine MoS2. The Mn-Mn bond lengths in ‘pizzas’ and ‘sandwiches’, except for the Mn3@MoS2(M) and Mn4@MoS2(M), are notably larger than those in the free Mnn clusters, also indicating a covalent-bond interaction between the Mn and S atoms. The Mn-Mo bond lengths in Mn2@MoS2(B) and Mn4@MoS2(B) are 2.762 and 2.800 Å, respectively. Notably, values of the farthest dMo-S in Mnn@MoS2(B) oscillate with the Mn numbers. The oscillating trend pervades to electronic and magnetic properties of the Mnn@MoS2 (B) sandwiches in the follow discussion.

Table 1 Adsorption energies Ead (in eV) and bond lengths d (in Å) of the Mnn (n = 1–4) clusters adsorbed on the monolayer and bilayer MoS2.
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The adsorption energies Ead of the Mnn clusters adsorbed on the ILC hosts were computed as follows.

where Etotal(Mnn@MoS2) and Etotal(MoS2) represent the total energies of the lowest-energy structures of the adsorbates and pristine MoS2, respectively and Etotal(Mnn) is the energy of the individual Mnn clusters. All adsorption energies are found largely below zero (see Table 1), indicating stability of MoS2 after the introductions of the Mnn clusters. Obviously, the absolute value of Ead increases with the numbers of the Mn atoms due to the increase of the covalent-bond interaction between the Mn and S atoms. To have a better view of the interactions between the Mnn clusters and MoS2 layers, the deformation electron density (DED) of the Mn3@MoS2(M) for the lowest-energy structures was plotted in Fig. 2a as an example. The DED is defined as the total charge density of a system with the density of the isolated atoms subtracted. The blue and silvery area indicate electron accumulation and depletion when atoms forming the Mn3@MoS2(M). When the Mn3 cluster is adsorbed on the MoS2 slab, the DED distributes not only surrounding the Mo and S atoms in the host MoS2 but also remarkably at the intervals between the Mn and S atoms and the guest Mn clusters (see Fig. 2a). Featuring covalent characters of the S-Mn bonds, the DED identifies strong interactions between the Mn and S in the Mnn@MoS2(M&B) and high stability of the structure due to such interactions.

Figure 2
figure 2

Electron densities of the Mn3@MoS2(M) complex.

(a) The deformation electron density (DED). Charge accumulations are obvious in blue regions and depletions in silvery regions. (b) Total electron density. (c) The net spin electron density. The surface isovalue for electron density is 0.04 e/Å3.

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Magnetic properties

The lowest-spin arrangements of individual clusters are all ferromagnetic from our present calculations. Magnetic moments of the Mnn (n = 1–4) clusters are 5, 10, 15 and 20 μB, respectively, in agreement with previous studies40,41,42. It is important to understand the host influence on the magnetic orders of the magnetic guests. For this purpose, we optimized all magnetic spin states of the lowest-energy structures of the ‘pizzas’ and ‘sandwiches’ from Fig. 1b,c. Table 2 gives the relative energies with respect to the most stable spin states of the Mnn clusters adsorbed on the ILC hosts at the lowest energy adsorption sites. Results show that magnetic moments of the impurity Mnn clusters are not quenched by the nonmagnetic host MoS2 substrate. The energetic magnetic spin state displays ferrimagnetic properties when ferromagnetic Mn clusters adsorbed on the MoS2. The Mnn@MoS2(M) pizzas prefer to have medium magnetic moments of 3, 6, 9 and 4 μB in comparison with their corresponding free Mnn clusters (5, 10, 15, 20 μB). The Mnn@MoS2(B) sandwiches exhibit favorable oscillatory behavior with relatively smaller magnetic moments of 3, 2, 3 and 2 μB. To reveal detailed contributions from each Mn atom in the ‘topping’ or ‘fillings’, we also studied the local spin state on the Mn atom of the Mnn@MoS2 (M&B) systems. Their magnetic moments are listed in Table S1 (see details in SI). The Mn atoms in Mnn@MoS2(M) pizzas are in ferromagnetic states except for theses of the Mn4@MoS2(M). On the Mn4@MoS2(M) pizza, three tiled Mn atoms have “spin-up” (majority) magnetic moments and one top Mn atom has “spin-down” (minority) magnetic moments. While in the Mnn@MoS2(B) sandwiches, the Mn atoms display ferrimagnetic order as shown in Table S1. Thus the guest Mnn clusters may serve as an ideal system to tailor magnetic properties when introduced on or between the MoS2 ‘crust’ or ‘bread slices’. Continued experimental and theoretical studies of similar TM clusters adsorbed on MoS2 systems may lead to discoveries of new families of dilute magnetic semiconductors with tunable magnetic properties.

Table 2 Magnetic moments M (μB) of the Mnn cluster adsorbed MoS2 complexes.
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It should be noted that the magnetic properties of the Mn7 cluster absorbed on graphene exhibits a magnetic moment of 6.3 μB per cell as given by first-principles calculations32. This value is 1.3 μB larger than 5.0 μB in an isolated Mn7 cluster. In the case of Mn doped MoS2 studied through a combination of DFT calculations and Monte Carlo simulations, the overall magnetic moment of the supercell is 1 μB corresponding to the single excess d electron provided by the Mn atom43. On the other hand, magnetic properties of nonmetal atoms adsorbed MoS2 monolayers were also investigated by first-principles calculations. The total magnetic moments of H-,B-, C-, N- and F-adsorbed MoS2 monolayers were found 1, 1, 2, 1 and 1 μB, respectively44. The magnetic motifs of all these three cases are different from that of the Mnn@MoS2 ‘pizzas’ and ‘sandwiches’ studied here. By comparing the magnetic properties between other cases and this work, more insights may be provided into the effect of the impurities types employed on a nonmagnetic layer host.

Mulliken population analysis shows that the total magnetic moment of the clusters is mainly localized in the Mn atoms as tabulated in Table 3. A small amount of magnetic moment is found in host Mo and S atoms. To visualize the spin distribution of the Mnn@MoS2(M) ‘pizza’, the isosurface spin density of the ‘pizza’ was plotted in Fig. 2. It can be seen from Fig. 2b,c that although the total charge density is extended over the whole Mn3@MoS2(M), the spin density is almost entirely located on the Mn3 cluster site, resulting in a robust magnetic moment of 9 μB for the Mn3@MoS2(M).

Table 3 Charge transfer and local magnetic moments of the Mnn cluster adsorbed MoS2 complexes.
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Electronic structures

The band structures of the Mnn@MoS2(M&B) complexes were plotted in Fig. 3 for the lowest-energy structures. These from the pristine monolayer and bilayer MoS2 were also given for comparison purposes. In the monolayer, a direct bandgap was found to have energies of 1.69 eV and 1.89 eV in our GGA and Heyd-Scuseria-Ernzerhof (HSE06) calculations implemented in CASTEP package45,46,47. The values are in good agreement with previous studies9,48,49,50,51,52,53,54,55. Although GGA at the PBE level calculations typically underestimates this bandgap, there is no difference between the GGA and HSE06 evaluations of the bandgap types. As Fig. 3 shows, the embedment of the Mnn clusters inserts additional defect states within the pristine MoS2 bandgap. The valence band maximum (VBM) and conduction band minimum (CBM) are primary from the 3d orbitals of the Mnn clusters. The partial density of states (PDOS) of Mnn@MoS2(M&B) in Fig. 4 clarifies theses defect states are from the Mnn clusters near the VBM and the CBM. Compared with the pristine MoS2 cases, Fermi energy shifts from the VBM towards the CBM with the increase of the Mn numbers. Figure 4 also shows that shapes of the total density of states for α electron (spin-up) and β electron (spin-down) near the Fermi energy are quite different in the contributions of the magnetism of the Mnn@MoS2. The bandgap of the pristine MoS2 is evidently reduced due to the absorptions of small TM clusters. Such a reduction can significantly affect material optical and transport properties. From the values listed in Table 3, the bandgap of the ‘pizzas’ decreases gradually with the successive Mn atoms. However, odd-even oscillation emerges again in bilayer system similar to its magnetic properties.

Figure 3
figure 3

Spin-polarized band structures of the Mnn adsorbed MoS2 systems.

(a) Band structures of the Mnn@MoS2 pizzas. (b) Band structures of the Mnn@MoS2 sandwiches. The blue and magenta lines represent the spin-up and spin-down components, respectively. The horizontal dash-dot lines indicate the Fermi level. The band structures of the pristine hosts are depicted at the very left column for comparison purpose.

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Figure 4
figure 4

Electronic partial density of states (PDOS) of the Mnn adsorbed MoS2 systems.

(a) The PDOS of spin-up (positive) and spin-down (negative) electrons of the Mnn@MoS2(M) pizzas. (b) The PDOS of spin-up (positive) and spin-down (negative) electrons of the Mnn@MoS2(B) sandwiches. The PDOS is obtained by Gaussian extension applied to the eigenvalues with a broadening width of 0.1 eV. The vertical dash-dot lines indicate the Fermi level.

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As the Mn clusters are adsorbed on MoS2, there is obvious hybridization between the atomic orbitals of the guest atom Mn and host atom S. We take the PDOS plots of Mo, S and Mn atoms of the Mn3@MoS2(M) as an example (see Fig. 5) to explicate the hybridization. Several sharp peak superpositions originate from the PDOS for d orbital of Mn and p orbital of S in the S-Mn bond below the Fermi level. And the PDOS for Mo and S atoms in S-Mo bond close to the Mn cluster is quite different from these spectator Mo and S atoms far away the Mn cluster. Similar behavior is observed in all other Mnn@MoS2 systems.

Figure 5
figure 5

The PDOS of atoms in the Mn3@MoS2(M) complex.

(a) Participator Mo atom near the Mn cluster. (b) Participator S atom contracting with Mn cluster. (c) Mn atom. (d) Spectator Mo atom away from the Mn cluster. (e) Spectator S atom away from Mn cluster. The illustration is the same as that in Fig. 4.

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Types of bands can be switched through the present doping route. A transition from an indirect to a direct bandgap in pristine MoS2 are found when the thickness is reduced from bilayer to a monolayer, in agreement with previous experimental reports9,56 and theoretical results57,58. After the Mnn clusters were introduced to the host MoS2 ‘crusts’, the Mnn@MoS2(M) pizza (n = 1,4) bandgaps keep direct as their host’s. However, the bandgap turns to indirect when n = 2,3 as shown in Fig. 3a. Excitingly, in the case of the Mn1@MoS2(B) ‘sandwich’, the indirect bandgap of the bilayer host was switched to a direct bandgap. The CBM and VBM are both aligned at the ĸ point. Such a direct band structure is similar to the monolayer’s ones, which have been considered as the crucial origin of the ILC unique material properties. The result indicates the bandgap of pristine MoS2 can be operated from an indirect to direct or direct to indirect bandgap by adsorbing small TM clusters like Mnn. This provides new opportunities for controlling electronic structures in nanoscale materials with novel optical behaviors.

Ranging from 0.053 to −0.215 and −0.32 to −1.715 au in the ‘pizza’ and ‘sandwiches’ systems, the net charge on the impurity Mn clusters clearly shows charge transfers between the ‘toppings’ and ‘fillings’ and the S atoms in the ‘crusts’ and ‘slices’. This leads high stabilities of the ‘pizza’ and ‘sandwiches’ following the partially ionic-like bonding of the Mn−S interaction through the charge transfers. Except for the Mn1@MoS2(M), charge transfers occur from the S atoms to the Mn atoms resulting in negative charges of the Mnn clusters. For the Mnn@MoS2(B), increases of the net charge values on the Mn clusters were found, illustrating enhancements of the sandwiches structures as the successive add-on dopant. The charge transfers between the Mn clusters and host MoS2 are one reason of the reducing magnetic moment of Mnn@MoS2 from the isolate Mn clusters, while strong hybridizations of the sulfur atoms in the MoS2 with the d states of the Mn cluster atoms is counted as another.

Thermostabilities

The thermodynamic stability was tested by using the Born−Oppenheimer molecular dynamics simulation implemented in the DMOL3 code at room temperature (T = 300 K). A sample of the dynamic simulations is shown in Fig. 6 for the Mn3@MoS2(M) pizza case. It is clear that the relative potential energy remains unchanged within the selected time scale. The ground-state structure is stable at room temperature. Such a thermostability is in line with the experimental evidences of the Au adsorbed MoS2 monolayer59 and the latest results of the water intercalated organic counterpart of the graphene35.

Figure 6
figure 6

Relative potential energy (eV) of the lowest-energy structures Mn3@MoS2(M).

The simulation time was set to 3 ps at a step interval of 1 fs in the molecular dynamics simulation.

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In conclusion, we have presented a new strategy of tailoring the inorganic layered crystal to the magnetic semiconductors by introducing magnetic clusters as adsorbates. Geometric optimizations show that the small clusters prefer to follow the host alignments to enhance the complex stabilities. The magnetic and electronic structures were thoroughly explored. It is found that the system magnetic properties and electronic structures can be manipulated by careful selections of the ‘pizza’ and ‘sandwich’ recipes. Moreover, switches between the direct and indirect bandgaps of the adsorbed MoS2 complexes were revealed. Benefiting from the uniqueness of the clusters and inorganic layered crystals, it is hoped that the present work will be served as a prototype in combinations of the cluster and layered crystal sciences and boost their applications in the semiconducting scopes.

Methods

All calculations were performed by using the DMOL3 package60,61. Results from the present package were cross checked with the calculations from CASTEP package. A relativistic semi-core pseudopotential was employed for the spin-unrestricted calculations with double-numerical basis where d polarization functions (DNP) were included. Generalized gradient approximation in the Perdue−Burke−Ernzerhof (PBE) functional form was chosen62. The effect of van der Waals interactions was introduced explicitly through an empirical correction scheme proposed by Ortmann, Bechstedt and Schmidt63. The quality of the self-consistent field (SCF) convergence tolerance was set as “fine”. A convergence criterion of 1 × 10−5 hartree was applied on the total energy and electron density, 2 × 10−3 hartree/Å on the gradient and 5 × 10−3 Å on lattice displacements. The 5 × 5 supercells were constructed from 75 atoms of 25 Mo atoms and 50 S atoms for the monolayer and 150 atoms including 50 Mo atoms and 100 S atoms for the bilayer. A vacuum region of 25 Å was selected in the z-direction to exclude mirror interactions between neighboring images. The Brillouin Zone integrations were carried out on a 10 × 10 × 1 Monkhorst−Pack k-points grad for the geometry optimizations and a 15 × 15 × 1 k-points grad for the band and density of states (DOS) properties. To elucidate system magnetic properties, we carried out a detailed calculation for each possible spin multiplicity (SM) ranging from 1 to 21 of the Mnn (n = 1–4) adsorbed MoS2 complexes.

Additional Information

How to cite this article: Zhang, M. et al. Magnetic MoS2 pizzas and sandwiches with Mnn (n=1–4) cluster toppings and fillings: A first-principles investigation. Sci. Rep. 6, 19504; doi: 10.1038/srep19504 (2016).