Magnetic MoS2 pizzas and sandwiches with Mnn (n = 1–4) cluster toppings and fillings: A first-principles investigation

The inorganic layered crystal (ILC) MoS2 in low dimensions is considered as one of the most promising and efficient semiconductors. To enable the magnetism and keep intrinsic crystal structures, we carried out a first-principles study of the magnetic and semiconductive monolayer MoS2 adsorbed with the Mnn (n = 1–4) clusters, and bilayer MoS2 intercalated with the same clusters. Geometric optimizations of the Mnn@MoS2 systems show the complexes prefer to have Mnn@MoS2(M) pizza and Mnn@MoS2(B) sandwich forms in the mono- and bi-layered cases, respectively. Introductions of the clusters will enhance complex stabilities, while bonds and charge transfers are found between external Mn clusters and the S atoms in the hosts. The pizzas have medium magnetic moments of 3, 6, 9, 4 μB and sandwiches of 3, 2, 3, 2 μB following the manganese numbers. The pizzas and sandwiches are semiconductors, but with narrower bandgaps compared to their corresponding pristine hosts. Direct bandgaps were found in the Mnn@MoS2(M) (n = 1,4) pizzas, and excitingly in the Mn1@MoS2(B) sandwich. Combining functional clusters to the layered hosts, the present work shows a novel material manipulation strategy to boost semiconductive ILCs applications in magnetics.

experiments 21 . Alternatives were suggested to replace both Mo and neighboring S atoms with the FeX 6 (X = S, C, N, O, F) clusters 22 , or a wetting deposition of the Co layer onto monolayer MoS 2 23 . Brewing magnetism into double-or few-layered MoS 2 are rather scarcely reported, despite of the magnification of efficiencies in the 3D piled-up electronics 4 . In a latest work, the Fe doped double layered MoS 2 was predicted to enhance the host stabilities as well as to magnetically exchange coupling between the host and dopants 24 . However, doping or growing dynamics of such hetero functional units normally debuts from a fast nucleation of the metallic ions 25,26 , resulting in rather small clusters or nanoparticles on the layered crystal surfaces or possibly among the layers [27][28][29] . Indeed, in addition to clusters' inimitable properties 30,31 , combining clusters with the monolayer graphene was predicted to increase the magnetic moment of the cluster [32][33][34] . Furthermore, the intercalated water molecules between graphene interlayers were observed experimentally and very unique properties have been revealed recently 35 . 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 MoS 2 'pizzas' with Mn n (n = 1-4) 'toppings' , and bilayer MoS 2 'sandwiches' with Mn n (n = 1-4) clusters 'fillings' . The manganese clusters were selected as the start clusters due to their magnetic robustness 36 , size-dependent magnetism 37 , as well as easier adsorptions on layered structures 38 . Hosts of the clusters were extended from monolayer MoS 2 '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 Mn n 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 Mn n 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 Mn n 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 calculations [39][40][41] . From the hosts' side, the 5 × 5 supercells of single-and two-layer MoS 2 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 MoS 2 , respectively, in good agreements with other density functional theory (DFT) calculations 42 . In general, the energy and magnetic properties of the Mn n @MoS 2 systems are sensitive to coordination and contact positions of the Mn n clusters with respect to the ILC hosts. In what follows, we name the systems of Mn n @ MoS 2 (M) for the Mn n cluster doped Monolayer complexes, and Mn n @MoS 2 (B) for the Bilayer ones. After a full optimization of all possible motifs including magnetic order effects, it is found that the Mn n @MoS 2 (M) prefer pizza structures. Manganese clusters maintain their initial geometries after being adsorbed on the MoS 2 monolayer. However, the Mn clusters evolve to a parallel layer motif when intercalated in the bilayers. The Mn n @ MoS 2 (B) have sandwich structures with the maximal coordination numbers to expand the interactions between the Mn n clusters and two layers of the MoS 2 .
Geometric arrangements of the Mn n clusters and their hosts were studied in details. For the Mn n @MoS 2 (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 MoS 2 site. For the Mn 4 @MoS 2 (M), the most stable structure is constructed by the tetrahedron Mn 4 cluster whose triangular face lays on the MoS 2 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 Mn 4 cluster sandwiched between two layers of the MoS 2 is unstable according to our calculation. In the figures, the dash-dot balls and lines refer to metastable positions of the Mn n clusters on the monolayer MoS 2 . However, in the case of inserting Mn n to bilayer MoS 2 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 MoS 2 , while the Mn atoms preferring to be under the S atom (featured 2 in Fig. 1c) and forming the most stable Mn n @MoS 2 (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 Mn n clusters adsorbed on the monolayer and bilayer MoS 2 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 MoS 2 honey comb structures remain unchanged after absorptions of the Mn n clusters. Very slight lattice distortions are found at the participator area near the Mn n clusters. From Table 1, it can be seen that the distances of the d S-Mo between the participator atoms of the MoS 2 became larger than those of the pristine MoS 2 in both the 'pizza' and 'sandwich' cases. These participator S atoms interact with the impurity Mn n 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 MoS 2 . The Mn-Mn bond lengths in 'pizzas' and 'sandwiches' , except for the Mn 3 @MoS 2 (M) and Mn 4 @ MoS 2 (M), are notably larger than those in the free Mn n clusters, also indicating a covalent-bond interaction between the Mn and S atoms. The Mn-Mo bond lengths in Mn 2 @MoS 2 (B) and Mn 4 @MoS 2 (B) are 2.762 and 2.800 Å, respectively. Notably, values of the farthest d Mo-S in Mn n @MoS 2 (B) oscillate with the Mn numbers. The oscillating trend pervades to electronic and magnetic properties of the Mn n @MoS 2 (B) sandwiches in the follow discussion.
The adsorption energies E ad of the Mn n clusters adsorbed on the ILC hosts were computed as follows. where E total (Mn n @MoS 2 ) and E total (MoS 2 ) represent the total energies of the lowest-energy structures of the adsorbates and pristine MoS 2 , respectively, and E total (Mn n ) is the energy of the individual Mn n clusters. All adsorption energies are found largely below zero (see Table 1), indicating stability of MoS 2 after the introductions of the Mn n clusters. Obviously, the absolute value of E ad 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 Mn n clusters and MoS 2 layers, the deformation electron density (DED) of the Mn 3 @MoS 2 (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 Mn 3 @MoS 2 (M). When the Mn 3 cluster is adsorbed on the MoS 2 slab, the DED distributes not only surrounding the Mo and S atoms in the host MoS 2 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 Mn n @MoS 2 (M&B) and high stability of the structure due to such interactions.  Table 2 gives the relative energies with respect to the most stable spin states of the Mn n clusters adsorbed on the ILC hosts at the lowest energy adsorption sites. Results show that magnetic moments of the impurity Mn n clusters are not quenched by the nonmagnetic host MoS 2 substrate. The energetic magnetic spin state displays ferrimagnetic properties when ferromagnetic Mn clusters adsorbed on the MoS 2 . The Mn n @MoS 2 (M) pizzas prefer to have medium magnetic moments of 3, 6, 9, and 4 μ B in comparison with their corresponding free Mn n clusters (5, 10, 15, 20 μ B ). The Mn n @MoS 2 (B) sandwiches exhibit favorable oscillatory behavior with relatively smaller magnetic moments of 3, 2, 3, and 2 μ B . 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 Mn n @MoS 2 (M&B) systems. Their magnetic moments are listed in Table S1 (see details in SI). The Mn atoms in Mn n @MoS 2 (M) pizzas are in ferromagnetic states except for theses of the Mn 4 @MoS 2 (M). On the Mn 4 @MoS 2 (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 Mn n @MoS 2 (B) sandwiches, the Mn atoms display ferrimagnetic order as shown in Table S1. Thus the guest Mn n clusters may serve as an ideal system to tailor magnetic properties when introduced on or between the MoS 2 'crust' or 'bread slices' . Continued experimental and theoretical studies of similar TM clusters adsorbed on MoS 2 systems may lead to discoveries of new families of dilute magnetic semiconductors with tunable magnetic properties. It should be noted that the magnetic properties of the Mn 7 cluster absorbed on graphene exhibits a magnetic moment of 6.3 μ B per cell as given by first-principles calculations 32 . This value is 1.3 μ B larger than 5.0 μ B in an isolated Mn 7 cluster. In the case of Mn doped MoS 2 studied through a combination of DFT calculations and Monte Carlo simulations, the overall magnetic moment of the supercell is 1 μ B corresponding to the single excess d electron provided by the Mn atom 43 . On the other hand, magnetic properties of nonmetal atoms adsorbed MoS 2 monolayers were also investigated by first-principles calculations. The total magnetic moments of H-,B-, C-, N-, and F-adsorbed MoS 2 monolayers were found 1, 1, 2, 1, and 1 μ B , respectively 44 . The magnetic motifs of all these three cases are different from that of the Mn n @MoS 2 '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 Mn n @MoS 2 (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 Mn 3 @MoS 2 (M), the spin density is almost entirely located on the Mn 3 cluster site, resulting in a robust magnetic moment of 9 μ B for the Mn 3 @MoS 2 (M).
Electronic structures. The band structures of the Mn n @MoS 2 (M&B) complexes were plotted in Fig. 3 for the lowest-energy structures. These from the pristine monolayer and bilayer MoS 2 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 package [45][46][47] . The values are in good agreement with previous studies 9, [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 Mn n clusters inserts additional defect states within the pristine MoS 2 bandgap. The valence band maximum (VBM) and conduction band minimum (CBM) are primary from the 3d orbitals of the Mn n clusters. The partial density of states (PDOS) of Mn n @MoS 2 (M&B) in Fig. 4 clarifies theses defect states are from the Mn n clusters near the VBM and the CBM. Compared with the pristine MoS 2 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 Mn n @MoS 2 . The bandgap of the pristine MoS 2 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.
As the Mn clusters are adsorbed on MoS 2 , 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 Mn 3 @MoS 2 (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 Mn n @MoS 2 systems.  Types of bands can be switched through the present doping route. A transition from an indirect to a direct bandgap in pristine MoS 2 are found when the thickness is reduced from bilayer to a monolayer, in agreement with previous experimental reports 9,56 and theoretical results 57,58 . After the Mn n clusters were introduced to the host MoS 2 'crusts' , the Mn n @MoS 2 (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 Mn 1 @MoS 2 (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 MoS 2 can be operated from an indirect to direct or direct to indirect bandgap by adsorbing small TM clusters like Mn n . 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 Mn 1 @MoS 2 (M), charge transfers occur from the S atoms to the Mn atoms resulting in negative charges of the Mn n clusters. For the Mn n @MoS 2 (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 MoS 2 are one reason of the reducing magnetic moment of Mn n @MoS 2 from the isolate Mn clusters, while strong hybridizations of the sulfur atoms in the MoS 2 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 Mn 3 @MoS 2 (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 MoS 2 monolayer 59 and the latest results of the water intercalated organic counterpart of the graphene 35 . 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 MoS 2 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 package 60,61 . 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 chosen 62 . The effect of van der Waals interactions was introduced explicitly through an empirical correction scheme proposed by Ortmann, Bechstedt, and Schmidt 63 . 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 Mn n (n = 1-4) adsorbed MoS 2 complexes.