Research Article  Open Access
Electronic Structure and Room Temperature of 2D Dilute Magnetic Semiconductors in Bilayer MoS_{2}Doped Mn
Abstract
The electronic structure and magnetic properties of manganese (Mn) doped bilayer (BL) molybdenum disulfide (MoS_{2}) are studied using the density function theory (DFT) plus onsite Hubbard potential correction (U). The results show that the substitution of Mn at the Mo sites of BL MoS_{2} is energetically favorable under sulfur (S) rich regime than Mo. The magnetic interaction between the two manganese (Mn) atoms in BL MoS_{2} is always ferromagnetic (FM) irrespective of the spatial distance between them, but the strength of ferromagnetic interaction decays with atomic distance. It is also found that two dopants in different layers of BL MoS_{2} communicate ferromagnetically. In addition to this, the detail investigation of BL MoS_{2} and its counterpart of monolayer indicates that interlayer interaction in BL MoS_{2} affects the magnetic interaction in Mndoped BL MoS_{2}. The calculated Curie temperature is 324, 418, and 381 K for impurity concentration of , , and , respectively, which is greater than room temperature, and the good dilute limit of dopant concentration is 0–6.25%. Based on the finding, it is proposed that Mndoped BL MoS_{2} are promising candidates for twodimensional (2D) dilute magnetic semiconductor (DMS) for hightemperature spintronics applications.
1. Introduction
It is known that graphene is the most wellknown member in the family of 2D materials. However, its gapless band structure has been deemed as a considerable drawback for realizing switching operation which is essential for digital logic devices [1]. On contrary to zero band gap graphene, other group of 2D materials so called transition metal dichalcogenides (TMDS) with chemical formula MX_{2}, where M stands for transition metals like molibidium (Mo), tungeston (W), and so on and X stands for chalcogen atoms like selfur (S), selenium (Se), and telenium (Te), and so on are more recently discovered [2]. The experimental study reveals that the weak van der Waals forces between each 2D monolayer of which they are formed allow thin multilayers to be easily exfoliated from their bulk form [3]. Among those families, monolayer MoS_{2} and few layer MoS_{2} have attracted interest due to their potential application [2, 4]; for instance, the monolayer (ML) MoS_{2} has emerged as a semiconductor with a large intrinsic direct band gap of approximately 1.8 eV [3], which makes it suitable for nanoelectronic and optoelectronic applications [5]. In MoS_{2} materials, the electronic structure depends on the number of layers which mean that there is a gradual transition from an indirect band gap (1.3 eV) in the bulk material to a direct gap in the ML material with band gap 1.9 eV which reveals that the interlayer van der Waals (VdW) interaction may affect the electronic structure [6]. In addition, it has been reported that the electronic structure of such system depends on stacking patterns [7]. There are five different stacking configurations for the bilayer MoS_{2} system [7], but the most stable one is AA’ [8].
On the contrary, during last few decades, the research in dilute magnetic semiconductors (DMSs) have attracted tremendous interest due to their great potential for different spin electronics (spintronics) applications [9]. Spintronics refers to new phenomena of electronic transport for which the electron spin plays a decisive role in contrast to conventional electronics for which the electron spin is practically irrelevant. For a full exploitation of spintronics, one should have materials which show simultaneously semiconducting properties and ferromagnetic ordering at operational temperature [10]. In last two decades, most of DMS research has focused on the transition metal (TM) doped IIIV and IIVI threedimensional (3D) semiconductors. However, the ferromagnetic transition temperature in wellstudied type of DMSs like Mn_{x} As is less than 200 K which is far from room temperature [11]. As a result of this, the search for DMS has recently been extended to twodimensional (2D) transition metal dichalcogenides (TMDs) like MoS_{2}, MoSe_{2}, and WS_{2}doped transition metal [4]. Recent theoretical study reveals that Mn and Fe are the best candidates to generate longrange room temperature in its Ml phase [4]. To date, several groups have reported experimentally [12] and theoretically the feasibility of MoS_{2} by substitutional doping with different (TM) : Mndoped monolayer (ML) MoS_{2} [13], iron (Fe) doped bilayer MoS_{2} [14], Nidoped ML MoS_{2} [15], and Codoped monolayer MoS_{2} [16]. In addition to this, in our previous ab initio study, we have shown that Vdoped ML and BL MoS_{2} are good candidates for nearly room temperature ferromagnetism [17]. However, electronic structure and magnetic interaction in Mndoped bilayer (BL) MoS_{2} has not yet been studied in detail. In this current study, Mndoped BL MoS_{2} are studied on the basis of spin polarized (DFT + U) formalism. The relative structural stability, electronic structure, and magnetic properties of MoS_{2}doped Mn are studied in detail. To understand magnetic ground state and the magnetic energy E, the energy difference between two dopants in FM and AF cofigurations in the ML and BL phase of MoS_{2} was calculated for different impurity concentrations. Furthermore, based on mean field theory together with empirical correction, the Curie temperature (Tc) is also estimated.
2. Computational Details
DFT + U calculations were performed using the planewave pseudopotential method with the aid of QUANTUM ESPRESSO code. Onsite Hubbard parameter, U = 4 eV, was assigned for dopants to take into account the strong correlation in the Mn 3d state [18]. Ultrasoft pseudopotentials (UPPs) were used to deal with the interaction between valence electrons and the ion core. The plane wave basis set is given a cutoff energy of 60 Ry used after performing the convergence test with respect to total energy. A unit cell with the periodic boundary condition was adopted to simulate the infinite xy plane. For the BL crystal, Grimmes DFTD2 dispersion correction [19] was applied to account for the longrange van der Waals interactions between layers. The equilibrium interlayer distance was obtained by careful minimization of total energy with respect to distance between layers. To investigate the doping effects of Mn impurities on bilayer MoS_{2}, the BL MoS_{2} was modeled by supercell of , , and which contains 36 S and 18 Mo, 64 S and 32 Mo, and 50 Mo and 100 S atoms, respectively. The vacuum space 20 Å thickness along the z axis was used to avoid any selfinteraction of the slabs for ML (to make sure there is no interaction along the zaxis). Integrations over the Brillouin zone (BZ) were sampled based on a Monkhorst pack 2D grid [20] based on the size of supercells.
3. Result and Discussion
3.1. Defect Formation Energy and Structural Stability
To understand relative stability of dopant atom (Mn) in BL MoS_{2}, dopant formation energy () was carried out employing the following equation [17, 21]:where E (Mn, MoS_{2}) and E (MoS_{2}) are total energy of doped and pure BL MoS_{2}, respectively, n_{i} is the corresponding number of species that has been added to or removed from the supercell, and and are chemical potentials of Mn and Mo, respectively. Both Mo and Srich conditions were considered for chemical potential calculation of Mo. In the Morich condition, the chemical potential for is obtained from its bulk bodycentered cubic (BCC) structure of Mo [21], whereas, under the Srich condition, is obtained from energy difference between formula unit of MoS_{2} and ring form of sulfur molecules. The dopant formation energy calculated using equation (1) for different impurity configurations of impurity atoms is summarized in Table 1. All calculated values under the Srich condition is negative which reveal that doping Mn under the Srich condition of BL MoS_{2} is favorable in comparison with the Morich condition in agreement with previous theoretical report [21] and experimental result [22]. Besides to this, the least formation energy −2.0144 eV is obtained in doping single Mn on BL MoS_{2} (6.25%) compared to ( Mn doping) which indicates that Mn dopants are more energetically favorable to occupy the substitutional lattice site (Mo) at low impurity concentration (dilute magnetic limit) than at high concentration.

3.2. Electronic Structures and Magnetism of Pure and Single MnDoped BL MoS_{2}
The calculated equilibrium lattice constant after optimization is , which is closer to the experimental value [23] and in good agreement with theoretical value 3.18 Å [24]. In addition to this, the calculated interlayer distance (the distance between two ML) of BL MoS_{2} is found to be 6.543 Å and the band gap calculated at this interlayer distance is 1.3 eV (Figure 1) closer with the previous reported value 1.29 Å [25]. Furthermore, the band gap increases with increasing interlayer distance, as shown in Figure 1(a). To investigate the effects of single Mn doping on the electronic and magnetic properties of pure BL MoS_{2}, and BL MoS_{2} model supercells which result in a magnetic impurity concentration of 3.125% and 5.55%, respectively, after doping a single Mn atom were considered (see Figure 2). As seen from Table 2, the total magnetic moment of the system is 1 and 1.02 after introducing single Mn in supercell of and , respectively.
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To understand how the states are distributed, the total density of state (DOS) for pure and single Mndoped BL MoS_{2} is plotted. As shown from Figure 3(a), for the pure system, the Fermi level is located at the middle and spin up and spin down states are symmetric indicating the pure BL MoS_{2} are nonmagnetic semiconductors. However, after introducing single Mn, the spin degeneracy of the band structure is broken and the minority of states remain semiconductors, whereas the majority (spin up state) impurity state is formed in the vicinity of the Fermi level; as a result, it behaves as metallic, leading to magnetic and half metallic behavior of the total DOS. On the contrary, with increasing concentration of Mn dopant (3.125% to 11.11%), the impurity state is broaden (moves closer to conduction band minimum (CBM)) Figures 3(b)–3(e) which reveals that the doped system behaves as the ntype of semiconductor. Furthermore, to understand the nature of band structure and defect state, the band structure of pure and single Mn doped in one of its layers is plotted. As shown from Figures 4(a) and 4(b), the pure system is nonmagnetic semiconductor with direct band gap measured to be 1.3 eV. However, in single Mndoped system, the majority band structure and the impurity states are formed above the Fermi level (within the gap) (Figure 4(c)). But, the minority state remains semiconductor, but the band gap is suppressed by 0.1 eV compared to the pure system (Figure 4(d)), which also gives further confirmation half metallic and magnetic behavior of the doped system. On the contrary, the impurity state closer to CBM reveals that the system is more likely the ntype of semiconductor. Based on those observation, it is suggested that the origin of magnetism as an isolated Mn atom with electron configuration has one more dorbital electron than Mo (with electron configuration ); thus, the extra one electron is responsible for the observed defect state in the gap.
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3.3. Magnetic Interaction between Dopants in Monolayer (ML) and Bilayer (BL) MoS_{2} Doped with a Pair of Mn Atoms
The magnetic interaction between dopants in doped ML and BL MoS_{2} systems is studied by calculating the total energy difference between FM and AF configurations at the same impurity separation [17]. The magnetic energy is given bywhere and are the total energies of the supercell in FM and AF states, respectively. Employing model supercells, , , and MoS_{2} result in doping concentrations , and , respectively. Five configurations with different dopantdopant (MnMn) separations were considered: nearestneighbor (N) configuration in which the two Mn atoms are in the nearest neighboring position with MnMn distance of 3.4 Å, the second nearestneighbor (NN) configurations in which the two Mn atoms are in the next nearestneighboring position with MnMn distance of 5.5 Å, and the third nearestneighbor (NNN) configuration in which the distance between the two doped Mn atoms are 6.4 Å; two Mn atoms in different layers of BL MoS_{2} are separated by interlayer distance (updn(d_{0}) = 6.53 Å), and two Mn atoms in different layers of BL MoS_{2} are separated by interlayer distance (updn(d_{1}) = 7.8 Å) results summarized in Tables 2 and 3. As can be seen from Tables 2 and 3, the calculated for all impurity configurations are negative which show that FM interaction is favorable for all concentrations of impurity in agreement with previous study in ML MoS_{2}doped Mn [26]. In addition to that, the strength of FM interaction decays from N to NNN for all concentrations of impurity. Furthermore, in order to get insights into FM interaction between the two nearest neighbor (N) Mn dopants, the total density of states (DOS) are plotted as shown in Figures 3(e) and 3(e); the dopants are ferromagnetically interacting, and the impurity states push towards the CBM with increasing impurity concentration (6.25–11.11%), which is in broad agreement with dilute magnetic semiconductor properties [11]. We further extend our investigation by doping two Mn in different layers BL MoS_{2}, as seen in the input structure in Figure 2(d) and Table 4, and and −0.0025 eV when two dopants are separated by d_{0} = 6.53 Å (at equilibrium interlayer distance) and , respectively. Interestingly, the result reveals that two dopants in different layers can interact ferromagnetically, and the strength of ferromagnetism suppresses with atomic distance and impurity concentration. This is also seen in the DOS plot in Figure 3(e), where spin degeneracy of spin up and spin down is breaking and system becomes ferromagnetic. For further information, the electronic band structure is drawn, as shown from the band plot for those system seen in Figures 4(e) and 4(f), the system becomes magnetic even when two dopants are in different layers, and this makes the physics of system under investigation more interesting that how two dopants in different layers are communicating. On the contrary, understanding mechanism of exchange interaction in magnetic system is another issue. Goodenough–Kanamori–Anderson rules which state that the magnetic ionligandmagnetic ion angle is 180° of two magnetic ions with partially filled d shells is strongly antiferromagnetic, whereas the magnetic ionligandmagnetic ion angle is 90° and is ferromagnetic super exchange. Thus, bond angle (MnSMn) is calculated as 93° which is closer to 90° and ensures that FM super exchange is primarily response for magnetic interaction in nearest neighbor dopants, in other words, Mn 3d orbital electrons interact antiferromagnetically with one of sulfur (S) 3p electrons then this state further interacts with other Mn 3d electrons; in this way, the two Mn atoms communicate ferromagnetically indirectly with aid of sulfur 3p state. We now turn to investigate the role of interlayer interaction in BL MoS_{2}, and we make magnetic energy, , comparison between pair of Mndoped MoS_{2} ML with BL MoS_{2} using a , , and supercells, and the results are listed in Tables 3 and 4, respectively. For instance, the calculated () are −0.1636, −0.2107, and −0.1844 eV for a pair of Mn doping in the first nearest neighbor (N) configurations in , , and in ML supercell, respectively, whereas −0.1666, −0.2137, and −0.192 eV for a pair of Mn doped in nearest neighbor configuration (N) in , and BL MoS_{2} supercells, respectively. The result show that ferromagnetism is more stable in Mndoped BL MoS_{2} than Mndoped BL MoS_{2}. The origin of discrepancy between BL and ML MoS_{2} in magnetic energy, , seems to be from interlayer interaction in BL MoS_{2}. Therefore, we report that interlayer interaction in Mndoped BL MoS_{2} system can affect its magnetic interaction, and similar finding was recently reported in irondoped BL MoS_{2} [14].



3.4. Ferromagnetic Transition Temperature (T_{c})
By mapping Heisenberg Hamiltonian together with mean field approximation, the Curie temperature (T_{c}) below which the system develops a longrange ferromagnetic ordering can be found as follows [27]:where is the magnetic energy obtained from the first principle spin polarized DFT calculation and N is the number of dopants in supercell. Using the value for first nearest neighbor impurity configurations (N) in Table 3 and N = 2, we have calculated ferromagnetic transition (T_{c}) for Mndoped BL MoS_{2}. However, it is well known that the magnetic ordering in the doped system is strongly influenced by percolation, and thus meanfield approximation cannot capture this behavior and tends to systematically overestimate T_{c} in these systems [13]. To overcome this, we make use of some empirical relation which connects the mean field value critical temperature with corrected critical temperature () as [28], where is the exact (corrected) critical temperature for 2D hexagonal lattice calculated using Ising model and is the predicted critical temperature using mean field theory. The calculated result is presented in Table 4. As shown in Table 4, in Mndoped BL MoS_{2} is found to be above the room temperature (RT), and a nonmonotonic behavior of T_{c} is observed; increases with Mn concentrations in a range of dilute limit (0 to 6.25%) and then decreases with further increasing Mn concentration above this value (6.25 to 11.11%), which confirm that, at high concentrations, the system exhibits FM instability due to some sort of direct interaction. Thus, the result indicates that ferromagnetism in this system is tunable by controlling the concentration of magnetic dopants (Mn), and such kind of properties are seen in wellknown IIIV DMS [10].
4. Conclusion
In conclusion, Mn dopant in BL MoS_{2} are energetically favorable to occupy the substitutional lattice site (Mo) under sulfur (S) rich regime than Mo. The magnetic interaction between dopants in Mndoped BL MoS_{2} is always ferromagnetic. Moreover, the strength of ferromagnetism decays with atomic distance. Interlayer interaction in Mndoped BL MoS_{2} affects its magnetic properties. Super exchange mechanism is primarily responsible for ferromagnetic interaction between a pair of dopants. The calculated T_{c} shows that good dilute limit of dopant concentration is , and further increasing dopant concentration results in FM instability. Based on the result, it is suggested that Mndoped BL MoS_{2} are promising candidates for 2D dilute magnetic superconductors for hightemperature spintronics applications.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest.
Acknowledgments
The authors acknowledge financial support from the Center for Science and Technology of the NonAligned and Other Developing Countries (NAM S & T Center), Supercomputer Education and Research Center (SERC) at Indian Institute of Sciences (IISc) for providing the computational facilities, and Arba Minch University, Arba Minch, Ethiopia.
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Copyright © 2020 Sintayehu Mekonnen Hailemariam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.