Tuning magnetic and optical properties in As–Ge (Si) co-doped MoS2 monolayer by defect-defect interaction

Modulating magnetic properties in monolayer MoS2 is important for the applications in spintronics and magnetism devices. In this work, we have studied the electronic, magnetic and optical properties of co-doped monolayer MoS2 with As–Ge (Si) doping on S surfaces through the first-principle calculations. Our results show that the magnetic properties of monolayer MoS2 can be tuned effectively by the distance of co-doped atoms. The projected density of state and the charge transfer demonstrate the interaction and superexchange coupling between As and Ge (Si) atoms are the key factor in the magnetic properties of co-doped structures. Furthermore, it is found that co-doping can also induce spin-polarized optical properties in low-energy region, which makes the co-doped MoS2 attractive candidates for spin-polarized photoelectric device applications.


Introduction
Molybdenum disulfide (MoS 2 ), a typical transition-metal dichalcogenide, has attracted extensive interest in recent years due to its unique physical properties and wide applications in electronic transistors [1,2], optoelectronic devices [3,4], and sensors [5,6].The intrinsic MoS 2 is a nonmagnetic semiconductor, therefore, it is of great significance to modulate its magnetic properties for the applications in spintronics [7,8], spin-polarized photoelectronic [4,9] and the magneto-optical effects [10,11].For instance, Cheng et al were able to make the diluted magnetic semiconductors by inducing the magnetic dopants into semiconductors, which can tune the magnetic states for the applications in spintronic devices [12][13][14].Kou et al studied the magnetic properties by strain and electric field on the zigzag MoS 2 nanoribbons [15].Ji et al found a giant magneto-optical Raman effect in MoS 2 by breaking the symmetry induced by the electron motions tuned by the external magnetic field [16].Therefore, tuning the magnetic properties of MoS 2 is essential to enhance the application of two-dimensional magnetic materials.
In the past studies, the efficient approaches to tune the magnetic properties of monolayer MoS 2 can be summarized into two types.The first type is the substitutional doping by transition-metal (TM) atoms [13,17,18].The TM atoms with the localized d electrons, such as Mn, Fe, Co, Ni, Cu and V, substituted Mo atom in monolayer MoS 2 can induce ferromagnetic states for spin-polarized carriers at the Fermi level [17,19,20].Fan et al modulated the electronic and magnetic properties of monolayer MoS 2 by embedded TM atoms, such as, Au, Rh, Pd, Pt and Ir [18,21].The magnetic properties of TM doped MoS 2 are dependent on the dopants and can be understood by the electronegativity [22] of the doped atoms and the crystal filed theory [23].However, the spin-diffusion length and spin relaxation times are always short due to the large spin-orbital coupling of heavy element atoms [24][25][26].Therefore, modulating the magnetic properties of MoS 2 by light atoms has attracted great attention recently [27][28][29].For example, Hu and Choi have reported that adsorption of atomic hydrogen on MoS 2 can induce obvious spin-polarization [30].Chen et al showed that the monolayer MoS 2 with nitrogen-doping is ferromagnetic [31], and Kaur and Kumar used the non-metal atom doped Janus transition metal dichalcogenides to tune the magnetic properties [32].The magnetic moment in light atom doped MoS 2 is usually attributed by the strong overlapping between d orbital of Mo and p orbital of non-metal atoms.
Up to now, most of the studies on the doping in MoS 2 are based on the single atom doping.However, different types of S vacancies in MoS 2 have been observed in micro-mechanical exfoliation, liquid exfoliation, physical and chemical vapor deposition, and high concentration of sulfur atom vacancies was also discovered in experiments [33][34][35][36][37][38].Hong et al have explored the atomic defects in MoS 2 monolayers in experiments and found that the defect density can be up to 3.5 × 10 13 cm −2 [33].Addou et al resolved a high intrinsic concentration of individual sulfur atom vacancies by STM [39].These high concentration S vacancies provide the opportunity to co-dope with different atoms in MoS 2 due to the high activity of S-vacancies [38,39].Therefore, it is significant to understand the electronic and magnetic properties of co-doped MoS 2 .
In this work, we have studied the electronic and magnetic properties of co-doped monolayer MoS 2 with doping atoms As and Ge (Si) on the same and different S surfaces by the first-principles calculations.Interestingly, our results show that the magnetic properties are modulated effectively according to the distance of As-Ge (Si), even though As or Ge (Si) single atom doping was illustrated to be nonmagnetic in previous theoretical studies [40].It is found that the distance-dependent interaction between As and Ge (Si) atoms is the key factor of magnetic properties based on the results of projected density of state (PDOS) and charge transfer.As the As-Ge (Si) distance increases, the charge transfer and orbital overlap between As and Ge (Si) atoms decrease, resulting in the decrease of magnetic moment from 1 µ B to 0 µ B .Furthermore, co-doping has great effects on the optical properties of MoS 2 and induces arresting spin-dependent optical properties.Our work provides a new approach to modulate the magnetic properties of MoS 2 without doping of TM atoms in spintronics device applications.

Methods
The calculations are based on the spin-polarized density function theory as implemented in the Vienna ab initio simulation package [41].The interactions between nucleus and valence electrons are described by the projector augmented wave method, and the interactions between electrons are treated by generalized gradient approximations proposed by Perdew, Burke and Ernzerh [42].The energy cutoff of 550 eV is used in the simulation for the plane-wave expansion basis set, and 7 × 7 × 1 Monkhorst-Pack k-point mesh is used for integration over the Brillouin zone.The 4 × 4 × 1 supercell, 5 × 5 × 1 supercell, and 6 × 6 × 1 supercell are adoped to calculate the electronic and magnetic properties by co-doping of monolayer MoS 2 (1H-MoS 2 ), with a vacuum layer of 15 Å on the z-direction to avoid spurious interactions.All conjugations are relaxed until the force on each atom is less than 0.01 eV Å −1 and the energy change per atom is less than 1.0 × 10 −5 eV.The optical properties are investigated by the frequency-dependent dielectric function ε(ω) = ε 1 (ω) + iε 2 (ω), the imaginary part ε 2 (ω) of the dielectric function was calculated by the equation of states [43] where the ω k is the k-point weight, and the indices c and v refer to conduction-band and valence-band states, respectively, and µ ck is the cell periodic part of the orbitals at the k point k, Ω is the unit cell volume, and ω is the photon energy.

Results and discussion
In order to investigate the distance-dependent interaction between As and Ge (Si), we propose seven configurations for As-Ge (Si) co-doping, including three co-doping configurations on the same sulfur surface and four on different sulfur surfaces, as shown in figure 1(a).According to the structural symmetry, (0, 1), (0, 2), and (0, 3) represent co-doping in the same sulfur layer with the nearest neighbor (NN), sub-next-neighbor (SNN), and third-next-neighbor (TNN) distances, respectively.While (0, −1), (0, −2), and (0, −3) represent the NN, SNN, and TNN positions of co-doping in opposite sulfur layers, respectively.The configuration (0, 0) is the unique co-doping structure of As and Ge (Si) atoms at the same doping positions in different sulfur layers.Meanwhile, the three Mo atoms connected with the Ge (Si) atom are labeled as Mo 1 , Mo 2 , and Mo 3 .
To estimate their stability, we calculate the formation energies of seven co-doped structures by , where E tot (V 2S ) and E co−doped tot (MoS 2 ) are the total energy of monolayer MoS 2 with two sulfur vacancies (V 2S ) and co-doped monolayer MoS 2 , E As and E Ge/Si correspond to their bulk energies per atom, respectively.The value of E f is more larger, the co-doped structure is more stable.As shown in figure 1(b), it is clear that the formation energies of all doped structures are in the range of 2.0 eV-3.5 eV, indicating that co-doped structures are more stable than monolayer MoS 2 with tow sulfur vacancies, and the formation energies are in the same range of other doping or co-doping MoS 2 systems [44][45][46].This suggests that stability and electronic properties of MoS 2 with vacancies can be effectively modified by co-doping.Furthermore, figure 1(b) shows that the E f with shorter doping distance is higher for SiAs-MoS 2 , indicating that the co-doped atoms tend to be the magnetic states.
In addition, we calculate the change of bond length of the As, Ge, and Si atoms with nearest Mo (d As -Mo , d Ge -Mo , and d Si -Mo ) of AsGe-MoS 2 and AsSi-MoS 2 in 4 × 4 × 1 supercell (figure 1(c)), and we also include the S-Mo bond in intrinsic monolayer MoS 2 (d S -Mo ) for comparison.It is obviously that the bond length of d Ge -Mo in (0, ±1) structures is the largest, which may result in the smallest formation energies.Meanwhile, the results clearly show that the bond length of d As -Mo in two co-doped structures have a little difference due to the interaction between the doped atoms, and d As -Mo of two co-doped structures are the same as this interaction vanished with doping atom distance increasing.We also calculate the energy difference ∆E (∆E = E nonmagnetic -E magnetic , where E nonmagnetic and E magnetic are the total energy of As-Ge(Si) co-doped structures with non-magnetic and magnetic states, respectively.)between the magnetic and nonmagnetic states of co-doped structures (figure 1(d)).The results shown that ∆E decrease with the distance increases and reduces to 0 eV at (0, 2) and (0, 3) of 4 × 4 × 1 supercell, (0, 3) 5 × 5 × 1 supercell, and (0, 5) 6 × 6 × 1 supercell in As-Ge(Si) co-doped structures, indicating the attenuating of magnetic moment as distance increases.In the following, we mainly take AsGe-MoS 2 of 4 × 4 × 1 supercell as an example to discuss and analyze.The net magnetic moment is displayed in figure 1(b) and it is interesting that the magnetic properties are dependent on the distance of As and Ge (Si) atoms.AsGe-MoS 2 (0, 0), and AsGe-MoS 2 (0, ±1) structures have 1 µ B magnetic moment, and AsGe-MoS 2 (0, ±2) and AsGe-MoS 2 (0, ±3) structures have 0.2 µ B and 0 µ B magnetic moments.This is very different with the MoS 2 with single As or Ge atom doping because it was illustrated to be nonmagnetic according to the spin-polarized PDOSs in figure 2 and previous theoretical studies [40].As shown in PDOS, it can be seen that there are defective states above the Fermi level in Ge-MoS 2 and Si-MoS 2 structure, which are mainly contributed from Ge-p/Si-p and Mo-d orbitals overlapping.For As-Ge and As-Si co-doped monolayer MoS 2 , (0, 0) and (0, ±1) systems are semiconductors, and (0, ±2) and (0, ±3) are metals.The spin-polarized features of (0, 0), (0, 1) and (0, 2) can be observed in the PDOS by the asymmetrical spin splitting at the Fermi level.However, the PDOS of spin-up and spin-down of (0, 3) structures are nonmagnetic as the PDOS of spin-up and spin-down are completely symmetrical without spin splitting.Thus, As and Ge (Si) atoms co-doping can effectively regulate the transition between semiconductor and metal properties of monolayer MoS 2 and induce tunable magnetic properties.
In order to understand the tunable magnetic properties, we investigate the feature of these defective states.It is found that co-doped atoms hybridize with their adjacent Mo atoms forming the covalent bonds as there are obvious orbitals overlapping between these atoms in all co-doped structures.However, it is interesting that orbitals overlapping between As-p and Ge-p/Si-p in defective states occurs only in the magnetic structures, indicating that As and Ge (Si) atoms interact with each other in magnetic structures.For AsGe-MoS 2 (0, 0) structure, there are two main defective states locating near Fermi level and 1.0 eV, where both As-p and Ge-p have larger contributions in these states and overlap with each other strongly.As As-Ge distance increases to AsGe-MoS 2 (0, 1), As-p and Ge-p orbitals still exhibit strong overlapping in defective states, but the contribution of As-p decreases.For AsGe-MoS 2 (0, 2) and AsGe-MoS 2 (0, 3) with further increased As-Ge distance, there is only very little contribution of As-p in the defective state at 0.7 eV, and the overlapping between Ge-p and As-p orbitals almost vanishes, which suggests that the defect-defect interaction decreases with the As-Ge distance increasing and results in smaller magnetic moments decreasing to 0 µ B gradually.Meanwhile, the conduction band maximum of the co-doped structure shifts up and the Fermi level crosses the valence band maximum as the As-Ge distance increases, and the co-doped structure transfers from the semiconductor to metal.The PDOS feature of AsGe-MoS 2 (0, 3) combines the feature of Ge and As single atom doped monolayer MoS 2 simply, which also indicates there is no interaction between As and Ge atoms in AsGe-MoS 2 (0, 3).At the same time, the PDOS of As and Si atoms co-doped systems have the same trend as AsGe-MoS 2 structures.The magnetic moments decreased with the As-p and Si-p orbitals overlapping weaken.Therefore, the distance-dependent interaction between the co-doped atoms plays the key role in the tunable magnetic properties.
As the magnetic property is always related to the charge transfer, we also investigate the charge transfer e As and e Si/Ge of As or Ge (Si) atom by the Bader charge in co-doped structures, respectively.According to the charge transfer of AsGe-MoS 2 (0, 1) in table 1, it is clear that As atom gains electrons and Ge atom losses electrons, but there is almost no charge transfer from Mo atom to As and Ge.This indicates that the charge  transfer occurs directly between As and Ge when As and Ge co-doped into MoS 2 -V 2S .Combining the charge transfer and the hybridization of As-p and Ge-p orbitals, it suggests that there is a superexchange coupling between As and Ge, which is similar as the superexchange coupling in monolayer CrS 2 [47].As the As-Ge distance increases from AsGe-MoS 2 (0, 1) to AsGe-MoS 2 (0, 3), the charge transfer disappears in AsGe-MoS 2 (0, 3) structures and the superexchange coupling weakens as well.For AsSi-MoS 2 systems, the charge transfer and the total magnetic moments decrease withe the distance of As and Si increase, which is similar to the regularities of AsGe-MoS 2 systems.Furthermore, as can be seen from the charge transfer and magnetic moments in table 1, similar magnetic properties is found with the supercell increasing from 4 × 4 × 1-5 × 5 × 1.Therefore, the tunable magnetic properties is robust with the doping concentration decreasing.For AsGe-MoS 2 (0, 0) structure, both As and Ge atoms gain electrons, which is different from the case of charge transfer in AsGe-MoS 2 (0, ±1) structures.Due to the larger electronegativity of As, As atom gains more electrons than Ge from the MoS 2 -V 2S .The differences between the three semiconductors can further be illustrated by the band structures and the spin charge densities as shown in figure 3. The features of band splitting for AsGe-MoS 2 (0, 1) and AsGe-MoS 2 (0, −1) are very similar but quite different from that of AsGe-MoS 2 (0, 0).Figures 3(d)-(f) demonstrate that the spin polarization charge for AsGe-MoS 2 (0, 0) structure is mainly around As and Mo 123 atoms, while it mainly locates at Ge and Mo 123 atoms for AsGe-MoS 2 (0, ±1) structures.
Spin-polarized electronic properties always induce excellent applications of 2D semiconductor materials, such as spin photocurrents, spin-valley effects and spin-dependent optical properties [9,[48][49][50].Thus, we study the spin-dependent optical properties by calculating the imaginary part ε 2 (ω) of the dielectric function of three semiconductor structures in figures 4(a)-(c).Figures 4(d)-(g) show the optical properties of (0, ±2) and (0, ±3) co-doped nonmagnetic structures.It is found that the optical properties are similar with the magnetic co-doped structures as the photon energy larger than 1 eV, while the optical transitions start from 0 eV as these nonmagnetic structure are metallic as shown figure 2. It is clearly demonstrated that the in-plane optical properties of AsGe-MoS 2 (0, 0) is isotropic at X and Y directions, but is anisotropic for AsGe-MoS 2 (0, ±1) structures.The reason is that the symmetries in X and Y directions are the same when As and Ge are doped at the (0, 0) position, but co-doping at different positions leads to asymmetric fractures in X Y directions.Furthermore, It is clear that the defective states are important for the optical properties and the threshold energies of ε 2 (ω) for the three structures are equal to the corresponding spin band gaps.There are two main optical peaks A 1 and B 1 in the low-energy region, which are related to the electron transitions between the valence bands (or defective states) and the defective states according to the transition matrix.Another important feature of the optical properties is that all semiconductors exhibit strong spin-dependent optical properties as ε 2 (ω) from the spin-up and spin-down channel are very different.For example, AsGe-MoS 2 (0, 0) structure only has the spin-down channel in the low-energy region (<1 eV), which means that only spin-down electrons can be excited when the energy of photon is in the energy range.These results suggest that the monolayer MoS 2 co-doped with As and Ge atoms on S surfaces are attractive candidates for spin-polarized photoelectric device applications.

Conclusion
In summary, we have studied the electronic, magnetic, and optical properties of As-Ge (Si) co-doped monolayer MoS 2 .It is found that co-doping can induce tunable magnetic properties in monolayer MoS 2 due to the distance-dependent As-Ge (Si) interaction.When the distance of As-Ge (Si) is less than NN, the co-doped MoS 2 structure is a magnetic semiconductor and possess 1 µ B magnetic moment.As the As-Ge (Si) distance increases to TNN, the co-doped structure transfers to a metal, and the magnetic moment of Ge-As (Si) vanishes to 0 µ B gradually due to the decreasing of the interaction between As and Ge (Si) atoms in 4 × 4 × 1 supercell.Similar decreasment of the magnetic moment are also found in large suprecell, confirming that the magnetic moment decreases with the weakening of the defect-defect interaction.Moreover, co-doping enhances the optical properties in the low-energy region and can realize the spin-dependent optical properties of monolayer MoS 2 , which makes co-doped MoS 2 are fascinating candidates for applications in spin optoelectronic devices.

Figure 1 .
Figure 1.(a) Top and side views of the atomic structures of monolayer MoS2 with the co-doped As and Ge (Si) atoms on S surfaces.The light blue, yellow, red and blue balls respect Mo, S, As and Ge (Si) elements, respectively.The red dashed circle represents the different positions of two doped atoms.(b) Formation energy and magnetic moments of seven co-doped structures.The black (green) line and the red (blue) dash line represent binding energy and magnetic moment of AsGe-MoS2 and AsSi-MoS2 structures, respectively.(c) dAs-Mo, dGe-Mo, and d Si-Mo are the bond distance of AsGe-MoS2 and AsSi-MoS2 co-doped structures in 4 × 4 × 1 supercell, respectively.(d) The energy difference between the magnetic and nonmagnetic states of AsGe-MoS2 and AsSi-MoS2 structures, respectively.

Table 1 .
The Bader charge and magnetic moments of As, or Ge(Si) single atom in 4 × 4 × 1 supercell, or 5 × 5 × 1 supercell AsGe-MoS2 structures.The positive (negative) number means an electron gained (lost) in Bader charge, and the positive (negative) number means the magnetic moments in two directions.