First Principles Prediction of the Magnetic Properties of Fe-X6 (X = S, C, N, O, F) Doped Monolayer MoS2

Using first-principles calculations, we have investigated the electronic structure and magnetic properties of Fe-X6 clusters (X = S, C, N, O, and F) incorporated in 4 × 4 monolayer MoS2, where a Mo atom is substituted by Fe and its nearest S atoms are substituted by C, N, O, and F. Single Fe and Fe-F6 substituions make the system display half-metallic properties, Fe-C6 and Fe-N6 substitutions lead to a spin gapless semiconducting behavior, and Fe-O6 doped monolayer MoS2 is semiconducting. Magnetic moments of 1.93, 1.45, 3.18, 2.08, and 2.21 μB are obtained for X = S, C, N, O, and F, respectively. The different electronic and magnetic characters originate from hybridization between the X and Fe/Mo atoms. Our results suggest that cluster doping can be an efficient strategy for exploring two-dimensional diluted magnetic semiconductors.


Calculation details
Our first principles calculations are based on density functional theory 17 and the projector augmented wave method 18 as implemented in the Vienna Ab initio Simulation Package 19 . The Perdew-Burke-Ernzerhof 20 spin-polarized generalized gradient approximation is used for the exchange-correlation potential and the plane-wave cutoff is set to 544 eV. We use a 4 3 4 3 1 MoS 2 supercell with a vacuum region of 10 Å , as shown in Fig. 1. The Brillouin-zone integrations are performed on a 4 3 4 3 1 k mesh. All structures are fully optimized until the force on each atom is less than 0.01 eV/Å and the total energy converged to 10 25 eV. In order to illustrate the nature of the charge transfer, we calculate the difference between the valence electron densities of the Fe-X 6 doped systems and the corresponding free atoms.

Results and discussion
The symmetry of monolayer MoS 2 with a Mo vacancy remains C 3v 13 , which is also valid for Fe-X 6 cluster doping. Under the structure relaxation the symmetry is maintained, since the distances between the Fe and six nearest X atoms are exactly the same. Table 1 gives the distances between the X and Fe (d Fe-X ) or Mo (d Mo-X ) atoms, and X-Fe-X bond angles for the Fe-X 6 doped systems. The Fe-X bond lengths are 2.29, 1.93, 1.98, 2.15, and 2.18 Å for X 5 S, C, N, O, and F, respectively, which is smaller than the bulk Mo-S distance (2.41 Å ), whereas the bond lengths between the X and nearest Mo atoms are 2.42, 2.04, 2.04, 2.03, and 2.21 Å . For pristine monolayer MoS 2 , the band gap of 1.7 eV is consistent with previous theoretical studies 12,21,22 and photoluminescence results 23 . Strong hybridization appears between the Mo d and S p states in both the VB and conduction band (CB). Furthermore, the VB maximum and CB minimum are governed by the Mo d orbital.
The band structure of Fe-X 6 doped monolayer MoS 2 is plotted in Fig. 2. Energy level splitting occurs between the spin-up and spindown channels near the Fermi level, which induces magnetic moments. For Fe-doped MoS 2 the spin-up CB minimum shifts down across the Fermi level and yields metallicity, while the spin-down channel remains semiconducting with a gap of 1.18 eV, indicating that the Fe-S 6 doped system is half-metallic. To test whether the halfmetallic character is sensitive to the concentration of the dopant, we have calculated the band structure of a 5 3 5 3 1 supercell, corres-ponding to a reduced concentration, and observe no relevant changes. The Fe-C 6 doped system shows a semiconducting character for each spin channel with band gaps of 0.40 and 0.32 eV for the spin-up and spin-down channels, respectively. The gap between the spin-up VB and spin-down CB is only 0.08 eV wide. Wang 24 and Hu 25 use the term ''gapless'' for an energy gap that is smaller than 0.1 eV. In this sense, Fe-C 6 doped monolayer MoS 2 is a spin gapless semiconductor. In the case of Fe-N 6 doping the system stays semiconducting with band gaps of 0.62 and 0.33 eV for the spin-up and spin-down channels, respectively. Since the gap between the spin-up CB and spin-down VB is 0.11 eV, as shown in Fig. 2(d), the system is also a spin gapless semiconductor. In both cases, no energy is required to excite electrons from the VB into the CB, where the excited electrons achieve 100% spin polarization at the Fermi level, as it is desirable for spintronics devices. One can flexibly tune the properties of spin gapless semiconducting materials externally by pressure, electric fields, impurities, etc 27 . Taking Fe-C 6 doping as an example, we further investigate the effect of the dopant concentration on the band structure for a larger 5 3 5 3 1 model of MoS 2 . It is found that the gap between the spin-up VB and spin-down CB increases to 0.16 eV, indicating that the system transforms into a semiconductor. The results demonstrate that the dopant concentration is important for the character of the system, in agreement with previous findings 25 . For Fe-O 6 doping we find 0.51 and 1.11 eV wide band gaps for the spin-up and spin-down channels, respectively. The gap between the spin-up CB and spin-down VB is 0.18 eV, so that the system retains the original semiconducting nature. For Fe-F 6 doping the spin-up channel shows a semiconducting character with a gap of 0.99 eV, whereas the CB crosses the Fermi level in the spindown channel, resulting in a half-metallic system. Overall, the introduction of Fe-X 6 clusters in monolayer MoS 2 can yield half-metallic and spin gapless semiconducting properties.
As the generalized gradient approximation usually underestimates the band gap of semiconductors and the spin gapless semiconducting behavior is judged from the state distribution around Fermi level, our conclusions may depend on this approximation. Hybrid functional with a certain percentage of Hartree-Fock exchange and many-body perturbation theory in the GW approximation generally lead to better agreement with experiments 26 . However, this is not a general truth but often depends on the material considered. The band gap of monolayer MoS 2 calculated in the generalized gradient approximation underestimates the experimental value of 1.8 eV by just 0.1 eV. The higher GW values of the band gap (G 0 W 0 : 2.82 eV 27 , GW: 2.97 eV 28 , 2.76 eV 29 , and GW 0 : 2.50 eV 30 ) contradict experiment, whereas our calculations can give a reliable description of the electronic and magnetic properties.
The density of states (DOS) of Fe-X 6 doped monolayer MoS 2 is addressed in Fig. 3. For Fe doping impurity states are formed 0.52 eV above the VB maximum and 0.09 eV below the CB minimum, reflecting n-doping. An increasing number of impurity states is formed when S is substituted by other X atoms. In the case of Fe-O 6 doping the impurity states are close to the CB minimum (n-doping), as shown in Fig. 3(e), and for Fe-F 6 doping they shift     even closer (n-doping). When substituting S with C they shift towards the VB maximum and appear even closer for Fe-N 6 doping for both spin channels, which is expected since the C and N atoms lack two and one electron, respectively, as compared to S. The primary contributions to the impurity states in the band gap stem from the Fe d states, the p states of the adjacent X atoms, and the d states of neighboring Mo atoms. Strong hybridization between the Fe d states and the p states of adjacent X atoms yields spin-polarization of the latter. In the immediate vicinity of the X atom only the moment of S is parallel to that of Fe, whereas those of the  Table 2. The moments are mainly due to the Fe d orbital, with minor contributions of the X and neighboring Mo atoms. The Fe-X bond length and Fe magnetic moment increase from C to F, as the atom size decreases and the hybridization between the X and Fe/Mo atoms is modified. An isolated Fe atom has a 3d 6 4s 2 electronic configuration with two additional valence electrons as compared to Mo (4d 5 5s 1 ), which reflects the magnetic moment of the supercell (1.93 m B ). The interaction between Fe and S weakens the Mo-S bonds and induces a magnetic moment of 0.11 m B per Mo atom. The moment is smaller for Mo atoms further away. Furthermore, the four unpaired C electrons (2s 2 2p 2 configuration) are shared with the neighboring Fe and Mo atoms, forming relatively strong bonds, as indicated by their bond lengths. The Fe d states show a weak spin splitting and thus a small magnetic moment. Figures 3(b)-(c) show near the Fermi level less hybridization between the C and neighboring Fe atoms, yielding a decreased magnetic moment. The smaller Mo magnetic moment is due to enhanced hybridization with C. For Fe-N 6 doped monolayer MoS 2 the Fe spin splitting is similar to the Fe-S 6 system. Due to stronger Fe-N than Fe-C hybridization, the Fe spin-up states are occupied and the occupation of the spin-down states decreases. Thus, the Fe magnetic moment is slightly larger than for C doping. By weaker Mo-N than Mo-C hybridization the Mo magnetic moment is reduced. The results for Fe-O 6 doping deviate from the above cases, while the valence electronic configuration of O (2s 2 2p 4 ) is the same as for S. The Fe spin splitting is larger than for Fe-S 6 doping, resulting in a larger magnetic moment, because the Fe-O is weaker than the Fe-S hybridization, which lowers the energy of the occupied d states and thus favors spin-up states. Because of stronger Mo-O hybridization, the Mo magnetic moment is slightly larger than for Fe-S 6 doping. F (2s 2 2p 5 ) has one more p electron than S. Weaker Fe-F than Fe-S hybridization results in enhanced Fe magnetic moments and the larger Mo magnetic moment as compared to Fe-S 6 doping originates from weaker Mo-F hybridization. It is found that the above results are insensitive to the Fe-X 6 dopant concentration. Figure 4 gives the charge density differences for Fe-X 6 doped monolayer MoS 2 . The charge density difference map in Fig. 4(b) demonstrates that Fe loses less electrons than Mo. Considering that Fe has one d and one s valence electron more than Mo, Fe acts as electron donor in monolayer MoS 2 . We observe that C gains more electrons than S, despite the fact that S is more electronegative than C. The Fe atom in the Fe-C 6 system loses more electrons than in the Fe-S 6 system, due to the stronger bonds between the C and Fe/Mo atoms. Some extra charge is found to accumulate around the N atoms. In the case of Fe-O 6 doping more electrons transfer from Fe and Mo to O as compared to the Fe-S 6 system, which is consistent   with the fact that O has a much higher electronegativity than S. For Fe-F 6 doping the charge density difference is very similar to the Fe-S 6 system far away from F, indicating that F has only a local effect on the electronic structure. More charge is transferred from Fe and Mo to F as compared to the Fe-S 6 system. The electron density around the X atoms becomes more localized from C to F as the atom size decreases. Furthermore, from C to F the charge transfer from Fe/Mo to X is enhanced with increasing electronegativity.

Conclusion
Our results for 4 3 4 3 1 monolayer MoS 2 reveal the following general aspects: (1) Single Fe and Fe-F 6 substitutions result in a half-metallic character, Fe-C 6 and Fe-N 6 substitutions lead to a spin gapless semiconducting behavior, and Fe-O 6 substitution retains the original semiconducting nature. (2) Spin polarization can be induced in monolayer MoS 2 with total magnetic moments of 1.93, 1.45, 3.18, 2.08, and 2.21 m B per 4 3 4 3 1 supercell for Fe-S 6 , Fe-C 6 , Fe-N 6 , Fe-O 6 , and Fe-F 6 doping, respectively. (3) The magnetic moments arise mainly from the Fe atoms with small contributions from the X and nearest-neighbor Mo atoms, due to hybridization between the X p and Fe/Mo d orbital. These findings can be instrumental for the future design of MoS 2 -based electronics.