Electronic and magnetic properties of n-type and p-doped MoS₂ monolayers

Abstract

The electronic and magnetic properties of n- and p-type impurities by means of group V and VII atoms substituting sulfur in a MoS₂ monolayer were investigated using first-principles methods based on density functional theory. Numerical results show that group V and VII atoms can induce magnetic properties, and the magnetic moment mainly originates from the dopant’s p orbital and neighbor Mo atoms’ d orbital. N-, P-, F-, and I-doped (or As-doped) MoS₂ exhibits magnetic nanomaterial (or metallic) features, and Cl- and Br-doped systems exhibit half-metallic ferromagnetism (HMF). Moreover, the formation energy calculations also indicate that it is energetically favorable and relatively easier to incorporate group V and VII atoms into a MoS₂ monolayer under Mo-rich experimental conditions. The formation energy of the F-doped system is the lowest, the next lowest formation energy is obtained in the Cl-doped system. By comparison, Cl-doped MoS₂ is more suitable for spin injection. This finding is important for the achievement of spin devices on MoS₂ nanostructures.

---

I. Introduction

Transition metal dichalcogenides (TMDs), with the chemical formula MX₂ (M = Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, and W, X = S, Se and Te), have been extensively studied. Layered semiconductor TMDs have proven to be important candidates for use as an absorber layer in low cost thin film solar cells.¹ This is due to their relatively small band gap (∼1–2 eV) and large absorption coefficient.² In particular, MoS₂ has been steadily attracting more attention. Recently, possible applications, including transistors,^3,4 photoemitting devices,⁵ photovoltaics,⁶ catalysis,⁷ hydrogen storage,⁸ lubricants,⁹ and Li-ion batteries¹⁰ have been proposed and investigated. Great attention has been paid to the exploration of the magnetic properties of transition-metal dichalcogenides for nanoscale spintronic devices. As is well-known, spintronic devices play an important role in their promising application in information technologies.^11,12 Highly spin-polarized ferromagnetism, especially half-metallic ferromagnetism (HMF) is a key ingredient for future high-performance spintronic devices.^13–15 HMF, where one spin direction behaves like a metal and the other is semiconducting were first predicted.¹⁶ Thus far, HMF has been found in different types of materials, such as pure organic compounds,¹⁷ organic–inorganic hybrid compounds,¹⁸ transition-metal oxides,¹⁹ transition-metal pnictides and chalcogenides,²⁰ Heusler alloys,^21,22 and zincblende compounds.^23,24 Dilute magnetic semiconductors (DMSs) with half-metallicity have been extensively studied due to their carrier-mediated ferromagnetism, which makes them ideal for spintronics applications by offering the possibility of electronic control of magnetism.^25,26 Manifestation of the ferromagnetic (FM) phase has been done with various treatments: vacancy-defect formation,^27–29 nanoribbon with zigzag edges,^30–33 and adsorption or substitution of a transition metal.^34–38 Transition-metal-doped semiconductors have been the subject of investigations for possible spintronics applications.^39–43 In particular, some groups have reported that intrinsic nonmagnetic elements such as dopants can produce HMF in some semiconductors.^29,44–50 While, the systematic study of the electronic and magnetic characteristics of n- and p-type impurities by means of group V and VII atoms substituting sulfur in a MoS₂ monolayer so far is still limited. In this paper, we investigate the structural, electronic and magnetic properties of (V, VII)-doped MoS₂, using first-principles calculations, which may find promising applications in spintronics devices.

The paper is organized as follows. In Sec. II we give an overview on the theoretical methods used in the work. In Sec. III we investigate the electronic and magnetic properties of (V, VII)-doped MoS₂ using first-principle calculations, we find that group V and VII atoms can induce magnetic properties, N-, P-, F-, and I-doped (or As-doped) MoS₂ exhibits magnetic nanomaterial (or metallic) features, Cl- and Br-doped MoS₂ exhibits half-metallic ferromagnetism (HMF) and the half-metallic gap is about 0.115 and 0.081 eV, respectively. The Cl-doped system is suitable for spin injection. Section IV summarizes the work.

II. Theoretical models and methods

Bulk MoS₂ is an indirect gap semiconductor, with a gap of ∼1.3 eV,^51,52 while as the material transitions to a monolayer the gap becomes direct with size ∼1.8 eV.^53,54 Layered MoS₂ consists of stacked S–Mo–S layers. MoS₂ layers have a P6₃/mmc space group symmetry with the Mo atoms having a trigonal prismatic coordination with the S atoms, as shown in Fig. 1. The bonds within the trilayers are covalent, adjacent layers are held together by weak van der Waals forces, enabling the well-known method of mechanical exfoliation. Thus, one can cleave the material down to single layer thickness.

Fig. 1 Schematic structure of MoS₂. The top and side views of the layered forms are shown. The purple and yellow balls represent Mo and S atoms, respectively.

Our calculations were performed within first-principles DFT using the projector augmented wave (PAW) method⁵⁵ within the Vienna ab initio simulation package (VASP).⁵⁶ Electron exchange and correlation effects were described within the generalized gradient approximation (GGA) in the Perdew–Burke–Ernzerhof (PBE) parametrization.⁵⁷ In all calculations, an energy cutoff of 500 eV for the plane-wave expansion of the wavefunctions was used. The valence electron configuration was S (3s2p4), Mo(4d55s1), N(2s2p3), P(3s2p3), As(4s2p3), F(2s2p5), Cl(3s2p5), Br(4s2p5) and I(5s2p5). The Brillouin-zone integrations were performed using special k-point sampling of the Monhkorst–Pack scheme. The k-points 9 × 9 × 1 were used for the two-dimensional 4 × 4 × 1 MoS₂ supercell. In order to avoid any artificial interaction between neighboring images, the vacuum layer along the z-direction was at least 15 Å for the MoS₂ supercell. All the structures were fully relaxed to minimize the total energy of the systems until a precision of 10⁻⁵ was reached. Both the atomic positions and cell parameters were optimized until the residual forces fell below 0.01 eV/Å.

III. Results and discussion

In this work, we investigate firstly the structural and electronic properties of the X-doped MoS₂ monolayer. The calculated Mo–X binding length (X denotes group V and VII atoms), d_Mo–X, magnetic moment, M_Mo, M_X, M_tot, total energy of the doped system, E_doped and the formation energy in different experimental conditions, E_form, are listed in Table 1. It can be seen that d_Mo–X, except for d_Mo–N, d_Mo–P and d_Mo–F, is more than d_Mo–S (2.407 Å), indicating a covalent-bond interaction between the Mo and X atoms. As the atomic size increases, d_Mo–X increases from N to As (or from F to I). The shortest d_Mo–X of 2.015 Å was found for a N impurity. We can also see from Table 1 that the total energy of the N-doped MoS₂ case is lowest, which indicates that the N-doped MoS₂ monolayer is much more stable than the other considered impurity cases. Our calculations demonstrate that a magnetic moment was observed for group V and VII atom substitution, and the total magnetic moment of the As-doped system was the smallest (0.053 μ_B) of those studied. However, the magnetic moment of all X-doped systems was less than 1 μ_B.

Table 1 The calculated Mo–X binding length, d_Mo–X, magnetic moment, M_Mo, M_X, M_tot, total energy of the doped system, E_tot, and the formation energy in different experimental conditions, E_form, of the X-doped MoS₂ monolayer

System	dX–Mo1 (Å)	dX–Mo2 (Å)	dX–Mo3 (Å)	MMo1 (μB)	MMo2 (μB)	MMo3 (μB)	X (μB)	Mtot (μB)	Edoped (eV)	Eform (eV)
										Mo-rich	S-rich
N	2.015	2.015	2.015	0.034	0.034	0.034	0.231	0.779	−351.04	0.574	2.02
P	2.387	2.387	2.389	0.094	0.089	0.093	0.169	0.72	−348.06	1.312	2.758
As	2.58	2.58	2.595	0.002	0.002	0.018	0.007	0.053	−347.24	4.184	5.63
F	2.364	2.364	2.154	0.294	0.301	0.081	0.066	0.853	−346.82	−1.469	−0.023
Cl	2.573	2.573	2.495	0.321	0.334	0.09	0.061	0.863	−345.07	0.216	1.662
Br	2.674	2.674	2.683	0.223	0.25	0.261	0.068	0.857	−344.38	1.058	2.504
I	2.824	2.824	3.004	0.115	0.115	0.485	0.074	0.823	−343.79	1.542	2.988

---

To probe the stability of the X-doped MoS₂ monolayer, the formation energy E_form can be calculated according to the following formula^58–62

E_form = E_(doped) − E_(pure) + n(μ_S − μ_X). (1)

Where E_(doped) and E_(pure) are the total energies of the MoS₂ monolayer with and without the X dopants. μ_S and μ_X are the chemical potentials for the S host and X dopant atoms, respectively, which depend on the material growth conditions and satisfy the boundary conditions. n is the number of S atoms replaced by X dopants. We use the energy per atom of X metal as μ_X. μ_S is defined within a range of values corresponding to Mo-rich or S-rich growth conditions. Under the Mo-rich conditions, Mo is assumed to be in thermodynamic equilibrium with the bulk solid phase and its chemical potential μ_Mo is assumed to be the energy per atom in bulk Mo. Then, μ_S can be obtained according to the relationship⁶³

2μ_S + μ_Mo = μ_MoS2 (2)

where μ_MoS2 is the total energy of one formula MoS₂. Under S-rich conditions, μ_S can be obtained from the total energy of bulk S. We can see from Table 1 that for the X-doped MoS₂, the formation energy is lower under Mo-rich conditions, which indicates that it is energetically favorable and relatively easier to incorporate the X atom into MoS₂ under Mo-rich experimental conditions. The formation energy of the F-doped system is the lowest, the next lowest formation energy being obtained for the Cl-doped system. The formation energy highly depends on the atomic size and electronegativity of the impurity atom. The F atom is more electronegative than that of other impurity atoms, but the atomic radius is the smallest of all the impurity atoms. So for the F-doped MoS₂ monolayer, the interaction with the host atoms is more strong and the formation energy is the lowest.

Next, we studied the electronic structures of the X-doped MoS₂ monolayer. Fig. 2 illustrates the results of the band structure for the pristine and X-doped MoS₂ monolayer. For the pristine monolayer MoS₂ 4 × 4 supercell, the direct band gap at the k-point is estimated to be E_g = 1.80 eV, which is very consistent with that of the primitive cell calculation.^53,54 Compared with the pristine case, flat impurity bands are introduced inside the band gap due to dopants in all doped cases. Furthermore, Fig. 2 also shows that for the N, P and As substitutions, the impurity states are close to the valance bands indicating p-type doping. For the F, Cl, Br and I substitutions, the impurity states are close to the conduction bands, which indicates n-type doping occurs in these cases. Moreover, from Fig. 2, we can see the spin-up and spin-down components are asymmetric for the X-doped systems. For N-, P-, F-, and I-doped MoS₂, the band structures indicate magnetic nanomaterial characteristics. For As-doped MoS₂, the calculated band structures show a magnetic metallic feature. For the Cl- and Br-doped MoS₂ monolayer, the calculated band structures show a half-metallic feature. The half-metallic (HM) gap is an important parameter to determine application in spintronic devices, which is defined as a minimum of E_c and E_v, where E_c is the bottom energy of the minority-spin conduction band with respect to the Fermi level and E_v is the absolute value of the top energy of the minority-spin valence band, also with respect to the Fermi level. According to this rule, the HM gap of the Cl- and Br-doped MoS₂ monolayer is about 0.115, and 0.081 eV, respectively. 100% spin polarization near the Fermi level here ensures a high degree of passage of preferred spin, and thus these systems may have potential for spin filter device applications. By comparison, we can see that the Cl-doped system is more suitable for spin injection.

Fig. 2 Band structures of pristine and one X-doped 4 × 4 × 1 MoS₂ monolayer. The black lines and red lines represent the spin-up and spin-down components, respectively, where the Fermi level is indicated by the dot line.

To gain more insight into the electronic and magnetic properties of the X-doped MoS₂ monolayer, the total density of states (TDOS) and partial total density of states (PDOS) of the dopants and neighbor Mo atoms are illustrated in Fig. 3. One can clearly see that the impurity levels of the group V atoms lie close to the valence band maximum (VBM), whereas those of the group VII atoms are close to the conduction band minimum (CBM). This is confirmed from the midgap impurity bands found in the corresponding band structures of Fig. 2. Further, it shows that the impurity bands of the N- and P-doped systems are mostly derived from the Mo dz² and X p_z orbitals near the Fermi level. For the As-doped system, the impurity bands are mostly derived from the Mo dx² − y² and As p_x and p_y orbitals near the Fermi level. For the group VII atom substitutions, we can see that the impurity bands mainly originate from the hybridization of Mo dxy and dyz, and the F atom p_z states near the Fermi level. For the case of the Cl-doped system, the impurity bands mainly originate from the hybridization of Mo dz² and dx² − y², and Cl atom p_x states near the Fermi level. For the case of the Br- and I-doped systems, the impurity bands mainly come from the hybridization of Mo dz², and X atom p_y states near the Fermi level. From Fig. 3, an asymmetrical distribution of DOS can be seen between the majority-spin and minority spin states which produces magnetism in all doped systems. We conclude the magnetic property mainly originates from the doped X atoms and neighboring three Mo atoms. The most important hybridization occurs at 0 eV, where the Fermi level crosses the spin-up states, resulting in the Cl and Br-doped system becoming half-metal. However, for the N, P, F, and I-doped systems, the spin states are not crossed by the Fermi level and distribute asymmetrically, resulting in these systems becoming magnetic nanomaterials. For the case of As-doped, the Fermi level crosses the spin-up and spin-down states and distributes asymmetrically, resulting in As-doped system becoming magnetic metal.

Fig. 3 TDOS and PDOS of X dopants and their neighboring Mo atoms in the X-doped 4 × 4 × 1 MoS₂.

Furthermore, the spin density of the X-doped MoS₂ monolayer is given in Fig. 4. We can see that a significant portion of the spin density is localized on the X atoms and neighboring three Mo atoms. For the N-, P-, and Br-doped systems, the spin density distribution of dopants and neighboring three Mo atoms is almost symmetrical, which can be attributed to the almost identical bond length of the X atoms and three Mo atoms (see Table 1). But for the F-, and Cl-doped systems, we can see the spin density distribution of the dopants and three Mo atoms is asymmetrical, the hybridization of the X atom and Mo1 and Mo2 is stronger than that of the X atom and Mo3. For the As- and I-doped systems, the hybridization of the X atom and Mo3 is stronger than that of the X atom and Mo1 and Mo2. From Table 1 and Fig. 4, we can see that the p orbital of the N and P atoms plays an important role in the total magnetism in the N- and P-doped systems, but the d orbital of the Mo atoms plays an important role in the total magnetism in As-, F-, Cl-, Br-, I-doped systems.

Fig. 4 Spin densities of one X dopant and its neighboring Mo atoms in X-doped MoS₂. Aqua isosurfaces represent positive spin densities (+0.001 e/ų).

IV. Conclusion

In summary, we investigated the electronic and magnetic properties of the V- and VII-doped MoS₂ monolayer using first-principles methods. We find that group V and VII atoms can induce magnetic properties, and the magnetic moment mainly originates from the dopant’s p orbital and neighboring Mo atoms’ d orbital. N-, P-, F-, and I-doped MoS₂ exhibits magnetic nanomaterial features, As-doped MoS₂ shows a magnetic metallic feature, the Cl- and Br-doped systems exhibit half-metallic ferromagnetism (HMF) with half-metallic gaps of about 0.115 and 0.081 eV, respectively. Moreover, the formation energy calculations also indicate that it is energetically favorably and relatively easier to incorporate group V and VII atoms into the MoS₂ monolayer under Mo-rich experimental conditions. The formation energy of the F-doped system is the lowest of those studied, the next lowest formation energy being obtained in the Cl-doped system. Cl-doped MoS₂ is more suitable for spin injection in the future. By comparison, we can see that the p orbital of the N and P atoms plays an important role in the total magnetism of the N- and P-doped systems, but the d orbital of the Mo atoms plays an important role in the total magnetism of the As-, F-, Cl-, Br-, I-doped systems. We believe that these results are helpful for the further study of the properties and applications of MoS₂ monolayer based diluted magnetic semiconductors.

Acknowledgements

This work is supported by a Grant from the National Natural Science Foundation of China (NSFC) under the Grant No. 11504092, National Undergraduate Training Programs for Innovation and Entrepreneurship (No. 201510476043), Natural science foundation research project of education department of Henan province (No. 2011A140018), Science and technology research key project of education department of Henan province (No. 14A140012), and High Performance Computing Center of Henan Normal University.

References

1. E. Gourmelon, O. Lignier, H. Hadouda, G. Couturier, J. C. Bernède, J. Tedd, J. Pouzet and J. Salardenne, Sol. Energy Mater. Sol. Cells, 1997, 46, 115.
2. P. P. Hankare, A. H. Manikshete, D. J. Sathe, P. A. Chate, A. A. Patil and K. M. Garadkar, J. Alloys Compd., 2009, 479, 657.
3. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti and A. Kis, Nat. Nanotechnol., 2011, 6, 147.
4. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman and M. S. Strano, Nat. Nanotechnol., 2012, 7, 699.
5. G. Eda, H. Yamaguchi, D. Voiry, T. Fujita, M. W. Chen and M. Chhowalla, Nano Lett., 2011, 11, 5111.
6. M. Thomalla and H. Tributsch, J. Phys. Chem. B, 2006, 110, 12167.
7. T. Drescher, F. Niefind, W. Bensch and W. Grunert, J. Am. Chem. Soc., 2012, 134, 18896.
8. A. M. Seayad and D. M. Antonelli, Adv. Mater., 2004, 16, 765.
9. M. Mosleh, N. D. Atnafu, J. H. Belk and O. M. Nobles, Wear, 2009, 267, 1220.
10. K. Chang and W. X. Chen, ACS Nano, 2011, 5, 4720.
11. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. Von Molnár, M. L. Roukes, A. Y. Chtchelkanova and D. M. Treger, Science, 2001, 294, 1488.
12. D. D. Awschalom and J. M. Kikkawa, Phys. Today, 1999, 52, 33.
13. S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. Von Molnár, M. L. Roukes, A. Y. Chtchelkanova and D. M. Treger, Science, 2001, 294, 1488.
14. D. D. Awschalom and J. M. Kikkawa, Phys. Today, 1999, 52, 33.
15. Y. H. Zhao, G. P. Zhao, Y. Liu and B. G. Liu, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 224417.
16. R. A. de Groot, F. M. Mueller, P. G. van Engen and K. H. J. Buschow, Phys. Rev. Lett., 1983, 50, 2024.
17. S. J. Luo and K. L. Yao, Phys. Rev. B: Condens. Matter Mater. Phys., 2003, 67, 214429.
18. H. M. Huang, S. J. Luo and K. L. Yao, J. Magn. Magn. Mater., 2009, 321, 2200.
19. S. M. Watts, S. Wirth, S. von Molnár, A. Barry and J. M. D. Coey, Phys. Rev. B: Condens. Matter Mater. Phys., 2000, 61, 9621.
20. P. Mavropoulos and I. Galanakis, J. Phys.: Condens. Matter, 2007, 19, 315221.
21. H. Z. Luo, Z. Y. Zhu, G. D. Liu, S. F. Xu, G. H. Wu, H. Y. Liu, J. P. Qu and Y. X. Li, J. Magn. Magn. Mater., 2008, 320, 421.
22. H. Rached, D. Rached, R. Khenata, A. H. Reshak and M. Rabah, Phys. Status Solidi B, 2009, 246, 1580.
23. I. Galanakis and Ph. Mavropoulos, Phys. Rev. B: Condens.Matter Mater. Phys., 2003, 67, 104417.
24. Y. Xing, Y. Liu, S. N. Li, Y. H. Zhao and W. H. Xie, Phys. Status Solidi B, 2010, 247, 2268.
25. H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto and Y. Iye, Appl. Phys. Lett., 1996, 69, 363.
26. T. Dietl, Nat. Mater., 2010, 9, 965.
27. C. Ataca and S. Ciraci, J. Phys. Chem. C, 2011, 115, 13303.
28. Y. Zhou, P. Yang, H. Zu, F. Gao and X. Zu, Nanoholes Nanodots and Antidots, Phys. Chem. Chem. Phys., 2013, 15, 10385–10394.
29. S. W. Han, Y. H. Hwang, S.-H. Kim, W. S. Yun, J. D. Lee, M. G. Park, S. Ryu, J. S. Park, D. H. Yoo and S.-P. Yoon, et al., Phys. Rev. Lett., 2013, 110, 247201.
30. Y. Ma, Y. Dai, M. Guo, C. Niu, J. Lu and B. Huang, Phys. Chem. Chem. Phys., 2011, 13, 15546–15553.
31. S. Tongay, S. S. Varnoosfaderani, B. R. Appleton, J. Wu and A. F. Hebardet, Appl. Phys. Lett., 2012, 101, 123105.
32. L. Kou, C. Tang, Y. Zhang, T. Heine, C. Chen and T. Frauenheim, J. Phys. Chem. Lett., 2012, 3, 2934–2941.
33. P. Lu, X. Wu, W. Guo and X. C. Zeng, Phys. Chem. Chem. Phys., 2012, 14, 13035–13040.
34. E. Durgun, D. I. Bilc, S. Ciraci and P. Ghosez, J. Phys. Chem. C, 2012, 116, 15713.
35. Y. Xie and J. M. Zhang, Comput. Theor. Chem., 2011, 976, 215.
36. Y. C. Cheng, Z. Y. Zhu, W. B. Mi, Z. B. Guo and U. Schwingenschlögl, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 87, 100401(R).
37. A. Ramasubramaniam and D. Naveh, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 87, 195201.
38. R. H. Mishra, W. Zhou, S. J. Pennycook, S. T. Pantelides and J. C. Idrobo, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 88, 144409.
39. H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto and Y. Iye, Appl. Phys. Lett., 1996, 69, 363.
40. K. Sato, L. Bergqvist, J. Kudrnovský, P. H. Dederichs, O. Eriksson, I. Turek, B. Sanyal, G. Bouzerar, H. Katayama-Yoshida, V. A. Dinh, T. Fukushima, H. Kizaki and R. Zeller, Rev. Mod. Phys., 2010, 82, 1633.
41. H. Ohno, Science, 1998, 281, 951.
42. X. Zhao, C. X. Xia, T. X. Wang and X. Q. Dai, Solid State Commun., 2015, 220, 31–35.
43. X. Zhao, C. X. Xia, T. X. Wang and X. Q. Dai, J. Alloys Compd., 2016, 654, 574–579.
44. C. W. Zhang and S. S. Yan, Appl. Phys. Lett., 2009, 95, 232108.
45. S. W. Fan, K. L. Yao, Z. L. Liu, G. Y. Gao, Y. Min and H. G. Cheng, J. Appl. Phys., 2008, 104, 043912.
46. H. Pan, Y. P. Feng, Q. Y. Wu, Z. G. Huang and J. Y. Lin, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 77, 125211.
47. S. S. Li, C. W. Zhang, F. Li, W. X. Ji, P. Li, M. J. Ren, P. J. Wang and M. Yuan, RSC Adv., 2014, 4, 24399–24405.
48. C. W. Zhang and S. S. Yan, Appl. Phys. Lett., 2009, 95, 232108.
49. F. B. Zheng, C. W. Zhang, S. S. Yan and F. Li, J. Nanopart. Res., 2013, 15, 1647.
50. Y. F. Chen, Q. G. Song, H. Y. Yan, X. Yang and T. Wei, Solid State Commun., 2011, 151, 619–623.
51. K. F. Mak, C. Lee, J. Hone, J. Shan and T. F. Heinz, Phys. Rev. Lett., 2010, 105, 136805.
52. A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C. Y. Chim, G. Galli and F. Wang, Nano Lett., 2010, 10, 1271–1275.
53. Y. H. Lee, X. Q. Zhang, W. Zhang, M. T. Chang, C. T. Lin, K. D. Chang, Y. C. Yu, J. T. W. Wang, C.-S. Chang and L. J. Li, et al., Adv. Mater., 2012, 24, 2320–2325.
54. W. Zhou, X. Zou, S. Najmaei, Z. Liu, Y. Shi, J. Kong, J. Lou, P. M. Ajayan, B. I. Yakobson and J.-C. Idrobo, Nano Lett., 2013, 13, 2615–2622.
55. P. E. Blochl, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 50, 17953.
56. G. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169.
57. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865.
58. C. X. Xia, Y. T Peng, S. Y. Wei and Y. Jia, Acta Mater., 2013, 61, 7720–7725.
59. C. X. Xia, Y. T Peng, H. Zhang, T. X. Wang, S. Y. Wei and Y. Jia, Phys. Chem. Chem. Phys., 2014, 16, 19674.
60. Y. T Peng, C. X. Xia, H. Zhang, T. X. Wang, S. Y. Wei and Y. Jia, Phys. Chem. Chem. Phys., 2014, 16, 18799.
61. Y. T Peng, C. X. Xia, H. Zhang, T. X. Wang, S. Y. Wei and Y. Jia, J. Appl. Phys., 2014, 116, 044306.
62. C. X. Xia, Y. Jia, M. Tao and Q. Zhang, Phys. Lett. A, 2013, 377, 1943.
63. X. Zhao, C. X. Xia, T. X. Wang, Y. T. Peng and X. Q. Dai, J. Alloys Compd., 2015, 649, 357–361.

---