Home
Search
Collections
Journals
About
Contact us
My IOPscience
Strain tuning of magnetism in Mn doped MoS2 monolayer
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 256003 (http://iopscience.iop.org/0953-8984/26/25/256003) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 129.187.254.47 This content was downloaded on 05/06/2014 at 18:07
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 256003 (6pp)
doi:10.1088/0953-8984/26/25/256003
Strain tuning of magnetism in Mn doped MoS2 monolayer Jingshan Qi1, Xiao Li2, Xiaofang Chen1 and Kaige Hu2 1
School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, People’s Republicof China 2 International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, People’s Republic of China E-mail: [email protected] and [email protected] Received 27 March 2014, revised 28 April 2014 Accepted for publication 6 May 2014 Published 5 June 2014 Abstract
We study the strain tuning of magnetism in Mn doped MoS2 monolayer system. With the increase of the tensile strain, the magnetic ground state changes from a state with total magnetic moment Mtot =1.0 μ B to another state with Mtot =3.0 μ B for single doping in a 4 × 4 supercell. Physical mechanism is elucidated from the effects of the local bonding and geometry symmetries on orbital hybridization. In addition, we find the ferromagnetic coupling is favored for small distances between Mn atoms corresponding to the uniform doping concentration of 25%. More importantly, the ferromagnetic state is highly stable and robust to tensile strains. Therefore, diluted magnetic semiconductors can be obtained and the strain engineering should be a very promising approach to tune the magnetic moments. Keywords: MoS2 monolayer, magnetism, strain (Some figures may appear in colour only in the online journal)
Since the discovery of new physics in grapheme [1, 2], twodimensional (2 D) atomic monolayer systems have been the focus of many recent researches in the condensed matter physics community [3–10]. Transition metal dichalcogenide MX2 monolayers (M are transition metals and X are S, Se, or Te) are alternative candidates for the appearance of interesting novel physical properties [5– 8, 10–12]. The semiconductor character of monolayer MoS2 (direct band gap of 1.8 eV [5]) makes it more attractive than graphene as the channel material for a field effect transistor (FET). MoS2 monolayers have been synthesized and applied to fabricate FET devices recently [13–16], showing large in-plane mobilities and high current on/off ratios [13]. Furthermore, doping of magnetic ions in the MoS2 crystal lattice provides a new playground to obtain diluted magnetic semiconductors in 2 D materials for spintronics applications. Cheng et.al studied MoS2 monolayers doped by transition metal atoms and found magnetism for Mn, Fe, Co and Zn doping cases [17]. On the other hand, reliable control of magnetic states is very crucial to the use of magnetic nanostructures in future spintronics and quantum information devices. Therefore it is highly desirable to find an alternative scheme to control 0953-8984/14/256003+6$33.00
magnetism for practical applications. Huang et.al reported a strain-controlled tuning of magnetism in transitionmetal-atom-decorated graphene [18]. However, the lack of a band gap in graphene hampers its application in semiconducting and photonic devices. In addition, several recent studies have investigated the relation between geometrical distortions and magnetic properties of monolayer structures [19–22]. So, strain engineering could be a promising approach to tune the magnetic properties for some special systems. Very recently, Mn doped monolayer MoS2 has motivate great interest and is theoretically predicted to be an atomically thin dilute magnetic semiconductor [23]. Therefore in this work, we take the Mn doped MoS2 monolayer as a primary example to demonstrate the effect of strain on magnetism and our strategy should be instructional to other transition metal atoms doping cases. We find that the strain engineering is a very promising approach to tune magnetic properties. With the increase of the tensile strain, the magnetic ground state change from the state with total magnetic moment Mtot = 1.0 μ B to another state with Mtot = 3.0 μ B for single doping in a 4 × 4 supercell. Because MoS2 monolayer demonstrates effective in-plane strain up to 11% [24], the strain engineering of magnetism found here 1
© 2014 IOP Publishing Ltd Printed in the UK
J Qi et al
J. Phys.: Condens. Matter 26 (2014) 256003
Figure 1. (a) Top view and (b) side view of a Mn doped MoS2 monolayer 4 × 4 supercell. A Mo atom is replaced by a Mn atom, corresponding to the uniform doping concentration of 6.25%. The local atomic structures of the relaxed Mn doped MoS2 monolayer with (c) the C2v symmetry and (d) the D3h symmetry are also shown.
should be an effective way to control the magnetic properties of Mn doped MoS2 monolayer systems. We also study the intrinsic magnetic coupling and find that the ferromagnetic (FM) coupling is favored for small distances between Mn atoms corresponding to the uniform doping concentration of 25%. More importantly, the FM state is highly stable and robust to tensile strains. Therefore, diluted magnetic semiconductors can be obtained and the strain engineering is a very promising approach to tune the magnetic moments. We perform first-principles calculations in a supercell configuration by using the VASP code [25]. We employ the projector augmented-wave (PAW [26]) method for ion-electron interactions and the generalized gradient approximation (GGA [27]) of the exchange-correlation functional. We use an energy cutoff of 400 eV for the plane-wave basis set. Calculations are performed in a 4 × 4 supercell of monolayer MoS2 with 48 atoms including 16 Mo atoms and 32 S atoms. One of the Mo atoms is replaced by a transition metal atom, corresponding to a uniform doping concentration of 6.25%, as shown in Figure 1. The supercell is adjusted to maintain a sufficiently large separation (20 Å) between adjacent monolayers. The 2 D Brillouin zone integrations are carried out by using a 7 × 7 × 1 k-point mesh. We also have tested several denser k-points meshes and higher cutoff energies, and found no significant differences. Atomic coordinates within the supercell are fully optimized without any symmetry constraints with the maximum residual force less than 0.01 eV/Å. We should mention that in [17]. Cheng et al found by GGA calculations that the relaxed structures of Mn doping monolayer MoS2 maintain C3v symmetry. However, we also performed GGA calculations and found that the C3v symmetry structure is only a metastable state and the C2v symmetry
structure is energetically more stable than the C3v symmetry structure. The energy difference ΔE between C3v and C2v symmetry structures is about 30 meV when η < 3% and C3v symmetry structures will spontaneously relax to C2v symmetry structures when η >3%. In addition, symmetry analysis shows that C3v symmetry in [17] should have higher D3h symmetry we use in the following. To include the strong correlation effects we perform GGA+U calculations [28] with U = 5.0 eV for Mn atoms. We take the Mn doped MoS2 monolayer as a primary example to demonstrate the strain effect. A biaxial strain η is defined as η = Δa / a, where a is the lattice constant of free MoS2 monolayer. η > 0 since only tensile strains are considered in the work. We find that under small tensile strains (η 4.5%). In figure 3 we show the isosurface plots of spin charge densities, ρs = ρ↑ − ρ↓ ( ρ↑ and ρ↓ represent the spin-up and spin-down charge density, respectively.), for Mn doped MoS2 monolayer under the strain of 3%. It turns out that the spin-up moments (green isosurface) locate mainly on Mn atoms, while the spin-down moments locate mainly on the surrounding S and Mo atoms. For D3h symmetry structures (l1 = l2 = l3), the six nearest-neighbor S atoms of a Mn atom have the same spin moment. For C2v symmetry structures (l1 = l2 < l3), the four nearest-neighbor S atoms with shorter Mn-S bonds have most of the spin moments, while the other two S atoms with longer Mn-S bonds have very small spin moments. With the increase of the strain, Mn-S bond lengths increase gradually and thus the covalent bonding between Mn atoms and surrounding S atoms becomes weaker and weaker. This makes electrons more and more local, leading to the slowly increasing of the local atomic magnetic moments with the increase of the tensile strain for C2v and D3h symmetry structures, shown in figure 2(c). Therefore, the magnetic moment is closely related with the local geometry surroundings. Because the symmetry affects the local Mn-S bonding (the D3h symmetry tends to enlarge the Mn-S bonds, while the C2v symmetry tends to contract the Mo-S bonds), Mtot is also related to the symmetry in a certain range of the strain (0–6%). Different magnetic moments in different structures of the C2v symmetry and the D3h symmetry can be further understood from the different orbital hybridization. The band structure of MoS2 monolayer changes a lot after doping due to the hybridization between Mn and MoS2 bands. In figure 4, we show the band structures of undoped and Mn doped MoS2 monolayer. Localized (flat) bands form in the band gap, which are hybridized orbitals of Mn, S and Mo. Compared to the D3h symmetry structures, the C2v symmetry structures have lower symmetry and smaller Mn-S average bond length (shown in figure 2 (b)), which affects the Mn-S bonding and local atomic magnetic moments. To understand the magnetic properties we show the variation of local atomic magnetic moments with the increase of strain in figure 2 (c). It shows that for the D3h symmetry the local magnetic moment on the Mn atom is large (about 4.3 μB)
Figure 2. (a) The energy difference ΔE between the states with
Mtot = 3.0μ B and Mtot = 1.0μ B varies with the increase of strain from 0 to 6%. Positive (negative) ΔE indicates that the state with Mtot = 1.0μ B is more (less) stable than the state with Mtot = 3.0μ B . (b) The average Mn-S bond length (Å) varies with the increase of strain for C2v and D3h symmetry structures, respectively. (c) The local atomic magnetic moment varies with the increase of strain for C2v and D3h symmetry structures, respectively.
In order to give a deep insight into the difference between the state with Mtot = 3.0 μ B and the state with Mtot = 1.0 μ B , we investigate the relaxed atomic structures of Mn doped MoS2 monolayer. We find that the structures have the D3h symmetry for the state with Mtot = 3.0 μ B , while the symmetry is reduced to C2v due to a Jahn-Teller distortion for the state with Mtot = 1.0 μ B . The local atomic structure around the Mn atom 3
J Qi et al
J. Phys.: Condens. Matter 26 (2014) 256003
Figure 3. Isosurface plots of the spin charge density, ρs = ρ↑ − ρ↓, for Mn doped MoS2 monolayer with the C2v symmetry (left) and the D3h
symmetry (right) under the strain of 3%. Isosurface values are set up to ±0.004 e/Å3. Green and red isosurfaces represent spin-up and s pin-down charge densities, respectively. Purple, blue and yellow balls represent Mn, Mo and S atoms, respectively.
Figure 4. Band structures of undoped (a) and Mn doped (b) MoS2 monolayer. In (b), the black and red curves represent spin-up and spindown energy bands, respectively.
due to large exchange splitting, indicating that the Mn atom is at a high-spin state. Due to proximity effects Mn atom further magnetizes the surrounding Mo and S atoms, leading to the opposite magnetic moments at the surrounding Mo and S atoms. Due to the small opposite magnetic moments at the surrounding Mo atoms (total about -0.50 μB) and S atoms (total about -0.75 μB), the total magnetic moment of the system is Mtot = 3.0 μB. For the C2v symmetry, the smaller average bond length indicates the stronger orbital hybridization between the Mn and surrounding S. In figure 5 we show the projected density of states (PDOS) for C2v and D3h symmetry structures under the same strain of 3%. In this case the D3h symmetry structure is metastable and it should reduce to the C2v symmetry structure under the structure relaxation. We can see that near the Fermi energy, the hybridization between Mn and S is different for C2v and D3h symmetry structures. For the C2v symmetry structure the hybridization between Mn dxz (dyz) and S px (py) states is stronger than that for the D3h symmetry structure due
to the same symmetry representation B1 (B2) and the shorter average Mn-S bond length. Consequently, the stronger hybridization between d↑xz (d↑yz) and px↑(py↑) leads to larger energy splitting. Therefore the higher energy d↑xz–px↑ (d↑yz–py↑) state (indicate by blue arrow in figure 5) moves to about 0.4 eV above the Fermi energy and becomes unoccupied. At the same time the spin-down Mo d and S p states (indicate by red arrow in figure 5) near the Fermi energy become occupied. Therefore in the structure relaxation from D3h to C2v, the local magnetic moment on the Mn atom becomes smaller (about 3.40 μ B) and the opposite magnetic moments on the surrounding Mo atoms (total about -0.8 μ B) and S atoms (total about -1.6 μ B) become larger, and thus the total magnetic moment of the system is reduced to Mtot = 1.0 μ B . However, for larger tensile strains (> 4.5%) the D3h symmetry structure becomes more energetically stable than the C2v symmetry structure, which means the C2v symmetry structure becomes metastable and it should reduce to the D3h symmetry structure under the structure 4
J Qi et al
J. Phys.: Condens. Matter 26 (2014) 256003
Table 1. The energy differences (ΔEFM-AFM = EFM − EAFM) between
the FM state and AFM state for Mn doped MoS2 monolayer as a function of strain η. The Mn–Mn distance is about 6.53 Å. η
0.0
ΔEFM-AFM (meV) –167
0.01
0.02
0.03
–145 –158 –146
0.04
0.05
0.06
–131 –143 –137
magnetic semiconductors can be obtained when the uniform doping concentration is increased to 25% and tensile strains can be used to tune the magnetic moments of such systems. In conclusion, we found that the strain engineering should be a very promising approach to tune the magnetic moment of Mn doped MX2 monolayer systems. With the increase of the tensile strain, the magnetic ground state changes from the state with Mtot = 1.0 μ B to the state with Mtot = 3.0 μ B for single doping in a 4 × 4 supercell. We found that the magnetic moment is closely related with the local atomic structure around the Mn atoms, because the Mn-S bonding and local geometry symmetry influences the orbital hybridization. Furthermore we find that the FM coupling is favored for the small distance between Mn atoms corresponding to the uniform doping concentration of 25%. The large energy difference between the FM and AFM states indicates the high FM stability. More importantly, the FM coupling is very robust to the tensile strain. Previous experiments have demonstrated the ability to dope MoS2 films, nanoparticles, and nanotubes with transition metals [29–32]. And in recent experiments, MoS2 monolayer demonstrates effective in-plane strain up to 11% [24]. Therefore, strain engineering of magnetism found here should be an effective way to control the magnetic properties of Mn doped MoS2 monolayer systems. We hope that our strategy can be proved experimentally in the future.
Figure 5. PDOS for C2v (a) and D3h (b) symmetry structures under the same strain of 3%. Positive (negative) values represent spinup and spin-down DOS, respectively. The intrinsic bandgaps are indicated by green arrows. Fermi energy is set at zero point.
relaxation. We also find similar results for Mn doped WS2 monolayer. The critical strain at which the magnetic ground state changes from the state (C2v) with Mtot =1.0 μ Bto the state (D3h) with Mtot =3.0 μ B is about 2%, which can be more easily realized experimentally. Therefore the strain tuning of magnetism found here should be general for semiconducting MX2 monolayers. To study the intrinsic magnetic coupling mechanism between the doped magnetic ions, in the following we focus on double atom substitution doping systems by using an 8 × 4 supercell. When the distance between two Mn atoms is 12.74 Å and 9.75 Å (corresponding to the uniform doping concentration of 6.25% and 11%, respectively), the FM and antiferromagnetic (AFM) states are almost degenerate (the energy difference ΔEFM-AFM = EFM − EAFMis smaller than 2 meV), indicating very weak magnetic coupling due to the large distance between the Mn atoms. When the distance between two Mn atoms is reduced to 6.53 Å (corresponding to the uniform doping concentration of 25%), the FM coupling state becomes more stable than the AFM coupling state. The large energy difference between the FM and AFM states (ΔEFM-AFM = –145 meV) indicates the high FM stability. It should be pointed out that we have checked paramagnetic (PM) state and found that the energy of PM state is very higher than the FM and AFM states. The large energy difference between the FM (AFM) and PM states (about 3.0 eV) indicates that the PM state is very far from the ground states and we can ignore it from now on. Because the magnetic moment is closely related with the local Mn-S bonding, the magnetic ground state should change from the state with Mtot =2.0 μ B to the state with Mtot = 6.0 μ Bwith the increase of strain, similar to single doping cases. Our calculations show that this transition indeed occurs when the strain increases up to about 4.5%. In addition, we also assess the robustness of the FM coupling to the tensile strain and find that the FM coupling state is still much more stable than the AFM coupling state with the increase of strain. ΔEFM-AFMchanges slightly in the range from -131 to -158 meV with the increase of strain from 0 to 6% (see table 1), indicating the high FM stability. Therefore, diluted
Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant No. 11204110, 11347005), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 12KJB140005) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). References [1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666 [2] Zhang Y B, Tan Y W, Stormer H L and Kim P 2005 Nature 438 201 [3] Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V and Geim A K 2005 Proc. Natl. Acad. Sci. USA 102 10451 [4] Dean C R et al 2010 Nat. Nanotechnol. 5 722 [5] Mak K F, Lee C, Hone J, Shan J and Heinz T F 2010 Phys. Rev. Lett. 105 136805 [6] Teweldebrhan D, Goyal V and Balandin A A 2010 Nano Lett. 10 1209 [7] Brivio J, Alexander D T L and Kis A 2011 Nano Lett. 11 5148 [8] Cao T et al 2012 Nat. Commun. 3 887 5
J Qi et al
J. Phys.: Condens. Matter 26 (2014) 256003
[22] Faccio R, Fernández-Werner L, Pardo H, Goyenola C, Ventura O N and Mombrú A l W 2010 J. Phys. Chem. C 114 18961 [23] Ramasubramaniam A and Naveh D 2013 Phys. Rev. B 87 195201 [24] Bertolazzi S, Brivio J and Kis A 2011 ACS Nano 5 9703 [25] Kresse G and Furthmuller J 1996 Comput. Mater. Sci. 6 15 [26] Kresse G and Joubert D 1999 Phys. Rev. B 59 1758 [27] Payne M C, Teter M P, Allan D C, Arias T A and Joannopoulos J D 1992 Rev. Mod. Phys. 64 1045 [28] Dudarev S L, Botton G A, Savrasov S Y, Humphreys C J and Sutton A P 1998 Phys. Rev. B 57 1505 [29] Hsu W K, Zhu Y Q, Yao N, Firth S, Clark R J H, Kroto H W and Walton D R M 2001 Adv. Funct. Mater. 11 69 [30] Durbin T D, Lince J R and Yarmoff J A 1992 J. Vac. Sci. Technol. A 10 2529 [31] Lince J R, Carré D J and Fleischauer P D 1987 Phys. Rev. B 36 1647 [32] Yadgarov L et al 2012 Angew. Chem. Int. Ed. 51 1148
[9] Feng J, Qian X, Huang C-W and Li J 2012 Nat. Photonics. 6 866 [10] Mak K F, He K, Shan J and Heinz T F 2012 Nat. Nanotechnol. 7 494 [11] Castellanos-Gomez A, Poot M, Steele G A, van der Zant H S J, Agrait N and Rubio-Bollinger G 2012 Adv. Mater. 24 772 [12] Xiao D, Liu G-B, Feng W, Xu X and Yao W 2012 Phys. Rev. Lett. 108 196802 [13] Radisavljevic B, Radenovic A, Brivio J, Giacometti V and Kis A 2011 Nat. Nanotechnol. 6 147 [14] Kim S et al 2012 Nat. Commun. 3 1011 [15] Li H et al 2012 Small 8 63 [16] Wang H et al 2012 Nano Lett. 12 4674 [17] Cheng Y C, Zhu Z Y, Mi W B, Guo Z B and Schwingenschlögl U 2013 Phys. Rev. B 87 100401 [18] Huang B, Yu J and Wei S-H 2011 Phys. Rev. B 84 075415 [19] Özçelik V O and Ciraci S 2012 Phys. Rev. B 86 155421 [20] Özçelik V O, Gurel H H and Ciraci S 2013 Phys. Rev. B 88 045440 [21] Fan X, Liu L, Lin J, Shen Z and Kuo J-L 2009 ACS Nano 3 3788
6
Search
Collections
Journals
About
Contact us
My IOPscience
Strain tuning of magnetism in Mn doped MoS2 monolayer
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 256003 (http://iopscience.iop.org/0953-8984/26/25/256003) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 129.187.254.47 This content was downloaded on 05/06/2014 at 18:07
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 256003 (6pp)
doi:10.1088/0953-8984/26/25/256003
Strain tuning of magnetism in Mn doped MoS2 monolayer Jingshan Qi1, Xiao Li2, Xiaofang Chen1 and Kaige Hu2 1
School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, People’s Republicof China 2 International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, People’s Republic of China E-mail: [email protected] and [email protected] Received 27 March 2014, revised 28 April 2014 Accepted for publication 6 May 2014 Published 5 June 2014 Abstract
We study the strain tuning of magnetism in Mn doped MoS2 monolayer system. With the increase of the tensile strain, the magnetic ground state changes from a state with total magnetic moment Mtot =1.0 μ B to another state with Mtot =3.0 μ B for single doping in a 4 × 4 supercell. Physical mechanism is elucidated from the effects of the local bonding and geometry symmetries on orbital hybridization. In addition, we find the ferromagnetic coupling is favored for small distances between Mn atoms corresponding to the uniform doping concentration of 25%. More importantly, the ferromagnetic state is highly stable and robust to tensile strains. Therefore, diluted magnetic semiconductors can be obtained and the strain engineering should be a very promising approach to tune the magnetic moments. Keywords: MoS2 monolayer, magnetism, strain (Some figures may appear in colour only in the online journal)
Since the discovery of new physics in grapheme [1, 2], twodimensional (2 D) atomic monolayer systems have been the focus of many recent researches in the condensed matter physics community [3–10]. Transition metal dichalcogenide MX2 monolayers (M are transition metals and X are S, Se, or Te) are alternative candidates for the appearance of interesting novel physical properties [5– 8, 10–12]. The semiconductor character of monolayer MoS2 (direct band gap of 1.8 eV [5]) makes it more attractive than graphene as the channel material for a field effect transistor (FET). MoS2 monolayers have been synthesized and applied to fabricate FET devices recently [13–16], showing large in-plane mobilities and high current on/off ratios [13]. Furthermore, doping of magnetic ions in the MoS2 crystal lattice provides a new playground to obtain diluted magnetic semiconductors in 2 D materials for spintronics applications. Cheng et.al studied MoS2 monolayers doped by transition metal atoms and found magnetism for Mn, Fe, Co and Zn doping cases [17]. On the other hand, reliable control of magnetic states is very crucial to the use of magnetic nanostructures in future spintronics and quantum information devices. Therefore it is highly desirable to find an alternative scheme to control 0953-8984/14/256003+6$33.00
magnetism for practical applications. Huang et.al reported a strain-controlled tuning of magnetism in transitionmetal-atom-decorated graphene [18]. However, the lack of a band gap in graphene hampers its application in semiconducting and photonic devices. In addition, several recent studies have investigated the relation between geometrical distortions and magnetic properties of monolayer structures [19–22]. So, strain engineering could be a promising approach to tune the magnetic properties for some special systems. Very recently, Mn doped monolayer MoS2 has motivate great interest and is theoretically predicted to be an atomically thin dilute magnetic semiconductor [23]. Therefore in this work, we take the Mn doped MoS2 monolayer as a primary example to demonstrate the effect of strain on magnetism and our strategy should be instructional to other transition metal atoms doping cases. We find that the strain engineering is a very promising approach to tune magnetic properties. With the increase of the tensile strain, the magnetic ground state change from the state with total magnetic moment Mtot = 1.0 μ B to another state with Mtot = 3.0 μ B for single doping in a 4 × 4 supercell. Because MoS2 monolayer demonstrates effective in-plane strain up to 11% [24], the strain engineering of magnetism found here 1
© 2014 IOP Publishing Ltd Printed in the UK
J Qi et al
J. Phys.: Condens. Matter 26 (2014) 256003
Figure 1. (a) Top view and (b) side view of a Mn doped MoS2 monolayer 4 × 4 supercell. A Mo atom is replaced by a Mn atom, corresponding to the uniform doping concentration of 6.25%. The local atomic structures of the relaxed Mn doped MoS2 monolayer with (c) the C2v symmetry and (d) the D3h symmetry are also shown.
should be an effective way to control the magnetic properties of Mn doped MoS2 monolayer systems. We also study the intrinsic magnetic coupling and find that the ferromagnetic (FM) coupling is favored for small distances between Mn atoms corresponding to the uniform doping concentration of 25%. More importantly, the FM state is highly stable and robust to tensile strains. Therefore, diluted magnetic semiconductors can be obtained and the strain engineering is a very promising approach to tune the magnetic moments. We perform first-principles calculations in a supercell configuration by using the VASP code [25]. We employ the projector augmented-wave (PAW [26]) method for ion-electron interactions and the generalized gradient approximation (GGA [27]) of the exchange-correlation functional. We use an energy cutoff of 400 eV for the plane-wave basis set. Calculations are performed in a 4 × 4 supercell of monolayer MoS2 with 48 atoms including 16 Mo atoms and 32 S atoms. One of the Mo atoms is replaced by a transition metal atom, corresponding to a uniform doping concentration of 6.25%, as shown in Figure 1. The supercell is adjusted to maintain a sufficiently large separation (20 Å) between adjacent monolayers. The 2 D Brillouin zone integrations are carried out by using a 7 × 7 × 1 k-point mesh. We also have tested several denser k-points meshes and higher cutoff energies, and found no significant differences. Atomic coordinates within the supercell are fully optimized without any symmetry constraints with the maximum residual force less than 0.01 eV/Å. We should mention that in [17]. Cheng et al found by GGA calculations that the relaxed structures of Mn doping monolayer MoS2 maintain C3v symmetry. However, we also performed GGA calculations and found that the C3v symmetry structure is only a metastable state and the C2v symmetry
structure is energetically more stable than the C3v symmetry structure. The energy difference ΔE between C3v and C2v symmetry structures is about 30 meV when η < 3% and C3v symmetry structures will spontaneously relax to C2v symmetry structures when η >3%. In addition, symmetry analysis shows that C3v symmetry in [17] should have higher D3h symmetry we use in the following. To include the strong correlation effects we perform GGA+U calculations [28] with U = 5.0 eV for Mn atoms. We take the Mn doped MoS2 monolayer as a primary example to demonstrate the strain effect. A biaxial strain η is defined as η = Δa / a, where a is the lattice constant of free MoS2 monolayer. η > 0 since only tensile strains are considered in the work. We find that under small tensile strains (η 4.5%). In figure 3 we show the isosurface plots of spin charge densities, ρs = ρ↑ − ρ↓ ( ρ↑ and ρ↓ represent the spin-up and spin-down charge density, respectively.), for Mn doped MoS2 monolayer under the strain of 3%. It turns out that the spin-up moments (green isosurface) locate mainly on Mn atoms, while the spin-down moments locate mainly on the surrounding S and Mo atoms. For D3h symmetry structures (l1 = l2 = l3), the six nearest-neighbor S atoms of a Mn atom have the same spin moment. For C2v symmetry structures (l1 = l2 < l3), the four nearest-neighbor S atoms with shorter Mn-S bonds have most of the spin moments, while the other two S atoms with longer Mn-S bonds have very small spin moments. With the increase of the strain, Mn-S bond lengths increase gradually and thus the covalent bonding between Mn atoms and surrounding S atoms becomes weaker and weaker. This makes electrons more and more local, leading to the slowly increasing of the local atomic magnetic moments with the increase of the tensile strain for C2v and D3h symmetry structures, shown in figure 2(c). Therefore, the magnetic moment is closely related with the local geometry surroundings. Because the symmetry affects the local Mn-S bonding (the D3h symmetry tends to enlarge the Mn-S bonds, while the C2v symmetry tends to contract the Mo-S bonds), Mtot is also related to the symmetry in a certain range of the strain (0–6%). Different magnetic moments in different structures of the C2v symmetry and the D3h symmetry can be further understood from the different orbital hybridization. The band structure of MoS2 monolayer changes a lot after doping due to the hybridization between Mn and MoS2 bands. In figure 4, we show the band structures of undoped and Mn doped MoS2 monolayer. Localized (flat) bands form in the band gap, which are hybridized orbitals of Mn, S and Mo. Compared to the D3h symmetry structures, the C2v symmetry structures have lower symmetry and smaller Mn-S average bond length (shown in figure 2 (b)), which affects the Mn-S bonding and local atomic magnetic moments. To understand the magnetic properties we show the variation of local atomic magnetic moments with the increase of strain in figure 2 (c). It shows that for the D3h symmetry the local magnetic moment on the Mn atom is large (about 4.3 μB)
Figure 2. (a) The energy difference ΔE between the states with
Mtot = 3.0μ B and Mtot = 1.0μ B varies with the increase of strain from 0 to 6%. Positive (negative) ΔE indicates that the state with Mtot = 1.0μ B is more (less) stable than the state with Mtot = 3.0μ B . (b) The average Mn-S bond length (Å) varies with the increase of strain for C2v and D3h symmetry structures, respectively. (c) The local atomic magnetic moment varies with the increase of strain for C2v and D3h symmetry structures, respectively.
In order to give a deep insight into the difference between the state with Mtot = 3.0 μ B and the state with Mtot = 1.0 μ B , we investigate the relaxed atomic structures of Mn doped MoS2 monolayer. We find that the structures have the D3h symmetry for the state with Mtot = 3.0 μ B , while the symmetry is reduced to C2v due to a Jahn-Teller distortion for the state with Mtot = 1.0 μ B . The local atomic structure around the Mn atom 3
J Qi et al
J. Phys.: Condens. Matter 26 (2014) 256003
Figure 3. Isosurface plots of the spin charge density, ρs = ρ↑ − ρ↓, for Mn doped MoS2 monolayer with the C2v symmetry (left) and the D3h
symmetry (right) under the strain of 3%. Isosurface values are set up to ±0.004 e/Å3. Green and red isosurfaces represent spin-up and s pin-down charge densities, respectively. Purple, blue and yellow balls represent Mn, Mo and S atoms, respectively.
Figure 4. Band structures of undoped (a) and Mn doped (b) MoS2 monolayer. In (b), the black and red curves represent spin-up and spindown energy bands, respectively.
due to large exchange splitting, indicating that the Mn atom is at a high-spin state. Due to proximity effects Mn atom further magnetizes the surrounding Mo and S atoms, leading to the opposite magnetic moments at the surrounding Mo and S atoms. Due to the small opposite magnetic moments at the surrounding Mo atoms (total about -0.50 μB) and S atoms (total about -0.75 μB), the total magnetic moment of the system is Mtot = 3.0 μB. For the C2v symmetry, the smaller average bond length indicates the stronger orbital hybridization between the Mn and surrounding S. In figure 5 we show the projected density of states (PDOS) for C2v and D3h symmetry structures under the same strain of 3%. In this case the D3h symmetry structure is metastable and it should reduce to the C2v symmetry structure under the structure relaxation. We can see that near the Fermi energy, the hybridization between Mn and S is different for C2v and D3h symmetry structures. For the C2v symmetry structure the hybridization between Mn dxz (dyz) and S px (py) states is stronger than that for the D3h symmetry structure due
to the same symmetry representation B1 (B2) and the shorter average Mn-S bond length. Consequently, the stronger hybridization between d↑xz (d↑yz) and px↑(py↑) leads to larger energy splitting. Therefore the higher energy d↑xz–px↑ (d↑yz–py↑) state (indicate by blue arrow in figure 5) moves to about 0.4 eV above the Fermi energy and becomes unoccupied. At the same time the spin-down Mo d and S p states (indicate by red arrow in figure 5) near the Fermi energy become occupied. Therefore in the structure relaxation from D3h to C2v, the local magnetic moment on the Mn atom becomes smaller (about 3.40 μ B) and the opposite magnetic moments on the surrounding Mo atoms (total about -0.8 μ B) and S atoms (total about -1.6 μ B) become larger, and thus the total magnetic moment of the system is reduced to Mtot = 1.0 μ B . However, for larger tensile strains (> 4.5%) the D3h symmetry structure becomes more energetically stable than the C2v symmetry structure, which means the C2v symmetry structure becomes metastable and it should reduce to the D3h symmetry structure under the structure 4
J Qi et al
J. Phys.: Condens. Matter 26 (2014) 256003
Table 1. The energy differences (ΔEFM-AFM = EFM − EAFM) between
the FM state and AFM state for Mn doped MoS2 monolayer as a function of strain η. The Mn–Mn distance is about 6.53 Å. η
0.0
ΔEFM-AFM (meV) –167
0.01
0.02
0.03
–145 –158 –146
0.04
0.05
0.06
–131 –143 –137
magnetic semiconductors can be obtained when the uniform doping concentration is increased to 25% and tensile strains can be used to tune the magnetic moments of such systems. In conclusion, we found that the strain engineering should be a very promising approach to tune the magnetic moment of Mn doped MX2 monolayer systems. With the increase of the tensile strain, the magnetic ground state changes from the state with Mtot = 1.0 μ B to the state with Mtot = 3.0 μ B for single doping in a 4 × 4 supercell. We found that the magnetic moment is closely related with the local atomic structure around the Mn atoms, because the Mn-S bonding and local geometry symmetry influences the orbital hybridization. Furthermore we find that the FM coupling is favored for the small distance between Mn atoms corresponding to the uniform doping concentration of 25%. The large energy difference between the FM and AFM states indicates the high FM stability. More importantly, the FM coupling is very robust to the tensile strain. Previous experiments have demonstrated the ability to dope MoS2 films, nanoparticles, and nanotubes with transition metals [29–32]. And in recent experiments, MoS2 monolayer demonstrates effective in-plane strain up to 11% [24]. Therefore, strain engineering of magnetism found here should be an effective way to control the magnetic properties of Mn doped MoS2 monolayer systems. We hope that our strategy can be proved experimentally in the future.
Figure 5. PDOS for C2v (a) and D3h (b) symmetry structures under the same strain of 3%. Positive (negative) values represent spinup and spin-down DOS, respectively. The intrinsic bandgaps are indicated by green arrows. Fermi energy is set at zero point.
relaxation. We also find similar results for Mn doped WS2 monolayer. The critical strain at which the magnetic ground state changes from the state (C2v) with Mtot =1.0 μ Bto the state (D3h) with Mtot =3.0 μ B is about 2%, which can be more easily realized experimentally. Therefore the strain tuning of magnetism found here should be general for semiconducting MX2 monolayers. To study the intrinsic magnetic coupling mechanism between the doped magnetic ions, in the following we focus on double atom substitution doping systems by using an 8 × 4 supercell. When the distance between two Mn atoms is 12.74 Å and 9.75 Å (corresponding to the uniform doping concentration of 6.25% and 11%, respectively), the FM and antiferromagnetic (AFM) states are almost degenerate (the energy difference ΔEFM-AFM = EFM − EAFMis smaller than 2 meV), indicating very weak magnetic coupling due to the large distance between the Mn atoms. When the distance between two Mn atoms is reduced to 6.53 Å (corresponding to the uniform doping concentration of 25%), the FM coupling state becomes more stable than the AFM coupling state. The large energy difference between the FM and AFM states (ΔEFM-AFM = –145 meV) indicates the high FM stability. It should be pointed out that we have checked paramagnetic (PM) state and found that the energy of PM state is very higher than the FM and AFM states. The large energy difference between the FM (AFM) and PM states (about 3.0 eV) indicates that the PM state is very far from the ground states and we can ignore it from now on. Because the magnetic moment is closely related with the local Mn-S bonding, the magnetic ground state should change from the state with Mtot =2.0 μ B to the state with Mtot = 6.0 μ Bwith the increase of strain, similar to single doping cases. Our calculations show that this transition indeed occurs when the strain increases up to about 4.5%. In addition, we also assess the robustness of the FM coupling to the tensile strain and find that the FM coupling state is still much more stable than the AFM coupling state with the increase of strain. ΔEFM-AFMchanges slightly in the range from -131 to -158 meV with the increase of strain from 0 to 6% (see table 1), indicating the high FM stability. Therefore, diluted
Acknowledgments This work is supported by the National Natural Science Foundation of China (Grant No. 11204110, 11347005), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 12KJB140005) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). References [1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666 [2] Zhang Y B, Tan Y W, Stormer H L and Kim P 2005 Nature 438 201 [3] Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V and Geim A K 2005 Proc. Natl. Acad. Sci. USA 102 10451 [4] Dean C R et al 2010 Nat. Nanotechnol. 5 722 [5] Mak K F, Lee C, Hone J, Shan J and Heinz T F 2010 Phys. Rev. Lett. 105 136805 [6] Teweldebrhan D, Goyal V and Balandin A A 2010 Nano Lett. 10 1209 [7] Brivio J, Alexander D T L and Kis A 2011 Nano Lett. 11 5148 [8] Cao T et al 2012 Nat. Commun. 3 887 5
J Qi et al
J. Phys.: Condens. Matter 26 (2014) 256003
[22] Faccio R, Fernández-Werner L, Pardo H, Goyenola C, Ventura O N and Mombrú A l W 2010 J. Phys. Chem. C 114 18961 [23] Ramasubramaniam A and Naveh D 2013 Phys. Rev. B 87 195201 [24] Bertolazzi S, Brivio J and Kis A 2011 ACS Nano 5 9703 [25] Kresse G and Furthmuller J 1996 Comput. Mater. Sci. 6 15 [26] Kresse G and Joubert D 1999 Phys. Rev. B 59 1758 [27] Payne M C, Teter M P, Allan D C, Arias T A and Joannopoulos J D 1992 Rev. Mod. Phys. 64 1045 [28] Dudarev S L, Botton G A, Savrasov S Y, Humphreys C J and Sutton A P 1998 Phys. Rev. B 57 1505 [29] Hsu W K, Zhu Y Q, Yao N, Firth S, Clark R J H, Kroto H W and Walton D R M 2001 Adv. Funct. Mater. 11 69 [30] Durbin T D, Lince J R and Yarmoff J A 1992 J. Vac. Sci. Technol. A 10 2529 [31] Lince J R, Carré D J and Fleischauer P D 1987 Phys. Rev. B 36 1647 [32] Yadgarov L et al 2012 Angew. Chem. Int. Ed. 51 1148
[9] Feng J, Qian X, Huang C-W and Li J 2012 Nat. Photonics. 6 866 [10] Mak K F, He K, Shan J and Heinz T F 2012 Nat. Nanotechnol. 7 494 [11] Castellanos-Gomez A, Poot M, Steele G A, van der Zant H S J, Agrait N and Rubio-Bollinger G 2012 Adv. Mater. 24 772 [12] Xiao D, Liu G-B, Feng W, Xu X and Yao W 2012 Phys. Rev. Lett. 108 196802 [13] Radisavljevic B, Radenovic A, Brivio J, Giacometti V and Kis A 2011 Nat. Nanotechnol. 6 147 [14] Kim S et al 2012 Nat. Commun. 3 1011 [15] Li H et al 2012 Small 8 63 [16] Wang H et al 2012 Nano Lett. 12 4674 [17] Cheng Y C, Zhu Z Y, Mi W B, Guo Z B and Schwingenschlögl U 2013 Phys. Rev. B 87 100401 [18] Huang B, Yu J and Wei S-H 2011 Phys. Rev. B 84 075415 [19] Özçelik V O and Ciraci S 2012 Phys. Rev. B 86 155421 [20] Özçelik V O, Gurel H H and Ciraci S 2013 Phys. Rev. B 88 045440 [21] Fan X, Liu L, Lin J, Shen Z and Kuo J-L 2009 ACS Nano 3 3788
6
