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Electronic, magnetic properties of transition metal doped Tl2S: First-principles study
Applied Surface Science 425 (2017) 393–399
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Electronic, magnetic properties of transition metal doped Tl2 S: First-principles study Nahong Song a,b , Yusheng Wang c,∗ , Weiyang Yu a , Liying Zhang a , Yuye Yang b , Yu Jia a,∗ a International Joint Research Laboratory for Quantum Functional Materials of Henan, School of Physics and Engineering, Zhengzhou University, Zhengzhou 450001, China b College of Computer and Information Engineering, University of Economics and Law, Zhengzhou, Henan 450000, China c College of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450011, China
a r t i c l e
i n f o
Article history: Received 16 May 2017 Received in revised form 28 June 2017 Accepted 4 July 2017 Available online 8 July 2017 Keywords: Tl2 S Magnetic coupling Diluted magnetic semiconductor
a b s t r a c t In this paper, the structural, electric and magnetic properties of transition metal (TM) doped monolayer Tl2 S are investigated by means of first-principles methods The results show that all the considered TM atoms are strongly bonded to the Tl vacancy site. The magnetic moment, the dilute magnetic semiconductor and metal characteristics are varied depending on the specific TM atoms. The TM doped Tl2 S (TM-Tl2 S) (from Sc to Ni) systems have fractional magnetic moments changing from 0.539 B to 4.479 B . However, Cu- and Zn-Tl2 S systems exit the nonmagnetic ground states. The spin polarized metallic states are achieved by Sc, Ti, V, Mn and Fe doping, while spin polarized semiconducting states are realized by Cr, Co and Ni doping. The charge transfer, the total magnetic moment and the band gap obtained with PBE method are less than the values obtained by PBE + U, which suggests that the Hubbard U plays an important role in TM-Tl2 S systems. In the case of two same types of TM atoms doped Tl2 S systems, there exist AFM in Sc-, V-, Mn-Tl2 S systems and FM only in Ti-Tl2 S system. Interestingly, the Cr-, Fe-, Co-, Ni-Tl2 S systems manifest paramagnetic. These findings may provide a new route for exploring two-dimensional diluted magnetic semiconductors experimentally and theoretically. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Much attention has been paid to two-dimensional (2D) materials after graphene was first isolated during the past decade, because 2D materials show many intriguing properties which are not found in their bulk counterparts [1–7] and are considered as cornerstones of the future nanoscale electronics and spintronics [8,9]. Recently, more and more 2D materials have been produced experimentally, such as transition-metal dichalcogenides, black phosphorus, arsenene and antimonene [10–16]. In the process of developing new 2D materials, lately, a few scientists have gradually begun to show solicitude for metal chalcogenides with layered structure. It is reported that group 13 chalcogenides generally are semiconducting in nature, forming binary and ternary compounds with a chain or layered structure [17–19]. Group 13 chalcogenides have much importance in the field of both fundamental research and technical applications because of exhibiting intrinsic vacancy structure, optical, electronic, and photoelectronic properties. Very recently,
∗ Corresponding authors. E-mail addresses: [email protected] (Y. Wang), [email protected] (Y. Jia). http://dx.doi.org/10.1016/j.apsusc.2017.07.018 0169-4332/© 2017 Elsevier B.V. All rights reserved.
thallium chalcogenides (Tl2 S) has received a great deal of attention due to Tl2 S having an unique anti-CdCl2 structure, where the chalcogen atom (S) is the central atom instead of the metal atom Tl, which is also the inverse of transition-metal dichalcogenides such as MoS2 [20–22]. Traditionally, Tl2 S, described as the rare mineral carlinite [23] with black, soft and extremely platy substance characteristics, has been synthesized [20,24]. Tl2 S nanorods were prepared via solvothermal route with the addition of KI [25]. Newly, study reported that single crystals of Tl2 S with layered structure were fabricated from pure (5N) elements in an evacuated silica tube (10−6 Torr) of 1.5 cm diameter and 20 cm length [26]. These lay a good foundation for further theoretical and experimental research to explore the nature of Tl2 S. The extensive research on diluted magnetic semiconductors (DMSs) has set off a craze in scientific community during past years due to the DMSs giving rise to potential applications in spintronics. Initially, the study concentrates almost entirely on the transition metal doped three-dimensional (3D) semiconductors. Lately, tremendous interest was motivated in two-dimensional (2D) materials such as graphene, h-BN, black phosphorene, transition metal dichalcogenides [27–30]. The metallic character prevents the graphene putting into the practical electronic devices, because it
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is very difficult to control the charge and magnetic states though graphene has been considered as a promising host material for TM implantation. The h-BN and black phosphorene overcome the difficulty of the band gap zero and proved to be the prospective host for the DMSs, however they are chemical instability if the systems are exposed to air. Cheng et al. reported MoX2 (X = Mn, Fe, Co, and Zn) are promising systems to explore two-dimensional DMSs [31]. Magnetism is observed for Mn, Fe, Co, Zn doping and the C3v symmetry is maintained, while Jahn-Teller distortions are found in other dopants of transition metals. This inspires our passion for researching electronic and magnetic properties of the TM doped Tl2 S (TM-Tl2 S). The study on the electrochemical and electronic properties of the Tl2 S reveals that Tl2 S displays a competent performance as a hydrogen evolution reaction electrocatalyst compared to a conventional glassy carbon electrode [31]. As far as we know, there has been rarely study on the stability of Tl2 S layer structure. The magnetic and electronic characters of TM-Tl2 S remain unexplored so far. Therefore, it is necessary to perform a systematic study of TM doped Tl2 S. In this work, we firstly verify that the Tl2 S monolayer is dynamically stable by calculating its phonon spectra. Then, we focus on exploring the electronic and magnetic properties of TM-Tl2 S systems. Our investigation may provide useful information regarding DMSs.
2. Computational details We address all the calculations of TM-Tl2 S using the spinpolarized density functional theory (DFT) by Vienna ab initio simulation package (VASP) [32–34]. The generalized gradient approximation (GGA) in Perdew-Burke-Ernzerhof (PBE) is used for an exchange functional, because GGA is very accurate to predict the magnetic states of TM atoms [28,35–37]. On the other hand, the electron correlation effect may play a role for magnetic properties of TM atoms due to the localized d orbital. Therefore, in order to get the magnetic states of TM-Tl2 S, we add the Hubbard U term to the DFT Hamiltonian and perform PBE + U calculations. The values of U are adopted as following: 4.0, 5.5, 3.3, 3.5, 3.5, 4.3, 3.3 and 6.5 eV for Sc-, Ti-, V-, Cr-, Mn-, Fe-, Co-and Ni-Tl2 S, respectively, which is verified reliably [30]. Moreover, a kinetic energy cutoff of 500 eV is selected for the plane wave expansion and high precision calculation. The Monkhorst−Pack k-point sampling 5 × 5 × 1 is used for the Brillouin zone integration. A vacuum space of 20 Å is introduced to avoid interactions between images. All the structures are fully optimized with respect to the ionic positions until the forces on all atoms are less than 0.01 eV/Å. All simulations are carried out for a 4 × 4 supercell with 16 S atoms and 31 Tl atoms with approximately a doping concentration of 2.08%, as shown in Fig. 1(b). In order to clarify the magnetic interaction between two impurities, we also introduce two same type TM atoms in one 4 × 4 supercell with impurity concentration about 4.2%.
3. Results and discussion The unit cell of monolayer Tl2 S has two Tl atoms and one S atom as shown in Fig. 1(a). The bond length of Tl S is 2.946 Å, which matches with previous results: the Tl−S distance varies between 2.82 Å and 3.09 Å [20]. The optimized lattice constants are a1 = a2 = 4.15 Å, which agree with the cell parameters of the single crystal reported by experiments [20]. In order to theoretically verify the monolayer Tl2 S being dynamically stable, the phonon spectra are calculated as shown in Fig. 1(d). The absence of imaginary frequencies demonstrates that the monolayer Tl2 S is stable when described by the chosen potential parameters. Therefore, this lays
Fig 1. (a) The optimized atomic structures of unit cell and 4 × 4 supercell of monolayer Tl2 S, (b) VTL defect of monolayer Tl2 S, (c) single TM substitutional doped Tl2 S, (d) the phonon dispersion of monolayer Tl2 S. The green and blue dashed circle indicates the VTl site. The wine red and grey spheres represent the S and Tl atoms, respectively. The TM atom is labeled into black. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
a foundation for theoretical research of monolayer Tl2 S properties and experimental synthesis of monolayer Tl2 S. For the TM doped system realization, such as TM-MoS2 , TMphosphorene, there are two steps as following: first creation of the vacancy (V) and then incorporation of TM dopants into the vacancy site. Therefore, our discussion begins with considering an individual Tl atom vacancy (VTl ) and an individual S atom vacancy (VS ), respectively. The vacancy structures are achieved by removing one S atom or one Tl atom from a 4 × 4 supercell of the perfect Tl2 S sheet. The vacancy formation energy (Evf ) is defined as: Evf = Ev + EM − Ep where Ev is the total energy of the Tl2 S monolayer sheet with the VS (VTl ), EM is the total energy of a free S (Tl) atom, Ep is the total energy of the perfect Tl2 S sheet. The calculated vacancy formation energies are 5.67 eV and 3.34 eV for a VS and a VTl , respectively. Hence the formation of a VTl requires less energy than that of a VS . On the contrary, in the MoS2 system, the formation of a Mo vacancy requires more energy than that of a S vacancy [27]. In the following, we pay attention to the monolayer Tl2 S with the VTl , which is energetically easier to be produced than the VS . Under the structure relaxation, similar to MoS2 with the S vacancy [38], the symmetry is maintained for the monolayer Tl2 S with the VTl (See Fig. 1(c)). There are no significant displacements for the neighboring Tl and S atoms with respect to the vacancy site, which is different from the clear distortion in graphene sheet with a single C vacancy [39] and in phosphorene sheet with a single P vacancy [30]. The ground state of monolayer Tl2 S with VTl (VS ) has no magnetism, which is the same as the MoS2 with the S vacancy [27] and the blue phosphorene sheet with a single P vacancy. While the vacancy cause a magnetic moment of 1.00 B /unit cell in the black phosphorene sheet with a single P vacancy [30]. Previous research reported that pulsed laser deposition can be used to dope graphene experimentally by single transition metal atom, such as Pt, Co, and In [35]. At the same time, Co doping can be picked up at the MoS2 edge by sulfidation of a mixture of ammonium heptamolybdate and cobalt nitrate [35]. Therefore, from a technical point of view, the same approaches may be applied to realize TM doped Tl2 S. Next, we turn to investigate the geometrical structures, stabilities, charge transfer and magnetic properties of the TM-Tl2 S systems. Various TM atoms (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn) were taken into account in this work. The typical atomic structures of TM-Tl2 S systems are shown in Fig. 1(c).
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Fig. 2. (a) The binding energy of TM (Ef ), (b) the average bond length of TM-S (dTM-S ) (Å), (c) the height of the doped TM atom relative to the Tl plane (h), (d) the TM transfer electronic charges obtained using Bader charge analysis.
Because the atomic radii of the considered TM atoms are smaller than that of Tl atom, the bond lengths of S-TMs (dS-TM ) are all smaller than the dS-Tl (2.94 Å) and the doped TM atoms slightly sink with respect to the Tl plane by 0.1 Å (see Fig. 2). On the contrary, the doped TM atoms slightly protrude the plane in TMMoS2 [38], TM-graphene [40] and TM-h-BN [41]. To discuss the stabilities of different dopants, the binding energies have been calculated as following: Eb = Ev + ETM −Etotal , where Ev is the energy of the relaxed monolayer Tl2 S with one VTl , ETM is the energy of the TM atom, and Etotal is the energy of the monolayer Tl2 S with one Tl atom substituted by one TM atom. As shown in Fig. 2, the binding strength for different TM atoms decreases in the order of Sc > Cu > V > Ti > Fe > Co > Mn > Ni > Cr > Zn, with the binding energies of 5.24, 4.34, 3.35, 3.19, 3.16, 2.94, 2.93, 2.58 and 1.91 eV, respectively. In Tl2 S compound, Tl atom exists in only a single oxidation state exhibiting the inert pair 6s2 configuration. Hence, each Tl vacancy can extract one electron from Tl2 S system, which results in p-type doping. As the isolated Sc and Cu atoms have 3d14s2 and 3d104s1 configuration respectively. The 3d1 valence electron for Sc and the 4s1 valence electron for Cu are equal to valence electron of Tl. Hence, the hybridization with the Tl vacancy state is strongly, inducing the large binding energies. For other TM atoms, the number of valence electron is more than that of Tl atom. Therefore, the hybridization between TM atoms and VTl becomes weak, which is proved by the decrease of the binding energy. Based on the structure and the stability of the above results, we turn to explore the electronic, magnetic properties and related physical mechanisms of TM-Tl2 S systems. As shown in Table 1, the TM-Tl2 S systems have fractional magnetic moments, which are different from the TM-phosphorene [30] and TM-graphene [42], in which the total magnetic moments have the integer values. We find that the magnetic moments of the TM impurities (MTM ) have a dominant contribution for the total magnetic moments. However, the magnetic moment of the Cu-Tl2 S (Zn-Tl2 S) is zero due to having no unpaired electrons. The magnetic moments of TM-Tl2 S systems (from Sc to Mn,) vary from 0.539 B to 4.479 B , which are significantly reduced compared with the magnetic moment values of the isolated TM atoms 1, 3, 5, 6, 5, 4, 3, and 2 B from Sc to Ni atoms, respectively, owing to their strong interaction with the defective Tl2 S substrate. To understand the magnetic properties of TM-Tl2 S systems, the transferred charges between TMs and Tl2 S are obtained by Bader charge analysis [43]. It is noticed from Fig. 2(d) that the TMs transfer fractional charges to Tl2 S substrate, which induce unpaired electrons for Sc to Ni and give rise to fractional magnetic moment of 0.443, 1.838, 2.617, 4.212, 4.439, 3.544, 1.968, 0.970 B , respectively. The charge transfers decrease monotonously as the atomic valence electron increases except for
Fig. 3. Spin density (up-down) with an isovalue of 0.0006 e/Å3 for single TM substitutional doped Tl2 S systems. Yellow and blue indicate the positive and negative spin densities, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the Cr. Due to the valence electron configuration 3d54s1 of Cr, the 3d shell is half-full according to Hund’s rule, therefore the charge is more difficult to be transferred to Tl2 S substrate, inducing the charge transfer intensely decreasing. In order to examine the effect of the on-site Coulomb interaction U on the magnetic properties of TM-Tl2 S systems, we perform the PBE and PBE + U calculations for all the considered magnetic systems. The magnetic moments obtained using PBE + U are larger than the PBE results, which indicates that the Hubbard U plays an important role on the spin moment for TM-Tl2 S system. Interestingly, the charge transfers obtained using PBE + U are larger than the PBE results for Sc, Ti, V, Mn, Fe, but smaller than the PBE results for the Cr, Co, Ni. In addition, to visualize the magnetic moment distribution of TMTl2 S systems, the spin density distributions are plotted in Fig. 3. The typical character of the magnetic moment contribution is that the magnetic moments are mainly localized on the doped TMs for almost all the systems, and the magnetic moments of adjacent S and Tl atoms are relatively small, which is similar to the above discussions in Table 1. The distributions of the magnetic moment are observed in other systems too, such as TM-MoS2 system [38], TM-phosphorene [44], TM-arsenene [45]. To further elaborate the mechanisms of the magnetic properties of TM-Tl2 S systems, we plot the total density of states (TDOS) and projected density of states (PDOS) of the TM atoms and its nearest S, Tl atoms in Fig. 4. Numerical results show that the spin-up and spin-down TDOS of monolayer Tl2 S and the monolayer Tl2 S with VTl are symmetric, which indicates that the monolayer Tl2 S system and the monolayer Tl2 S with VTl possess the properties of nonmagnetic ground states (see Fig. 4(a) and (b)). It can be seen from Fig. 4(a) that for monolayer Tl2 S, the valence band maximum (VBM) is dominated by the hybridization of pz orbitals of S and Tl atoms, while the conduction band minimum (CBM) is mainly contributed by the degenerate px , py orbitals of Tl atom. For the monolayer Tl2 S with VTl , the pz orbitals of S and Tl atoms hybridize at Fermi level, inducing the metallic character. Meanwhile, the CBM contributed by the degenerate px , py orbitals of Tl atom moves up. For Cu and Zn-Tl2 S systems, the spin-up and spin-down states of TDOS also are symmetric, which indicates that Cu and Zn substituting Tl atom can induce hardly magnetic moments. This is also consistent with the calculated magnetic moments being zero in Table 1. The hybridization between the degenerate dx2 -y2 and dxy orbitals
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Table 1 The TM transfer electronic charges obtained using Bader charge analysis, total magnetic moment (Mtot ), magnetic moment of the TM impurity (MTM ) and the nearest S and Tl atom (MS and MTl ) for a single TM substitutional doped Tl2 S systems obtained in the PBE + U method. The values in parentheses are obtained in the PBE method. TM-Tl2S
Q(e) (PBE/PBE + U)
Mtot (B ) (PBE/PBE + U)
MTM (B ) (PBE/PBE + U)
MS (B ) (PBE/PBE + U)
MTl (B ) (PBE/PBE + U)
Egap (eV) (PBE/PBE + U)
Sc Ti V Cr Mn Fe Co Ni Cu Zn
−1.52(−1.43) −1.19(−1.17) −1.16(−1.03) −0.77(−0.83) −1.04(−0.85) −0.91(−0.73) −0.44(−0.45) −0.35(−0.38) −0.38 −0.79
0.539(0.468) 1.915(1.515) 2.592(2.568) 4.25(3.990) 4.479(3.959) 3.688 (3.241) 1.964(1.910) 0.974(0.893) 0 0
0.443(0.338) 1.838(1.475) 2.617(2.500) 4.212(3.866) 4.439(3.937) 3.544(3.054) 1.968(1.822) 0.970(0.763) 0 0
−0.006(−0.005) −0.035(−0.025) −0.024(−0.030) −0.029(−0.016) 0.008(0.019) 0.035(0.051) 0.003(0.033) 0.001(0.033) 0 0
0.014(0.016) 0.013(0.009) 0.001(0.011) 0.015(0.020) −0.003(−0.01) 0.003(−0.001) −0.004(−0.007) −0.002(−0.001) 0 0
0(0) 0(0) 0(0) 0.72(0.44) 0(0) 0 0.85(0.40) 0.98(0.36) 1.3 0
of Cu and the pz orbitals of S and Tl atoms devotes to VBM, while Cu d orbital dedicates hardly CBM in Cu-Tl2 S systems. In Zn-Tl2 S systems, the degenerate px , py orbitals of Tl atom moving down cross the Fermi level, leading to the metallic state. We can see from Fig. 4(e)–(m) that the hybridization of TM 3d orbitals and p orbitals of the nearest S, Tl atoms results in the splitting of the energy levels near the Fermi level in the spin-polarized systems, which are responsible for the magnetic moments. In addition, the magnetic moments mainly originate from different d orbitals given a detailed explanation below. For Sc-Tl2 S system, the magnetic moment of Sc
atom comes from Sc dz2 orbital entirely due to dz2 being localized asymmetrically. For Ti-Tl2 S system, it is clearly seen that the Ti dz2 and dx2 -y2 orbitals are asymmetrically localized at the Fermi level, showing two narrow peaks and overlapping fractionally with each other. Consequently, in the majority-spin channel, both of them are fractionally occupied, resulting in the appearance of the magnetic moments and metallicity. For V-Tl2 S system, the V dyz and V dxz orbitals are localized asymmetrically at −1.6 eV, inducing the magnetic moments. For Cr-Tl2 S system, the Cr dx2 -y2 and dxy orbitals mainly contribute to the magnetic moments near the Fermi level.
Fig. 4. PDOS for single TM doped Tl2 S systems.
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Fig. 5. Band structures for single TM substitutional doped Tl2 S systems.
For Mn-, Fe-, Co- and Ni- Tl2 S systems, complicated phenomenon occurs because TM atom has more than 5 electrons of 3d and some of the nonbonding orbitals are filled. For Mn-, Fe-, and Ni-Tl2 S systems, they share the same features that the 3d orbitals are localized at a relatively deeper energy level because they have partially occupied non-bonding 3d orbitals, which are dyz, dxy, dz2 of the Mn atom, dz2 of the Fe atom and dxz, dyz of Ni atom respectively, leading to the magnetic moments. For Co-Tl2 S system, the Co-3d orbitals are split into e1 (dz2 ) orbital and four-fold degenerate e2 (dxy, dxz, dyz, dx2 -y2 ) orbital near the Fermi level, therefore e1 orbital and four-fold degenerate e2 are mainly responsible for the magnetic moment. From the above analysis of TDOS and PDOS, it is clearly seen that the magnetic moments are well localized at the TM atom site, which is consistent with the spin density distribution plotted. It is also significant further to analyze the band structures of various considered systems. As shown in Fig. 5(a), the monolayer Tl2 S is semiconductor with a direct band gap of 1.37 eV, which is larger than that of the Tl2 S bulk (0.8 eV) [31]. However, the monolayer Tl2 S with the VTl becomes to the metal, due to the Tl defect inducing the VBM moving up. It can be seen that the band structures depend highly on the specific impurity atom for TM-Tl2 S systems in Fig. 5. For Cu-Tl2 S system, a direct band gap of 1.30 eV is found, which is comparable to the band gap 1.37 eV of Tl2 S. Hence Cu-Tl2 S system still preserve the nonmagnetic semiconductor character. In addition, the nonmagnetic states are found in Zn-Tl2 S system and the CBM crosses the Fermi level at . Consequently, Zn-Tl2 S system becomes to nonmagnetic metal. For Sc-, Ti-, V-, Mn-, Fe-Tl2 S systems, due to the CBM and the VBM moving down compared with the monolayer Tl2 S, both the spin up and spin down bands cross the Fermi level at , which indicates that the metallic states are achieved. More importantly, for Cr-, Co-, Ni- Tl2 S systems, the
band gaps with spin polarization are found (see Fig. 5(i), (l), (m)), which indicates the properties of DMS. The analysis from the band structures are consistent with above results from the PDOS. It is worth mentioning that the band gaps obtained from PBE + U are larger than those obtained from PBE in Cr-, Co-, Ni- Tl2 S systems (see Table 1). This indicates that the Hubbard U in Cr-, Co-, Ni- Tl2 S systems plays a big part in increasing the band gaps, which is also found in Ti-doped blue phosphorene [30]. In order to determine the magnetic interactions between two same TM impurity atoms in TM-Tl2 S systems, we substitute two Tl atoms with same TM atoms in a 4 × 4 supercell with a doping concentration of about 4.2%. Another TM dopant atom substitutes Tl atom marked by a blue dashed circle as shown in Fig. 1(a). Since both Zn- and Cu-Tl2 S systems display nonmagnetic ground state for single TM substituting doped Tl2 S, we exclude these two systems. For the sake of finding the magnetic ground states, we consider ferromagnetic (FM) and antiferromagnetic (AFM) spin configurations. The total energies of FM and AFM configurations, the total energy difference [E = EFM − EAFM ], the total magnetic moment, the binding energy using the PBE + U method are presented in Table 2. Numerical results show that the binding energies are larger than the values in the single TM substitutional doped Tl2 S systems, except for Sc which slightly deceases from 5.24 eV (in the single Sc doped Tl2 S system) to 4.69 eV. This indicates that two same TM atoms doped Tl2 S are energetically favorable except for Sc. In addition, we can see that FM and AFM coupling between two TMs depends on the specific TM atoms. For the Sc-, V-, MnTl2 S systems, they exhibit the characteristic of AFM due to the total energy difference being positive. While Ti-Tl2 S system has FM ground state. For the Cr-, Fe-, Co-, Ni-Tl2 S systems, the FM and AFM configurations are almost degenerated indicating that they exhibit paramagnetic behaviors. The spin density of two TM doped
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Fig. 6. Spin density (up-down) with an isovalue of 0.0006 e/Å3 for two TM atoms doped Tl2 S systems: (a) ScAFM -Tl2 S, (b) TiFM -Tl2 S, (c)VAFM -Tl2 S, (d) CrAFM -Tl2 S, (e) (d) CrFM -Tl2 S, (f) MnAFM -Tl2 S, (g) FeAFM -Tl2 S, (h) FeFM -Tl2 S, (i) CoAFM -Tl2 S, (j) CoFM -Tl2 S, (k) NiAFM -Tl2 S, (l) NiFM -Tl2 S. Yellow and blue indicate the positive and negative spin densities, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 2 Total energies of FM and AFM states, the energy differences E = EFM − EAFM , the binding energies and total magnetic moment (Mtotal ) for the two TM atoms doped Tl2 S systems. The values are obtained in the PBE + U method.
Sc Ti V Cr Mn Fe Co Ni
EFM (eV)
EAFM (meV)
EFM-AFM (meV)
Eb (eV)
Mtot (B ) (PBE/PBE + U)
−163.1906 −161.6426 −164.26475 −166.30011 −166.15534 −162.51444 −160.78516 −156.78897
−163.19747 −161.63291 −164.29866 −166.30071 −166.16393 −162.51468 −160.78534 −156.78808
6.78 −9.69 33.91 0.6 8.59 0.24 0.18 −0.9
4.69 4.43 6.10 7.35 7.54 5.81 5.01 3.07
−0.229 3.19 0.08 0(8.50) 0.23 0.661(3.83) 0(3.93) 0.001(1.95)
show that the Hubbard U have an important effect on the charge transfers, magnetic moments and band gaps. The magnetic coupling between magnetic moments induced by TM varies with the specific TM atoms. For instance, the magnetic coupling is found to be AFM in Sc-, V-, Mn-Tl2 S systems. On the contrary, the magnetic coupling is FM in Ti-Tl2 S system. Interestingly, the Cr-, Fe-, Co-, NiTl2 S systems manifest paramagnetic. In a word, the electronic and magnetic properties of Tl2 S can be modulated by doping different TM atoms. We expect the conclusions obtained from Tl2 S may be valid for group 13 chalcogenides. Investigation of further materials from group 13 chalcogenides is promising to find new 2D materials applied to nanoelectronic devices and spintronics. Acknowledgements
Tl2 S using the PBE + U method are presented in Fig. 6. The yellow color represents spin up, while the blue color represents spin down densities. Like in the single TM doped Tl2 S systems, the magnetic moments are mainly from the TM atoms, while Tl and S atoms show negligible spin polarization. It can be seen from Fig. 6 that the Sc, V, Mn have AFM coupling, while Ti has FM coupling, which are agree with the results in Table 2. For the double Cr-, Fe-, Co-, Ni- atoms doped Tl2 S systems, we display both the FM and AFM configurations because they are degenerated. It is clearly displayed that the spectral shapes of spin density are the same as found in the single substitutional doped Tl2 S systems, which suggests the same d orbitals are in charge of the magnetic moments. 4. Conclusion In conclusion, the structural, electronic, and magnetic properties of various TM atoms doped Tl2 S have been systematically studied by using first-principles DFT calculations. The results show that all the TM atoms are strongly bonded to VTl , which mainly results from the hybridization between the d orbitals of the TM and p orbitals of its nearest S, Tl atoms. Among the single TM doped Tl2 S systems, we found no spin polarized ground states in the Cu- and Zn-Tl2 S systems. In other systems, the spin polarized ground states are found. The TM-Tl2 S systems have fractional magnetic moments. The magnetic moment of each TM atom originates mainly from different d orbitals in spin polarized TM-Tl2 S systems. In addition, the band structures are strongly dependent on specific TM atom. The Sc-, Ti-, V-, Mn-, Fe- and Zn-Tl2 S systems show the metallic behavior. However, the Cu-Tl2 S system is still semiconductor with the direct gap as the monolayer Tl2 S. More importantly, the Cr-, Co, Ni-Tl2 S systems possess spin polarized semiconducting feature, although the band gaps vary as the TM atoms change, which suggests that the monolayer Tl2 S will be a new DMS. Research findings
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Electronic, magnetic properties of transition metal doped Tl2 S: First-principles study Nahong Song a,b , Yusheng Wang c,∗ , Weiyang Yu a , Liying Zhang a , Yuye Yang b , Yu Jia a,∗ a International Joint Research Laboratory for Quantum Functional Materials of Henan, School of Physics and Engineering, Zhengzhou University, Zhengzhou 450001, China b College of Computer and Information Engineering, University of Economics and Law, Zhengzhou, Henan 450000, China c College of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450011, China
a r t i c l e
i n f o
Article history: Received 16 May 2017 Received in revised form 28 June 2017 Accepted 4 July 2017 Available online 8 July 2017 Keywords: Tl2 S Magnetic coupling Diluted magnetic semiconductor
a b s t r a c t In this paper, the structural, electric and magnetic properties of transition metal (TM) doped monolayer Tl2 S are investigated by means of first-principles methods The results show that all the considered TM atoms are strongly bonded to the Tl vacancy site. The magnetic moment, the dilute magnetic semiconductor and metal characteristics are varied depending on the specific TM atoms. The TM doped Tl2 S (TM-Tl2 S) (from Sc to Ni) systems have fractional magnetic moments changing from 0.539 B to 4.479 B . However, Cu- and Zn-Tl2 S systems exit the nonmagnetic ground states. The spin polarized metallic states are achieved by Sc, Ti, V, Mn and Fe doping, while spin polarized semiconducting states are realized by Cr, Co and Ni doping. The charge transfer, the total magnetic moment and the band gap obtained with PBE method are less than the values obtained by PBE + U, which suggests that the Hubbard U plays an important role in TM-Tl2 S systems. In the case of two same types of TM atoms doped Tl2 S systems, there exist AFM in Sc-, V-, Mn-Tl2 S systems and FM only in Ti-Tl2 S system. Interestingly, the Cr-, Fe-, Co-, Ni-Tl2 S systems manifest paramagnetic. These findings may provide a new route for exploring two-dimensional diluted magnetic semiconductors experimentally and theoretically. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Much attention has been paid to two-dimensional (2D) materials after graphene was first isolated during the past decade, because 2D materials show many intriguing properties which are not found in their bulk counterparts [1–7] and are considered as cornerstones of the future nanoscale electronics and spintronics [8,9]. Recently, more and more 2D materials have been produced experimentally, such as transition-metal dichalcogenides, black phosphorus, arsenene and antimonene [10–16]. In the process of developing new 2D materials, lately, a few scientists have gradually begun to show solicitude for metal chalcogenides with layered structure. It is reported that group 13 chalcogenides generally are semiconducting in nature, forming binary and ternary compounds with a chain or layered structure [17–19]. Group 13 chalcogenides have much importance in the field of both fundamental research and technical applications because of exhibiting intrinsic vacancy structure, optical, electronic, and photoelectronic properties. Very recently,
∗ Corresponding authors. E-mail addresses: [email protected] (Y. Wang), [email protected] (Y. Jia). http://dx.doi.org/10.1016/j.apsusc.2017.07.018 0169-4332/© 2017 Elsevier B.V. All rights reserved.
thallium chalcogenides (Tl2 S) has received a great deal of attention due to Tl2 S having an unique anti-CdCl2 structure, where the chalcogen atom (S) is the central atom instead of the metal atom Tl, which is also the inverse of transition-metal dichalcogenides such as MoS2 [20–22]. Traditionally, Tl2 S, described as the rare mineral carlinite [23] with black, soft and extremely platy substance characteristics, has been synthesized [20,24]. Tl2 S nanorods were prepared via solvothermal route with the addition of KI [25]. Newly, study reported that single crystals of Tl2 S with layered structure were fabricated from pure (5N) elements in an evacuated silica tube (10−6 Torr) of 1.5 cm diameter and 20 cm length [26]. These lay a good foundation for further theoretical and experimental research to explore the nature of Tl2 S. The extensive research on diluted magnetic semiconductors (DMSs) has set off a craze in scientific community during past years due to the DMSs giving rise to potential applications in spintronics. Initially, the study concentrates almost entirely on the transition metal doped three-dimensional (3D) semiconductors. Lately, tremendous interest was motivated in two-dimensional (2D) materials such as graphene, h-BN, black phosphorene, transition metal dichalcogenides [27–30]. The metallic character prevents the graphene putting into the practical electronic devices, because it
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is very difficult to control the charge and magnetic states though graphene has been considered as a promising host material for TM implantation. The h-BN and black phosphorene overcome the difficulty of the band gap zero and proved to be the prospective host for the DMSs, however they are chemical instability if the systems are exposed to air. Cheng et al. reported MoX2 (X = Mn, Fe, Co, and Zn) are promising systems to explore two-dimensional DMSs [31]. Magnetism is observed for Mn, Fe, Co, Zn doping and the C3v symmetry is maintained, while Jahn-Teller distortions are found in other dopants of transition metals. This inspires our passion for researching electronic and magnetic properties of the TM doped Tl2 S (TM-Tl2 S). The study on the electrochemical and electronic properties of the Tl2 S reveals that Tl2 S displays a competent performance as a hydrogen evolution reaction electrocatalyst compared to a conventional glassy carbon electrode [31]. As far as we know, there has been rarely study on the stability of Tl2 S layer structure. The magnetic and electronic characters of TM-Tl2 S remain unexplored so far. Therefore, it is necessary to perform a systematic study of TM doped Tl2 S. In this work, we firstly verify that the Tl2 S monolayer is dynamically stable by calculating its phonon spectra. Then, we focus on exploring the electronic and magnetic properties of TM-Tl2 S systems. Our investigation may provide useful information regarding DMSs.
2. Computational details We address all the calculations of TM-Tl2 S using the spinpolarized density functional theory (DFT) by Vienna ab initio simulation package (VASP) [32–34]. The generalized gradient approximation (GGA) in Perdew-Burke-Ernzerhof (PBE) is used for an exchange functional, because GGA is very accurate to predict the magnetic states of TM atoms [28,35–37]. On the other hand, the electron correlation effect may play a role for magnetic properties of TM atoms due to the localized d orbital. Therefore, in order to get the magnetic states of TM-Tl2 S, we add the Hubbard U term to the DFT Hamiltonian and perform PBE + U calculations. The values of U are adopted as following: 4.0, 5.5, 3.3, 3.5, 3.5, 4.3, 3.3 and 6.5 eV for Sc-, Ti-, V-, Cr-, Mn-, Fe-, Co-and Ni-Tl2 S, respectively, which is verified reliably [30]. Moreover, a kinetic energy cutoff of 500 eV is selected for the plane wave expansion and high precision calculation. The Monkhorst−Pack k-point sampling 5 × 5 × 1 is used for the Brillouin zone integration. A vacuum space of 20 Å is introduced to avoid interactions between images. All the structures are fully optimized with respect to the ionic positions until the forces on all atoms are less than 0.01 eV/Å. All simulations are carried out for a 4 × 4 supercell with 16 S atoms and 31 Tl atoms with approximately a doping concentration of 2.08%, as shown in Fig. 1(b). In order to clarify the magnetic interaction between two impurities, we also introduce two same type TM atoms in one 4 × 4 supercell with impurity concentration about 4.2%.
3. Results and discussion The unit cell of monolayer Tl2 S has two Tl atoms and one S atom as shown in Fig. 1(a). The bond length of Tl S is 2.946 Å, which matches with previous results: the Tl−S distance varies between 2.82 Å and 3.09 Å [20]. The optimized lattice constants are a1 = a2 = 4.15 Å, which agree with the cell parameters of the single crystal reported by experiments [20]. In order to theoretically verify the monolayer Tl2 S being dynamically stable, the phonon spectra are calculated as shown in Fig. 1(d). The absence of imaginary frequencies demonstrates that the monolayer Tl2 S is stable when described by the chosen potential parameters. Therefore, this lays
Fig 1. (a) The optimized atomic structures of unit cell and 4 × 4 supercell of monolayer Tl2 S, (b) VTL defect of monolayer Tl2 S, (c) single TM substitutional doped Tl2 S, (d) the phonon dispersion of monolayer Tl2 S. The green and blue dashed circle indicates the VTl site. The wine red and grey spheres represent the S and Tl atoms, respectively. The TM atom is labeled into black. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
a foundation for theoretical research of monolayer Tl2 S properties and experimental synthesis of monolayer Tl2 S. For the TM doped system realization, such as TM-MoS2 , TMphosphorene, there are two steps as following: first creation of the vacancy (V) and then incorporation of TM dopants into the vacancy site. Therefore, our discussion begins with considering an individual Tl atom vacancy (VTl ) and an individual S atom vacancy (VS ), respectively. The vacancy structures are achieved by removing one S atom or one Tl atom from a 4 × 4 supercell of the perfect Tl2 S sheet. The vacancy formation energy (Evf ) is defined as: Evf = Ev + EM − Ep where Ev is the total energy of the Tl2 S monolayer sheet with the VS (VTl ), EM is the total energy of a free S (Tl) atom, Ep is the total energy of the perfect Tl2 S sheet. The calculated vacancy formation energies are 5.67 eV and 3.34 eV for a VS and a VTl , respectively. Hence the formation of a VTl requires less energy than that of a VS . On the contrary, in the MoS2 system, the formation of a Mo vacancy requires more energy than that of a S vacancy [27]. In the following, we pay attention to the monolayer Tl2 S with the VTl , which is energetically easier to be produced than the VS . Under the structure relaxation, similar to MoS2 with the S vacancy [38], the symmetry is maintained for the monolayer Tl2 S with the VTl (See Fig. 1(c)). There are no significant displacements for the neighboring Tl and S atoms with respect to the vacancy site, which is different from the clear distortion in graphene sheet with a single C vacancy [39] and in phosphorene sheet with a single P vacancy [30]. The ground state of monolayer Tl2 S with VTl (VS ) has no magnetism, which is the same as the MoS2 with the S vacancy [27] and the blue phosphorene sheet with a single P vacancy. While the vacancy cause a magnetic moment of 1.00 B /unit cell in the black phosphorene sheet with a single P vacancy [30]. Previous research reported that pulsed laser deposition can be used to dope graphene experimentally by single transition metal atom, such as Pt, Co, and In [35]. At the same time, Co doping can be picked up at the MoS2 edge by sulfidation of a mixture of ammonium heptamolybdate and cobalt nitrate [35]. Therefore, from a technical point of view, the same approaches may be applied to realize TM doped Tl2 S. Next, we turn to investigate the geometrical structures, stabilities, charge transfer and magnetic properties of the TM-Tl2 S systems. Various TM atoms (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn) were taken into account in this work. The typical atomic structures of TM-Tl2 S systems are shown in Fig. 1(c).
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Fig. 2. (a) The binding energy of TM (Ef ), (b) the average bond length of TM-S (dTM-S ) (Å), (c) the height of the doped TM atom relative to the Tl plane (h), (d) the TM transfer electronic charges obtained using Bader charge analysis.
Because the atomic radii of the considered TM atoms are smaller than that of Tl atom, the bond lengths of S-TMs (dS-TM ) are all smaller than the dS-Tl (2.94 Å) and the doped TM atoms slightly sink with respect to the Tl plane by 0.1 Å (see Fig. 2). On the contrary, the doped TM atoms slightly protrude the plane in TMMoS2 [38], TM-graphene [40] and TM-h-BN [41]. To discuss the stabilities of different dopants, the binding energies have been calculated as following: Eb = Ev + ETM −Etotal , where Ev is the energy of the relaxed monolayer Tl2 S with one VTl , ETM is the energy of the TM atom, and Etotal is the energy of the monolayer Tl2 S with one Tl atom substituted by one TM atom. As shown in Fig. 2, the binding strength for different TM atoms decreases in the order of Sc > Cu > V > Ti > Fe > Co > Mn > Ni > Cr > Zn, with the binding energies of 5.24, 4.34, 3.35, 3.19, 3.16, 2.94, 2.93, 2.58 and 1.91 eV, respectively. In Tl2 S compound, Tl atom exists in only a single oxidation state exhibiting the inert pair 6s2 configuration. Hence, each Tl vacancy can extract one electron from Tl2 S system, which results in p-type doping. As the isolated Sc and Cu atoms have 3d14s2 and 3d104s1 configuration respectively. The 3d1 valence electron for Sc and the 4s1 valence electron for Cu are equal to valence electron of Tl. Hence, the hybridization with the Tl vacancy state is strongly, inducing the large binding energies. For other TM atoms, the number of valence electron is more than that of Tl atom. Therefore, the hybridization between TM atoms and VTl becomes weak, which is proved by the decrease of the binding energy. Based on the structure and the stability of the above results, we turn to explore the electronic, magnetic properties and related physical mechanisms of TM-Tl2 S systems. As shown in Table 1, the TM-Tl2 S systems have fractional magnetic moments, which are different from the TM-phosphorene [30] and TM-graphene [42], in which the total magnetic moments have the integer values. We find that the magnetic moments of the TM impurities (MTM ) have a dominant contribution for the total magnetic moments. However, the magnetic moment of the Cu-Tl2 S (Zn-Tl2 S) is zero due to having no unpaired electrons. The magnetic moments of TM-Tl2 S systems (from Sc to Mn,) vary from 0.539 B to 4.479 B , which are significantly reduced compared with the magnetic moment values of the isolated TM atoms 1, 3, 5, 6, 5, 4, 3, and 2 B from Sc to Ni atoms, respectively, owing to their strong interaction with the defective Tl2 S substrate. To understand the magnetic properties of TM-Tl2 S systems, the transferred charges between TMs and Tl2 S are obtained by Bader charge analysis [43]. It is noticed from Fig. 2(d) that the TMs transfer fractional charges to Tl2 S substrate, which induce unpaired electrons for Sc to Ni and give rise to fractional magnetic moment of 0.443, 1.838, 2.617, 4.212, 4.439, 3.544, 1.968, 0.970 B , respectively. The charge transfers decrease monotonously as the atomic valence electron increases except for
Fig. 3. Spin density (up-down) with an isovalue of 0.0006 e/Å3 for single TM substitutional doped Tl2 S systems. Yellow and blue indicate the positive and negative spin densities, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the Cr. Due to the valence electron configuration 3d54s1 of Cr, the 3d shell is half-full according to Hund’s rule, therefore the charge is more difficult to be transferred to Tl2 S substrate, inducing the charge transfer intensely decreasing. In order to examine the effect of the on-site Coulomb interaction U on the magnetic properties of TM-Tl2 S systems, we perform the PBE and PBE + U calculations for all the considered magnetic systems. The magnetic moments obtained using PBE + U are larger than the PBE results, which indicates that the Hubbard U plays an important role on the spin moment for TM-Tl2 S system. Interestingly, the charge transfers obtained using PBE + U are larger than the PBE results for Sc, Ti, V, Mn, Fe, but smaller than the PBE results for the Cr, Co, Ni. In addition, to visualize the magnetic moment distribution of TMTl2 S systems, the spin density distributions are plotted in Fig. 3. The typical character of the magnetic moment contribution is that the magnetic moments are mainly localized on the doped TMs for almost all the systems, and the magnetic moments of adjacent S and Tl atoms are relatively small, which is similar to the above discussions in Table 1. The distributions of the magnetic moment are observed in other systems too, such as TM-MoS2 system [38], TM-phosphorene [44], TM-arsenene [45]. To further elaborate the mechanisms of the magnetic properties of TM-Tl2 S systems, we plot the total density of states (TDOS) and projected density of states (PDOS) of the TM atoms and its nearest S, Tl atoms in Fig. 4. Numerical results show that the spin-up and spin-down TDOS of monolayer Tl2 S and the monolayer Tl2 S with VTl are symmetric, which indicates that the monolayer Tl2 S system and the monolayer Tl2 S with VTl possess the properties of nonmagnetic ground states (see Fig. 4(a) and (b)). It can be seen from Fig. 4(a) that for monolayer Tl2 S, the valence band maximum (VBM) is dominated by the hybridization of pz orbitals of S and Tl atoms, while the conduction band minimum (CBM) is mainly contributed by the degenerate px , py orbitals of Tl atom. For the monolayer Tl2 S with VTl , the pz orbitals of S and Tl atoms hybridize at Fermi level, inducing the metallic character. Meanwhile, the CBM contributed by the degenerate px , py orbitals of Tl atom moves up. For Cu and Zn-Tl2 S systems, the spin-up and spin-down states of TDOS also are symmetric, which indicates that Cu and Zn substituting Tl atom can induce hardly magnetic moments. This is also consistent with the calculated magnetic moments being zero in Table 1. The hybridization between the degenerate dx2 -y2 and dxy orbitals
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Table 1 The TM transfer electronic charges obtained using Bader charge analysis, total magnetic moment (Mtot ), magnetic moment of the TM impurity (MTM ) and the nearest S and Tl atom (MS and MTl ) for a single TM substitutional doped Tl2 S systems obtained in the PBE + U method. The values in parentheses are obtained in the PBE method. TM-Tl2S
Q(e) (PBE/PBE + U)
Mtot (B ) (PBE/PBE + U)
MTM (B ) (PBE/PBE + U)
MS (B ) (PBE/PBE + U)
MTl (B ) (PBE/PBE + U)
Egap (eV) (PBE/PBE + U)
Sc Ti V Cr Mn Fe Co Ni Cu Zn
−1.52(−1.43) −1.19(−1.17) −1.16(−1.03) −0.77(−0.83) −1.04(−0.85) −0.91(−0.73) −0.44(−0.45) −0.35(−0.38) −0.38 −0.79
0.539(0.468) 1.915(1.515) 2.592(2.568) 4.25(3.990) 4.479(3.959) 3.688 (3.241) 1.964(1.910) 0.974(0.893) 0 0
0.443(0.338) 1.838(1.475) 2.617(2.500) 4.212(3.866) 4.439(3.937) 3.544(3.054) 1.968(1.822) 0.970(0.763) 0 0
−0.006(−0.005) −0.035(−0.025) −0.024(−0.030) −0.029(−0.016) 0.008(0.019) 0.035(0.051) 0.003(0.033) 0.001(0.033) 0 0
0.014(0.016) 0.013(0.009) 0.001(0.011) 0.015(0.020) −0.003(−0.01) 0.003(−0.001) −0.004(−0.007) −0.002(−0.001) 0 0
0(0) 0(0) 0(0) 0.72(0.44) 0(0) 0 0.85(0.40) 0.98(0.36) 1.3 0
of Cu and the pz orbitals of S and Tl atoms devotes to VBM, while Cu d orbital dedicates hardly CBM in Cu-Tl2 S systems. In Zn-Tl2 S systems, the degenerate px , py orbitals of Tl atom moving down cross the Fermi level, leading to the metallic state. We can see from Fig. 4(e)–(m) that the hybridization of TM 3d orbitals and p orbitals of the nearest S, Tl atoms results in the splitting of the energy levels near the Fermi level in the spin-polarized systems, which are responsible for the magnetic moments. In addition, the magnetic moments mainly originate from different d orbitals given a detailed explanation below. For Sc-Tl2 S system, the magnetic moment of Sc
atom comes from Sc dz2 orbital entirely due to dz2 being localized asymmetrically. For Ti-Tl2 S system, it is clearly seen that the Ti dz2 and dx2 -y2 orbitals are asymmetrically localized at the Fermi level, showing two narrow peaks and overlapping fractionally with each other. Consequently, in the majority-spin channel, both of them are fractionally occupied, resulting in the appearance of the magnetic moments and metallicity. For V-Tl2 S system, the V dyz and V dxz orbitals are localized asymmetrically at −1.6 eV, inducing the magnetic moments. For Cr-Tl2 S system, the Cr dx2 -y2 and dxy orbitals mainly contribute to the magnetic moments near the Fermi level.
Fig. 4. PDOS for single TM doped Tl2 S systems.
N. Song et al. / Applied Surface Science 425 (2017) 393–399
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Fig. 5. Band structures for single TM substitutional doped Tl2 S systems.
For Mn-, Fe-, Co- and Ni- Tl2 S systems, complicated phenomenon occurs because TM atom has more than 5 electrons of 3d and some of the nonbonding orbitals are filled. For Mn-, Fe-, and Ni-Tl2 S systems, they share the same features that the 3d orbitals are localized at a relatively deeper energy level because they have partially occupied non-bonding 3d orbitals, which are dyz, dxy, dz2 of the Mn atom, dz2 of the Fe atom and dxz, dyz of Ni atom respectively, leading to the magnetic moments. For Co-Tl2 S system, the Co-3d orbitals are split into e1 (dz2 ) orbital and four-fold degenerate e2 (dxy, dxz, dyz, dx2 -y2 ) orbital near the Fermi level, therefore e1 orbital and four-fold degenerate e2 are mainly responsible for the magnetic moment. From the above analysis of TDOS and PDOS, it is clearly seen that the magnetic moments are well localized at the TM atom site, which is consistent with the spin density distribution plotted. It is also significant further to analyze the band structures of various considered systems. As shown in Fig. 5(a), the monolayer Tl2 S is semiconductor with a direct band gap of 1.37 eV, which is larger than that of the Tl2 S bulk (0.8 eV) [31]. However, the monolayer Tl2 S with the VTl becomes to the metal, due to the Tl defect inducing the VBM moving up. It can be seen that the band structures depend highly on the specific impurity atom for TM-Tl2 S systems in Fig. 5. For Cu-Tl2 S system, a direct band gap of 1.30 eV is found, which is comparable to the band gap 1.37 eV of Tl2 S. Hence Cu-Tl2 S system still preserve the nonmagnetic semiconductor character. In addition, the nonmagnetic states are found in Zn-Tl2 S system and the CBM crosses the Fermi level at . Consequently, Zn-Tl2 S system becomes to nonmagnetic metal. For Sc-, Ti-, V-, Mn-, Fe-Tl2 S systems, due to the CBM and the VBM moving down compared with the monolayer Tl2 S, both the spin up and spin down bands cross the Fermi level at , which indicates that the metallic states are achieved. More importantly, for Cr-, Co-, Ni- Tl2 S systems, the
band gaps with spin polarization are found (see Fig. 5(i), (l), (m)), which indicates the properties of DMS. The analysis from the band structures are consistent with above results from the PDOS. It is worth mentioning that the band gaps obtained from PBE + U are larger than those obtained from PBE in Cr-, Co-, Ni- Tl2 S systems (see Table 1). This indicates that the Hubbard U in Cr-, Co-, Ni- Tl2 S systems plays a big part in increasing the band gaps, which is also found in Ti-doped blue phosphorene [30]. In order to determine the magnetic interactions between two same TM impurity atoms in TM-Tl2 S systems, we substitute two Tl atoms with same TM atoms in a 4 × 4 supercell with a doping concentration of about 4.2%. Another TM dopant atom substitutes Tl atom marked by a blue dashed circle as shown in Fig. 1(a). Since both Zn- and Cu-Tl2 S systems display nonmagnetic ground state for single TM substituting doped Tl2 S, we exclude these two systems. For the sake of finding the magnetic ground states, we consider ferromagnetic (FM) and antiferromagnetic (AFM) spin configurations. The total energies of FM and AFM configurations, the total energy difference [E = EFM − EAFM ], the total magnetic moment, the binding energy using the PBE + U method are presented in Table 2. Numerical results show that the binding energies are larger than the values in the single TM substitutional doped Tl2 S systems, except for Sc which slightly deceases from 5.24 eV (in the single Sc doped Tl2 S system) to 4.69 eV. This indicates that two same TM atoms doped Tl2 S are energetically favorable except for Sc. In addition, we can see that FM and AFM coupling between two TMs depends on the specific TM atoms. For the Sc-, V-, MnTl2 S systems, they exhibit the characteristic of AFM due to the total energy difference being positive. While Ti-Tl2 S system has FM ground state. For the Cr-, Fe-, Co-, Ni-Tl2 S systems, the FM and AFM configurations are almost degenerated indicating that they exhibit paramagnetic behaviors. The spin density of two TM doped
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Fig. 6. Spin density (up-down) with an isovalue of 0.0006 e/Å3 for two TM atoms doped Tl2 S systems: (a) ScAFM -Tl2 S, (b) TiFM -Tl2 S, (c)VAFM -Tl2 S, (d) CrAFM -Tl2 S, (e) (d) CrFM -Tl2 S, (f) MnAFM -Tl2 S, (g) FeAFM -Tl2 S, (h) FeFM -Tl2 S, (i) CoAFM -Tl2 S, (j) CoFM -Tl2 S, (k) NiAFM -Tl2 S, (l) NiFM -Tl2 S. Yellow and blue indicate the positive and negative spin densities, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 2 Total energies of FM and AFM states, the energy differences E = EFM − EAFM , the binding energies and total magnetic moment (Mtotal ) for the two TM atoms doped Tl2 S systems. The values are obtained in the PBE + U method.
Sc Ti V Cr Mn Fe Co Ni
EFM (eV)
EAFM (meV)
EFM-AFM (meV)
Eb (eV)
Mtot (B ) (PBE/PBE + U)
−163.1906 −161.6426 −164.26475 −166.30011 −166.15534 −162.51444 −160.78516 −156.78897
−163.19747 −161.63291 −164.29866 −166.30071 −166.16393 −162.51468 −160.78534 −156.78808
6.78 −9.69 33.91 0.6 8.59 0.24 0.18 −0.9
4.69 4.43 6.10 7.35 7.54 5.81 5.01 3.07
−0.229 3.19 0.08 0(8.50) 0.23 0.661(3.83) 0(3.93) 0.001(1.95)
show that the Hubbard U have an important effect on the charge transfers, magnetic moments and band gaps. The magnetic coupling between magnetic moments induced by TM varies with the specific TM atoms. For instance, the magnetic coupling is found to be AFM in Sc-, V-, Mn-Tl2 S systems. On the contrary, the magnetic coupling is FM in Ti-Tl2 S system. Interestingly, the Cr-, Fe-, Co-, NiTl2 S systems manifest paramagnetic. In a word, the electronic and magnetic properties of Tl2 S can be modulated by doping different TM atoms. We expect the conclusions obtained from Tl2 S may be valid for group 13 chalcogenides. Investigation of further materials from group 13 chalcogenides is promising to find new 2D materials applied to nanoelectronic devices and spintronics. Acknowledgements
Tl2 S using the PBE + U method are presented in Fig. 6. The yellow color represents spin up, while the blue color represents spin down densities. Like in the single TM doped Tl2 S systems, the magnetic moments are mainly from the TM atoms, while Tl and S atoms show negligible spin polarization. It can be seen from Fig. 6 that the Sc, V, Mn have AFM coupling, while Ti has FM coupling, which are agree with the results in Table 2. For the double Cr-, Fe-, Co-, Ni- atoms doped Tl2 S systems, we display both the FM and AFM configurations because they are degenerated. It is clearly displayed that the spectral shapes of spin density are the same as found in the single substitutional doped Tl2 S systems, which suggests the same d orbitals are in charge of the magnetic moments. 4. Conclusion In conclusion, the structural, electronic, and magnetic properties of various TM atoms doped Tl2 S have been systematically studied by using first-principles DFT calculations. The results show that all the TM atoms are strongly bonded to VTl , which mainly results from the hybridization between the d orbitals of the TM and p orbitals of its nearest S, Tl atoms. Among the single TM doped Tl2 S systems, we found no spin polarized ground states in the Cu- and Zn-Tl2 S systems. In other systems, the spin polarized ground states are found. The TM-Tl2 S systems have fractional magnetic moments. The magnetic moment of each TM atom originates mainly from different d orbitals in spin polarized TM-Tl2 S systems. In addition, the band structures are strongly dependent on specific TM atom. The Sc-, Ti-, V-, Mn-, Fe- and Zn-Tl2 S systems show the metallic behavior. However, the Cu-Tl2 S system is still semiconductor with the direct gap as the monolayer Tl2 S. More importantly, the Cr-, Co, Ni-Tl2 S systems possess spin polarized semiconducting feature, although the band gaps vary as the TM atoms change, which suggests that the monolayer Tl2 S will be a new DMS. Research findings
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