- Email: [email protected]
Ab initio study of electronic and magnetic properties in TM-doped 2D silicon carbide
Physica E 85 (2017) 280–284
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Ab initio study of electronic and magnetic properties in TM-doped 2D silicon carbide
crossmark
⁎
M. Luoa, , Y.H. Shenb, T.L. Yinb,c a b c
Department of Electronic Engineering, Shang Hai Jian Qiao University, Shanghai 201306, PR China Key Laboratory of Polar Materials and Devices, East China Normal University, Shanghai 200241, PR China School of Electronics and Information, Nantong University, Nantong 226019, PR China
A R T I C L E I N F O
A BS T RAC T
Keywords: SiC Magnetic properties First-principles calculation Antiferromagnetic Haldane-Anderson model
The magnetic properties of SiC monolayer with different TM atoms and substitutional sites are investigated using first-principles method. Magnetism is observed for all the TM dopants. The magnetic moments and binding energies are quite different between Si (TMSi) and C (TMC) sites. Dependent to the larger magnetic moments and binding energy, we also investigate the interaction between two Mn atoms in the TMSi system. The results show that the ferromagnetic states are originated by the p–d hybridization mechanism between Mn and its neighboring C atoms. Moreover, the antiferromagnetic coupling is observed with increasing Mn-Mn distance, which can be explained by two-impurity Haldane-Anderson model using quantum Monte Carlo method.
1. Introduction Silicon carbide (SiC) has attracted much interest due to its corrosion resistance, large band gap, high mechanical strength, low density, high hardness, high thermal conductivity and low thermal expansion coefficient [1–5]. Similar to graphene, the SiC monolayer (2D-SiC) with a honeycomb structure could be energetically stable [6,7] and SiC Monolayer exhibits a large direct band gap [8]. Several theoretical studies investigated the structure and electronic properties of SiC nano scales [9,10]. Due to its wide band gap (3.2 eV), SiC has potential applications in electronics and optics. Recently a large number of researches have given special attention to the properties of metal doped 2D materials [11–15] and high catalytic activity has been verified. However, few theoretical studies have been focused on the magnetic properties of 3d transition metal (TM) doped SiC monolayers [16,17]. In order to find its potential applications, we study the TM doped SiC monolayer by using first-principles calculations. In this work, the magnetic properties of SiC monolayer with different TM atoms and substitutional sites are investigated using first-principles method. Magnetism is observed for all the TM dopants, but the magnetic behavior is quite different between Si and C substituted systems, shown TMSi and TMC, respectively. Among all the TMSi monolayers, the MnSi system has large magnetic moments and also shows a most stable structure. Therefore, the interaction
⁎
Corresponding author. E-mail address: [email protected] (M. Luo).
http://dx.doi.org/10.1016/j.physe.2016.08.028 Received 25 July 2016; Received in revised form 25 August 2016; Accepted 29 August 2016 Available online 17 September 2016 1386-9477/ © 2016 Elsevier B.V. All rights reserved.
between two Mn atoms in the MnSi system is investigated. The results show the p–d hybridization mechanism between the Mn and its neighboring C atoms results in its ferromagnetic state. Moreover, the antiferromagnetic coupling is observed with increasing Mn-Mn distance which can be explained by two-impurity Haldane-Anderson model using quantum Monte Carlo method. 2. Method Our calculations are performed first-principles method based on density functional theory (DFT) within the generalized gradient approximations (GGA-PBE) [18] as implemented in the VASP package [19]. The projector augmented-wave (PAW) [20] pseudo potential method is used and the cut off energy is 450 eV. The 4×4×2 k-point grids were used in both 5×5×1 and 10×5×1 supercells. The lattice parameter and bond length of SiC monolayer is 3.094 and 1.786 Å [21], respectively. The separation between two layers is 20 Å. All the calculations are self-consistent and the total energy convergence criterion is set at the value of 10−5 eV. 3. Result and discussions 3.1. Electronic structure and magnetism of TM doped SiC monolayer Firstly, we calculate the equilibrium structure of pure SiC mono-
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Fig. 1. Schematic structure showing (a) pristine SiC monolayer (side view) and TM-substituted SiC monolayer (top view); (b) the hexagonal structure viewed along the c axis, and the configurations in two Mn atoms-doped SiC monolayer of 10×5×1 supercell; (c) band structure of pristine SiC monolayer.
systems. Because of this, we come to investigate the interaction between two-Mn-doped system of 10×5×1 supercell, and several possible configurations of Mn dopants are discussed as shown in Fig. 1(b). We use i to mark the dopant Mn (0, i) and we position one Mn dopant atom in a fixed site [denoted 0 in Fig. 1(b)] and the other Mn dopant substitutes a Si atom at one of the marked positions i=1–5. As shown in Table 2, it is found that the ferromagnetic coupling depends on Mn-Mn distance. In addition, the stability of FM states is determined by the total energy difference for the above possible configurations. The total energy difference is estimated asΔE = EAFM − EFM , where EFM and EAFM are the total energies of two Mn atoms aligned ferromagnetically (FM) and antiferromagnetically (AFM), respectively. For the nearest Mn-Mn distance, as shown in Table 2, ΔE is 150 meV which indicates the interaction between two Mn atoms is FM. However, the situation changes with increasing MnMn distance; the FM state disappears and the AFM state appears. For the cases of (0, 2) and (0, 3) in the 10×5×1 supercell, ΔE are about −41 and −12 meV, respectively. Moreover, the (0, 1) case has the lowest total energy, which indicates that the nearest two-Mn-doped SiC monolayer should be the most stable candidates for the 2D silicon carbide.. In order to understand the FM interaction between the nearest two Mn dopants, the TDOS and PDOS are shown in Fig. 4. From Fig. 4(a)– (b), the d state of Mn overlaps with that of p state of the C atom. In the minority spin channel, the p state of the connecting C atoms contributes significantly to the unoccupied states, which indicates a strong hybridization between Mn and its neighboring C atoms. The polarized spins in C p states couple with the d localized spins of Mn, showing a pd like interaction chain, which results in an indirect FM interaction between Mn and C atoms. Because of the p-d interaction, the minority spin states are lifted upward together with the downward shift of the majority spin states, which lower the total energy of the system [23]. Thus, the p-d hybridization is responsible for FM in Mn-doped SiC monolayer.. For the nearest two Mn dopants, the calculated magnetic moment is 6.00 μB. It is hypothesized that the different local distortion may result in different spin distributions of the local moment. As illustrated in Fig. 5, the main spin densities are localized around two Mn dopants. The interaction between a Mn dopant and its neighboring C atoms is
layer, which is shown in Fig. 1. Fig. 1(a) shows the schematic structure of TM-doped SiC monolayer of 5×5×1 supercell (50 atoms). The band structure of pure SiC monolayer is shown in Fig. 1(c), it has π and π* bands around K point at the Fermi level symmetrically and has a direct band gap of 2.52 eV, which agree with the previous studies [10,22]. These results verified the reliability of our methods.. Next, we study the magnetic properties of several TM (Co, Cu, Mn, Fe, and Ni) atoms substituted SiC monolayers. There are possible two TM substitutional sites in the SiC monolayer. We have shown the TMSi and TMC for the Si and C site substituted by TM atoms in Fig. 1(b), respectively. The total magnetic moments (μtotal), binding energy and bonding length are shown in Table 1. Here, the binding energy is estimated as Eb=(Epure+ETM)−ET, where Epure and ET is the total energy of SiC monolayer with one vacancy and with a TM dopant, respectively; ETM is the energy of a TM atom. From our calculations, the values of μtotal are in the range of 0.299–1.571 and 1.963–2.999 μB for TMC and TMSi cases, respectively. The results indicate the stronger magnetic coupling in the TMSi systems. Also, we analyze the electronic properties of TMSi- and TMC-doped SiC monolayer, respectively. The total density of states (DOS) and projected density of states (PDOS) for TM-doped SiC monolayer are shown in Fig. 2. From Fig. 2(a) and (j), the spin-up and spin-down density in all the TM-doped systems are nonmagnetic and that is why the systems are nonmagnetic. For example, in the Mn-doped system, we see in Fig. 2(d) and (i), there are obvious spin spitting around the Fermi level and the symmetry of spin-up and spin-down breaks and the system exhibits magnetic behavior. We also see the hybridization between Mn and C atoms is stronger than that of Mn-Si, and then the magnetic moment of the MnSi-doped system is larger.. 3.2. Magnetic coupling in Mn-substituted SiC monolayer In Fig. 3, we have depicted the Eb variations of both TMC and TMSi cases. As it is shown the values of Eb in TMSi structures are entirely higher than those of the TMC structures, which indicate the TMSi systems are more stable. Although the binding energy difference of CoSi, CuSi, FeSi, MnSi, and NiSi structures is small. The MnSi system has the biggest value. Hence, we deduce that the stable structure is an essential property of MnSi system which is an advantage over other 281
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Table 1 Binding energy (Eb), total magnetic moment (μtotal) and TM-C and TM-Si bond lengths in the TM-substituted SiC monolayer of 5×5×1 supercell. Structure
Eb (eV)
μtotal (μB)
lTM-Si (Å)
Structure
Eb (eV)
μtotal (μB)
lTM-C (Å)
CoC CuC MnC FeC NiC
3.95 3.46 4.52 4.27 3.53
0.566 0.359 1.052 1.571 0.299
2.044 2.070 2.086 2.058 2.039
CoSi CuSi MnSi FeSi NiSi
4.23 3.87 4.98 4.45 4.00
2.138 1.963 2.121 2.999 2.451
1.794 1.827 1.806 1.791 1.885
Fig. 2. Spin-polarized DOS and PDOS of TM-substituted SiC monolayer of 5×5×1 supercell (TM denotes Co–Ni). The Fermi level is marked by blue dashed line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 2 Optimized Mn-Mn distance (dMn-Mn), total magnetic moments (Mtot), total energies (Etot), energy differences between AFM and FM (ΔE) and the configurations of Mn atoms are as shown in Fig. 1(b). Structure
Configuration
dMn-Mn (Å)
Mtot (μB)
Etot (eV)
ΔE (eV)
Si48Mn2C50
1 2 3 4 5
3.087 6.290 9.372 12.457 15.542
6.00 – – – –
679.421 679.113 679.096 678.523 678.045
0.150 −0.041 −0.012 −0.002 −0.002
It is noteworthy that a much larger Mn-Mn distance is considered in the 10×5×1 supercell. For the cases of (0, 4) and (0, 5) shown in Fig. 1(b), the total energy difference ΔE is about −2 meV. The results indicate that the AFM interaction between two Mn atoms is reduced seriously with increasing Mn-Mn distance. Such exotic phenomena has been observed before [24,25]. Ruderman-Kittel-Kasuya-Yosida (RKKY) theory has been used to discuss magnetic impurities in ordinary metals successfully, which is a carrier mediated indirect coupling due to the Friedel oscillations of the polarized carriers around the impurities. However, quite different behaviors were experimentally
Fig. 3. The binding energy of the TMSi and TMC structure in the 5×5×1 supercell.
ferromagnetically, which indicates a p character of the spin-polarized states of C atoms. Therefore, the total magnetic moment (6.00 μB) mainly arises from the spin-up d states of two Mn atoms (5.03 μB), and the spin-up p states of their nearest-neighboring C atoms (0.84 μB).. 282
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Fig. 4. (a) DOS for two-Mn-doped SiC monolayer in the 10×5×1 supercell, and (b) its nearest five C atoms, respectively.
Fig. 5. Calculated spin density distribution in Mn-doped SiC monolayer of 10×5×1 supercell. Yellow and cyan isosurfaces represent positive and negative spin densities (0.008 e/Å3), respectively.
observed when magnetic impurities are doped into a semiconductor, the Haldane–Anderson impurity model had been introduced to study TM impurities in semiconductors [26] and quantum Monte Carlo (QMC) calculations [27] have supported this picture for the generation of FM correlations between magnetic impurities in semiconductors. Therefore, we studied the spin interaction in the (Mn, Si)C monolayer using the same model. The Haldane-Anderson model is estimated as
H=
∑
(εkα − μ) ck+ασ c kασ +
k, α, σ
∑
+ Vkm ck+ασ dmσ + Vmk dmσ c kασ
k, m, α, σ
+ + (Ed − μ) ∑ d mσ d mσ + U ∑ n md ↑ d md ↓ m, σ
m
(1)
where ckασ and d mσ is the Annihilation Operator of the valence electron and the local electron, respectively. α presents the valence band α = c D or conduction band α = υ and their formations are εkc = 2 (k / k 0 )2 + Eg D
and εkυ = − 2 (k / k 0 )2 , respectively. Vkm = Veik ⋅ R , k is wave vector and R is the distance between the two TM (Ni) atoms. k 0 is estimated as the wave vector of half occupied valence band and takes as 0 ≤ k 0 ≤ 2 . The strength of hybridization is taken as Δ = πρ0 V 2 . ρ = k 03 /(2πD ) is taken as the density of states in half-filled valence band. D = 12 ,Eg = 2.53,Ed = μ − U /2 and μ is the chemical potential. In order
Fig. 6. (a) Magnetic correlation function vs k0R at Δ/U=2, μ=0.1, β=16. (b) The total energy difference (ΔE) between the AFM and FM vs Mn-Mn distance.
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Acknowledgments
to induce the local magnetic moment of dopants, the coefficients of electron correlation are taken as U = 2 and β = 1/ kB T , respectively. According to calculated results of QMC, we get the spin correlation 1 − exp(−βJ ) function as σ1z σ2z = 3 + exp(−βJ12 ) , where the σiz = ni ↑ − ni ↓ . J12 is the 12 integral of Heisenberg function. The time step of Mastsubara is taken z z as Δτ = 0.5. σ1 σ2 can be read directly from the QMC. Hence, we simulate the magnetic correlation function to the k 0 R , as shown in Fig. 6. From Fig. 6(a), we can see that the magnetic coupling between two TM (Mn) atoms is localized in a small range and switched from FM to AFM with increasing Mn-Mn distance. Then the AFM coupling reduces exponentially which indicates the FM states would never appear again. The simulation describes the trend between the calculated energy difference (ΔE) and the Mn-Mn distance (R) shown in Fig. 6(b) reasonably. In the present model, the FM and AFM coupling between two TM (Mn) dopants are influenced by many factors such as Δ/U, μ, T and β. As we know, the long range FM interaction between the TM dopants while the hybridization is weak which can be well explained by the Zener-RKKY theory [28]. However, the oscillation of RKKY has been depressed by the strong p-d hybridization between the Mn atoms and C atoms and then a long range AFM interaction is observed. More detailed studies need to be done in the future..
The work is supported by the Shanghai Committee of Science and Technology, China (Grant no. ZHT. K1507). We also thank the Supercomputer Center of ECNU for using the Dawn 5000A supercomputer. References [1] P.A. Ivanov, V.E. Chelnokov, Semicond. Sci. Technol. 7 (1992) 863. [2] T. Narushima, T. Goto, T. Hirai, Y. Iguchi, Mater. Trans. JIM 38 (1997) 821. [3] S.Z. Wang, L.Y. Xu, B.Y. Shu, B. Xiao, J.Y. Zhuang, E.W. Shi, J. Inorg. Mater. 14 (1999) 527. [4] J.B. Casady, R.W. Johnson, Solid State Electron. 39 (10) (1996) 1409. [5] K. Watari, J. Ceram. Soc. Jpn. 109 (2001) S7. [6] F. Claeyssens, C.L. Freeman, N.L. Allan, Y. Sun, M.N.R. Ashfolda, J.H. Harding, J. Mater. Chem. 15 (2015) 139. [7] C.L. Freeman, F. Claeyssens, N.L. Allan, Phys. Rev. Lett. 96 (2006) 066102. [8] H.C. Hsueh, G.Y. Guo, S.G. Louie, Phys. Rev. B 84 (2011) 085404. [9] P. Lou, J.Y. Lee, J. Phys. Chem. C 113 (2009) 21213. [10] E. Bekaroglu, M. Topsakal, S. Cahangirov, S. Ciraci, Phys. Rev. B 81 (2010) 075433. [11] Y.C. Cheng, Z.Y. Zhu, W.B. Mi, Z.B. Guo, U. Schwingenschl̈ogl, Phys. Rev. B 87 (2013) 100401. [12] V. Krasheninnikov, P.O. Lehtinen, A.S. Foster, P. Pyykkö, R.M. Nieminen, Phys. Rev. Lett. 102 (2009) 126807. [13] B. Huang, H. Xiang, J. Yu, S.H. Wei, Phys. Rev. Lett. 108 (2012) 206802. [14] W.S. Yun, S. Han, S.C. Hong, I.G. Kim, J. Lee, Phys. Rev. B 85 (2012) 033305. [15] M. Chhowalla, H.S. Shin, G. Eda, L.J. Li, K.P. Loh, H. Zhang, Nat. Chem. 5 (2013) 263. [16] E. Bekaroglu, M. Topsakal, S. Cahagirov, S. Ciraci, Phys. Rev. B 81 (2010) 075433. [17] M.B. Javan, J. Magn. Magn. Mater. 401 (2016) 656. [18] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [19] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169. [20] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [21] S.S. Lin, J. Phys. Chem. C 116 (2012) 3951. [22] X. Lin, S. Lin, Y. Xu, A.A. Hakro, T. Hasan, B. Zhang, B. Yu, J. Luo, E. Li, H. Chen, J. Mater. Chem. C 1 (2013) 2131. [23] C. Zener, Phys. Rev. 81 (1951) 440. [24] M. Luo, Z. Tang, J. Zheng, Z.Q. Zhu, J.H. Chu, J. Appl. Phys. 108 (2010) 053703. [25] J.H. Chung, S.J. Chung, Sanghoon Lee, B.J. Kirby, J.A. Borchers, Y.J. Cho, X. Liu, J.K. Furdyna, Phys. Rev. Lett. 101 (2008) 237202. [26] F.D.M. Haldane, P.W. Anderson, Phys. Rev. B 13 (1976) 2553. [27] N. Bulut, K. Tanikawa, S. Takahashi, S. Maekawa, Phys. Rev. B 76 (2007) 045220. [28] J. Kanamori, K. Terakura, J. Phys. Soc. Jpn. 70 (2001) 1433.
4. Conclusion We used the density function theory to study the magnetic properties of SiC monolayers with series TM (Co, Cu, Mn, Fe, and Ni) atoms. The substitutions of Si and C sites of SiC sheet are discussed, which are shown TMSi and TMC, respectively. The TMSi and TMC systems show different magnetic behaviors for all the TM dopants. The magnetic moments and binding energies are larger in the TMSi systems. Especially, the MnSi system is the most stable structure among all the doped systems. Then, we investigate the interaction between two Mn atoms in the MnSi system. The results show that the ferromagnetic states originated by the p–d hybridization mechanism between the Mn and its neighboring C atoms. Moreover, the antiferromagnetic state is observed with increasing Mn-Mn distance which can be explained by two-impurity Haldane-Anderson model using quantum Monte Carlo method.
284
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Ab initio study of electronic and magnetic properties in TM-doped 2D silicon carbide
crossmark
⁎
M. Luoa, , Y.H. Shenb, T.L. Yinb,c a b c
Department of Electronic Engineering, Shang Hai Jian Qiao University, Shanghai 201306, PR China Key Laboratory of Polar Materials and Devices, East China Normal University, Shanghai 200241, PR China School of Electronics and Information, Nantong University, Nantong 226019, PR China
A R T I C L E I N F O
A BS T RAC T
Keywords: SiC Magnetic properties First-principles calculation Antiferromagnetic Haldane-Anderson model
The magnetic properties of SiC monolayer with different TM atoms and substitutional sites are investigated using first-principles method. Magnetism is observed for all the TM dopants. The magnetic moments and binding energies are quite different between Si (TMSi) and C (TMC) sites. Dependent to the larger magnetic moments and binding energy, we also investigate the interaction between two Mn atoms in the TMSi system. The results show that the ferromagnetic states are originated by the p–d hybridization mechanism between Mn and its neighboring C atoms. Moreover, the antiferromagnetic coupling is observed with increasing Mn-Mn distance, which can be explained by two-impurity Haldane-Anderson model using quantum Monte Carlo method.
1. Introduction Silicon carbide (SiC) has attracted much interest due to its corrosion resistance, large band gap, high mechanical strength, low density, high hardness, high thermal conductivity and low thermal expansion coefficient [1–5]. Similar to graphene, the SiC monolayer (2D-SiC) with a honeycomb structure could be energetically stable [6,7] and SiC Monolayer exhibits a large direct band gap [8]. Several theoretical studies investigated the structure and electronic properties of SiC nano scales [9,10]. Due to its wide band gap (3.2 eV), SiC has potential applications in electronics and optics. Recently a large number of researches have given special attention to the properties of metal doped 2D materials [11–15] and high catalytic activity has been verified. However, few theoretical studies have been focused on the magnetic properties of 3d transition metal (TM) doped SiC monolayers [16,17]. In order to find its potential applications, we study the TM doped SiC monolayer by using first-principles calculations. In this work, the magnetic properties of SiC monolayer with different TM atoms and substitutional sites are investigated using first-principles method. Magnetism is observed for all the TM dopants, but the magnetic behavior is quite different between Si and C substituted systems, shown TMSi and TMC, respectively. Among all the TMSi monolayers, the MnSi system has large magnetic moments and also shows a most stable structure. Therefore, the interaction
⁎
Corresponding author. E-mail address: [email protected] (M. Luo).
http://dx.doi.org/10.1016/j.physe.2016.08.028 Received 25 July 2016; Received in revised form 25 August 2016; Accepted 29 August 2016 Available online 17 September 2016 1386-9477/ © 2016 Elsevier B.V. All rights reserved.
between two Mn atoms in the MnSi system is investigated. The results show the p–d hybridization mechanism between the Mn and its neighboring C atoms results in its ferromagnetic state. Moreover, the antiferromagnetic coupling is observed with increasing Mn-Mn distance which can be explained by two-impurity Haldane-Anderson model using quantum Monte Carlo method. 2. Method Our calculations are performed first-principles method based on density functional theory (DFT) within the generalized gradient approximations (GGA-PBE) [18] as implemented in the VASP package [19]. The projector augmented-wave (PAW) [20] pseudo potential method is used and the cut off energy is 450 eV. The 4×4×2 k-point grids were used in both 5×5×1 and 10×5×1 supercells. The lattice parameter and bond length of SiC monolayer is 3.094 and 1.786 Å [21], respectively. The separation between two layers is 20 Å. All the calculations are self-consistent and the total energy convergence criterion is set at the value of 10−5 eV. 3. Result and discussions 3.1. Electronic structure and magnetism of TM doped SiC monolayer Firstly, we calculate the equilibrium structure of pure SiC mono-
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Fig. 1. Schematic structure showing (a) pristine SiC monolayer (side view) and TM-substituted SiC monolayer (top view); (b) the hexagonal structure viewed along the c axis, and the configurations in two Mn atoms-doped SiC monolayer of 10×5×1 supercell; (c) band structure of pristine SiC monolayer.
systems. Because of this, we come to investigate the interaction between two-Mn-doped system of 10×5×1 supercell, and several possible configurations of Mn dopants are discussed as shown in Fig. 1(b). We use i to mark the dopant Mn (0, i) and we position one Mn dopant atom in a fixed site [denoted 0 in Fig. 1(b)] and the other Mn dopant substitutes a Si atom at one of the marked positions i=1–5. As shown in Table 2, it is found that the ferromagnetic coupling depends on Mn-Mn distance. In addition, the stability of FM states is determined by the total energy difference for the above possible configurations. The total energy difference is estimated asΔE = EAFM − EFM , where EFM and EAFM are the total energies of two Mn atoms aligned ferromagnetically (FM) and antiferromagnetically (AFM), respectively. For the nearest Mn-Mn distance, as shown in Table 2, ΔE is 150 meV which indicates the interaction between two Mn atoms is FM. However, the situation changes with increasing MnMn distance; the FM state disappears and the AFM state appears. For the cases of (0, 2) and (0, 3) in the 10×5×1 supercell, ΔE are about −41 and −12 meV, respectively. Moreover, the (0, 1) case has the lowest total energy, which indicates that the nearest two-Mn-doped SiC monolayer should be the most stable candidates for the 2D silicon carbide.. In order to understand the FM interaction between the nearest two Mn dopants, the TDOS and PDOS are shown in Fig. 4. From Fig. 4(a)– (b), the d state of Mn overlaps with that of p state of the C atom. In the minority spin channel, the p state of the connecting C atoms contributes significantly to the unoccupied states, which indicates a strong hybridization between Mn and its neighboring C atoms. The polarized spins in C p states couple with the d localized spins of Mn, showing a pd like interaction chain, which results in an indirect FM interaction between Mn and C atoms. Because of the p-d interaction, the minority spin states are lifted upward together with the downward shift of the majority spin states, which lower the total energy of the system [23]. Thus, the p-d hybridization is responsible for FM in Mn-doped SiC monolayer.. For the nearest two Mn dopants, the calculated magnetic moment is 6.00 μB. It is hypothesized that the different local distortion may result in different spin distributions of the local moment. As illustrated in Fig. 5, the main spin densities are localized around two Mn dopants. The interaction between a Mn dopant and its neighboring C atoms is
layer, which is shown in Fig. 1. Fig. 1(a) shows the schematic structure of TM-doped SiC monolayer of 5×5×1 supercell (50 atoms). The band structure of pure SiC monolayer is shown in Fig. 1(c), it has π and π* bands around K point at the Fermi level symmetrically and has a direct band gap of 2.52 eV, which agree with the previous studies [10,22]. These results verified the reliability of our methods.. Next, we study the magnetic properties of several TM (Co, Cu, Mn, Fe, and Ni) atoms substituted SiC monolayers. There are possible two TM substitutional sites in the SiC monolayer. We have shown the TMSi and TMC for the Si and C site substituted by TM atoms in Fig. 1(b), respectively. The total magnetic moments (μtotal), binding energy and bonding length are shown in Table 1. Here, the binding energy is estimated as Eb=(Epure+ETM)−ET, where Epure and ET is the total energy of SiC monolayer with one vacancy and with a TM dopant, respectively; ETM is the energy of a TM atom. From our calculations, the values of μtotal are in the range of 0.299–1.571 and 1.963–2.999 μB for TMC and TMSi cases, respectively. The results indicate the stronger magnetic coupling in the TMSi systems. Also, we analyze the electronic properties of TMSi- and TMC-doped SiC monolayer, respectively. The total density of states (DOS) and projected density of states (PDOS) for TM-doped SiC monolayer are shown in Fig. 2. From Fig. 2(a) and (j), the spin-up and spin-down density in all the TM-doped systems are nonmagnetic and that is why the systems are nonmagnetic. For example, in the Mn-doped system, we see in Fig. 2(d) and (i), there are obvious spin spitting around the Fermi level and the symmetry of spin-up and spin-down breaks and the system exhibits magnetic behavior. We also see the hybridization between Mn and C atoms is stronger than that of Mn-Si, and then the magnetic moment of the MnSi-doped system is larger.. 3.2. Magnetic coupling in Mn-substituted SiC monolayer In Fig. 3, we have depicted the Eb variations of both TMC and TMSi cases. As it is shown the values of Eb in TMSi structures are entirely higher than those of the TMC structures, which indicate the TMSi systems are more stable. Although the binding energy difference of CoSi, CuSi, FeSi, MnSi, and NiSi structures is small. The MnSi system has the biggest value. Hence, we deduce that the stable structure is an essential property of MnSi system which is an advantage over other 281
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Table 1 Binding energy (Eb), total magnetic moment (μtotal) and TM-C and TM-Si bond lengths in the TM-substituted SiC monolayer of 5×5×1 supercell. Structure
Eb (eV)
μtotal (μB)
lTM-Si (Å)
Structure
Eb (eV)
μtotal (μB)
lTM-C (Å)
CoC CuC MnC FeC NiC
3.95 3.46 4.52 4.27 3.53
0.566 0.359 1.052 1.571 0.299
2.044 2.070 2.086 2.058 2.039
CoSi CuSi MnSi FeSi NiSi
4.23 3.87 4.98 4.45 4.00
2.138 1.963 2.121 2.999 2.451
1.794 1.827 1.806 1.791 1.885
Fig. 2. Spin-polarized DOS and PDOS of TM-substituted SiC monolayer of 5×5×1 supercell (TM denotes Co–Ni). The Fermi level is marked by blue dashed line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 2 Optimized Mn-Mn distance (dMn-Mn), total magnetic moments (Mtot), total energies (Etot), energy differences between AFM and FM (ΔE) and the configurations of Mn atoms are as shown in Fig. 1(b). Structure
Configuration
dMn-Mn (Å)
Mtot (μB)
Etot (eV)
ΔE (eV)
Si48Mn2C50
1 2 3 4 5
3.087 6.290 9.372 12.457 15.542
6.00 – – – –
679.421 679.113 679.096 678.523 678.045
0.150 −0.041 −0.012 −0.002 −0.002
It is noteworthy that a much larger Mn-Mn distance is considered in the 10×5×1 supercell. For the cases of (0, 4) and (0, 5) shown in Fig. 1(b), the total energy difference ΔE is about −2 meV. The results indicate that the AFM interaction between two Mn atoms is reduced seriously with increasing Mn-Mn distance. Such exotic phenomena has been observed before [24,25]. Ruderman-Kittel-Kasuya-Yosida (RKKY) theory has been used to discuss magnetic impurities in ordinary metals successfully, which is a carrier mediated indirect coupling due to the Friedel oscillations of the polarized carriers around the impurities. However, quite different behaviors were experimentally
Fig. 3. The binding energy of the TMSi and TMC structure in the 5×5×1 supercell.
ferromagnetically, which indicates a p character of the spin-polarized states of C atoms. Therefore, the total magnetic moment (6.00 μB) mainly arises from the spin-up d states of two Mn atoms (5.03 μB), and the spin-up p states of their nearest-neighboring C atoms (0.84 μB).. 282
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Fig. 4. (a) DOS for two-Mn-doped SiC monolayer in the 10×5×1 supercell, and (b) its nearest five C atoms, respectively.
Fig. 5. Calculated spin density distribution in Mn-doped SiC monolayer of 10×5×1 supercell. Yellow and cyan isosurfaces represent positive and negative spin densities (0.008 e/Å3), respectively.
observed when magnetic impurities are doped into a semiconductor, the Haldane–Anderson impurity model had been introduced to study TM impurities in semiconductors [26] and quantum Monte Carlo (QMC) calculations [27] have supported this picture for the generation of FM correlations between magnetic impurities in semiconductors. Therefore, we studied the spin interaction in the (Mn, Si)C monolayer using the same model. The Haldane-Anderson model is estimated as
H=
∑
(εkα − μ) ck+ασ c kασ +
k, α, σ
∑
+ Vkm ck+ασ dmσ + Vmk dmσ c kασ
k, m, α, σ
+ + (Ed − μ) ∑ d mσ d mσ + U ∑ n md ↑ d md ↓ m, σ
m
(1)
where ckασ and d mσ is the Annihilation Operator of the valence electron and the local electron, respectively. α presents the valence band α = c D or conduction band α = υ and their formations are εkc = 2 (k / k 0 )2 + Eg D
and εkυ = − 2 (k / k 0 )2 , respectively. Vkm = Veik ⋅ R , k is wave vector and R is the distance between the two TM (Ni) atoms. k 0 is estimated as the wave vector of half occupied valence band and takes as 0 ≤ k 0 ≤ 2 . The strength of hybridization is taken as Δ = πρ0 V 2 . ρ = k 03 /(2πD ) is taken as the density of states in half-filled valence band. D = 12 ,Eg = 2.53,Ed = μ − U /2 and μ is the chemical potential. In order
Fig. 6. (a) Magnetic correlation function vs k0R at Δ/U=2, μ=0.1, β=16. (b) The total energy difference (ΔE) between the AFM and FM vs Mn-Mn distance.
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Acknowledgments
to induce the local magnetic moment of dopants, the coefficients of electron correlation are taken as U = 2 and β = 1/ kB T , respectively. According to calculated results of QMC, we get the spin correlation 1 − exp(−βJ ) function as σ1z σ2z = 3 + exp(−βJ12 ) , where the σiz = ni ↑ − ni ↓ . J12 is the 12 integral of Heisenberg function. The time step of Mastsubara is taken z z as Δτ = 0.5. σ1 σ2 can be read directly from the QMC. Hence, we simulate the magnetic correlation function to the k 0 R , as shown in Fig. 6. From Fig. 6(a), we can see that the magnetic coupling between two TM (Mn) atoms is localized in a small range and switched from FM to AFM with increasing Mn-Mn distance. Then the AFM coupling reduces exponentially which indicates the FM states would never appear again. The simulation describes the trend between the calculated energy difference (ΔE) and the Mn-Mn distance (R) shown in Fig. 6(b) reasonably. In the present model, the FM and AFM coupling between two TM (Mn) dopants are influenced by many factors such as Δ/U, μ, T and β. As we know, the long range FM interaction between the TM dopants while the hybridization is weak which can be well explained by the Zener-RKKY theory [28]. However, the oscillation of RKKY has been depressed by the strong p-d hybridization between the Mn atoms and C atoms and then a long range AFM interaction is observed. More detailed studies need to be done in the future..
The work is supported by the Shanghai Committee of Science and Technology, China (Grant no. ZHT. K1507). We also thank the Supercomputer Center of ECNU for using the Dawn 5000A supercomputer. References [1] P.A. Ivanov, V.E. Chelnokov, Semicond. Sci. Technol. 7 (1992) 863. [2] T. Narushima, T. Goto, T. Hirai, Y. Iguchi, Mater. Trans. JIM 38 (1997) 821. [3] S.Z. Wang, L.Y. Xu, B.Y. Shu, B. Xiao, J.Y. Zhuang, E.W. Shi, J. Inorg. Mater. 14 (1999) 527. [4] J.B. Casady, R.W. Johnson, Solid State Electron. 39 (10) (1996) 1409. [5] K. Watari, J. Ceram. Soc. Jpn. 109 (2001) S7. [6] F. Claeyssens, C.L. Freeman, N.L. Allan, Y. Sun, M.N.R. Ashfolda, J.H. Harding, J. Mater. Chem. 15 (2015) 139. [7] C.L. Freeman, F. Claeyssens, N.L. Allan, Phys. Rev. Lett. 96 (2006) 066102. [8] H.C. Hsueh, G.Y. Guo, S.G. Louie, Phys. Rev. B 84 (2011) 085404. [9] P. Lou, J.Y. Lee, J. Phys. Chem. C 113 (2009) 21213. [10] E. Bekaroglu, M. Topsakal, S. Cahangirov, S. Ciraci, Phys. Rev. B 81 (2010) 075433. [11] Y.C. Cheng, Z.Y. Zhu, W.B. Mi, Z.B. Guo, U. Schwingenschl̈ogl, Phys. Rev. B 87 (2013) 100401. [12] V. Krasheninnikov, P.O. Lehtinen, A.S. Foster, P. Pyykkö, R.M. Nieminen, Phys. Rev. Lett. 102 (2009) 126807. [13] B. Huang, H. Xiang, J. Yu, S.H. Wei, Phys. Rev. Lett. 108 (2012) 206802. [14] W.S. Yun, S. Han, S.C. Hong, I.G. Kim, J. Lee, Phys. Rev. B 85 (2012) 033305. [15] M. Chhowalla, H.S. Shin, G. Eda, L.J. Li, K.P. Loh, H. Zhang, Nat. Chem. 5 (2013) 263. [16] E. Bekaroglu, M. Topsakal, S. Cahagirov, S. Ciraci, Phys. Rev. B 81 (2010) 075433. [17] M.B. Javan, J. Magn. Magn. Mater. 401 (2016) 656. [18] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [19] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169. [20] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [21] S.S. Lin, J. Phys. Chem. C 116 (2012) 3951. [22] X. Lin, S. Lin, Y. Xu, A.A. Hakro, T. Hasan, B. Zhang, B. Yu, J. Luo, E. Li, H. Chen, J. Mater. Chem. C 1 (2013) 2131. [23] C. Zener, Phys. Rev. 81 (1951) 440. [24] M. Luo, Z. Tang, J. Zheng, Z.Q. Zhu, J.H. Chu, J. Appl. Phys. 108 (2010) 053703. [25] J.H. Chung, S.J. Chung, Sanghoon Lee, B.J. Kirby, J.A. Borchers, Y.J. Cho, X. Liu, J.K. Furdyna, Phys. Rev. Lett. 101 (2008) 237202. [26] F.D.M. Haldane, P.W. Anderson, Phys. Rev. B 13 (1976) 2553. [27] N. Bulut, K. Tanikawa, S. Takahashi, S. Maekawa, Phys. Rev. B 76 (2007) 045220. [28] J. Kanamori, K. Terakura, J. Phys. Soc. Jpn. 70 (2001) 1433.
4. Conclusion We used the density function theory to study the magnetic properties of SiC monolayers with series TM (Co, Cu, Mn, Fe, and Ni) atoms. The substitutions of Si and C sites of SiC sheet are discussed, which are shown TMSi and TMC, respectively. The TMSi and TMC systems show different magnetic behaviors for all the TM dopants. The magnetic moments and binding energies are larger in the TMSi systems. Especially, the MnSi system is the most stable structure among all the doped systems. Then, we investigate the interaction between two Mn atoms in the MnSi system. The results show that the ferromagnetic states originated by the p–d hybridization mechanism between the Mn and its neighboring C atoms. Moreover, the antiferromagnetic state is observed with increasing Mn-Mn distance which can be explained by two-impurity Haldane-Anderson model using quantum Monte Carlo method.
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