- Email: [email protected]
Electronic structure and spin properties study on 2D h-BN nanosheet with Ti or Fe doping
Solid State Communications 307 (2020) 113803
Contents lists available at ScienceDirect
Solid State Communications journal homepage: http://www.elsevier.com/locate/ssc
Electronic structure and spin properties study on 2D h-BN nanosheet with Ti or Fe doping Min Wang a, b, Fanfan Meng b, Denglu Hou a, *, Yilin Han c, Jie Ren d, Chenxiang Bai e, Baozhu Wang b, Tiege Zhou f a
Hebei Advanced Thin Films Laboratory, Institute of Physics, Hebei Normal University, Shijiazhuang, 050024, PR China School of Information Science and Engineering, Hebei University of Science and Technology, Shijiazhuang, 050018, PR China Department of Construction Engineering, Hebei Vocational College of Politics and Law, Shijiazhuang, 050061, PR China d School of Science, Hebei University of Science and Technology, Shijiazhuang, 050018, PR China e School of Microelectronics, Tianjin University, Tianjin, 300072, PR China f College of Electronic Information and Optical Engineering, Nankai University, Tianjin, 300071, PR China b c
A R T I C L E I N F O
A B S T R A C T
Communicated by A. Nikita
The electronic structure and spin properties of Titanium (Ti) or Iron (Fe) doped hexagonal boron nitride (h-BN) nanosheet have been studied by using ab initio study based on density functional theory (DFT). GGA þ U cal culations show that one Ti or Fe atom can introduce local magnetic states into the system. Impurity levels will be generated in band gap, and this will lead to spin polarization. The calculated magnetic moments are 1.0 μB and 2.9 μB for Ti and Fe, respectively. Furthermore, the magnetic moments are all contributed by the d orbitals of doped atoms in h-BN monolayer. The studies of magnetic coupling reveal that two Ti atoms are mainly coupled antiferromagnetically at different distances between Ti atoms in h-BN monolayer. The Ti-doped system is coupled ferromagnetically only when Ti–Ti distance is 6.625 Å. While the magnetic coupling exhibits regular oscillation characteristics in the system with two Fe atoms doping at different distances. This novel property in Fe-doped h-BN nanosheet provides a new way to control the spin property of material. Our research is beneficial to the development of spintronics.
Keywords: Two-dimensional nanosheet Electronic structure Magnetism First principle
1. Introduction Information technology (IT) is the cornerstone of today’s social development. It is urgent to develop high-speed and low-energy tech nologies in the field of IT. Spintronics was proposed as a new method ology. Compared to conventional electronics in IT domain, spintronics can introduce the electron’s spin degree to electronic device [1]. It can increase the speed of reading and writing in data storage by one thou sand times [2]. Therefore, searching for materials with good spin properties of electron has become a research hot spot. Two-dimensional (2D) material boron nitride (BN) has been attracted wide attention due to its special electronic quality and latent application in the next-generation of electronic device [2–4]. Hexagonal boron nitride (h-BN) is a typical two-dimensional mate rial. Unlike graphene, h-BN monolayer without doping is a semi conductor with a wide-band gap at room temperature [5,6]. Therefore, the pristine h-BN is not an ideal material for electronic applications.
However, research has found that the geometric structure and electron spin state of h-BN can be changed by adsorbing or doping other atoms, thus showing its value in the field of spintronics [6]. Y. Liu et al. [6] have studied the h-BN with Si doping. The results show that silicon atom can cause serious lattice distortion in BN, leading to the bending of h-BN sheet. Furthermore, two spin localized states were produced by the Si-dopant in the band gap of BN. The magnetic moment is 1 μB, which is mainly localized around the Si-dopant. BN nanotubes with carbon doping have been studied by R. Q. Wu et al. [7]. The calculated results reveal that carbon atom can introduce spin polarization instead of B or N atom. Furthermore, the magnetic moments mainly come from the 2p electron of the carbon. Using first principles calculation, R. Beiranvand et al. [8] have studied the electronic properties in h-BN nanosheet. The results show that the band structure of BN has the semiconductor character with the forbidden gap of about 4.96 eV. BN optical properties reveal that the optical conductivity begins at the gap of about 2.92 eV and 6.73 eV in both parallel and perpendicular electric field
* Corresponding author. E-mail address: [email protected] (D. Hou). https://doi.org/10.1016/j.ssc.2019.113803 Received 9 August 2019; Received in revised form 26 November 2019; Accepted 7 December 2019 Available online 10 December 2019 0038-1098/© 2019 Elsevier Ltd. All rights reserved.
M. Wang et al.
Solid State Communications 307 (2020) 113803
Fig. 1. Structure of h-BN monolayer supercell. Boron and nitrogen atoms are labeled as green and gray circles (in all structural graphs), respectively. The number 1 to 6 represent the distance between the doped atoms from the first nearest neighbor to the sixth nearest neighbor, respectively.
polarizations, respectively. Based on DFT calculations, D. S. Fartab et al. [9] have studied the magnetism in h-BN with Li doping. The optimized BN sheet will produce serious local distortion. The defect of occupying N position is more stable than that of B position. Moreover, that a single B atom was replaced by Li can increase the concentration of holes and form a p-type semiconductor. Although previous studies have discussed the properties of defects in BN, most of them focused on the effect of lattice distortion on magne tism. The magnetic coupling between defects was rarely addressed. However, this is particularly critical for further exploring the spin characteristics of defects in BN. In this article, the electronic structure and magnetism in h-BN monolayer with Titanium (Ti) or iron (Fe) doping have been studied. We will systematically study the magnetic coupling between the impurity atoms and reveal the corresponding spin properties. 2. Computational details In this paper, Vienna ab initio simulation package (VASP) is used to calculate the electronic structure and magnetic properties in h-BN with or without doping [10]. Projector augmented plane-wave (PAW) method is adopted [11]. Plane wave cutoff energy is 500 eV. k-mesh was set to be 5 � 5 � 1 Monkhorst-Pack grids. The exchange-correlation potential was described by the generalized gradient approximation (GGA) [12]. Furthermore, the on-site coulomb repulsion parameter U [13] on Ti or Fe 3d orbitals was applied. The valence configuration is 3d24s2for Ti, while Fe is 3d64s2. We selected the appropriate U-value through previous studies [14–16], which were proved to be effective. The U-value was selected as 3.3 eV for Ti, and 3.0 eV for Fe. The energy convergence error is 10 5 eV for the electronic loops and 10 4 eV for the ionic relaxations. In this work, h-BN by a (6 � 6) monolayer cell was modeled, 72 atoms in total, see Fig. 1. The vacuum spacing between the adjacent hBN slabs along the c axis was set to be 18 Å to eliminate the interaction between the layers, and it was tested for a good convergence.
Fig. 2. Calculated densities of states (DOS) of: (a) Perfect h-BN monolayer, (b) and (c) are the h-BN doped with one Ti and Fe, respectively. Fermi energy is set to be zero in all DOS plots.
3. Results and discussion 3.1. The electronic structure and magnetic properties 3.1.1. The h-BN monolayer without doping From Fig. 1, the nearest neighbor to B atom is three N atoms in h-BN monolayer. In the picture, a planar hexagon is formed by B and N atoms. Obviously, two-dimensional (2D) h-BN has a honeycomb structure. In our calculations, the B–N bond length is 1.443 Å after structural relax ation, which is in good agreement with the value of 1.45 Å in the 2
M. Wang et al.
Solid State Communications 307 (2020) 113803
Fig. 3. (a) The SDM of h-BN with one Ti atom doping, (b) Local structure diagram for the monolayer.
magnetic moment of about 1.0 μB. The PDOS in Fig. 2 (b) reveals that the magnetic moment is mainly contributed by d-orbital electrons of the impurity Ti. The spin-density map (SDM) also confirms this in Fig. 3 (a), spin electrons are mainly localized around the Ti atom. Because the electronegativity and atomic radius of Ti or Fe are closer to that of B atom, the boron is replaced by transition metal (TM) atom (Ti or Fe). In order to further prove our analysis, the total energy of h-BN that Ti or Fe is replaced by N atom in the monolayer was also calculated. The calculated results show that TM atoms are easier to replace B than N in the h-BN monolayer. The energy difference between them is about 3.93 eV for Ti, while 6.37 eV for Fe. In Fig. 3 (b), it is obvious that Ti atom can cause distortion of nearby lattice. The bond length of Ti–N is about 1.78 Å after relaxation, which is larger than B–N. However, the Ti atom does not break away from the h-BN monolayer surface. Next, we can use molecular orbital theory (MOT) to explain it. From Fig. 3, we can see that the local structure of Ti and surrounding B atoms has D3h symmetry. There are six irreducible representations in D3h group. They are A0 1, A0 2, E0 , A00 1, A00 2 and E00 , respectively. E0 and E00 are two-dimensional, while the rest are one-dimensional. 3d orbitals will split under the action of D3h group. In Fig. 4, dyz and dxz are a pair of degenerate levels with E00 symmetry. dxy and dx2-y2 are another pair of degenerate levels with E0 symmetry. The remaining dz2 orbital has A0 1 symmetry. Similarly, px and py are a pair of degenerate levels with E0 symmetry. pz has A00 2 symmetry. According to MOT, the bonding con ditions are similar energy, symmetry matching and maximum overlap of the orbits. The nonbonding A0 1 orbital is formed by dz2. dx2-y2 and px form bonding orbital σ E0 and antibonding orbital σ*E0 . Similarly, bonding orbital π E0 and antibonding orbital π*E0 are formed by dxy and py. The remaining pz, dyz and dxz form non-bonded orbitals A200 , E100 and E200 , respectively. There are five valence electrons in the outermost layer of the local structure. These valence electrons are arranged in molecular orbitals in order of energy from low to high. Obviously, there is still a spin electron left in the orbital πE0 . Therefore, the magnetic moment of h-
Fig. 4. Molecular orbital diagram of Ti-doped h-BN monolayer.
experiment [17]. The total density of state (TDOS) and projected densities of states (PDOS) of h-BN monolayer with or without doping were all shown in Fig. 2. In the diagram, the pristine h-BN monolayer is an insulator with a band gap of about 4.5 eV, which is also accord with previous study [17]. From Fig. 2 (a), the conduction band is above the 4 eV level, and is mainly composed of p orbitals of B atoms, while the valence band is mainly composed of p orbitals of N atoms. The majority and minority spin channels are symmetrically distributed, so the TDOS of h-BN is clearly not spin-polarized. 3.1.2. The h-BN monolayer with Ti doping When one B atom is replaced by one Ti atom in the h-BN, the spin distributions are asymmetric. It is obviously that the monolayer becomes magnetic. Compared with the undoped monolayer, the Ti atom can introduce one impurity level in the forbidden band. The impurity state is located at about 0.23 eV below the Fermi energy (see Fig. 2 b). The calculated results show that one Ti atom can introduce a
Fig. 5. (a) The SDM of h-BN with one Fe atom, (b) Local structure diagram for the monolayer. 3
M. Wang et al.
Solid State Communications 307 (2020) 113803
Fig. 6. Molecular orbital diagram of Fe-doped h-BN monolayer. Fig. 9. Energy difference (ΔE) between antiferromagnetic (EAFM) and ferro magnetic (EFM) states in h-BN with two Fe doping at different distances. ΔE ¼ EAFM – EFM.
deformation was also produced by the doped-Fe atom. The deformation occurs only in the plane, see Fig. 5 (b). After relaxation, the bond lengths of Fe–N are 1.69 Å, 1.70 Å and 1.72 Å, respectively. In Fig. 6, dyz and dxz, dxy and dx2-y2 are still degenerate levels in the system. Compared with Ti-doped system, dz2 has higher energy than dxy and dx2-y2 in Fe-doped system. Bonding orbital σE0 and antibonding orbital σ*E0 are formed by the combination of dx2-y2 and px. Bonding orbital π E0 and antibonding orbital π*E0 are formed by the combination of dxy and py. A0 1, E100 , E200 and A0 2 are non-bonded orbits formed by dz2, dyz, dxz and pz, respectively. The nine electrons in the outermost layer of the system will be filled in the molecular orbital in turn. However, the split energy (Δ0) between E200 and A0 2 is smaller than the exchange (P) be tween them. So the last three electrons will occupy the E100 , E200 and A0 2 orbitals in parallel. Thus, the calculated magnetic moment in the Fedoped system is about 2.9 μB. This is consistent with the theoretical analysis.
Fig. 7. Energy difference (ΔE) between antiferromagnetic (EAFM) and ferro magnetic (EFM) states in h-BN with two Ti doping at different distances. ΔE ¼ EAFM – EFM.
BN monolayer with Ti doped is 1 μB, which is consistent with the calculated result.
3.2. The magnetic coupling of Ti or Fe doped h-BN monolayer
3.1.3. The h-BN monolayer with Fe doping In Fig. 2, when Fe atom is introduced into h-BN monolayer, impurity levels were also produced in the band gap, which are 0.3 eV and 0.4 eV below Fermi level, 1.1 eV and 2.5 eV above Fermi level. The calculated magnetic moment is 2.9 μB, which is mainly contributed by d-orbital electrons of Fe atom. The SDM was shown in Fig. 5 (a). Local structural
3.2.1. Magnetic coupling in Ti-doped system In order to further explore the effect of magnetic properties in the Tidoped system, the magnetic coupling of two Ti atoms at different dis tances has been studied. In the supercell, there are six different dis tances, see Fig. 1. They are 2.504 Å, 4.337 Å, 5.008 Å, 6.625 Å, 7.512 Å and 8.674 Å, respectively. The exchange parameters can be calculated to
Fig. 8. TDOS and PDOS diagrams of the h-BN with two Ti atoms doping at different distances. dTi-Ti denotes the distance between two Ti atoms. 4
M. Wang et al.
Solid State Communications 307 (2020) 113803
Fig. 10. TDOS and PDOS diagrams of the h-BN with two Fe atoms doping at different distances.- dFe-Fe denotes the distance between two Fe atoms.
determine the magnetic exchange interaction [18,19]. Here, we calcu lated the energy difference between ferromagnetic (EFM) and antifer romagnetic (EAFM) states at different distances [2]. And the calculated results were shown in Fig. 7. In Fig. 7, when the distance between two Ti atoms is 6.625 Å, the ground state of the Ti-doped h-BN monolayer is ferromagnetic. The calculated magnetic moment in the system is 1.5 μB. The others are antiferromagnetic coupling. It can be concluded that FM superexchange is more favorable at the Ti–Ti distance of 6.625 Å. Therefore, although the impurity Ti can produce local magnetic moment, it is not easy to produce long-range magnetic order due to the antiferromagnetic coupling between Ti atoms at different distances. In Fig. 8, the system will maintain the characteristics of semiconductor regardless of the distance. The impurity levels in the forbidden band are mainly contributed by d-orbital of doped Ti atoms.
4. Conclusion
3.2.2. Magnetic coupling in Fe-doped system Similarly, there are also six Fe–Fe distances in the Fe doped system. The distances were shown in Fig. 9, which are similar to that of Ti-doped system. The calculated results show that the ground state of the Fedoped system is ferromagnetic when the Fe–Fe distance is 2.504 Å, 5.008 Å or 7.512 Å. The magnetic moments are 7.3 μB, 7.4 μB and 9.1 μB, respectively. However, when the Fe–Fe distance is 4.337 Å, 6.625 Å or 8.674 Å, the antiferromagnetic coupling in the Fe-doped system is more stable. The magnetic coupling between the impurity Fe atoms in the hBN exhibits regular oscillating characteristics with the change of Fe–Fe distance. In Fig. 10, the system maintains the characteristics of semi conductor at each doping distance, which is consistent with that of Tidoped system. The impurity levels in the band gap increase signifi cantly after introducing another Fe atom into the system. In addition, the amplitude of ΔE oscillations decreases gradually with the increase of Fe–Fe distance. The sensitivity in magnetic coupling can be attributed to the competition of FM superexchange interaction, AFM superexchange interaction and AFM direct exchange interaction [2]. FM superexchange is more stable when the Fe–Fe distance is 2.504 Å, 5.008 Å or 7.512 Å. And the energy differences (ΔE) between EAFM and EFM are 21.32 meV, 226.96 meV and 185.33 meV, respectively. AFM superexchange in the system is more favorable at other distances. The ΔE’s are 621.26 meV, 348.57 meV and 116.78 meV at the Fe–Fe distance of 4.337 Å, 6.625 Å and 8.674 Å, respectively. From the above discussion, the spin prop erties of electrons can be controlled by controlling the doping distance, which provides a new way for the development of spintronics.
The data required to reproduce these findings are available from the corresponding authors upon reasonable request.
In conclusion, Ti or Fe-doped h-BN monolayer has been studied based on GGA þ U calculations. The calculated results show that Ti or Fe atom can both produce the high-spin states in the system. The magnetic moment of Ti-doped system is 1.0 μB, while 2.9 μB for the Fe-doped h-BN monolayer. Further studies show that the magnetic moments mainly come from the d orbitals of transition metal atoms. In addition, the magnetic coupling between Ti atoms in h-BN monolayer is mainly AFM coupling, except for the case of Ti–Ti distance 6.625 Å. However, the magnetic coupling between Fe atoms in h-BN monolayer shows regular oscillating at the different distances. Our research provides a new way to control the spin properties in the material. Data availability
Declaration of competing interest All the authors declared that they have no conflicts of interest to this work. In short, there are no conflicts of interest. Acknowledgements This work was supported by Project funded by China Postdoctoral Science Foundation [grant number 2018M640245], Project funded by Hebei Province Postdoctoral Science Foundation [grant number B2018003013], the Natural Science Foundation of Hebei, China [grant number F2017208031], the Natural Science Foundation of Nation, China [grant number 51674096], the Fundamental Research Funds for the Central Universities, Nankai University [grant number 63191740]. References [1] X. Li, J. Yang, First-principles design of spintronics materials, Natl. Sci. Rev. 3 (2016) 365–381, https://doi.org/10.1093/nsr/nww026. [2] M. Wang, S. Tang, J. Ren, B. Wang, Y. Han, Y. Dai, Magnetism in boron nitride monolayer induced by cobalt or nickel doping, J. Supercond. Nov. Magnetism 31 (2018) 1559–1565, https://doi.org/10.1007/s10948-017-4353-5. [3] J. Meng, D. Li, Y. Niu, H. Zhao, C. Liang, Z. He, Structural, electronic, and magnetic properties of 3D metal trioxide and tetraoxide superhalogen cluster-doped monolayer BN, Phys. Lett. A 380 (2010) 2300–2306, https://doi.org/10.1016/j. physleta.2016.04.042.
5
M. Wang et al.
Solid State Communications 307 (2020) 113803 [12] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865–3868, https://doi.org/10.1103/ PhysRevLett.77.3865. [13] S.L. Dudarev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Electronenergy-loss spectra and the structural stability of nickel oxide: an LSDAþU study, Phys. Rev. B 57 (1998) 1505–1509, https://doi.org/10.1103/PhysRevB.57.1505. [14] M. Wang, M. Feng, X. Zuo, First principles study of the electronic structure and magnetism of oxygen-deficient anatase TiO2 (0 0 1) surface, Appl. Surf. Sci. 292 (2014) 475–479, https://doi.org/10.1016/j.apsusc.2013.11.165. [15] C. Chao, P.J. Hirschfeld, H. Cheng, Proximity of antiferromagnetism and superconductivity in Lao1-xFxFeAs: effective Hamiltonian from ab initio studies, Phys. Rev. B 77 (2008) 1–5, https://doi.org/10.1103/PhysRevB.77.220506. [16] A. Walsh, Y. Yan, M.M.A. Jassin, S. Wei, Electronic, energetic, and chemical effects of intrinsic defects and Fe-doping of CoAl2O4: a DFTþU study, J. Phys. Chem. B 112 (2008) 12044–12050, https://doi.org/10.1021/jp711566k. [17] J. Zhou, Q. Wang, Q. Sun, P. Jena, Electronic and magnetic properties of a BN sheet decorated with hydrogen and fluorine, Phys. Rev. B 81 (2010) 1–7, https://doi. org/10.1103/PhysRevB.81.085442. [18] D. Comtesse, H.C. Herper, A. Hucht, P. Entel, A first-principles study aided with Monte Carlo simulations of carbon doped iron-manganese alloys, Eur. Phys. J. B 85 (2012) 343, https://doi.org/10.1140/epjb/e2012-30321-x. [19] Y. Yue, Fe2C monolayer: an intrinsic ferromagnetic MXene, J. Magn. Magn. Mater. 434 (2017) 164–168, https://doi.org/10.1016/j.jmmm.2017.03.058.
[4] J.A. Gonҫalves, R.J.C. Batista, R. Tromer, S. Azevedo, Study of the stability and electronic properties of h-BN nanoribbons with reconstructed edges, Chem. Phys. Lett. 727 (2019) 126–132, https://doi.org/10.1016/j.cplett.2019.04.057. [5] H. Mei, X. Cai, M. Tang, Q. Hui, Q. Song, M. Wang, Electronic and mechanic properties of a new cubic boron nitride, Comput. Mater. Sci. 162 (2019) 111–115, https://doi.org/10.1016/j.commatsci.2019.02.034. [6] Y. Liu, B. Gao, D. Xu, H. Wang, J. Zhao, Theoretical study on Si-doped hexagonal boron nitride (h-BN) sheet: electronic, magnetic properties, and reactivity, Phys. Lett. A 378 (2014) 2989–2994, https://doi.org/10.1016/j.physleta.2014.07.053. [7] R.Q. Wu, L. Liu, G.W. Peng, Y.P. Feng, Magnetism in BN nanotubes induced by carbon doping, Appl. Phys. Lett. 86 (2005) 1–3, https://doi.org/10.1063/ 1.1890477. [8] R. Beiranvand, S. Valedbagi, Electronic and optical properties of h-BN nanosheet: a first principles calculation, Diam. Relat. Mater. 58 (2015) 190–195, https://doi. org/10.1016/j.diamond.2015.07.008. [9] D.S. Fartab, A.A. Kordbacheh, Lithium doping and vacancy effects on the structural, Electronic and magnetic properties of hexagonal boron nitride sheet: a first-principles calculation, Superlattice Microstruct. 118 (2018) 185–195, https:// doi.org/10.1016/j.spmi.2018.04.002. [10] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169–11186, https://doi.org/10.1103/PhysRevB.54.11169. [11] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmentedwave method, Phys. Rev. B 59 (1999) 1758–1775, https://doi.org/10.1103/ PhysRevB.59.1758.
6
Contents lists available at ScienceDirect
Solid State Communications journal homepage: http://www.elsevier.com/locate/ssc
Electronic structure and spin properties study on 2D h-BN nanosheet with Ti or Fe doping Min Wang a, b, Fanfan Meng b, Denglu Hou a, *, Yilin Han c, Jie Ren d, Chenxiang Bai e, Baozhu Wang b, Tiege Zhou f a
Hebei Advanced Thin Films Laboratory, Institute of Physics, Hebei Normal University, Shijiazhuang, 050024, PR China School of Information Science and Engineering, Hebei University of Science and Technology, Shijiazhuang, 050018, PR China Department of Construction Engineering, Hebei Vocational College of Politics and Law, Shijiazhuang, 050061, PR China d School of Science, Hebei University of Science and Technology, Shijiazhuang, 050018, PR China e School of Microelectronics, Tianjin University, Tianjin, 300072, PR China f College of Electronic Information and Optical Engineering, Nankai University, Tianjin, 300071, PR China b c
A R T I C L E I N F O
A B S T R A C T
Communicated by A. Nikita
The electronic structure and spin properties of Titanium (Ti) or Iron (Fe) doped hexagonal boron nitride (h-BN) nanosheet have been studied by using ab initio study based on density functional theory (DFT). GGA þ U cal culations show that one Ti or Fe atom can introduce local magnetic states into the system. Impurity levels will be generated in band gap, and this will lead to spin polarization. The calculated magnetic moments are 1.0 μB and 2.9 μB for Ti and Fe, respectively. Furthermore, the magnetic moments are all contributed by the d orbitals of doped atoms in h-BN monolayer. The studies of magnetic coupling reveal that two Ti atoms are mainly coupled antiferromagnetically at different distances between Ti atoms in h-BN monolayer. The Ti-doped system is coupled ferromagnetically only when Ti–Ti distance is 6.625 Å. While the magnetic coupling exhibits regular oscillation characteristics in the system with two Fe atoms doping at different distances. This novel property in Fe-doped h-BN nanosheet provides a new way to control the spin property of material. Our research is beneficial to the development of spintronics.
Keywords: Two-dimensional nanosheet Electronic structure Magnetism First principle
1. Introduction Information technology (IT) is the cornerstone of today’s social development. It is urgent to develop high-speed and low-energy tech nologies in the field of IT. Spintronics was proposed as a new method ology. Compared to conventional electronics in IT domain, spintronics can introduce the electron’s spin degree to electronic device [1]. It can increase the speed of reading and writing in data storage by one thou sand times [2]. Therefore, searching for materials with good spin properties of electron has become a research hot spot. Two-dimensional (2D) material boron nitride (BN) has been attracted wide attention due to its special electronic quality and latent application in the next-generation of electronic device [2–4]. Hexagonal boron nitride (h-BN) is a typical two-dimensional mate rial. Unlike graphene, h-BN monolayer without doping is a semi conductor with a wide-band gap at room temperature [5,6]. Therefore, the pristine h-BN is not an ideal material for electronic applications.
However, research has found that the geometric structure and electron spin state of h-BN can be changed by adsorbing or doping other atoms, thus showing its value in the field of spintronics [6]. Y. Liu et al. [6] have studied the h-BN with Si doping. The results show that silicon atom can cause serious lattice distortion in BN, leading to the bending of h-BN sheet. Furthermore, two spin localized states were produced by the Si-dopant in the band gap of BN. The magnetic moment is 1 μB, which is mainly localized around the Si-dopant. BN nanotubes with carbon doping have been studied by R. Q. Wu et al. [7]. The calculated results reveal that carbon atom can introduce spin polarization instead of B or N atom. Furthermore, the magnetic moments mainly come from the 2p electron of the carbon. Using first principles calculation, R. Beiranvand et al. [8] have studied the electronic properties in h-BN nanosheet. The results show that the band structure of BN has the semiconductor character with the forbidden gap of about 4.96 eV. BN optical properties reveal that the optical conductivity begins at the gap of about 2.92 eV and 6.73 eV in both parallel and perpendicular electric field
* Corresponding author. E-mail address: [email protected] (D. Hou). https://doi.org/10.1016/j.ssc.2019.113803 Received 9 August 2019; Received in revised form 26 November 2019; Accepted 7 December 2019 Available online 10 December 2019 0038-1098/© 2019 Elsevier Ltd. All rights reserved.
M. Wang et al.
Solid State Communications 307 (2020) 113803
Fig. 1. Structure of h-BN monolayer supercell. Boron and nitrogen atoms are labeled as green and gray circles (in all structural graphs), respectively. The number 1 to 6 represent the distance between the doped atoms from the first nearest neighbor to the sixth nearest neighbor, respectively.
polarizations, respectively. Based on DFT calculations, D. S. Fartab et al. [9] have studied the magnetism in h-BN with Li doping. The optimized BN sheet will produce serious local distortion. The defect of occupying N position is more stable than that of B position. Moreover, that a single B atom was replaced by Li can increase the concentration of holes and form a p-type semiconductor. Although previous studies have discussed the properties of defects in BN, most of them focused on the effect of lattice distortion on magne tism. The magnetic coupling between defects was rarely addressed. However, this is particularly critical for further exploring the spin characteristics of defects in BN. In this article, the electronic structure and magnetism in h-BN monolayer with Titanium (Ti) or iron (Fe) doping have been studied. We will systematically study the magnetic coupling between the impurity atoms and reveal the corresponding spin properties. 2. Computational details In this paper, Vienna ab initio simulation package (VASP) is used to calculate the electronic structure and magnetic properties in h-BN with or without doping [10]. Projector augmented plane-wave (PAW) method is adopted [11]. Plane wave cutoff energy is 500 eV. k-mesh was set to be 5 � 5 � 1 Monkhorst-Pack grids. The exchange-correlation potential was described by the generalized gradient approximation (GGA) [12]. Furthermore, the on-site coulomb repulsion parameter U [13] on Ti or Fe 3d orbitals was applied. The valence configuration is 3d24s2for Ti, while Fe is 3d64s2. We selected the appropriate U-value through previous studies [14–16], which were proved to be effective. The U-value was selected as 3.3 eV for Ti, and 3.0 eV for Fe. The energy convergence error is 10 5 eV for the electronic loops and 10 4 eV for the ionic relaxations. In this work, h-BN by a (6 � 6) monolayer cell was modeled, 72 atoms in total, see Fig. 1. The vacuum spacing between the adjacent hBN slabs along the c axis was set to be 18 Å to eliminate the interaction between the layers, and it was tested for a good convergence.
Fig. 2. Calculated densities of states (DOS) of: (a) Perfect h-BN monolayer, (b) and (c) are the h-BN doped with one Ti and Fe, respectively. Fermi energy is set to be zero in all DOS plots.
3. Results and discussion 3.1. The electronic structure and magnetic properties 3.1.1. The h-BN monolayer without doping From Fig. 1, the nearest neighbor to B atom is three N atoms in h-BN monolayer. In the picture, a planar hexagon is formed by B and N atoms. Obviously, two-dimensional (2D) h-BN has a honeycomb structure. In our calculations, the B–N bond length is 1.443 Å after structural relax ation, which is in good agreement with the value of 1.45 Å in the 2
M. Wang et al.
Solid State Communications 307 (2020) 113803
Fig. 3. (a) The SDM of h-BN with one Ti atom doping, (b) Local structure diagram for the monolayer.
magnetic moment of about 1.0 μB. The PDOS in Fig. 2 (b) reveals that the magnetic moment is mainly contributed by d-orbital electrons of the impurity Ti. The spin-density map (SDM) also confirms this in Fig. 3 (a), spin electrons are mainly localized around the Ti atom. Because the electronegativity and atomic radius of Ti or Fe are closer to that of B atom, the boron is replaced by transition metal (TM) atom (Ti or Fe). In order to further prove our analysis, the total energy of h-BN that Ti or Fe is replaced by N atom in the monolayer was also calculated. The calculated results show that TM atoms are easier to replace B than N in the h-BN monolayer. The energy difference between them is about 3.93 eV for Ti, while 6.37 eV for Fe. In Fig. 3 (b), it is obvious that Ti atom can cause distortion of nearby lattice. The bond length of Ti–N is about 1.78 Å after relaxation, which is larger than B–N. However, the Ti atom does not break away from the h-BN monolayer surface. Next, we can use molecular orbital theory (MOT) to explain it. From Fig. 3, we can see that the local structure of Ti and surrounding B atoms has D3h symmetry. There are six irreducible representations in D3h group. They are A0 1, A0 2, E0 , A00 1, A00 2 and E00 , respectively. E0 and E00 are two-dimensional, while the rest are one-dimensional. 3d orbitals will split under the action of D3h group. In Fig. 4, dyz and dxz are a pair of degenerate levels with E00 symmetry. dxy and dx2-y2 are another pair of degenerate levels with E0 symmetry. The remaining dz2 orbital has A0 1 symmetry. Similarly, px and py are a pair of degenerate levels with E0 symmetry. pz has A00 2 symmetry. According to MOT, the bonding con ditions are similar energy, symmetry matching and maximum overlap of the orbits. The nonbonding A0 1 orbital is formed by dz2. dx2-y2 and px form bonding orbital σ E0 and antibonding orbital σ*E0 . Similarly, bonding orbital π E0 and antibonding orbital π*E0 are formed by dxy and py. The remaining pz, dyz and dxz form non-bonded orbitals A200 , E100 and E200 , respectively. There are five valence electrons in the outermost layer of the local structure. These valence electrons are arranged in molecular orbitals in order of energy from low to high. Obviously, there is still a spin electron left in the orbital πE0 . Therefore, the magnetic moment of h-
Fig. 4. Molecular orbital diagram of Ti-doped h-BN monolayer.
experiment [17]. The total density of state (TDOS) and projected densities of states (PDOS) of h-BN monolayer with or without doping were all shown in Fig. 2. In the diagram, the pristine h-BN monolayer is an insulator with a band gap of about 4.5 eV, which is also accord with previous study [17]. From Fig. 2 (a), the conduction band is above the 4 eV level, and is mainly composed of p orbitals of B atoms, while the valence band is mainly composed of p orbitals of N atoms. The majority and minority spin channels are symmetrically distributed, so the TDOS of h-BN is clearly not spin-polarized. 3.1.2. The h-BN monolayer with Ti doping When one B atom is replaced by one Ti atom in the h-BN, the spin distributions are asymmetric. It is obviously that the monolayer becomes magnetic. Compared with the undoped monolayer, the Ti atom can introduce one impurity level in the forbidden band. The impurity state is located at about 0.23 eV below the Fermi energy (see Fig. 2 b). The calculated results show that one Ti atom can introduce a
Fig. 5. (a) The SDM of h-BN with one Fe atom, (b) Local structure diagram for the monolayer. 3
M. Wang et al.
Solid State Communications 307 (2020) 113803
Fig. 6. Molecular orbital diagram of Fe-doped h-BN monolayer. Fig. 9. Energy difference (ΔE) between antiferromagnetic (EAFM) and ferro magnetic (EFM) states in h-BN with two Fe doping at different distances. ΔE ¼ EAFM – EFM.
deformation was also produced by the doped-Fe atom. The deformation occurs only in the plane, see Fig. 5 (b). After relaxation, the bond lengths of Fe–N are 1.69 Å, 1.70 Å and 1.72 Å, respectively. In Fig. 6, dyz and dxz, dxy and dx2-y2 are still degenerate levels in the system. Compared with Ti-doped system, dz2 has higher energy than dxy and dx2-y2 in Fe-doped system. Bonding orbital σE0 and antibonding orbital σ*E0 are formed by the combination of dx2-y2 and px. Bonding orbital π E0 and antibonding orbital π*E0 are formed by the combination of dxy and py. A0 1, E100 , E200 and A0 2 are non-bonded orbits formed by dz2, dyz, dxz and pz, respectively. The nine electrons in the outermost layer of the system will be filled in the molecular orbital in turn. However, the split energy (Δ0) between E200 and A0 2 is smaller than the exchange (P) be tween them. So the last three electrons will occupy the E100 , E200 and A0 2 orbitals in parallel. Thus, the calculated magnetic moment in the Fedoped system is about 2.9 μB. This is consistent with the theoretical analysis.
Fig. 7. Energy difference (ΔE) between antiferromagnetic (EAFM) and ferro magnetic (EFM) states in h-BN with two Ti doping at different distances. ΔE ¼ EAFM – EFM.
BN monolayer with Ti doped is 1 μB, which is consistent with the calculated result.
3.2. The magnetic coupling of Ti or Fe doped h-BN monolayer
3.1.3. The h-BN monolayer with Fe doping In Fig. 2, when Fe atom is introduced into h-BN monolayer, impurity levels were also produced in the band gap, which are 0.3 eV and 0.4 eV below Fermi level, 1.1 eV and 2.5 eV above Fermi level. The calculated magnetic moment is 2.9 μB, which is mainly contributed by d-orbital electrons of Fe atom. The SDM was shown in Fig. 5 (a). Local structural
3.2.1. Magnetic coupling in Ti-doped system In order to further explore the effect of magnetic properties in the Tidoped system, the magnetic coupling of two Ti atoms at different dis tances has been studied. In the supercell, there are six different dis tances, see Fig. 1. They are 2.504 Å, 4.337 Å, 5.008 Å, 6.625 Å, 7.512 Å and 8.674 Å, respectively. The exchange parameters can be calculated to
Fig. 8. TDOS and PDOS diagrams of the h-BN with two Ti atoms doping at different distances. dTi-Ti denotes the distance between two Ti atoms. 4
M. Wang et al.
Solid State Communications 307 (2020) 113803
Fig. 10. TDOS and PDOS diagrams of the h-BN with two Fe atoms doping at different distances.- dFe-Fe denotes the distance between two Fe atoms.
determine the magnetic exchange interaction [18,19]. Here, we calcu lated the energy difference between ferromagnetic (EFM) and antifer romagnetic (EAFM) states at different distances [2]. And the calculated results were shown in Fig. 7. In Fig. 7, when the distance between two Ti atoms is 6.625 Å, the ground state of the Ti-doped h-BN monolayer is ferromagnetic. The calculated magnetic moment in the system is 1.5 μB. The others are antiferromagnetic coupling. It can be concluded that FM superexchange is more favorable at the Ti–Ti distance of 6.625 Å. Therefore, although the impurity Ti can produce local magnetic moment, it is not easy to produce long-range magnetic order due to the antiferromagnetic coupling between Ti atoms at different distances. In Fig. 8, the system will maintain the characteristics of semiconductor regardless of the distance. The impurity levels in the forbidden band are mainly contributed by d-orbital of doped Ti atoms.
4. Conclusion
3.2.2. Magnetic coupling in Fe-doped system Similarly, there are also six Fe–Fe distances in the Fe doped system. The distances were shown in Fig. 9, which are similar to that of Ti-doped system. The calculated results show that the ground state of the Fedoped system is ferromagnetic when the Fe–Fe distance is 2.504 Å, 5.008 Å or 7.512 Å. The magnetic moments are 7.3 μB, 7.4 μB and 9.1 μB, respectively. However, when the Fe–Fe distance is 4.337 Å, 6.625 Å or 8.674 Å, the antiferromagnetic coupling in the Fe-doped system is more stable. The magnetic coupling between the impurity Fe atoms in the hBN exhibits regular oscillating characteristics with the change of Fe–Fe distance. In Fig. 10, the system maintains the characteristics of semi conductor at each doping distance, which is consistent with that of Tidoped system. The impurity levels in the band gap increase signifi cantly after introducing another Fe atom into the system. In addition, the amplitude of ΔE oscillations decreases gradually with the increase of Fe–Fe distance. The sensitivity in magnetic coupling can be attributed to the competition of FM superexchange interaction, AFM superexchange interaction and AFM direct exchange interaction [2]. FM superexchange is more stable when the Fe–Fe distance is 2.504 Å, 5.008 Å or 7.512 Å. And the energy differences (ΔE) between EAFM and EFM are 21.32 meV, 226.96 meV and 185.33 meV, respectively. AFM superexchange in the system is more favorable at other distances. The ΔE’s are 621.26 meV, 348.57 meV and 116.78 meV at the Fe–Fe distance of 4.337 Å, 6.625 Å and 8.674 Å, respectively. From the above discussion, the spin prop erties of electrons can be controlled by controlling the doping distance, which provides a new way for the development of spintronics.
The data required to reproduce these findings are available from the corresponding authors upon reasonable request.
In conclusion, Ti or Fe-doped h-BN monolayer has been studied based on GGA þ U calculations. The calculated results show that Ti or Fe atom can both produce the high-spin states in the system. The magnetic moment of Ti-doped system is 1.0 μB, while 2.9 μB for the Fe-doped h-BN monolayer. Further studies show that the magnetic moments mainly come from the d orbitals of transition metal atoms. In addition, the magnetic coupling between Ti atoms in h-BN monolayer is mainly AFM coupling, except for the case of Ti–Ti distance 6.625 Å. However, the magnetic coupling between Fe atoms in h-BN monolayer shows regular oscillating at the different distances. Our research provides a new way to control the spin properties in the material. Data availability
Declaration of competing interest All the authors declared that they have no conflicts of interest to this work. In short, there are no conflicts of interest. Acknowledgements This work was supported by Project funded by China Postdoctoral Science Foundation [grant number 2018M640245], Project funded by Hebei Province Postdoctoral Science Foundation [grant number B2018003013], the Natural Science Foundation of Hebei, China [grant number F2017208031], the Natural Science Foundation of Nation, China [grant number 51674096], the Fundamental Research Funds for the Central Universities, Nankai University [grant number 63191740]. References [1] X. Li, J. Yang, First-principles design of spintronics materials, Natl. Sci. Rev. 3 (2016) 365–381, https://doi.org/10.1093/nsr/nww026. [2] M. Wang, S. Tang, J. Ren, B. Wang, Y. Han, Y. Dai, Magnetism in boron nitride monolayer induced by cobalt or nickel doping, J. Supercond. Nov. Magnetism 31 (2018) 1559–1565, https://doi.org/10.1007/s10948-017-4353-5. [3] J. Meng, D. Li, Y. Niu, H. Zhao, C. Liang, Z. He, Structural, electronic, and magnetic properties of 3D metal trioxide and tetraoxide superhalogen cluster-doped monolayer BN, Phys. Lett. A 380 (2010) 2300–2306, https://doi.org/10.1016/j. physleta.2016.04.042.
5
M. Wang et al.
Solid State Communications 307 (2020) 113803 [12] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865–3868, https://doi.org/10.1103/ PhysRevLett.77.3865. [13] S.L. Dudarev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Electronenergy-loss spectra and the structural stability of nickel oxide: an LSDAþU study, Phys. Rev. B 57 (1998) 1505–1509, https://doi.org/10.1103/PhysRevB.57.1505. [14] M. Wang, M. Feng, X. Zuo, First principles study of the electronic structure and magnetism of oxygen-deficient anatase TiO2 (0 0 1) surface, Appl. Surf. Sci. 292 (2014) 475–479, https://doi.org/10.1016/j.apsusc.2013.11.165. [15] C. Chao, P.J. Hirschfeld, H. Cheng, Proximity of antiferromagnetism and superconductivity in Lao1-xFxFeAs: effective Hamiltonian from ab initio studies, Phys. Rev. B 77 (2008) 1–5, https://doi.org/10.1103/PhysRevB.77.220506. [16] A. Walsh, Y. Yan, M.M.A. Jassin, S. Wei, Electronic, energetic, and chemical effects of intrinsic defects and Fe-doping of CoAl2O4: a DFTþU study, J. Phys. Chem. B 112 (2008) 12044–12050, https://doi.org/10.1021/jp711566k. [17] J. Zhou, Q. Wang, Q. Sun, P. Jena, Electronic and magnetic properties of a BN sheet decorated with hydrogen and fluorine, Phys. Rev. B 81 (2010) 1–7, https://doi. org/10.1103/PhysRevB.81.085442. [18] D. Comtesse, H.C. Herper, A. Hucht, P. Entel, A first-principles study aided with Monte Carlo simulations of carbon doped iron-manganese alloys, Eur. Phys. J. B 85 (2012) 343, https://doi.org/10.1140/epjb/e2012-30321-x. [19] Y. Yue, Fe2C monolayer: an intrinsic ferromagnetic MXene, J. Magn. Magn. Mater. 434 (2017) 164–168, https://doi.org/10.1016/j.jmmm.2017.03.058.
[4] J.A. Gonҫalves, R.J.C. Batista, R. Tromer, S. Azevedo, Study of the stability and electronic properties of h-BN nanoribbons with reconstructed edges, Chem. Phys. Lett. 727 (2019) 126–132, https://doi.org/10.1016/j.cplett.2019.04.057. [5] H. Mei, X. Cai, M. Tang, Q. Hui, Q. Song, M. Wang, Electronic and mechanic properties of a new cubic boron nitride, Comput. Mater. Sci. 162 (2019) 111–115, https://doi.org/10.1016/j.commatsci.2019.02.034. [6] Y. Liu, B. Gao, D. Xu, H. Wang, J. Zhao, Theoretical study on Si-doped hexagonal boron nitride (h-BN) sheet: electronic, magnetic properties, and reactivity, Phys. Lett. A 378 (2014) 2989–2994, https://doi.org/10.1016/j.physleta.2014.07.053. [7] R.Q. Wu, L. Liu, G.W. Peng, Y.P. Feng, Magnetism in BN nanotubes induced by carbon doping, Appl. Phys. Lett. 86 (2005) 1–3, https://doi.org/10.1063/ 1.1890477. [8] R. Beiranvand, S. Valedbagi, Electronic and optical properties of h-BN nanosheet: a first principles calculation, Diam. Relat. Mater. 58 (2015) 190–195, https://doi. org/10.1016/j.diamond.2015.07.008. [9] D.S. Fartab, A.A. Kordbacheh, Lithium doping and vacancy effects on the structural, Electronic and magnetic properties of hexagonal boron nitride sheet: a first-principles calculation, Superlattice Microstruct. 118 (2018) 185–195, https:// doi.org/10.1016/j.spmi.2018.04.002. [10] G. Kresse, J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169–11186, https://doi.org/10.1103/PhysRevB.54.11169. [11] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmentedwave method, Phys. Rev. B 59 (1999) 1758–1775, https://doi.org/10.1103/ PhysRevB.59.1758.
6