- Email: [email protected]
M-C21, an anti-ferromagnetic carbon bulk materials
Solid State Communications 302 (2019) 113707
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Communication
M-C21, an anti-ferromagnetic carbon bulk materials a
Zhenhai Lai , Xi Zhu a b
T
a,b,∗
School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China Shenzhen Institute of Artificial Intelligence and Robotics for Society, Shenzhen, Guangdong, 518172, China
A B S T R A C T
A new carbon allotrope named M-C21 with anti-ferromagnetic ground state is predicted and theoretically studied by Ab initio density functional theory (DFT) method. This new structure displays F-43 M space group for the non-magnetic and ferromagnetic states and IMM2 space group for the anti-ferromagnetic state. The magnetic property in the M-C21 carbon origins from the space confined carbon radicals, which couples with the nearby magnetic carbon atoms through superexchange mechanism. The M-C21 carbon could be possibly synthesized through dehydrogenation from the mixture of Centro-hexaquinacene and methane. This work provides a new theoretic solution for the design and synthesis the magnetic carbon materials for future applications.
1. Introduction The magnetic carbon materials are of extreme importance for fundamental research and industry applications, the success of creating magnetic carbon is supposed to accelerate the carbon nano electronics for the next generation by releasing the freedom of spin. However, due to the strong covalent bond character in most of the carbon allotropes, including graphite and diamond, it is depressing to create perfect magnetic units due to the super stable ground states, however, by theory, it has been proposed several luminous strategies [1–4] to disclose the intrinsic magnetic information in full carbon materials. There are some experiments argued for the detection of the magnetic state in variant carbon samples [5,6], however, due to the sample quality, the detail of the atomic structure information is unavailable, which subsequently lead to the mechanism of magnetism remaining unknown and under debate, generally, there are some common factors which are believed to lead to the magnetism, including lattice vacancies [7,8], adatoms [9], negative Gaussian curvature [10], and carbon radical in hybrid structures [4]etc. Though there are about 500 carbon allotropes [11] reported experimentally and predicted theoretically, the magnetic full carbon allotropes are still rare in literature, it is of both fundamental importance and application motivation to investigate more on the structure and property of magnetic carbon allotropes. 2. Results and discussion Here in this work, we provided a new carbon allotrope with 3D bulk structures, with 21 carbon atoms in the primitive lattice cell, named as M-C21, and investigate the crystal and electronic properties. The crystal structure design is based on the carbon radical methodology in
∗
nanobuds [4], we hybrid the traditional sp3 and sp2 type atoms to form the isolated 3 fold carbon radical. The calculations were carried out using the density functional theory (DFT) [12] as implemented in the Abinit code [13]. Local density approximation (LDA) [14,15] and Generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) functional [16] are used for exchange and correlation. Norm-conserving pseudopotentials were used with a 500 eV kinetic energy cut-off, a smallest allowed K-spacing 0.02 Å−1 is used for the sampling of the Brillouin zone. The structures are fully optimized until the maximal atomic force is converged to 1 × 10−5 eV/Å and the lattice stress is less than 0.1 GPa. For the ferro-magnetic (FM) and nonmagnetic (NM) states, the calculations were performed in the primitive cell, while for the anti-ferromagnetic (AFM) calculation, we consider both the AFM states inside the primitive cell and the AFM states in the nearest double cell, there is no symmetry constrain for all the FM/AFM/ NM ground state calculation. The idea of constructing this structures is based on the carbon radical methodology in nanobuds [4], we hybrid the traditional sp3 and sp2 type atoms to form the isolated 3 fold carbon radical. Fig. 1 (a) and (b) show the conventional cell and primitive cell of M-C21, the lattice parameter for the conventional cell is a = 9.17 Å, with space group F4¯ 3M, (number 216), it can be divided into two sub units as shown in the primitive cell in Fig. 1 (b), one is the carbon polyhedron colored by red (C1) and gray (C2), which are connected by 3-folded bonds; the other are the blue and yellow ones (C3,C4) in the carbon polyhedron, which are 4-folded bonds. The bond geometry of the carbon tetrahedron, as shown in Fig. 1 (b), are b1 = 1.53 Å, and bond angle a1 = 109.5°, which are of typical sp3 hybridized bonding; For the carbon polyhedron composed by red and gray carbon atoms, the bond length is b2 = 1.36 Å, and bond angle is a2 = 125.0°, these are of typical sp2 carbon hybridized bonding. Moreover, the gray ones (C2),
Corresponding author. School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China. E-mail address: [email protected] (X. Zhu).
https://doi.org/10.1016/j.ssc.2019.113707 Received 20 March 2019; Received in revised form 29 July 2019; Accepted 19 August 2019 Available online 23 August 2019 0038-1098/ © 2019 Elsevier Ltd. All rights reserved.
Solid State Communications 302 (2019) 113707
Z. Lai and X. Zhu
Fig. 1. atomic structure for the M-C21 carbon allotrope, (a) shows the conventional cell, (b) shows the primitive cell, the yellow and blue color represents C3 and C4, the carbon atoms with 4 –fold bonds, the red color represents C1, the carbon atoms with double bonds, the gray color represents C2, the carbon atoms of carbon radicals, the three kinds of carbon-carbon bonds and bond angles are identified with b1,b2 and b3, a1,a2 and a3 respectively. (c), the possible synthesis pass from the dehydrogenation between the Centrohexaquinacene and Methane radical (marked in red).
Table 1 Space groups, lattice parameters (a and c in Å), mass density (ρ in g/cm3), C–C bond length (dC − C in Å) atomic cohesive energy (Ecoh in eV) and bulk modulus (B in GPa) of diamond, graphite and M-C21.The LDA and PBE data are from this work. Structure
Space group
Method
a (Å)
Diamond
Fd3¯ m
Graphite
P63/mmc
M-C21
F4¯ 3m
LDA PBE EXP [24] LDA GGA EXP [25] PBE
3.54 3.57 3.57 2.45 2.46 2.46 9.17
c(Å)
6.60 6.85 6.71
ρ (g/cm3)
dC-C(Å)
Ecoh (eV/atom)
B (GPa)
3.61 3.50 3.52 2.34 2.22 2.27 2.17
1.53 1.58 1.54 1.41 1.42 1.42 1.53, 1.36, 1.47
8.93 7.78 7.37 8.92 7.90 7.34 7.27
505 464 443 310 294 290 261
diamond, however, it is lower than many other predicted carbon allotrope, such as T-carbon [17], BC8 carbon, Rh6 carbon [18] and pentagraphene [19]. Fig. 1 (c) shows the possible synthesis strategy for the M-C21 carbon. Starting from two reactants Centrohexaquinacene and Methane radical, through dehydrogenation. The dehydrogenation methodology is a typical bottom-up technology and is widely applied in structure synthesis [20], even the full carbon diamond crystal can be synthesized through the dehydrogenation progress of admantane molecule below 500 °C [21]. The activation energy for the benzene dehydrogenation (benzene to biphenyl) is around 287 kJ/mol [22]. This energy is far from dissociating the C–H bonds (440 kJ/mol) [23]. Theoretically, the
are radical carbon atoms with direct 3 folded bonds with bond length b3 = 1.47 Å and bond angle a3 = 120.0°, this bond length is between the traditional sp3 (1.54 Å) and sp2 (1.34 Å), and also longer than the bond length in graphite (1.42 Å), indicating the strong hybridization between the sp2 and sp3 type bonding. Table 1 summarizes the comparison of space groups, lattice parameters, mass density, carboncarbon bond lengths, atomic cohesive energy and bulk modulus among diamond, graphite and M-C21 carbons, the mass density of M-C21 is only 2.17 g/cm3, which is as low as that of layer graphite, this is because as a bulk materials, the crystal structure of M-C21 is not fully packed. The atomic cohesive energy Ecoh of M-C21 is 7.27 eV based on the PBE function, it is about 0.6–0.7 eV/atom higher than graphite and 2
Solid State Communications 302 (2019) 113707
Z. Lai and X. Zhu
Fig. 3. (a) Potential energy per atom variation (Epot/atom) plot with the volume per atom, comparison among diamond, graphite and M-C21. (b) Potential energy per atom variation (Epot/atom) during NPT molecular dynamics under 600 K, 800 K, 1000 K and 1atm pressure respectively.
Fig. 2. Simulated phonon band structures and partial phonon dos for M-C21, the geometric shape in the p-dos plot corresponds to the various types of carbon atoms in Fig. 1 (b). The AFM and FM states are colored by black and red respectively.
dehydrogenation strategy is a possible way for the synthesis of M-C21 carbon structure. To check the thermal stability, we plot the phonon band structures of M-C21 carbon as shown in Fig. 2, there is no negative frequency over the entire Brillion zone, indicating that the structure is stable at 0 K and 0 GPa condition, the highest frequency is around 47.1 (1571.2 cm−1) THz for the A1 mode at Γ point for the ferromagnetic (FM) states and 47.2 (1574.2 cm−1) THz with the same A1 mode for anti-ferromagnetic (AFM) state because of the slightly bond length reduction and bond strength increase in the AFM state. Due to the lower of symmetry of the AFM state, the T2 mode in FM state split into 2 A1 and B2 modes. The highest frequency mode is a typical C–C double bond vibration, according to the partial DOS, the double bonded C1 type carbon atoms' contribution is dominant, and there are also some C2 components since the C2 and C1 types are connected, the major C1 contribution lies at range 1180 cm−1, the typical sp3 high frequency mode 1400 cm−1 disappears here because there is no whole diamond like sub units in the M-C21 at all. For the C3 and C4 types, we can see besides the high frequency, it is almost degenerated with the C1 type in other vibration widows. Other than the thermal stability, we also check the total energy with the volume variation, as shown in Fig. 3 (a), we can see that the diamond and graphite are more stable than the M-C21, and the M-C21 is stable (continues E-V curve) even the volume is compressed into 1/2 of the origin one, corresponding a 130 GPa external pressure, and when the volume is double, the structure is still stable from the E-V curve shape. We also perform NPT molecular dynamics under 1000 K, 800 K and 600 K under 1 atm to check the structure stability of M-C21 under high temperature condition, with a 900 eV kinetic cutoff energy in the DFT calculation with the AFM states. As shown in Fig. 3 (b), we can see even for the 1000 K case, the potential energy per atom Epot/atom increases 0.15 eV/atom, which is within 0.5% in volume variation as compared with Fig. 3 (a), indicating the M-C21 structure is extra stable even under 1000 K. Next, we investigate the electronic structure of the M-C21 phase, as discussed above, without considering the conjugation, the C2 type carbon atoms is 3-fold carbon which is unsaturated, it can carry unpaired spins. Fig. 4 plots the spin-polarized and structure and projected density of states (DOS), we find that the ground state of M-C21 is AFM, which is 6.7 meV per atom and 30.5 meV per atom energy favor than the FM phase and NM phase respectively. As discussed above, the four C2 type carbon atoms have unpaired spins and our simulation finds each atom have 1 μ B absolute magnetic moment, thus each unit cell has
Fig. 4. (a), Spin-polarized electronic band structures and (b), projected density of states (DOS) plot of the anti-ferromagnetic M-C21 carbon. The up and down green arrow represent the up and down spin respectively, The insert figure in (b) up left side shows the color mapped spin-density with iso-value 0.03 e/Å3, (c), the locally magnified spin density with iso-value 0.005 e/Å3 illustrates the super-exchange mechanism for the anti-ferromagnetism.
4 μ B magnetic moments for the FM states. For the AFM state, any nearby two C2 type carbon atoms have different spin states, and all the spin density is localized only in the C2 type carbon atom, as shown in the up left insert figure in Fig. 4 (b), the AFM ground state is also semiconductor, however, if we look further into the spin density, and reduce the iso-value into 0.005 e/Å3, as shown in Fig. 4 (c), we can see the two C2 type carbon atoms which connecting two C1 types atoms have different spin states from the nearby C2 type atoms, these makes the local structure a typical super-exchange AFM system, where the nearby two p orbitals have different spins, due to the bulk periodic character of M-C21, these kind of super-exchange will boost the long range magnetism. In the full carbon systems, these kinds of super-exchanges magnetism has been predicted existing in the graphene nanoribbon with zigzag edges [26], the exchange energy is around 2 meV [26], here in the 3D case in M-C21 carbon, the exchange energy can reach 30.5 meV, which guarantees the robust magnetic property in the full carbon materials. In summary, by first principle density functional theory calculation, we predicted a new carbon allotrope in bulk phase, M-C21, we performed calculation on the phonon spectrum, energy-volume curve and potential energy during high temperature molecular dynamics, and we 3
Solid State Communications 302 (2019) 113707
Z. Lai and X. Zhu
find this new carbon allotrope is stable when the pressure reach 130 GPa and temperature reach 1000 K. The most significance is, due to the special carbon bonding, it has radical like carbon atoms in the crystal structures, which makes the AFM ground state with super-exchange interactions, this work provides paves new ways to develop new magnetic bulk carbon allotropes both in theory and synthesis.
Lett. 93 (2004) 187202. [8] Y. Zhang, S. Talapatra, S. Kar, R. Vajtai, S.K. Nayak, P.M. Ajayan, Phys. Rev. Lett. 99 (2007) 107201. [9] P.O. Lehtinen, A.S. Foster, A. Ayuela, A. Krasheninnikov, K. Nordlund, R.M. Nieminen, Phys. Rev. Lett. 91 (2003) 017202. [10] N. Park, M. Yoon, S. Berber, J. Ihm, E. Osawa, D. Tománek, Phys. Rev. Lett. 91 (2003) 237204. [11] R. Hoffmann, A.A. Kabanov, A.A. Golov, D.M. Proserpio, Angew. Chem. Int. Ed. 55 (2016) 10962–10976. [12] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864–B871. [13] X. Gonze, B. Amadon, P.M. Anglade, J.M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Côté, T. Deutsch, L. Genovese, P. Ghosez, M. Giantomassi, S. Goedecker, D.R. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, M.J.T. Oliveira, G. Onida, Y. Pouillon, T. Rangel, G.M. Rignanese, D. Sangalli, R. Shaltaf, M. Torrent, M.J. Verstraete, G. Zerah, J.W. Zwanziger, Comput. Phys. Commun. 180 (2009) 2582–2615. [14] D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566–569. [15] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048–5079. [16] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. [17] X.-L. Sheng, Q.-B. Yan, F. Ye, Q.-R. Zheng, G. Su, Phys. Rev. Lett. 106 (2011) 155703. [18] S. Zhang, Q. Wang, X. Chen, P. Jena, Proc. Natl. Acad. Sci. 110 (2013) 18809–18813. [19] S. Zhang, J. Zhou, Q. Wang, X. Chen, Y. Kawazoe, P. Jena, Proc. Natl. Acad. Sci. 112 (2015) 2372–2377. [20] Z. Wang, A. Błaszczyk, O. Fuhr, S. Heissler, C. Wöll, M. Mayor, Nat. Commun. 8 (2017) 14442. [21] Y.-C. Chen, L. Chang, RSC Adv. 3 (2013) 1514–1518. [22] R. Dasgupta, B.R. Maiti, Ind. Eng. Chem. Process Des. Dev. 25 (1986) 381–386. [23] Y.R. Luo, Comprehensive Handbook of Chemical Bond Energies, CRC Press, 2007. [24] C. Kittel, Introduction to Solid State Physics, Wiley, 2004. [25] J. Furthmüller, J. Hafner, G. Kresse, Phys. Rev. B 50 (1994) 15606–15622. [26] J. Jung, T. Pereg-Barnea, A.H. MacDonald, Phys. Rev. Lett. 102 (2009) 227205.
Acknowledgment This work is supported by Shenzhen Fundamental Research foundation (JCYJ20170818103918295, JCYJ20180508162801893) Chinese National Science Foundation (Grant. No. 21805234) and President's funds from CUHK-Shenzhen. This work is partially supported by Robotic Discipline Development Fund (2016-1418) from Shenzhen Govement. References [1] A.N. Andriotis, M. Menon, R.M. Sheetz, L. Chernozatonskii, Phys. Rev. Lett. 90 (2003) 026801. [2] F. Cervantes-Sodi, G. Csányi, S. Piscanec, A.C. Ferrari, Phys. Rev. B 77 (2008) 165427. [3] O. Hod, V. Barone, G.E. Scuseria, Phys. Rev. B 77 (2008) 035411. [4] X. Zhu, H. Su, Phys. Rev. B 79 (2009) 165401. [5] P. Esquinazi, D. Spemann, R. Höhne, A. Setzer, K.H. Han, T. Butz, Phys. Rev. Lett. 91 (2003) 227201. [6] J. Narayan, A. Bhaumik, J. Appl. Phys. 118 (2015) 215303. [7] P.O. Lehtinen, A.S. Foster, Y. Ma, A.V. Krasheninnikov, R.M. Nieminen, Phys. Rev.
4
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Communication
M-C21, an anti-ferromagnetic carbon bulk materials a
Zhenhai Lai , Xi Zhu a b
T
a,b,∗
School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China Shenzhen Institute of Artificial Intelligence and Robotics for Society, Shenzhen, Guangdong, 518172, China
A B S T R A C T
A new carbon allotrope named M-C21 with anti-ferromagnetic ground state is predicted and theoretically studied by Ab initio density functional theory (DFT) method. This new structure displays F-43 M space group for the non-magnetic and ferromagnetic states and IMM2 space group for the anti-ferromagnetic state. The magnetic property in the M-C21 carbon origins from the space confined carbon radicals, which couples with the nearby magnetic carbon atoms through superexchange mechanism. The M-C21 carbon could be possibly synthesized through dehydrogenation from the mixture of Centro-hexaquinacene and methane. This work provides a new theoretic solution for the design and synthesis the magnetic carbon materials for future applications.
1. Introduction The magnetic carbon materials are of extreme importance for fundamental research and industry applications, the success of creating magnetic carbon is supposed to accelerate the carbon nano electronics for the next generation by releasing the freedom of spin. However, due to the strong covalent bond character in most of the carbon allotropes, including graphite and diamond, it is depressing to create perfect magnetic units due to the super stable ground states, however, by theory, it has been proposed several luminous strategies [1–4] to disclose the intrinsic magnetic information in full carbon materials. There are some experiments argued for the detection of the magnetic state in variant carbon samples [5,6], however, due to the sample quality, the detail of the atomic structure information is unavailable, which subsequently lead to the mechanism of magnetism remaining unknown and under debate, generally, there are some common factors which are believed to lead to the magnetism, including lattice vacancies [7,8], adatoms [9], negative Gaussian curvature [10], and carbon radical in hybrid structures [4]etc. Though there are about 500 carbon allotropes [11] reported experimentally and predicted theoretically, the magnetic full carbon allotropes are still rare in literature, it is of both fundamental importance and application motivation to investigate more on the structure and property of magnetic carbon allotropes. 2. Results and discussion Here in this work, we provided a new carbon allotrope with 3D bulk structures, with 21 carbon atoms in the primitive lattice cell, named as M-C21, and investigate the crystal and electronic properties. The crystal structure design is based on the carbon radical methodology in
∗
nanobuds [4], we hybrid the traditional sp3 and sp2 type atoms to form the isolated 3 fold carbon radical. The calculations were carried out using the density functional theory (DFT) [12] as implemented in the Abinit code [13]. Local density approximation (LDA) [14,15] and Generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) functional [16] are used for exchange and correlation. Norm-conserving pseudopotentials were used with a 500 eV kinetic energy cut-off, a smallest allowed K-spacing 0.02 Å−1 is used for the sampling of the Brillouin zone. The structures are fully optimized until the maximal atomic force is converged to 1 × 10−5 eV/Å and the lattice stress is less than 0.1 GPa. For the ferro-magnetic (FM) and nonmagnetic (NM) states, the calculations were performed in the primitive cell, while for the anti-ferromagnetic (AFM) calculation, we consider both the AFM states inside the primitive cell and the AFM states in the nearest double cell, there is no symmetry constrain for all the FM/AFM/ NM ground state calculation. The idea of constructing this structures is based on the carbon radical methodology in nanobuds [4], we hybrid the traditional sp3 and sp2 type atoms to form the isolated 3 fold carbon radical. Fig. 1 (a) and (b) show the conventional cell and primitive cell of M-C21, the lattice parameter for the conventional cell is a = 9.17 Å, with space group F4¯ 3M, (number 216), it can be divided into two sub units as shown in the primitive cell in Fig. 1 (b), one is the carbon polyhedron colored by red (C1) and gray (C2), which are connected by 3-folded bonds; the other are the blue and yellow ones (C3,C4) in the carbon polyhedron, which are 4-folded bonds. The bond geometry of the carbon tetrahedron, as shown in Fig. 1 (b), are b1 = 1.53 Å, and bond angle a1 = 109.5°, which are of typical sp3 hybridized bonding; For the carbon polyhedron composed by red and gray carbon atoms, the bond length is b2 = 1.36 Å, and bond angle is a2 = 125.0°, these are of typical sp2 carbon hybridized bonding. Moreover, the gray ones (C2),
Corresponding author. School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China. E-mail address: [email protected] (X. Zhu).
https://doi.org/10.1016/j.ssc.2019.113707 Received 20 March 2019; Received in revised form 29 July 2019; Accepted 19 August 2019 Available online 23 August 2019 0038-1098/ © 2019 Elsevier Ltd. All rights reserved.
Solid State Communications 302 (2019) 113707
Z. Lai and X. Zhu
Fig. 1. atomic structure for the M-C21 carbon allotrope, (a) shows the conventional cell, (b) shows the primitive cell, the yellow and blue color represents C3 and C4, the carbon atoms with 4 –fold bonds, the red color represents C1, the carbon atoms with double bonds, the gray color represents C2, the carbon atoms of carbon radicals, the three kinds of carbon-carbon bonds and bond angles are identified with b1,b2 and b3, a1,a2 and a3 respectively. (c), the possible synthesis pass from the dehydrogenation between the Centrohexaquinacene and Methane radical (marked in red).
Table 1 Space groups, lattice parameters (a and c in Å), mass density (ρ in g/cm3), C–C bond length (dC − C in Å) atomic cohesive energy (Ecoh in eV) and bulk modulus (B in GPa) of diamond, graphite and M-C21.The LDA and PBE data are from this work. Structure
Space group
Method
a (Å)
Diamond
Fd3¯ m
Graphite
P63/mmc
M-C21
F4¯ 3m
LDA PBE EXP [24] LDA GGA EXP [25] PBE
3.54 3.57 3.57 2.45 2.46 2.46 9.17
c(Å)
6.60 6.85 6.71
ρ (g/cm3)
dC-C(Å)
Ecoh (eV/atom)
B (GPa)
3.61 3.50 3.52 2.34 2.22 2.27 2.17
1.53 1.58 1.54 1.41 1.42 1.42 1.53, 1.36, 1.47
8.93 7.78 7.37 8.92 7.90 7.34 7.27
505 464 443 310 294 290 261
diamond, however, it is lower than many other predicted carbon allotrope, such as T-carbon [17], BC8 carbon, Rh6 carbon [18] and pentagraphene [19]. Fig. 1 (c) shows the possible synthesis strategy for the M-C21 carbon. Starting from two reactants Centrohexaquinacene and Methane radical, through dehydrogenation. The dehydrogenation methodology is a typical bottom-up technology and is widely applied in structure synthesis [20], even the full carbon diamond crystal can be synthesized through the dehydrogenation progress of admantane molecule below 500 °C [21]. The activation energy for the benzene dehydrogenation (benzene to biphenyl) is around 287 kJ/mol [22]. This energy is far from dissociating the C–H bonds (440 kJ/mol) [23]. Theoretically, the
are radical carbon atoms with direct 3 folded bonds with bond length b3 = 1.47 Å and bond angle a3 = 120.0°, this bond length is between the traditional sp3 (1.54 Å) and sp2 (1.34 Å), and also longer than the bond length in graphite (1.42 Å), indicating the strong hybridization between the sp2 and sp3 type bonding. Table 1 summarizes the comparison of space groups, lattice parameters, mass density, carboncarbon bond lengths, atomic cohesive energy and bulk modulus among diamond, graphite and M-C21 carbons, the mass density of M-C21 is only 2.17 g/cm3, which is as low as that of layer graphite, this is because as a bulk materials, the crystal structure of M-C21 is not fully packed. The atomic cohesive energy Ecoh of M-C21 is 7.27 eV based on the PBE function, it is about 0.6–0.7 eV/atom higher than graphite and 2
Solid State Communications 302 (2019) 113707
Z. Lai and X. Zhu
Fig. 3. (a) Potential energy per atom variation (Epot/atom) plot with the volume per atom, comparison among diamond, graphite and M-C21. (b) Potential energy per atom variation (Epot/atom) during NPT molecular dynamics under 600 K, 800 K, 1000 K and 1atm pressure respectively.
Fig. 2. Simulated phonon band structures and partial phonon dos for M-C21, the geometric shape in the p-dos plot corresponds to the various types of carbon atoms in Fig. 1 (b). The AFM and FM states are colored by black and red respectively.
dehydrogenation strategy is a possible way for the synthesis of M-C21 carbon structure. To check the thermal stability, we plot the phonon band structures of M-C21 carbon as shown in Fig. 2, there is no negative frequency over the entire Brillion zone, indicating that the structure is stable at 0 K and 0 GPa condition, the highest frequency is around 47.1 (1571.2 cm−1) THz for the A1 mode at Γ point for the ferromagnetic (FM) states and 47.2 (1574.2 cm−1) THz with the same A1 mode for anti-ferromagnetic (AFM) state because of the slightly bond length reduction and bond strength increase in the AFM state. Due to the lower of symmetry of the AFM state, the T2 mode in FM state split into 2 A1 and B2 modes. The highest frequency mode is a typical C–C double bond vibration, according to the partial DOS, the double bonded C1 type carbon atoms' contribution is dominant, and there are also some C2 components since the C2 and C1 types are connected, the major C1 contribution lies at range 1180 cm−1, the typical sp3 high frequency mode 1400 cm−1 disappears here because there is no whole diamond like sub units in the M-C21 at all. For the C3 and C4 types, we can see besides the high frequency, it is almost degenerated with the C1 type in other vibration widows. Other than the thermal stability, we also check the total energy with the volume variation, as shown in Fig. 3 (a), we can see that the diamond and graphite are more stable than the M-C21, and the M-C21 is stable (continues E-V curve) even the volume is compressed into 1/2 of the origin one, corresponding a 130 GPa external pressure, and when the volume is double, the structure is still stable from the E-V curve shape. We also perform NPT molecular dynamics under 1000 K, 800 K and 600 K under 1 atm to check the structure stability of M-C21 under high temperature condition, with a 900 eV kinetic cutoff energy in the DFT calculation with the AFM states. As shown in Fig. 3 (b), we can see even for the 1000 K case, the potential energy per atom Epot/atom increases 0.15 eV/atom, which is within 0.5% in volume variation as compared with Fig. 3 (a), indicating the M-C21 structure is extra stable even under 1000 K. Next, we investigate the electronic structure of the M-C21 phase, as discussed above, without considering the conjugation, the C2 type carbon atoms is 3-fold carbon which is unsaturated, it can carry unpaired spins. Fig. 4 plots the spin-polarized and structure and projected density of states (DOS), we find that the ground state of M-C21 is AFM, which is 6.7 meV per atom and 30.5 meV per atom energy favor than the FM phase and NM phase respectively. As discussed above, the four C2 type carbon atoms have unpaired spins and our simulation finds each atom have 1 μ B absolute magnetic moment, thus each unit cell has
Fig. 4. (a), Spin-polarized electronic band structures and (b), projected density of states (DOS) plot of the anti-ferromagnetic M-C21 carbon. The up and down green arrow represent the up and down spin respectively, The insert figure in (b) up left side shows the color mapped spin-density with iso-value 0.03 e/Å3, (c), the locally magnified spin density with iso-value 0.005 e/Å3 illustrates the super-exchange mechanism for the anti-ferromagnetism.
4 μ B magnetic moments for the FM states. For the AFM state, any nearby two C2 type carbon atoms have different spin states, and all the spin density is localized only in the C2 type carbon atom, as shown in the up left insert figure in Fig. 4 (b), the AFM ground state is also semiconductor, however, if we look further into the spin density, and reduce the iso-value into 0.005 e/Å3, as shown in Fig. 4 (c), we can see the two C2 type carbon atoms which connecting two C1 types atoms have different spin states from the nearby C2 type atoms, these makes the local structure a typical super-exchange AFM system, where the nearby two p orbitals have different spins, due to the bulk periodic character of M-C21, these kind of super-exchange will boost the long range magnetism. In the full carbon systems, these kinds of super-exchanges magnetism has been predicted existing in the graphene nanoribbon with zigzag edges [26], the exchange energy is around 2 meV [26], here in the 3D case in M-C21 carbon, the exchange energy can reach 30.5 meV, which guarantees the robust magnetic property in the full carbon materials. In summary, by first principle density functional theory calculation, we predicted a new carbon allotrope in bulk phase, M-C21, we performed calculation on the phonon spectrum, energy-volume curve and potential energy during high temperature molecular dynamics, and we 3
Solid State Communications 302 (2019) 113707
Z. Lai and X. Zhu
find this new carbon allotrope is stable when the pressure reach 130 GPa and temperature reach 1000 K. The most significance is, due to the special carbon bonding, it has radical like carbon atoms in the crystal structures, which makes the AFM ground state with super-exchange interactions, this work provides paves new ways to develop new magnetic bulk carbon allotropes both in theory and synthesis.
Lett. 93 (2004) 187202. [8] Y. Zhang, S. Talapatra, S. Kar, R. Vajtai, S.K. Nayak, P.M. Ajayan, Phys. Rev. Lett. 99 (2007) 107201. [9] P.O. Lehtinen, A.S. Foster, A. Ayuela, A. Krasheninnikov, K. Nordlund, R.M. Nieminen, Phys. Rev. Lett. 91 (2003) 017202. [10] N. Park, M. Yoon, S. Berber, J. Ihm, E. Osawa, D. Tománek, Phys. Rev. Lett. 91 (2003) 237204. [11] R. Hoffmann, A.A. Kabanov, A.A. Golov, D.M. Proserpio, Angew. Chem. Int. Ed. 55 (2016) 10962–10976. [12] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864–B871. [13] X. Gonze, B. Amadon, P.M. Anglade, J.M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Côté, T. Deutsch, L. Genovese, P. Ghosez, M. Giantomassi, S. Goedecker, D.R. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, M.J.T. Oliveira, G. Onida, Y. Pouillon, T. Rangel, G.M. Rignanese, D. Sangalli, R. Shaltaf, M. Torrent, M.J. Verstraete, G. Zerah, J.W. Zwanziger, Comput. Phys. Commun. 180 (2009) 2582–2615. [14] D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566–569. [15] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048–5079. [16] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. [17] X.-L. Sheng, Q.-B. Yan, F. Ye, Q.-R. Zheng, G. Su, Phys. Rev. Lett. 106 (2011) 155703. [18] S. Zhang, Q. Wang, X. Chen, P. Jena, Proc. Natl. Acad. Sci. 110 (2013) 18809–18813. [19] S. Zhang, J. Zhou, Q. Wang, X. Chen, Y. Kawazoe, P. Jena, Proc. Natl. Acad. Sci. 112 (2015) 2372–2377. [20] Z. Wang, A. Błaszczyk, O. Fuhr, S. Heissler, C. Wöll, M. Mayor, Nat. Commun. 8 (2017) 14442. [21] Y.-C. Chen, L. Chang, RSC Adv. 3 (2013) 1514–1518. [22] R. Dasgupta, B.R. Maiti, Ind. Eng. Chem. Process Des. Dev. 25 (1986) 381–386. [23] Y.R. Luo, Comprehensive Handbook of Chemical Bond Energies, CRC Press, 2007. [24] C. Kittel, Introduction to Solid State Physics, Wiley, 2004. [25] J. Furthmüller, J. Hafner, G. Kresse, Phys. Rev. B 50 (1994) 15606–15622. [26] J. Jung, T. Pereg-Barnea, A.H. MacDonald, Phys. Rev. Lett. 102 (2009) 227205.
Acknowledgment This work is supported by Shenzhen Fundamental Research foundation (JCYJ20170818103918295, JCYJ20180508162801893) Chinese National Science Foundation (Grant. No. 21805234) and President's funds from CUHK-Shenzhen. This work is partially supported by Robotic Discipline Development Fund (2016-1418) from Shenzhen Govement. References [1] A.N. Andriotis, M. Menon, R.M. Sheetz, L. Chernozatonskii, Phys. Rev. Lett. 90 (2003) 026801. [2] F. Cervantes-Sodi, G. Csányi, S. Piscanec, A.C. Ferrari, Phys. Rev. B 77 (2008) 165427. [3] O. Hod, V. Barone, G.E. Scuseria, Phys. Rev. B 77 (2008) 035411. [4] X. Zhu, H. Su, Phys. Rev. B 79 (2009) 165401. [5] P. Esquinazi, D. Spemann, R. Höhne, A. Setzer, K.H. Han, T. Butz, Phys. Rev. Lett. 91 (2003) 227201. [6] J. Narayan, A. Bhaumik, J. Appl. Phys. 118 (2015) 215303. [7] P.O. Lehtinen, A.S. Foster, Y. Ma, A.V. Krasheninnikov, R.M. Nieminen, Phys. Rev.
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