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Tunable electronic and magnetic properties of substitutionally doped graphene
Physica E 119 (2020) 113985
Contents lists available at ScienceDirect
Physica E: Low-dimensional Systems and Nanostructures journal homepage: www.elsevier.com/locate/physe
Tunable electronic and magnetic properties of substitutionally doped graphene Artur P. Durajski a ,∗, Anita E. Auguscik a , Radosław Szcze¸śniak a,b a b
Institute of Physics, Cze¸stochowa University of Technology, Ave. Armii Krajowej 19, 42-200 Cze¸stochowa, Poland Institute of Physics, Jan Długosz University in Cze¸stochowa, Ave. Armii Krajowej 13/15, 42-200 Cze¸stochowa, Poland
ARTICLE
INFO
ABSTRACT
Keywords: Graphene Electronic properties Magnetic properties Doping DFT calculations
The van der Waals materials provide a playground to study new phenomena in two-dimensional magnetism. Here, we discuss the possibility of induction of a magnetic state in graphene by modifying its band structure by substitutional doping. Based on a density-functional theory we study the structural, electronic and magnetic properties of graphene doped with V, Cr, Mn, Fe, Co, Ni, and Cu atoms. It was observed that substitutionally doping, strongly influences the structural as well as the electronic properties of the resulting layers. Our study identified four candidates (graphene doped with V, Cr, Fe, and Co atoms) whose ferromagnetic order is energetically the most favorable. In the case of V- and Cr-doped graphene, Curie temperatures obtained analytically far exceed the room temperature. Furthermore, the Mn-doped system prefers antiferromagnetic order and in the case of Ni and Cu dopants, we observed nonmagnetic behavior. Although the addition of the Hubbard parameter 𝑈 slightly modified the magnetic properties the graphene sheets doped with V and Cr atoms are found to have the high Curie temperature (∼500-800 K). Our studies demonstrate, that the obtained results can be valuable in designing nanodevices for applications.
1. Introduction
physical properties of investigated systems [18,19]. Beyond the superconductivity, the studies on the magnetic properties of graphene also attract wide attention. The fact that pristine graphene is not magnetic limits its application in areas such as magnetic storage and spintronics. However, recent theoretical and experimental results indicate that adsorption of metal adatoms and substitutional doping is a promising way to modulate the electronic properties and induce a ferromagnetic state of graphene-based systems [20–27]. However, it remains a challenge to tune this ferromagnetism at ambient temperature. In this work, we report our first-principles calculation results of the influence of substitutional doping of 3𝑑 transition metals (i.e. V, Cr, Mn, Fe, Co, Ni, and Cu) on the geometric structure, the electronic structure and the magnetic properties of the graphene sheet. The ferromagnetic spin-order with a Curie temperature much higher than room temperature we obtained in the case of V- and Cr-doped graphene. This paper is organized as follows. In the next section, we briefly describe the method and calculation details. Then, we present our results together with accurate discussions, including the doping effect on electronic and magnetic behaviors of graphene. Next, to include the strong correlation effects, calculations in the DFT+U approach have been performed. Finally, we summarize and conclude our paper.
After the first mechanical exfoliation of graphene from graphite in 2004 [1], two-dimensional (2D) hexagonal structures have been widely studied due to their unique electronic and magnetic properties as well as potential applications [2–6]. Among many remarkable features, graphene is characterized by good charge and heat transport, and outstanding thermomechanical and optical properties that make this material an attractive candidate for the future generation of nanoelectronic and nanophotonic devices, gas sensors, biosensors, and batteries for energy storage [7]. However, in pristine graphene, the electronic density of states at the Fermi energy is zero, and thus the graphene is a semiconductor with zero band gap or a semimetal [8,9] which limits its suitability for many applications. Therefore, to make it really useful, its electronic structure should be modified desirably. A possible approach of tuning the characteristics of graphene is to introduce in-plane defects and impurities or controlling decoration/intercalation of mono/multilayer graphene [10–15]. For instance, the superconducting state was observed experimentally in Li-decorated monolayer graphene around 5.9 K [16] and in Ca-intercalated graphene laminates at 6.4 K [17]. Moreover, it was shown that the pristine bilayer graphene and Liintercalated graphene exhibit nonsuperconducting behavior, suggesting the significant influence of intercalated atoms and its species on the
∗ Corresponding author. E-mail address: [email protected] (A.P. Durajski).
https://doi.org/10.1016/j.physe.2020.113985 Received 3 October 2019; Received in revised form 21 January 2020; Accepted 27 January 2020 Available online 31 January 2020 1386-9477/© 2020 Elsevier B.V. All rights reserved.
Physica E: Low-dimensional Systems and Nanostructures 119 (2020) 113985
A.P. Durajski et al.
Fig. 1. Schematics showing the evolution of the geometric structure of Cu-doped graphene during the relaxation procedure. The C atoms are shown in yellow and the Cu atoms are shown in brown. The forces are visualized by blue arrows. The views show different stages from the initial (a) to the fully relaxed configuration (d). Figures (b) and (c) present intermediate steps. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Structural parameters for the substitutionally doped graphene through the seven atoms considered in this work. The properties listed are the lattice parameter (𝑎), doping atom height (ℎ𝐷𝐴 ), height of three nearest-neighbor C atoms lifted up from the plane (ℎ𝐶 ) and doping atom–carbon atom bond length (𝑑𝐷𝐴−𝐶 ).
2. Computational methods First-principles calculations are performed within the framework of the density-functional theory (DFT) [28] with Grimme semi-empirical correction (DFT-D2 method) on the van der Waals interactions, as implemented in the Quantum Espresso (QE) package [29,30]. The generalized gradient approximation of Perdew–Burke–Ernzerhof (GGAPBE) is used for the exchange–correlation functional together with the projector-augmented wave (PAW) method. Spin polarization is allowed in all calculations. The kinetic energy cutoff for the wavefunction is set to 40 Ry and the kinetic energy cutoff for charge density is 400 Ry. The model system consists of a 6 × 6 supercell of graphene (containing 72 C atoms) with four 3𝑑 transition metal atoms substituting four C atoms, corresponding to about 5.5% dopant concentration. To avoid the interaction between graphene layers, a vacuum layer of 12 Å is added along the graphene plane normal. To obtain the optimized structures, the atomic positions are fully relaxed by using the Broyden–Fletcher– Goldfarb–Shanno (BFGS) quasi-Newton algorithm until all forces are smaller than 0.01 eV/Å. The Brillouin zone is sampled utilizing an 8 × 8 × 1 k-mesh in the Monkhorst–Pack scheme and the Marzari– Vanderbilt cold smearing with a smearing factor of 0.005 Ry is used in all calculations. A 32 × 32 × 1 Monkhorst–Pack grid is applied for the calculation of the density of states (DOS). We have carefully checked all these parameters, and we found they are good for a strict energy-convergence criterion.
Dopant
𝑎 (Å)
ℎ (Å)
𝑑𝐷𝐴−𝐶 (Å)
ℎ𝐶 (Å)
V Cr Mn Fe Co Ni Cu
14.9716 14.9526 14.9382 14.8574 14.9357 14.9194 14.9570
1.2652 1.2147 1.1790 1.1989 1.0853 1.0852 1.2197
1.8606 1.8157 1.7799 1.7726 1.7637 1.7922 1.8800
0.2106 0.2316 0.2597 0.2869 0.2158 0.1719 0.1919
carbon atom, the metal atoms displace outwards from the graphene surface and the geometric structure of substitutionally doped graphene undergoes a significant rearrangement. The doping atoms protrude out of the graphene sheet at a height (ℎ) of 1.085 − 1.265 Å and the three nearest-neighbor C atoms are also elevated above the graphene surface by 0.172 − 0.287 Å. The doping atom–carbon atom bond length is in the range of 1.764 − 1.880 Å, which is quite large compared to C–C bonds. This is associated with a distortion of hexagon structures adjacent to the doping atom [33]. A summary of the obtained results is shown in Table 1. Moreover, in Fig. 1 we showed the evolution of the geometric structure of Cu-doped graphene during the relaxation procedure.
3. Results and discussion
The binding energy (𝐸𝑏 ) of the substitutional metal atoms in the graphene sheet is calculated using the following formula:
3.1. Effect of doping on geometric of graphene
𝐸𝑏 = 𝐸𝐷𝐴 + 𝐸𝐶 − 𝐸𝐶+𝐷𝐴
Before the study of substitutionally doped graphene, pristine graphene was investigated to check the reliability of our calculations. Primarily, we optimized the 72-atom graphene supercell to get a relaxed structure. The relaxed distance between adjacent carbon atoms in the plane (C–C bond length) was found to be 1.42 Å and the lattice parameters of the supercell were 𝑎 = 𝑏 = 14.79 Å which is in excellent agreement with the previous results [31,32]. This indicating thereby the correctness of our calculations. Then, this optimized graphene sheet was doped with 3𝑑 transition metal atoms V, Cr, Mn, Fe, Co, Ni, and Cu. As the atomic radii of these elements are larger than that of the
where 𝐸𝐷𝐴 is the ground state energy of an isolated dopant atom, 𝐸𝐶 is the energy of the graphene with vacancies and 𝐸𝐶+𝐷𝐴 represents the total energy of substitutionally doped graphene systems. All energies were calculated for the fixed supercells. The binding energy for the 3𝑑 transition metal atoms is in the range of 7.75–4.21 eV. The positive values indicate that all investigated systems have stable configurations. Quantitatively, as we can see in Fig. 2, the maximum bonding energy corresponds to Co atom, which has a 4𝑠2 3𝑑 7 electronic configuration. The weakest binding has been found for Cu atom having 4𝑠1 3𝑑 10 electronic configuration. 2
(1)
Physica E: Low-dimensional Systems and Nanostructures 119 (2020) 113985
A.P. Durajski et al.
semiconducting behavior, which agrees with the results of the previous study [4]. It means that perfect graphene is nonmagnetic, but the presence of vacancies or dopant atoms can induce magnetism, by breaking the symmetry of the 𝜋-electron system. Analyzing the results obtained for doped graphene, it is observed that the total DOS gets altered and localized levels start appearing, especially in the vicinity of the Fermi level. Moreover, for the V-, Cr-, Fe-, and Co-doped graphene the total DOS near the Fermi level is distinctly asymmetric. For these cases, the calculated energy difference between the ferromagnetic and antiferromagnetic states (𝛥𝐸𝐹 𝑀−𝐴𝐹 𝑀 ) shows that the ferromagnetic state is energetically more favorable than the antiferromagnetic spin ordering, which is in good agreement with the total magnetic moment (𝑀) in Table 2. Interestingly, the Mn-doped graphene acquires antiferromagnetism, which is in good accordance with the previous results [34]. The symmetry of the spin up and spin down bands confirms the nonmagnetic nature of the Ni- and Cu-doped systems. The ferromagnetic graphene-based material with Curie temperature (𝑇𝐶 ) higher than room temperature can be a good candidate for nanomagnetic applications [21]. Herein, based on the mean-field approximation [35], we estimated 𝑇𝐶 using the following formula [36]:
Fig. 2. Binding energies per one dopant atom (main part) and the total energies (inset) of the graphene sheet with four 3𝑑 transition metal atoms adsorbed.
3.2. Effect of doping on electronic structures of graphene
𝛥𝐸 3 𝑘 𝑇 = − 𝐹 𝑀−𝐴𝐹 𝑀 , 2 𝐵 𝐶 𝑛
(2)
where 𝑘𝐵 = 8.6173 × 10−5 is the Boltzmann constant and 𝑛 is the number of the dopants in the supercell (in our case 𝑛 = 4). As we can see in Table 2, the estimated Curie temperatures for V- and Cr-doped graphene are 823.9 and 498.2 K, well above the room temperature. It should be noted, that recently the similar results were obtained for the N-doped graphene that also exhibits ferromagnetic properties with high
The density of states (DOS) has been calculated to investigate the electronic properties of graphene with transition metal atoms as substitutional impurities. Fig. 3 demonstrates the results for the pristine graphene sheet and, subsequently, results obtained for all doped systems. The DOS of the pristine graphene exhibits a zero band gap
Fig. 3. A comparison of the spin-polarized density of states (DOS) of ideal pristine and doped graphene supercells. The Fermi level set to zero is indicated as the vertical dashed line. 3
Physica E: Low-dimensional Systems and Nanostructures 119 (2020) 113985
A.P. Durajski et al. Table 2 Total magnetic moment (𝑀), energy difference between the FM and AFM phase (𝛥𝐸𝐹 𝑀−𝐴𝐹 𝑀 ) and Curie temperature (𝑇𝐶 ) for the substitutionally doped graphene in the ferromagnetic state. Dopant
𝑀 (𝜇𝐵 )
𝛥𝐸𝐹 𝑀−𝐴𝐹 𝑀 (eV)
𝑇𝐶 (K)
V Cr Fe Co
2.78 7.95 4.24 3.48
−0.425977 −0.257563 −0.008111 −0.052077
823.9 498.2 15.7 100.7
Table 3 The value of Hubbard U parameter and the corresponding total magnetic moment (M), the energy difference between the FM and AFM phase (𝛥𝐸𝐹 𝑀−𝐴𝐹 𝑀 ) and Curie temperature (𝑇𝐶 ) for the V-, Cr-, and Co-doped graphene in the ferromagnetic state. Dopant
U (eV)
𝑀 (𝜇𝐵 )
𝛥𝐸𝐹 𝑀−𝐴𝐹 𝑀 (eV)
𝑇𝐶 (K)
V Cr Co
3.90 3.21 7.83
3.97 8.00 3.20
−0.404508 −0.250691 −0.053287
782.3 484.9 103.1
𝑇𝐶 (> 600 K) [21]. Moreover, Park et al. reported that ferromagnetic semiconductor properties can be observed in the monolayer graphene after manganese-oxide doping. The transport measurements indicate the Curie temperature of this system is 270 K [37]. 3.3. Effects of the Hubbard on-site Coulombic correction on the electronic properties of doped graphene Due to the fact that in investigated 3𝑑 transition metals 𝑑 orbitals are partially filled, the description of properties of these systems can be particularly difficult using traditional DFT methods. Indeed, strong correlation effects might exist as well as quantum spin fluctuations which are not well described by DFT in the GGA approximation [38]. Therefore, to include the strong correlation effects, calculations in the DFT+U approach [39,40], implemented in the QE package, have been performed for the study of the electronic properties of substitutionally doped graphene. In particular, the linear-response approach was used to compute U from first principles [41]. This method derives Hubbard parameters from the response of the Hubbard sites electronic occupations to a small perturbation of the potential acting on the Hubbard manifold of the d or f electrons [41,42]. For V-, Cr-, Fe-, and Co-doped graphene supercells the estimated values of 𝑈 are 3.90, 3.21, 4.17, and 7.83 eV, respectively. Entering the 𝑈 parameter into the calculations of electronic properties causes that antiferromagnetic ordering of Fe-doped graphene is energetically more favorable than ferromagnetic one. This result confirm that the Hubbard correction is able to significantly change the magnetic properties of modified graphene with respect to GGA. Fig. 4 compares the total DOS of V-, Cr-, and Co-doped graphene in the ferromagnetic state obtained with and without 𝑈 parameter. As we can see at the Fermi level the changes are not significant or drastic, hence, the Curie temperatures calculated using the DFT+U approach and collected in Table 3 are slightly different from those calculated using the DFT approach. Unfortunately, due to the lack of experimental data, we cannot say unequivocally, which method providing a more accurate estimation of the electronic and magnetic properties of these materials.
Fig. 4. A comparison of the spin-polarized density of states computed in DFT (colored background areas) and DFT+U approach (solid lines). The Fermi level set to zero is marked as the vertical dashed line.
that magnetic properties are affected by the implementation of the Hubbard 𝑈 term in DFT calculations, as confirmed by changing the type of magnetic ordering from the ferro- to antiferromagnetic in Fe-doped graphene. Interestingly, the graphene sheets doped with V and Cr atoms analyzed with and without 𝑈 are found to have high Curie temperature (∼500–800 K). This discovery opens up vast opportunities for utilizing two-dimensional doped graphene magnets in room-temperature spintronics devices. We expect that our findings can stimulate further experimental studies for the remarkable properties of substitutionally doped graphene and lead to the verification of predictions presented herein. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
4. Conclusions CRediT authorship contribution statement
Within the first-principles calculations, here we systematically investigate the structural, electronic and magnetic properties of graphene sheets doped with V, Cr, Mn, Fe, Co, Ni, and Cu atoms. Our results reveal the effects of substitutional doping on the density of states of a graphene monolayer and show the opportunity to induce a ferromagnetic state in V-, Cr-, Fe- and Co-doped system. Moreover, we found
Artur P. Durajski: Conceptualization, Methodology, Software, Supervision. Anita E. Auguscik: Conceptualization, Data curation, Investigation, Visualization, Writing - original draft. Radosław Szcze¸śniak: Investigation, Writing - review & editing. 4
Physica E: Low-dimensional Systems and Nanostructures 119 (2020) 113985
A.P. Durajski et al.
Acknowledgments
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A.P. Durajski acknowledges the financial support from the Czestochowa University of Technology, Poland under Grant No. BS/MN200-301/2019 and from the Polish Ministry of Science and Higher Education under the scholarship for young outstanding scientists No. 406/STYP/13/2018. All authors are grateful to the Czestochowa University of Technology - MSK CzestMAN, Poland for granting access to the computing infrastructure built in the projects No. POIG.02.03.0000-028/08 ‘‘PLATON - Science Services Platform’’ and No. POIG.02.03. 00-00-110/13 ‘‘Deploying high-availability, critical services in Metropolitan Area Networks (MAN-HA)’’. References [1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306 (2004) 666. [2] R. Wang, X.-G. Ren, Z. Yan, L.-J. Jiang, W.E.I. Sha, G.-C. Shan, Front. Phys. 14 (2018) 13603. [3] M.J. Allen, V.C. Tung, R.B. Kaner, Chem. Rev. 110 (2010) 132. [4] A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Modern Phys. 81 (2009) 109. [5] M. Huefner, C. May, S. Kicin, K. Ensslin, T. Ihn, M. Hilke, K. Suter, N.F. de Rooij, U. Staufer, Phys. Rev. B 79 (2009) 134530. [6] D. Szczesniak, A.P. Durajski, A. Khater, D. Ghader, Europhys. Lett. 114 (4) (2016) 48001. [7] H. Zhao, Q. Guo, F. Xia, H. Wang, Nanophotonics 4 (2015) 128. [8] G. Lu, K. Yu, Z. Wen, J. Chen, Nanoscale 5 (2013) 1353. [9] H.H. Radamson, in: S. Kasap, P. Capper (Eds.), Springer Handbook of Electronic and Photonic Materials, Springer International Publishing, Cham, 2017, p. 1173. [10] K.T. Chan, J.B. Neaton, M.L. Cohen, Phys. Rev. B 77 (2008) 235430. [11] M. Sun, W. Tang, Q. Ren, Y. Zhao, S. Wang, J. Yu, Y. Du, Y. Hao, Physica E 80 (2016) 142. [12] J. Dai, J. Yuan, J. Phys. Condens. Matter 22 (2010) 225501. [13] P.T. Araujo, M. Terrones, M.S. Dresselhaus, Mater. Today 15 (2012) 98. [14] J. Pesic, V. Damljanovic, R. Gajic, K. Hingerl, M. Belic, Europhys. Lett. 112 (2015) 67006. [15] J. Pesic, R. Gajic, K. Hingerl, M. Belic, Europhys. Lett. 108 (2014) 67005.
5
Contents lists available at ScienceDirect
Physica E: Low-dimensional Systems and Nanostructures journal homepage: www.elsevier.com/locate/physe
Tunable electronic and magnetic properties of substitutionally doped graphene Artur P. Durajski a ,∗, Anita E. Auguscik a , Radosław Szcze¸śniak a,b a b
Institute of Physics, Cze¸stochowa University of Technology, Ave. Armii Krajowej 19, 42-200 Cze¸stochowa, Poland Institute of Physics, Jan Długosz University in Cze¸stochowa, Ave. Armii Krajowej 13/15, 42-200 Cze¸stochowa, Poland
ARTICLE
INFO
ABSTRACT
Keywords: Graphene Electronic properties Magnetic properties Doping DFT calculations
The van der Waals materials provide a playground to study new phenomena in two-dimensional magnetism. Here, we discuss the possibility of induction of a magnetic state in graphene by modifying its band structure by substitutional doping. Based on a density-functional theory we study the structural, electronic and magnetic properties of graphene doped with V, Cr, Mn, Fe, Co, Ni, and Cu atoms. It was observed that substitutionally doping, strongly influences the structural as well as the electronic properties of the resulting layers. Our study identified four candidates (graphene doped with V, Cr, Fe, and Co atoms) whose ferromagnetic order is energetically the most favorable. In the case of V- and Cr-doped graphene, Curie temperatures obtained analytically far exceed the room temperature. Furthermore, the Mn-doped system prefers antiferromagnetic order and in the case of Ni and Cu dopants, we observed nonmagnetic behavior. Although the addition of the Hubbard parameter 𝑈 slightly modified the magnetic properties the graphene sheets doped with V and Cr atoms are found to have the high Curie temperature (∼500-800 K). Our studies demonstrate, that the obtained results can be valuable in designing nanodevices for applications.
1. Introduction
physical properties of investigated systems [18,19]. Beyond the superconductivity, the studies on the magnetic properties of graphene also attract wide attention. The fact that pristine graphene is not magnetic limits its application in areas such as magnetic storage and spintronics. However, recent theoretical and experimental results indicate that adsorption of metal adatoms and substitutional doping is a promising way to modulate the electronic properties and induce a ferromagnetic state of graphene-based systems [20–27]. However, it remains a challenge to tune this ferromagnetism at ambient temperature. In this work, we report our first-principles calculation results of the influence of substitutional doping of 3𝑑 transition metals (i.e. V, Cr, Mn, Fe, Co, Ni, and Cu) on the geometric structure, the electronic structure and the magnetic properties of the graphene sheet. The ferromagnetic spin-order with a Curie temperature much higher than room temperature we obtained in the case of V- and Cr-doped graphene. This paper is organized as follows. In the next section, we briefly describe the method and calculation details. Then, we present our results together with accurate discussions, including the doping effect on electronic and magnetic behaviors of graphene. Next, to include the strong correlation effects, calculations in the DFT+U approach have been performed. Finally, we summarize and conclude our paper.
After the first mechanical exfoliation of graphene from graphite in 2004 [1], two-dimensional (2D) hexagonal structures have been widely studied due to their unique electronic and magnetic properties as well as potential applications [2–6]. Among many remarkable features, graphene is characterized by good charge and heat transport, and outstanding thermomechanical and optical properties that make this material an attractive candidate for the future generation of nanoelectronic and nanophotonic devices, gas sensors, biosensors, and batteries for energy storage [7]. However, in pristine graphene, the electronic density of states at the Fermi energy is zero, and thus the graphene is a semiconductor with zero band gap or a semimetal [8,9] which limits its suitability for many applications. Therefore, to make it really useful, its electronic structure should be modified desirably. A possible approach of tuning the characteristics of graphene is to introduce in-plane defects and impurities or controlling decoration/intercalation of mono/multilayer graphene [10–15]. For instance, the superconducting state was observed experimentally in Li-decorated monolayer graphene around 5.9 K [16] and in Ca-intercalated graphene laminates at 6.4 K [17]. Moreover, it was shown that the pristine bilayer graphene and Liintercalated graphene exhibit nonsuperconducting behavior, suggesting the significant influence of intercalated atoms and its species on the
∗ Corresponding author. E-mail address: [email protected] (A.P. Durajski).
https://doi.org/10.1016/j.physe.2020.113985 Received 3 October 2019; Received in revised form 21 January 2020; Accepted 27 January 2020 Available online 31 January 2020 1386-9477/© 2020 Elsevier B.V. All rights reserved.
Physica E: Low-dimensional Systems and Nanostructures 119 (2020) 113985
A.P. Durajski et al.
Fig. 1. Schematics showing the evolution of the geometric structure of Cu-doped graphene during the relaxation procedure. The C atoms are shown in yellow and the Cu atoms are shown in brown. The forces are visualized by blue arrows. The views show different stages from the initial (a) to the fully relaxed configuration (d). Figures (b) and (c) present intermediate steps. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Structural parameters for the substitutionally doped graphene through the seven atoms considered in this work. The properties listed are the lattice parameter (𝑎), doping atom height (ℎ𝐷𝐴 ), height of three nearest-neighbor C atoms lifted up from the plane (ℎ𝐶 ) and doping atom–carbon atom bond length (𝑑𝐷𝐴−𝐶 ).
2. Computational methods First-principles calculations are performed within the framework of the density-functional theory (DFT) [28] with Grimme semi-empirical correction (DFT-D2 method) on the van der Waals interactions, as implemented in the Quantum Espresso (QE) package [29,30]. The generalized gradient approximation of Perdew–Burke–Ernzerhof (GGAPBE) is used for the exchange–correlation functional together with the projector-augmented wave (PAW) method. Spin polarization is allowed in all calculations. The kinetic energy cutoff for the wavefunction is set to 40 Ry and the kinetic energy cutoff for charge density is 400 Ry. The model system consists of a 6 × 6 supercell of graphene (containing 72 C atoms) with four 3𝑑 transition metal atoms substituting four C atoms, corresponding to about 5.5% dopant concentration. To avoid the interaction between graphene layers, a vacuum layer of 12 Å is added along the graphene plane normal. To obtain the optimized structures, the atomic positions are fully relaxed by using the Broyden–Fletcher– Goldfarb–Shanno (BFGS) quasi-Newton algorithm until all forces are smaller than 0.01 eV/Å. The Brillouin zone is sampled utilizing an 8 × 8 × 1 k-mesh in the Monkhorst–Pack scheme and the Marzari– Vanderbilt cold smearing with a smearing factor of 0.005 Ry is used in all calculations. A 32 × 32 × 1 Monkhorst–Pack grid is applied for the calculation of the density of states (DOS). We have carefully checked all these parameters, and we found they are good for a strict energy-convergence criterion.
Dopant
𝑎 (Å)
ℎ (Å)
𝑑𝐷𝐴−𝐶 (Å)
ℎ𝐶 (Å)
V Cr Mn Fe Co Ni Cu
14.9716 14.9526 14.9382 14.8574 14.9357 14.9194 14.9570
1.2652 1.2147 1.1790 1.1989 1.0853 1.0852 1.2197
1.8606 1.8157 1.7799 1.7726 1.7637 1.7922 1.8800
0.2106 0.2316 0.2597 0.2869 0.2158 0.1719 0.1919
carbon atom, the metal atoms displace outwards from the graphene surface and the geometric structure of substitutionally doped graphene undergoes a significant rearrangement. The doping atoms protrude out of the graphene sheet at a height (ℎ) of 1.085 − 1.265 Å and the three nearest-neighbor C atoms are also elevated above the graphene surface by 0.172 − 0.287 Å. The doping atom–carbon atom bond length is in the range of 1.764 − 1.880 Å, which is quite large compared to C–C bonds. This is associated with a distortion of hexagon structures adjacent to the doping atom [33]. A summary of the obtained results is shown in Table 1. Moreover, in Fig. 1 we showed the evolution of the geometric structure of Cu-doped graphene during the relaxation procedure.
3. Results and discussion
The binding energy (𝐸𝑏 ) of the substitutional metal atoms in the graphene sheet is calculated using the following formula:
3.1. Effect of doping on geometric of graphene
𝐸𝑏 = 𝐸𝐷𝐴 + 𝐸𝐶 − 𝐸𝐶+𝐷𝐴
Before the study of substitutionally doped graphene, pristine graphene was investigated to check the reliability of our calculations. Primarily, we optimized the 72-atom graphene supercell to get a relaxed structure. The relaxed distance between adjacent carbon atoms in the plane (C–C bond length) was found to be 1.42 Å and the lattice parameters of the supercell were 𝑎 = 𝑏 = 14.79 Å which is in excellent agreement with the previous results [31,32]. This indicating thereby the correctness of our calculations. Then, this optimized graphene sheet was doped with 3𝑑 transition metal atoms V, Cr, Mn, Fe, Co, Ni, and Cu. As the atomic radii of these elements are larger than that of the
where 𝐸𝐷𝐴 is the ground state energy of an isolated dopant atom, 𝐸𝐶 is the energy of the graphene with vacancies and 𝐸𝐶+𝐷𝐴 represents the total energy of substitutionally doped graphene systems. All energies were calculated for the fixed supercells. The binding energy for the 3𝑑 transition metal atoms is in the range of 7.75–4.21 eV. The positive values indicate that all investigated systems have stable configurations. Quantitatively, as we can see in Fig. 2, the maximum bonding energy corresponds to Co atom, which has a 4𝑠2 3𝑑 7 electronic configuration. The weakest binding has been found for Cu atom having 4𝑠1 3𝑑 10 electronic configuration. 2
(1)
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semiconducting behavior, which agrees with the results of the previous study [4]. It means that perfect graphene is nonmagnetic, but the presence of vacancies or dopant atoms can induce magnetism, by breaking the symmetry of the 𝜋-electron system. Analyzing the results obtained for doped graphene, it is observed that the total DOS gets altered and localized levels start appearing, especially in the vicinity of the Fermi level. Moreover, for the V-, Cr-, Fe-, and Co-doped graphene the total DOS near the Fermi level is distinctly asymmetric. For these cases, the calculated energy difference between the ferromagnetic and antiferromagnetic states (𝛥𝐸𝐹 𝑀−𝐴𝐹 𝑀 ) shows that the ferromagnetic state is energetically more favorable than the antiferromagnetic spin ordering, which is in good agreement with the total magnetic moment (𝑀) in Table 2. Interestingly, the Mn-doped graphene acquires antiferromagnetism, which is in good accordance with the previous results [34]. The symmetry of the spin up and spin down bands confirms the nonmagnetic nature of the Ni- and Cu-doped systems. The ferromagnetic graphene-based material with Curie temperature (𝑇𝐶 ) higher than room temperature can be a good candidate for nanomagnetic applications [21]. Herein, based on the mean-field approximation [35], we estimated 𝑇𝐶 using the following formula [36]:
Fig. 2. Binding energies per one dopant atom (main part) and the total energies (inset) of the graphene sheet with four 3𝑑 transition metal atoms adsorbed.
3.2. Effect of doping on electronic structures of graphene
𝛥𝐸 3 𝑘 𝑇 = − 𝐹 𝑀−𝐴𝐹 𝑀 , 2 𝐵 𝐶 𝑛
(2)
where 𝑘𝐵 = 8.6173 × 10−5 is the Boltzmann constant and 𝑛 is the number of the dopants in the supercell (in our case 𝑛 = 4). As we can see in Table 2, the estimated Curie temperatures for V- and Cr-doped graphene are 823.9 and 498.2 K, well above the room temperature. It should be noted, that recently the similar results were obtained for the N-doped graphene that also exhibits ferromagnetic properties with high
The density of states (DOS) has been calculated to investigate the electronic properties of graphene with transition metal atoms as substitutional impurities. Fig. 3 demonstrates the results for the pristine graphene sheet and, subsequently, results obtained for all doped systems. The DOS of the pristine graphene exhibits a zero band gap
Fig. 3. A comparison of the spin-polarized density of states (DOS) of ideal pristine and doped graphene supercells. The Fermi level set to zero is indicated as the vertical dashed line. 3
Physica E: Low-dimensional Systems and Nanostructures 119 (2020) 113985
A.P. Durajski et al. Table 2 Total magnetic moment (𝑀), energy difference between the FM and AFM phase (𝛥𝐸𝐹 𝑀−𝐴𝐹 𝑀 ) and Curie temperature (𝑇𝐶 ) for the substitutionally doped graphene in the ferromagnetic state. Dopant
𝑀 (𝜇𝐵 )
𝛥𝐸𝐹 𝑀−𝐴𝐹 𝑀 (eV)
𝑇𝐶 (K)
V Cr Fe Co
2.78 7.95 4.24 3.48
−0.425977 −0.257563 −0.008111 −0.052077
823.9 498.2 15.7 100.7
Table 3 The value of Hubbard U parameter and the corresponding total magnetic moment (M), the energy difference between the FM and AFM phase (𝛥𝐸𝐹 𝑀−𝐴𝐹 𝑀 ) and Curie temperature (𝑇𝐶 ) for the V-, Cr-, and Co-doped graphene in the ferromagnetic state. Dopant
U (eV)
𝑀 (𝜇𝐵 )
𝛥𝐸𝐹 𝑀−𝐴𝐹 𝑀 (eV)
𝑇𝐶 (K)
V Cr Co
3.90 3.21 7.83
3.97 8.00 3.20
−0.404508 −0.250691 −0.053287
782.3 484.9 103.1
𝑇𝐶 (> 600 K) [21]. Moreover, Park et al. reported that ferromagnetic semiconductor properties can be observed in the monolayer graphene after manganese-oxide doping. The transport measurements indicate the Curie temperature of this system is 270 K [37]. 3.3. Effects of the Hubbard on-site Coulombic correction on the electronic properties of doped graphene Due to the fact that in investigated 3𝑑 transition metals 𝑑 orbitals are partially filled, the description of properties of these systems can be particularly difficult using traditional DFT methods. Indeed, strong correlation effects might exist as well as quantum spin fluctuations which are not well described by DFT in the GGA approximation [38]. Therefore, to include the strong correlation effects, calculations in the DFT+U approach [39,40], implemented in the QE package, have been performed for the study of the electronic properties of substitutionally doped graphene. In particular, the linear-response approach was used to compute U from first principles [41]. This method derives Hubbard parameters from the response of the Hubbard sites electronic occupations to a small perturbation of the potential acting on the Hubbard manifold of the d or f electrons [41,42]. For V-, Cr-, Fe-, and Co-doped graphene supercells the estimated values of 𝑈 are 3.90, 3.21, 4.17, and 7.83 eV, respectively. Entering the 𝑈 parameter into the calculations of electronic properties causes that antiferromagnetic ordering of Fe-doped graphene is energetically more favorable than ferromagnetic one. This result confirm that the Hubbard correction is able to significantly change the magnetic properties of modified graphene with respect to GGA. Fig. 4 compares the total DOS of V-, Cr-, and Co-doped graphene in the ferromagnetic state obtained with and without 𝑈 parameter. As we can see at the Fermi level the changes are not significant or drastic, hence, the Curie temperatures calculated using the DFT+U approach and collected in Table 3 are slightly different from those calculated using the DFT approach. Unfortunately, due to the lack of experimental data, we cannot say unequivocally, which method providing a more accurate estimation of the electronic and magnetic properties of these materials.
Fig. 4. A comparison of the spin-polarized density of states computed in DFT (colored background areas) and DFT+U approach (solid lines). The Fermi level set to zero is marked as the vertical dashed line.
that magnetic properties are affected by the implementation of the Hubbard 𝑈 term in DFT calculations, as confirmed by changing the type of magnetic ordering from the ferro- to antiferromagnetic in Fe-doped graphene. Interestingly, the graphene sheets doped with V and Cr atoms analyzed with and without 𝑈 are found to have high Curie temperature (∼500–800 K). This discovery opens up vast opportunities for utilizing two-dimensional doped graphene magnets in room-temperature spintronics devices. We expect that our findings can stimulate further experimental studies for the remarkable properties of substitutionally doped graphene and lead to the verification of predictions presented herein. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
4. Conclusions CRediT authorship contribution statement
Within the first-principles calculations, here we systematically investigate the structural, electronic and magnetic properties of graphene sheets doped with V, Cr, Mn, Fe, Co, Ni, and Cu atoms. Our results reveal the effects of substitutional doping on the density of states of a graphene monolayer and show the opportunity to induce a ferromagnetic state in V-, Cr-, Fe- and Co-doped system. Moreover, we found
Artur P. Durajski: Conceptualization, Methodology, Software, Supervision. Anita E. Auguscik: Conceptualization, Data curation, Investigation, Visualization, Writing - original draft. Radosław Szcze¸śniak: Investigation, Writing - review & editing. 4
Physica E: Low-dimensional Systems and Nanostructures 119 (2020) 113985
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Acknowledgments
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