Magnetic and Electronic Properties of $\beta$-Graphyne Doped with Rare-Earth Atoms

Juan Ren(任娟)$^{1,2\hyperlink{s}{**}}$, Song-Bin Zhang(张松斌)$^{1\hyperlink{s}{**}}$, Ping-Ping Liu(刘萍萍)$^{3}$

doi:10.1088/0256-307X/36/7/076101

⇦Chinese Physics Letters, 2019, Vol. 36, No. 7, Article code 076101⇨ Magnetic and Electronic Properties of $\beta$-Graphyne Doped with Rare-Earth Atoms * Juan Ren (任娟)1,2**, Song-Bin Zhang (张松斌)1**, Ping-Ping Liu (刘萍萍)3 Affiliations 1School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119 2School of Science, Xi'an Technological University, Xi'an 710032 3College of Materials and Engineering, Yangtze Normal University, Chongqing 408000 Received 21 March 2019, online 20 June 2019 ^*Supported by the Scientific Research Plan Projects of Shannxi Education Department under Grant No 17JK0366, and the Natural Science Foundation of Shaanxi Science and Technology Department under Grant Nos 2018JQ1042, 2017ZDXM-GY-114 and 2018GY-044.
^**Corresponding author. Email: renjuan@xatu.edu.cn; song-binzhang@snnu.edu.cn Citation Text: Ren J, Zhang S B and Liu P P 2019 Chin. Phys. Lett. 36 076101 Abstract Structural, electronic and magnetic properties of La-, Ce-, Pr-, Nd-, Pm-, Sm- and Eu-doped $\beta$-graphyne are investigated by comprehensive ab initio calculation based on density functional theory. The adsorption energies indicate that the dopings are suitable. The doped $\beta$-graphyne undergoes transition from semiconductor to metal. Furthermore, the doping of Nd, Pm, Sm and Eu atoms can induce magnetization. The results are useful for spintronics and the design of future electronic devices. DOI:10.1088/0256-307X/36/7/076101 PACS:61.48.Gh, 73.22.Pr, 75.75.-c, 71.15.Mb © 2019 Chinese Physics Society Article Text Carbon is a very common element that exists in many forms in the atmosphere and in the earth's crust and living things. The most known naturally occurring carbon, which exists mainly in two most stable allotropes (diamond and graphite consisting of $sp^{3}$- and $sp^{2}$-hybridized carbon atoms, respectively). Many carbon allotropes are prepared or predicted theoretically with the development of nanotechnology and computer simulation technology. Here, the most remarkable and well known achievements are the discovery of OD fullerenes,[1] 1D nanotubes,[2] and 2D graphene[3] that is a kind of $sp^{2}$-hybridized carbon materials. Back in 1987, Baughman et al.[4] firstly proposed the structure of graphynes, and ten years later, Haley et al.[5] designed graphdiynes of $sp^{1}+sp^{2}$ carbon allotropes. The structure of graphyne can be regarded as carbon and carbon triple bond inserted into carbon single bond of graphene since $sp$ and $sp^{2}$ hybrids can be mixed in different proportions. To date, although large scale graphyne materials have not been successfully prepared experimentally, the substructures of graphyne have been synthesized. The first success was achieved in synthesis of large-area graphyne by Li et al. in 2010.[6] They used the coupling reaction taking place under the hexaenyl benzene by the catalytic of copper sheet, and then they synthesized graphyne nanotubes successfully.[7] These experiments have proved that the success synthesis of graphyne is very promising. The successful fabrication of graphyne has been receiving growing attention. The $sp$- and $sp^{2}$-hybridized carbon atoms in graphyne endow these new carbon materials with outstanding properties, including uniformly distributed pores, tunable electronic properties, good chemical stability, excellent mechanical, optical and energy storage properties.[8–12] Due to the presence of acetylenic fragments, graphyne holds four typical geometrical structures, namely, $\alpha$-graphyne, $\beta $-graphyne, $\gamma $-graphyne, and (6,6,12)-graphyne. Functionalization of graphyne is an effective approach to tune the electronic and magnetic properties of nanostructures. As far as we know, the current research on functionalized graphyne is mainly concentrated in lithium batteries, hydrogen storage media, and as a gas sensor.[13–15] There are a few calculations on the magnetic properties. In 2012, He et al.[16] have systematically studied the electronic and magnetic properties of $3d$ transition-metal atom (V, Cr, Mn, Fe, Co and Ni) adsorbed on graphdiyne and graphyne. The adsorbed complexes are excellent candidates for spintronics. Sholeh et al.[17] investigated the adsorptions of transition metal (Fe, Co and Ni) on the external surface of graphyne nanotubes. The results show that the Fe- and Co-adsorbed complexes are magnetic and the Ni-adsorbed complexes are nonmagnetic. Recently, the doping properties of $\gamma$-graphyne with all $3d$, $4d$, and $5d$ transition metal adatoms adsorbed are calculated through density functional theory. This offers an attractive way of modifying their electronic and magnetic properties.[18] The very recent results show that the electronic and magnetic properties of graphyne can be modulated by different hydrogenating manners.[19] However, to our knowledge, the adsorption doping of rare-earth (RE) atoms on $\beta$-graphyne has been rarely studied. Rare-earth metals have large atomic radii, at the same time, the $\beta$-graphyne constitutes larger rings compared with the six-member rings of graphene, making it possible to introduce rare-earth metals in the same plane as the defect-free carbon sheet. On the other hand, $4f$ rare-earth metal atoms have larger magnetic moments compared to $3d$ transition metals. In this work, we investigate the adsorption doping of rare-earth (RE) atoms (La, Ce, Pr, Nd, Pm, Sm and Eu) on $\beta$-graphyne by comprehensive first-principles calculations. The computational method details are given, and the systems of RE atoms adsorbed on $\beta$-graphyne are discussed. The results of adsorption energies, Mulliken charge, and magnetic moments corresponding to various systems are presented. In each doping, the electronic structure, the spin charge density, and density of states (DOSs) of the functional systems are analyzed in detail. The results demonstrate that the $\beta$-graphyne can be magnetized by doping of some RE atoms. All structural optimization and property calculations are calculated with the DMol$^{3}$ code,[20,21] which is a validated density functional theory. The exchange and correlation terms are described by the generalized gradient approximation (GGA) with the Perdew-Wang 91(PW91).[22,23] The DFT semi core pseudopotential (DSPP) is performed for the relativistic effect, which replaces core electrons as a single effective potential. The basis set consists of the double numerical plus (DNP) polarization atomic orbitals. Structural optimizations are obtained without any symmetry constraints using a convergence tolerance of energy of $1.0\times 10^{-5}$ Hartree, a maximum force of 0.002 Hartree/Å, and a maximum displacement of 0.005 Å. The orbital cutoff is set to be global with a value of 4.5 Å, the smearing is 0.005 Ha. The lattice constants of the $\beta$-graphyne model are first fully optimized with a 15 Å vacuum space to eliminate the interaction between periodic images. For the $\beta$-graphyne, $2\times 2\times1$ supercells are investigated with the Brillouin zone $k$-point meshes of $5\times 5\times1$ during geometry optimization and their electronic properties for all the systems. The charge and magnetic moment are obtained by Mulliken population analyses. The successful fabrications of graphyne provide an opportunity to design magnetic properties by doping the foreign atoms. We choose a $2\times 2\times1$ supercell for the present investigation. Firstly, the structure of pure $\beta$-graphyne is presented in Fig. 1(a). The results show that the band gap of pure $\beta$-graphyne is 0.027 eV for spin-up and spin-down channels, and the bond lengths of $sp^{2}$–$sp^{2}$, $sp^{2}$–$sp$ and $sp$–$sp$ are 1.389, 1.235, and 1.454 Å, respectively, which are in good agreement with the previous calculations.[24] Thus the calculated approach is credible. The structures of the rare-earth metal doped $\beta$-graphyne are optimized by considering spin polarization. The results show that all rare-earth metal atoms prefer to locate inside the acetylenic six-member ring with $\beta$-graphyne in plane. To evaluate the stability, we calculate the adsorption energy. The mean binding energy between the RE atoms and the $\beta$-graphyne is expressed as $$ \Delta E=E({\rm graphyne})+E({\rm RE})-E({\rm RE\_doped}), $$ where $E({\rm graphyne})$ is the total energy of pure optimized $\beta$-graphyne, $E({\rm RE})$ is the spin-polarized total energy of a single rare-earth atom (La, Ce, Pr, Nd, Pm, Sm and Eu) in its ground state, and $E({\rm RE\_doped})$ is the spin polarized total energy for the optimized configuration of RE-doped $\beta$-graphyne. In Table 1, we list the adsorption energies, band gap, the magnetic moments of the RE impurities ($\mu_{\rm RE}$), RE-doped $\beta$-graphyne ($\mu_{\rm total}$), and the nearest-neighboring C atoms ($\mu_{\rm C}$) of RE-doped $\beta$-graphyne, Mulliken charge of RE atoms, respectively. The adsorption energies of the RE (RE=La, Ce, Pr, Nd, Pm, Sm and Eu) doped $\beta$-graphyne are 3.476, 6.342, 3.741, 4.949, 4.369, 3.905 and 3.642 eV, respectively. The results indicate that the RE atoms are suitable for adsorption doping on $\beta$-graphyne. It is sufficient to indicate that the RE atoms tend to uniformly disperse on the $\beta$-graphyne sheet against clustering.

Fig. 1. (a) The positions of rare-earth metal atoms doped on $\beta$-graphyne, with red for rare-earth metal atoms and gray for carbon atoms. (b) The band structure of pure $\beta$-graphyne.

**Table 1.** The adsorption energies (eV), magnetic moments of the RE impurities ($\mu_{\rm RE}$), RE-doped $\beta$-graphyne ($\mu_{\rm total}$), and the nearest-neighboring C atoms ($\mu_{\rm C}$) of RE-adsorbed $\beta$-graphyne, Mulliken charge of RE atoms, respectively. GY: graphyne.
Systems	Adsorption energy(eV)	$\mu (\mu_{\rm B})$			Charge (a.u.)
Systems	Adsorption energy(eV)	$\mu_{\rm RE}$	$\mu_{\rm C}$	$\mu_{\rm tot}$	Charge (a.u.)
La-GY	3.476	0	0	0	1.041
Ce-GY	6.342	0	0	0	1.223
Pr-GY	3.741	0	0	0	1.102
Nd-GY	4.949	4.120	$-$0.04	4.108	1.114
Pm-GY	4.369	5.203	$-$0.036	5.167	1.113
Sm-GY	3.905	6.257	$-$0.027	6.230	1.202
Eu-GY	3.642	7.259	$-$0.044	7.215	1.175

Firstly, the properties of magnetic and electronic structures of pure $\beta$-graphyne doped with rare-earth metals in considering supercells have been investigated in detail. From the results in Table 1, we can see that no magnetisms are observed when La, Ce, Pr atoms are adsorbed on $\beta$-graphyne. However, the local magnetic moments of Nd, Pm, Sm and Eu are 4.120, 5.203, 6.257 and 7.259$\mu_{\rm B}$, respectively. The introduction of external atoms Nd, Pm, Sm and Eu can bring high values of magnetic moments. The carbon atoms near the metal atoms have only a small contribution to the total magnetic moments. The band structures of RE (RE=La, Ce, Pr, Nd, Pm, Sm and Eu) doped $\beta$-graphyne are presented in Fig. 2. The calculated results show that all the doping systems become metalline with a band gap of zero. It is clear that there are band lines across the Fermi energy level in Fig. 2.

Fig. 2. Band structures of RE (RE=La, Ce, Pr, Nd, Pm, Sm and Eu) doped $\beta$-graphyne. The horizontal dotted line represents the Fermi energy level.

Fig. 3. The spin charge density distributions of certain RE-doped $\beta$-graphyne: (a) Nd-GY, (b) Pm-GY, (c) Sm-GY and (d)Eu-GY. The blue and yellow colors (isovalues=0.002 e/Å) represent positive (spin-up) and negative (spin-down) values, respectively.

For further investigation, we analyze the electron distribution on orbitals of RE and surrounding C atoms. For example, the electronic configurations of Ce and Eu are [Xe]$6s^{0.956(\uparrow ), 0.451(\downarrow )}$ $5d^{1.115(\uparrow ), 0.048(\downarrow )}$ $4f^{1.423(\uparrow ), 0.007(\downarrow )}$; [Xe]$6s^{0.975(\uparrow ), 0.870(\downarrow )}5d^{0.151(\uparrow ), 0.006(\downarrow)}$ $4f^{6.998(\uparrow ), 0.000(\downarrow )}$ as single atoms, and they become [Xe]$6s^{1.102(\uparrow ), 1.102(\downarrow )}$ $5d^{0.427(\uparrow ), 0.427(\downarrow )}$ $4f^{0.784(\uparrow ), 0.784(\downarrow )}$; [Xe]$6s^{1.178(\uparrow ), 1.075(\downarrow )}5d^{0.290(\uparrow ), 0.138(\downarrow )}$ $4f^{7.002(\uparrow ), 0.007(\downarrow )}$ of Ce and Eu in the doping systems. In the pure $\beta$-graphyne, the electronic configuration of the C atom is [He]$2s^{3.230}2p^{2.538}$, and in the adsorption doped $\beta$-graphyne the nearest-neighboring C atoms change to [He]$2s^{3.230}2p^{2.598}$ and [He]$2s^{3.334}2p^{2.582}$. As we know, the magnetic moments of Ce and Eu atoms are predominantly contributed by the polarized $5d6s$ electrons and localized $4f$ electrons. Most of the $5d6s$ electrons of La, Ce and Pr transfer to neighboring C-$2p$ orbitals whereas $4f$ electrons of Nd, Pm, Sm and Eu remain in the orbitals. It is understandable that the magnetic moments of Nd-, Pm-, Sm- and Eu-doped systems are preserved, whereas those of La-, Ce- and Pr-doped systems are zero. The spin charge density distributions of certain RE-doped $\beta$-graphyne are shown in Figs. 3(a) (Nd-), 3(b) (Pm-), 3(c) (Sm-) and 3(d) (Eu-doped $\beta$-graphyne). The blue and yellow colors represent positive (spin-up) and negative (spin-down) values, respectively. It is clear that the magnetic moments are mainly from the RE atoms and small contributions to the nearest-neighboring C atoms. In Table 1, the results are reported that the Mulliken charges of rare-metal (RE=La, Ce, Pr, Nd, Pm, Sm and Eu atoms) are 1.041, 1.223, 1.102, 1.114, 1.113, 1.202 and 1.175 a.u., respectively. It is proved that rare-earth atoms donate electrons to the neighboring carbon atoms of $\beta$-graphyne. After metal doping, there are charge transfers between the metal atoms and $\beta$-graphyne. These results are consistent with the electronic configurations.

Fig. 4. The total density of states (TDOS) and partial density of states (PDOS) of (a) La-, (b) Ce-, (c) Pr-, (d) Nd-, (e) Pm-, (f) Sm- and (g) Eu-doped $\beta$-graphyne. The vertical dotted line indicates the Fermi level.

In the following we calculate the total density of states (TDOS) and partial density of states (PDOS) of pure and La-, Ce-, Pr-, Nd-, Pm-, Sm- and Eu-doped $\beta$-graphyne in Fig. 4. In Fig. 4(a), we can see that the spin-up and spin-down PDOSs of La atoms are completely symmetric. Near the Fermi level, the density of states for La-$5d$, $6s$ and C-$2p$ orbitals take place with hybridization and across the Fermi energy level. Thus the La-doped $\beta$-graphyne becomes metalline. The results agree with the Mulliken analysis that some electrons transfer between La-$5d$, $6s$ and C-$2p$ orbitals. Similarly, there are no magnetic properties for Ce- and Pr-doped systems, the PDOS of Ce and Pr atoms are also symmetric. As shown in Figs. 4(d)–4(g), for the Nd-, Pm-, Sm- and Eu-doped $\beta$-graphyne, there is clear spin polarization between the PDOS of the two spin channels at/nearby Fermi level. Especially, we can see that the spin-up and spin-down PDOSs of Nd, Pm, Sm and Eu are unsymmetrical, indicating the magnetic states of the decorated systems. PDOSs indicate that the spin polarization mainly comes from the $4f$ and $5d$ electrons, which are responsible for the induced magnetic moments. Namely, the mechanism of magnetic moment emergence resides on unpaired $4f$ and $5d$ electrons. In the case of the Sm-doped system, the spin-up PDOS of Sm-$4f$ orbital is much localized with a sharp peak at $-$0.483 eV, but the spin-down PDOS is zero. The results prove that the positive magnetic moments of Sm-doped $\beta$-graphyne are mostly contributed by the $4f$ electrons. For the Pm-doped $\beta$-graphyne in Fig. 4(e), the PDOS of Pm is similar with Sm. In the case of Eu, there is some difference between the Sm and Pm-doped systems. The filled spin-up and spin-down Eu-$6p$ states appear at 0–10 eV, whereas the two states are symmetric. For the Eu-doped $\beta$-graphyne, the magnetic moments are also contributed by the $4f$ and $5d$ electrons. In conclusion, the structural, electronic and magnetic properties of La-, Ce-, Pr-, Nd-, Pm-, Sm- and Eu-doped $\beta$-graphyne have been investigated by comprehensive ab initio calculation based on density functional theory. The adsorption energies indicate that the dopings are suitable. The electronic structure of $\beta$-graphyne can be regulated by metal dopings. Interestingly, the pure $\beta$-graphyne with a band gap of 0.027 eV becomes metalline after adsorption doping of La, Ce, Pr, Nd, Pm, Sm and Eu atoms. Furthermore, the doping of Nd, Pm, Sm and Eu atoms can induce magnetization. These results may be helpful for understanding influence of RE metals on $\beta$-graphyne. References C60: BuckminsterfullereneHelical microtubules of graphitic carbonElectric Field Effect in Atomically Thin Carbon FilmsStructure‐property predictions for new planar forms of carbon: Layered phases containing s p ² and s p atomsCarbon Networks Based on Dehydrobenzoannulenes: Synthesis of Graphdiyne SubstructuresArchitecture of graphdiyne nanoscale filmsConstruction of Tubular Molecule Aggregations of Graphdiyne for Highly Efficient Field EmissionGRAPHYNE-BASED SINGLE ELECTRON TRANSISTOR: AB INITIO ANALYSISBoron-substituted graphyne as a versatile material with high storage capacities of Li and H2: a multiscale theoretical studyGraphyne- and graphdiyne-based nanoribbons: Density functional theory calculations of electronic structuresNanoindentation Models of Monolayer Graphene and Graphyne under Point Load Pattern Studied by Molecular DynamicsA potentiometric solid state copper electrode based on nanostructure polypyrrole conducting polymer film doped with 5-sulfosalicylic acidGraphyne and Graphdiyne: Promising Materials for Nanoelectronics and Energy Storage ApplicationsLi decorated 6,6,12-graphyne: A new star for hydrogen storage materialThermodynamically Stable Calcium-Decorated Graphyne as a Hydrogen Storage MediumMagnetic Properties of Single Transition-Metal Atom Absorbed Graphdiyne and Graphyne Sheet from DFT+U CalculationsStudy of the Influence of Transition Metal Atoms on Electronic and Magnetic Properties of Graphyne Nanotubes Using Density Functional TheoryFunctionalization of γ-graphyne by transition metal adatomsTuning the electronic and magnetic properties of graphyne by hydrogenationFrom molecules to solids with the DMol3 approachHardness conserving semilocal pseudopotentialsDensity functional approach to study structural properties and electric field gradients in rare earth materialsFirst-principles study of anatase and rutile

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