Magnetic properties of X-C2N (X=Cl, Br and I) monolayers: A first-principles study

The electronic and magnetic properties of X-C2N (X=F, Cl, Br and I) monolayers have been systematically investigated from first-principles calculations. The F atom can be strongly adsorbed on the top of the host carbon atoms, while the Cl, Br and I atoms favor the top of the host nitrogen atoms of C2N monolayers. These functionalized X-C2N (X=F, Cl, Br and I) monolayers exhibit interesting electronic and magnetic features. The F-C2N monolayer system shows a nonmagnetic metallic state, while the X-C2N (X=Cl, Br and I) monolayer systems exhibit the magnetic semiconducting ground state. Moreover, the ferromagnetic state is energetically more stable configuration for the X-C2N (X=Cl, Br and I) monolayer systems. Magnetic analysis further elaborates that the induced magnetism in the X-C2N (X=Cl, Br and I) monolayer systems mainly arises from the local magnetic moments of the halogen adatoms. Thus, the chemical functionalization of nitrogenated honey graphene through halogen atoms adsorption has promising applications in electronic devices.


I. INTRODUCTION
Two-dimensional (2D) materials have been studied extensively by theoretical calculations and experiments since the discovery of graphene in 2004. 1-6 Many new 2D materials have been realized after graphene. Silicene, germanene and phosphorene have been synthesised on substrates. [7][8][9][10][11][12] In these 2D materials, graphene has a planar configuration without buckling height. By contrast, the silicene, germanene and phosphorene all show nonzero buckling height. [13][14][15][16][17][18][19][20] Besides the singleelement 2D materials, compounds consisting of boron, carbon and nitrogen have intrigued much attention. [21][22][23][24][25][26][27][28][29][30] In particular, the C 2 N monolayer has been realized in experiments. 31 The C 2 N crystal was successfully synthesized by a simple wet chemical reaction. 31 The lattice structure of C 2 N was confirmed with various characterization techniques, including scanning tunnelling microscopy. 31 Since the successful synthesis of the C 2 N monolayer, many applications of the C 2 N monolayers have been proposed. Ca-embedded C 2 N monolayer is a promising CO 2 adsorbent among the two dimensional materials. 32 The isovalent atom doped holey C 2 N monolayers show interesting electronic characteristics and optical properties. 33 The Sc, Ti, V, Cr, Mn, Fe, Co and Ni atom-embedded C 2 N monolayers induce a ferromagnetic ground state, while Cu atom-embedded C 2 N monolayer possesses paramagnetic characteristics in the 2D C 2 N monolayer. 34 In the meanwhile, the Zn atom-embedded C 2 N monolayer exhibits a nonmagnetic ground state. 34 The zigzag C 2 N nanoribbons with edge modifications have been proposed to be multi-functional spin devices. The C 2 N crystal shows a finite band-gap of approximately 1.96 eV in experiments. 31 Especially, the highest valence bands of the C 2 N monolayer are quasi-flat and the density of states (DOS) of the C 2 N monolayer shows a van Hove singularity near the valence band maximum (VBM). [32][33][34][35][36][37][38][39][40][41][42] Van Hove singularities in a 2D material may lead to phase transitions such as ferromagnetism and superconductivity. [43][44][45] We have already reported such type of ferromagnetic half metallic phase transition with the help of hole doping in the pristine C 2 N monolayer system from the first-principles calculations. 45 Furthermore, electron doping has also proved as an effective way to induce significant magnetism in the pristine C 2 N monolayer. [43][44][45] Thus, it is important to study the chemical adsorption of halogen adatoms on the C 2 N monolayer because the halogen atoms are highly prone to accepting electrons to further increase their stability.
In this paper, we have systematically investigated the electronic and magnetic properties of the X-C 2 N (X=F, Cl, Br and I) monolayers by utilizing first-principles calculations. We find that the Cl, Br, and I adatoms can be strongly adsorbed on the top of the host nitrogen atoms, while the F atoms favor the top of the host carbon atoms of the C 2 N monolayer. The F-C 2 N monolayer system shows a nonmagnetic metallic state, while the chemically functionalized X-C 2 N (X=Cl, Br and I) monolayer systems exhibit the magnetic semiconducting ground state with the ferromagnetic state being more energetically stable. Additionally, the magnetic analysis reveals the origin of such induced magnetism in the X-C 2 N (X=Cl, Br and I) monolayer systems, which mainly arises from the local magnetic moments of the halogen adatoms.
The outline of this paper is as follows: Section II describes the calculation methods. In Sec. III, we show the structures of X-C 2 N (X=F, Cl, Br and I) monolayers and discuss the electronic and magnetic properties of the system. Section IV is the summary.

II. METHODS
We have performed spin-polarized density functional theory (DFT) calculations implemented in the Vienna ab initio simulation package (VASP). 46,47 We have adopted the projector-augmented wave (PAW) potentials to model the core electrons, while to model the valance electrons a plane wave basis set with an energy cutoff of 500 eV is adopted. For exchange and correlation, we have utilized the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzernhof (PBE). 48 A (2×2) C 2 N supercell including 72 nonmetal atoms and an adsorbed halogen atom is employed. The vacuum region between adjacent C 2 N layers is kept larger than 15 Å to avoid images interactions. The Brillouin zone (BZ) sampling is obtained using a 6 × 6 × 1 Monkhorst-Pack grid for relaxation calculations while a 12 × 12 × 1 Monkhorst-Pack grid is adopted for the static calculations. 49 The tolerance of the energy convergence is set to 10 −5 eV. We have relaxed all the structures until the forces on each atom become smaller than 0.01 eV/Å.

III. RESULTS AND DISCUSSIONS
The lattice structure of the pristine C 2 N monolayer is shown in Fig. 1. We give the top view and side view of a 2 × 2 supercell of the pristine C 2 N monolayer. A primitive cell of the pristine C 2 N monolayer contains twelve carbon (C) atoms and six nitrogen (N) atoms, as depicted in Fig. 1(a). The pristine C 2 N monolayer possesses planar configuration without any buckling. The lattice constant of the pristine C 2 N monolayer is 8.328Å, which agrees well with the experiment measurement and previous theoretical studies. 31,[43][44][45] The B 1 and B 2 C-C bond lengths are 1.470Å and 1.430Å, respectively. The B 3 C-N bond length is 1.336Å. The structure of the pristine C 2 N monolayer can be considered as carbon rings further connected by nitrogen atoms.
We have considered adsorption of a single halogen atom on the 2×2 supercell of the C 2 N monolayer. One side adsorption of nanosheet may induce curved structure. [50][51][52] In our case, the coverage of adsorption atoms is about 1.4%, which is small and the effect of the adsorption induced stress will be weak. Eight possible adsorption sites are chosen on the C 2 N monolayer i.e. three hollow sites (H 1 , H 2 and H 3 ), three bridge sites (B 1 , B 2 and B 3 ), and two top sites (T 1 and T 2 ). More precisely, H 1 represents the largest hollow sites of the C 2 N monolayer, whereas H 2 and H 3 denote the hollow sites of the C-N rings and the C-C rings of the C 2 N monolayer, respectively. Furthermore, B 1 and B 2 represent two different C-C bridge sites whereas B 3 represents the C-N bridge sites. Similarly, T 1 and T 2 denote the top sites of the carbon and nitrogen atoms, respectively. The most stable adsorption site identified for the Cl-C 2 N, Br-C 2 N and I-C 2 N monolayer systems is the T 2 site which represents the atop site of the host nitrogen atoms of the C 2 N monolayer. The optimized structures of X-C 2 N (X=Cl, Br and I) monolayers with the adsorbed halogen atoms on their most stable adsorption sites are presented in Fig. 2 with Cl-C 2 N as an example. The binding energy is defined as E = E d −E 0 −E m , where E d and E 0 are the energies with and without the adsorbed halogen atoms, respectively. Whereas E m is the energy of a free halogen atom. The binding energy of Cl-C 2 N, Br-C 2 N and I-C 2 N with the halogen atoms on the most stable adsorption sites T 2 are 446 meV, 275 meV and 177 meV, respectively. In the eight adsorption sites we have considered, the B 3 site can be regarded as the most unique unstable adsorption site. Because all the halogen atoms likely to be reside on the T 1 sites after structure relaxation, which may comes from the symmetry issue because the B 3 site is one of the most unique unsymmetrical site in the eight adsorption sites chosen.
The properties of the C 2 N monolayers with the adsorbed halogen atoms in their most stable adsorption sites are listed in Table I   , the height from the halogen atom to the C 2 N plane (h), the angle between the X-N (X=Cl, Br and I) bond (or F-C bond) and the C 2 N plane (θ), the nearest C-N bond length (l C N ) of the halogen atom, the X-N (X=Cl, Br and I) bond (or F-C bond) length (l), the band gap (E g ) and the total magnetic moment of the system (µ tot ). properties of the X-C 2 N (X=F, Cl, Br and I) monolayers, thus the lattice constants of the X-C 2 N (X=F, Cl, Br and I) monolayers are about 2 times of the lattice constant (8.328Å) of the primitive cell of the C 2 N monolayer. The conclusions can be made from the lattice constants calculations of the X-C 2 N (X=F, Cl, Br and I) monolayers which are as follows: (1) The lattice constants of X-C 2 N (X=F, Cl, Br and I) monolayers are entirely insensitive to the kind of the adsorb halogen atoms.
(2) The X-C 2 N (X=F, Cl, Br and I) monolayers are stable. The optimize heights obtained from the adsorbed halogen atoms (F, Cl, Br and I) and the C 2 N monolayer plane are 2.059Å, 2.223Å, 2.389Å and 2.404Å, respectively. Although the most stable adsorption sites for the corresponding adsorbed halogen atoms (Cl, Br and I) are all T 2 , the projection positions of these three types of halogen atoms on the C 2 N plane are not the positions of the nitrogen atoms. To depict the departure of these three types of halogen atoms from the rigorous T 2 sites, we define an angle (θ) which is the angle between the X-N (X=Cl, Br and I) bond and the C 2 N plane. The θ for Cl, Br and I are 60.058 • , 59.393 • and 51.394 • , respectively. The θ for F means the angle is 90.000 • between the F-C bond and the C 2 N plane. The C-N bond lengths are 1.337Å for Cl-C 2 N, Br-C 2 N and I-C 2 N, which demonstrates again the stability of the C 2 N monolayer after the adsorption of the halogen atoms. The X-N bond lengths for Cl, Br and I are 2.395Å, 2.605Å and 2.969Å, respectively. The difference of the X-N (X=Cl, Br and I) bond lengths arises partially from the different radius of the halogen atoms.
The electronic band structures of the pristine C 2 N, the Cl-C 2 N, the Br-C 2 N and the I-C 2 N monolayer systems are shown in Figs. 3(a)-3(d). The electronic band structures of the F-C 2 N are shown at last as its properties are different from those of the X-C 2 N (X=Cl, Br and I) monolayers. The band gap of the C 2 N monolayer is 1.670eV, which agrees well with the previous calculations. [43][44][45] The band gap is smaller than the experiment result (1.96eV), 31 which may come from the use of the PBE exchange and correlation functional because the PBE usually underestimates the band gaps  of the semiconductors and insulators. The valence band maximum (VBM) and the conduction band minimum (CBM) locate at the Γ point. Some flat electronic bands emerge near the VBM and a sharp van Hove singularity emerges in the density of states of the C 2 N monolayer. Since the van Hove singularity of the pristine C 2 N monolayer locates near the VBM, we can tailor the electronic and magnetic features of the C 2 N monolayer by utilizing the available van Hove singularity. The hole-doped C 2 N monolayers show half metallic nature with ferromagnetic ground state whereas the electron-doping in the C 2 N monolayer induce significant magnetic moments. [43][44][45] Since the halogen atoms are highly prone to accepting electrons to increase their stability, thus we expect significant modification in the electronic and magnetic behaviors of the functionalized structures, which are further confirmed from the spin polarized band structures of the Cl-C 2 N, the Br-C 2 N and the I-C 2 N monolayer systems. The calculated bandgaps of the Cl-C 2 N, the Br-C 2 N and the I-C 2 N monolayer systems are 0.825eV, 0.629eV and 0.398eV, respectively. The bandgaps of the X-C 2 N (X=Cl, Br and I) monolayers are smaller than the bandgap (1.670eV) of the pristine C 2 N monolayer. Strikingly, some flat subbands emerge near the Fermi level in the the Cl-C 2 N, Br-C 2 N and I-C 2 N monolayer systems. It can also be noticed that the highest valence band and the lowest conduction band of the X-C 2 N (X=Cl, Br and I) monolayers are fully spin polarized, which suggests that all the conduction electrons available in the spin-down channel can be utilized at room temperature. The calculated net magnetic moment induced in the Cl-C 2 N, the Br-C 2 N and the I-C 2 N monolayer systems is 1.000µ B . Moreover, it can also be noticed from the spin polarized electronic band structures provided in the Figs. 3(c) and 3(d) which means the X-C 2 N (X=Cl, Br and I) monolayers are magnetic semiconductors. Conventionally, in the common diluted magnetic semiconductors, the magnetism often originates from the doping of transition metal atoms. [53][54][55] It is important to notice that in the Cl-C 2 N, the Br-C 2 N and the I-C 2 N monolayer systems, the magnetism originate from the halogen atoms.
We have also shown the distribution of charge density of spin-up state minus spin-down state of the X-C 2 N (X=Cl, Br and I) monolayers in Fig. 4. The ferromagnet of the X-C 2 N (X=Cl, Br and I) monolayers is localized on the halogen atoms. Halogen atoms are extensively utilized to tailor the electronic and magnetic properties of the 2D materials. [56][57][58][59][60] Additionally, it is reported that fluorination can successfully induce half-metallicity in the zigzag boron nitride nanoribbons or zinc oxide layers. 56,57 Thus the underlying magnetism mechanism in these proposed materials (Cl-C 2 N, Br-C 2 N and I-C 2 N monolayers) is similar to those of Refs. 56-60. To understand the magnetism of the X-C 2 N (X=Cl, Br and I) monolayers from another perspective, the density of states (DOS) and the projected density of states (PDOS) of the Cl-C 2 N and Br-C 2 N are plotted in Fig. 5. Considering the similarity of the electronic band structures of the Br-C 2 N and I-C 2 N monolayer systems, we take the DOS and PDOS of the Br-C 2 N as an example to explore the magnetism. The C and N atoms in Fig. 5 represent the nearest C atom and the nearest N atom of the corresponding halogen atom. The Cl-C 2 N and Br-C 2 N possess band gaps of 0.825eV and 0.629eV, FIG. 4. Distribution of charge density of spin-up state minus spin-down state for (a) the Cl-C 2 N (b) the Br-C 2 N and (c) the I-C 2 N, respectively. The isosurface value is taken to be 0.002 eÅ −3 . The green, the orange and the purple colors label the spin-up charges of the Cl-C 2 N, the Br-C 2 N and the I-C 2 N monolayer systems, respectively. respectively, which agrees well with the electronic band structures in Fig. 3. The peaks of the DOS near the VBM and CBM in Fig. 5 have a good correspondence with the flat sub-bands in Fig. 3. Figures 5(a) and 5(b) shows that the hybridized p-orbitals of dopants and p-orbitals of the nearest C and N atoms mainly contribute to the induced impurity states. The peaks near the Fermi level of the DOS of the Cl-C 2 N and Br-C 2 N come mostly from the p orbitals of the N atoms and the halogen atoms. A strong hybridization emerges between the p orbitals of the N atom and the p orbitals of the halogen atoms. The p-p hybridization leads to the split of the energy level near the Fermi energy, the split from the p-p hybridization is the origin of the induced magnetism in the X-C 2 N (X=Cl, Br and I) monolayers. In order to explore the magnetic ground state of the X-C 2 N (X=Cl, Br and I) monolayers, an antiferromagnetic (AFM) configuration has been considered in Fig. 6. Our calculations indicate that the local magnetic moment of the X-C 2 N (X=Cl, Br and I) monolayers is insensitive with the size of the supercell. One X atom (X=Cl, Br and I) induces 1.000µ B local magnetic moment for (1×1), (1×2) or (2×2) X-C 2 N (X=Cl, Br and I) supercells. The geometry, the energy for the ferromagnetic (FM), AFM, nonmagnetic (NM) configuration have been calculated for the X-C 2 N (X=Cl, Br and I) monolayers. We set the energy of FM of the X-C 2 N (X=Cl, Br and I) monolayers as 0. The energy of AFM of the X-C 2 N (X=Cl, Br and I) monolayers are calculated to be 1.03meV, 0.65meV and 0.22meV, respectively. The energy of NM of the X-C 2 N (X=Cl, Br and I) monolayers are 1.006eV, 0.951eV and 0.959eV, respectively. The ferromagnetic state is the most energetically stable configuration for the X-C 2 N (X=Cl, Br and I) monolayers. The corresponding magnetic moment for a (2×2) X-C 2 N (X=Cl, Br and I) supercell is 4.000 µ B for the FM state.
At last, we give the optimized structure and electronic structure of F-C 2 N with the F atom in the most stable adsorption site in Fig. 7. The most stable adsorption site of the F atom is the top site of the C atom in the C 2 N monolayer, which is different from the most stable adsorption sites of Cl, Br and I atoms. The F-C bond length is 1.468Å and the height from the F atom to the C 2 N plane is 2.059Å. Figure 7(b) shows that a small distortion occurs when the F atoms adsorbed on the top site of the C atom. The height from the nearest C atom of the F atom to the C 2 N plane is 0.602Å. The F-C 2 N exhibits metallic feature as the Fermi level cross with an impurity band, as illustrated in Fig. 7(c), which is different from the semiconductor features of the X-C 2 N (X=Cl, Br and I) monolayers. The F-C 2 N exhibits nonmagnetic characteristics with the symmetry of the DOS in Fig. 7(d), which is different from the ferromagnetic ground states of the X-C 2 N (X=Cl, Br and I) monolayers. The adsorption site, the electronic and magnetic properties of F-C 2 N are different from that of the X-C 2 N (X=Cl, Br and I) monolayers.

IV. CONCLUSION
We have studied the electronic and magnetic features of the X-C 2 N (X=F, Cl, Br and I) monolayers from first-principles calculations. The F atom can be strongly adsorbed on top of the host carbon atoms, while the Cl, Br and I atoms favor top of the host nitrogen atoms of C 2 N monolayers. The F-C 2 N monolayer system shows a nonmagnetic metallic state, while the Cl-C 2 N, the Br-C 2 N and the I-C 2 N monolayers exhibit a net magnetic moment of 1.000µ B . Moreover, the ferromagnetic state is energetically most stable configuration for the X-C 2 N (X=Cl, Br and I) monolayers. The spatial spin charge density distributions further demonstrate that the induced magnetism in the X-C 2 N (X=Cl, Br and I) monolayers originates from the adsorbed halogen atoms. The Cl-C 2 N, the Br-C 2 N and the I-C 2 N monolayer systems show different bandgaps in the electronic band structures. The electronic subbands near the Fermi energy of the X-C 2 N (X=Cl, Br and I) monolayers are fully spin polarized.
Functionalization of the C 2 N monolayer through these halogen-atoms adsorption appears to be a promising way to extend its applications.