Electron spin-polarization and spin-gapless states in an oxidized carbon nitride monolayer

Abstract

Electron spin-polarization in metal-free organic materials is currently drawing considerable attention due to their applications in organic electronics. Using first-principles calculations, we propose a stable two-dimensional (2D) honeycomb lattice oxidized carbon nitride material, C₂NO. The energetic favorability, phonon spectrum and molecular dynamics simulation confirm the stability and plausibility of the C₂NO material. The electronic structure of the metal-free organic material is spin-polarized, yielding magnetic moments of 1.0 μ_B in one primitive cell. More interestingly, the spin-polarized electronic band lines have a zero band gap at the Fermi level, exhibiting spin-gapless features. These unique properties are promising for spin detectors and generators for electromagnetic radiation over a wide range of wavelengths based on the spin photoconductivity.

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Introduction

Spin gapless semiconductors (SGSs), inspired by the unique properties of gapless semiconductors like graphene, were first proposed theoretically in diluted magnetic semiconductors.¹ In contrast to the gapless semiconductors such as graphene,² HgCdTe, HgCdSe, and HgZnSe,³ SGSs have one gapless spin channel while the other spin channel is semiconducting. Such interesting features are quite promising for spintronic devices, including spin detectors and generators, spin photodiodes and spin image detectors. It has been demonstrated that Co-doped PbPdO₂ ¹ and some Heusler compounds (Mn₂CoAl and Co-doped PbPdO₂)^4–6 are SGSs with parabolic energy-momentum dispersion near the Fermi level. The transition-metal (TM) atoms with un-paired d-electrons contribute to the electron spin-polarization in these SGSs. In view of the toxicity of TM atoms to environment, metal-free and environmentally-friendly SGSs are highly desirable.

Stable electron spin-polarization and ferromagnetism have been demonstrated in different metal-free compounds, such as graphite,⁷ boron nitride,^8,9 graphene-like carbon nitrides,¹⁰ silicon carbide,¹¹ and so on. The electron spin-polarization in these materials was attributed to the unpaired electrons of the defects, such as vacancy defects and adatoms.^12–14 More interestingly, theoretical investigations imply that spin-gapless states can be achieved in a new family of graphene-like carbon nitride frameworks.¹⁵ The energy-momentum dispersion near the Fermi level is linear or parabolic depending on the building blocks of the frameworks. This opens an avenue for the development of metal-free SGSs.

Graphitic carbon nitrides have been studied for more than one hundred years.¹⁶ s-Triazine (C₃N₃) and tri-triazine (C₆N₇) are the two prevailing building blocks which are jointed together directly or by sp²-hybridized nitrogen (or carbon) atoms.¹⁷ Some of the graphitic carbon nitrides have been realized using different approaches.^18–25 For example, the synthesized graphitic carbon nitride with stoichiometry of C₃N₄ (denoted as g-C₃N₄) has the tri-triazine units being jointed together via sp²-hybridized nitrogen atoms.^26–29 The semiconducting nature and band alignment are suitable for hydrogen generation via photocatalytic water splitting.³⁰ Additionally, an interesting framework of carbon nitride with stoichiometry of CN (denoted as g-CN) composing of directly-linked s-triazine was fabricated in recent experiments.²⁷ First-principles calculations indicated that topologically nontrivial electronic states near the Fermi level can be characterized by a ruby model.³¹ The porous structures of these graphitic carbon nitrides are also suitable for gas separation³² and water desalination.³³

In this work, we demonstrated from first-principles that the g-CN framework can be tuned to a SGS by substituting half of the nitrogen atoms with oxygen atoms (denoted as g-C₂NO). The g-C₂NO has a spin-polarized electronic structure with magnetic moments of 1.0 μ_B in one unit cell and stable ferromagnetic ordering. More interestingly, it is gapless in one spin channel, while other spin channel is semiconducting, featured by SGSs. The spin-polarized carriers exhibit different effective masses, arising from different parabolic energy-momentum dispersion relations. These interesting properties offer an effective approach in design of metal-free SGSs which are promising for spintronics devices.

Method

First-principle calculations were performed by utilizing the plane-wave basis Vienna ab initio simulation package known as VASP code,^34,35 implementing the density functional theory (DFT).³⁶ The electron–electron interactions were treated within a generalized gradient approximation (GGA) in the form of Perdew–Burke–Ernzerhof (PBE) for the exchange-correlation functional.^37,38 The energy cutoff employed for plane-wave expansion of electron wavefunctions were set to 520 eV. The Brillouin zone (BZ) integration was sampled on a grid of 5 × 5 × 1 k-points for structure optimization and 18 × 18 × 1 k-points for the electronic structure calculations. The supercells containing twelve atoms are repeated periodically along a₁ and a₂ (Fig. 1) while a vacuum region of about 15 Å was applied along the z-direction (a₃) to avoid mirror interaction between adjacent supercells. Structure optimization was carried out using a conjugate gradient (CG) method until the remanent force on each atom is less than 0.001 eV Å⁻¹. The phonon spectra were calculated using a Phonopy package in combination with VASP calculations.^39,40

Fig. 1 Schematic representation of g-C₂NO with the unit cell indicated by the dashed lines. The two basis vectors are represented by a₁ and a₂. The different atoms (C, O, N) are indicated by the balls with different colors.

Results and discussion

The atomic structure of g-C₂NO is built by replacing half of the nitrogen atoms of g-CN¹⁵ with oxygen atoms, as shown in Fig. 1. The primitive cell of g-C₂NO contains an s-triazine unit and a C₃O₃ hexagon which are jointed together by a C–C bond. Similar to g-CN, g-C₂NO lattice has a planar configuration with a perfect six-fold symmetry. However, in contrast to g-CN, the inversion symmetry is lifted in g-C₂NO. The optimized lattice constant (length of lattice vectors) of g-C₂NO is 7.057 Å, slightly shorter than that of g-CN (7.119 Å). The C–N bonds in s-triazine units are 1.353 Å in length, longer than that in g-CN (1.340 Å), and the ∠C–N–C bond angle 112.7° is close to that 114.4° in g-CN lattice. The C–O bonds in the C₃O₃ hexagon have the length of 1.346 Å, which is longer than that in CO₂ molecule. The C–C bond between the s-triazine and C₃O₃ units is about 1.425 Å and the ∠C–O–C bond angle is about 120.3°, both of which are very close to the values in graphene (1.420 Å and 120°).

We adopted three strategies to confirm the stability of the g-C₂NO lattice. Firstly, we calculated the formation energy E_form of g-C₂NO by the definition:

E_form = E_g-C2NO + 3 × μ_N − E_g-CN − 3 × μ_O

where E_g-C2NO and E_g-CN represent the total energy of g-C₂NO and g-CN lattices, μ_N and μ_O are the chemical potentials calculated from gas molecules. This definition corresponds to a hypothetical reaction:

C₆N₆ (g-CN) + 3/2O₂ → C₆N₃O₃ (g-C₂NO) + 3/2N₂

Our calculations showed that the formation energy of g-C₂NO is about −0.423 eV per atom. The negative value of E_form implies that this reaction is exothermic and thus the g-C₂NO is energetically favorable. Secondly, we calculated the phonon spectrum of the g-C₂NO using the force-constants obtained from first-principles calculations. The phonon spectrum along the highly symmetric directions in BZ is plotted in Fig. 2(a). Obviously, no imaginary frequency modes can be found in the phonon spectrum. We also calculated the phonon spectrum of the g-C₂NO under tensile strain and found that it is free from imaginary frequency modes as the strain less than 5%. These confirm the kinetic stability of the g-C₂NO lattice. Finally, we preformed first-principles molecular dynamics simulation (MDS) on a 4 × 4 supercell of g-C₂NO at the room temperature (300 K) with a time step of 1.0 fs. After running 3000 steps, the geometry of g-C₂NO is well preserved without any structural destruction. The total energy of the system converges to a steady-state value, as shown in Fig. 2(b). Although the time scale is limited due to the computational load restriction, the MDS result suggests the dynamic stability the g-C₂NO at room temperature.

Fig. 2 (a) Phonon dispersion curves obtained by force-constant of g-C₂NO are presented along the high symmetric points in the BZ for none pressure. (b)The relative energy as a function of the molecular dynamic simulation step (including 192 atoms) at 300 K. The inset panel at the top left corner is the input structure of g-C₂NO at the beginning. The bottom right inset panels are the structure at 3000 fs.

The electronic structure of g-C₂NO was then calculated from first-principles. Compared with g-CN, the substitutions of N with O atoms introduce additional electrons as O atom has one more electron than N, which increases the energy of Fermi level of g-C₂NO. The presence of C₃O₃ units also breaks the symmetry of g-CN and consequently alters the band structures. Therefore, it is not surprising that the electronic structures of g-C₂NO differ significantly from g-CN. g-C₂NO has a spin-polarized ground state with magnetic moments of 1.0 μ_B in one unit cell. The spin-polarized state is energetically more favorable than the spin-unpolarized state by about 94.3 meV per unit cell. Starting from different initial spin configurations, self-consistent calculations give two typical magnetic orderings of the magnetic moments, as shown in Fig. 3. Ferromagnetic (FM) ordering (Fig. 3(a)) is energetically more favorable than antiferromagnetic (AFM) ordering (Fig. 3(b)) by about 82.9 meV per unit cell. Although these energy differences are relatively small, the electron spin-polarization and ferromagnetism of g-C₂NO are still detectable at low temperature.

Fig. 3 Spin-polarized electron density profiles of g-C₂NO. (a) The FM ordering. (b) AFM orderings. Spin up and spin down components are indicated by yellow and blue. The isosurface value of spin-polarized electron density was set to 0.005 Å⁻³. (c) Energy spectrums of the clusters (inset pictures) in the vicinity of the Fermi level. The energy at the Fermi level was set to zero.

The electron spin-polarization and ferromagnetism of g-C₂NO is understandable from the molecular orbital analysis. The energy eigenvalue spectrums of s-triazine and C₃O₃ in the vicinity of the Fermi level calculated from DFT are plotted in Fig. 3(c). For s-triazine, the highest occupied molecular orbitals doubly-degenerate with the two spin branches occupied equally, while for C₃O₃, the two spin-down states are partially-filled with small spin splitting. When they are jointed together via C–C bridges, the degeneracy of the two spin-down states is lifted. One is fully occupied while other is empty, leading to net magnetic moment of 1.0 μ_B. The unoccupied spin-down state will act as an acceptor level, allowing a virtual hopping for FM arrangement in g-C₂NO lattice. This is reason why FM ordering is energetically more favorable than AFM.

The spin-resolved electronic band structures of g-C₂NO are plotted in Fig. 4(a). It is clear that the band lines in the proximity of Fermi level are spin-polarized with the largest spin-splitting of 0.48 eV at the Γ point. The valence band and the conduction band nearest to the Fermi level are belong to the same spin channel which touch at a single point (Γ point) at the Fermi level, while another spin channel has a band gap of 1.15 eV, exhibiting clear features of SGSs. It is noteworthy that the two bands nearest to the Fermi level have parabolic energy-momentum dispersion relations and thus can be described by the effective mass model. We evaluated the effective masses (m*) of electrons and holes of these two bands using the expression:

m*(k) = (h/2π)²/(d²E(k)/dk²)

Fig. 4 (a) Spin-resolved band structure line along the high symmetric points in the BZ. And electron density of states (DOS) is set at left. Enlarged views of the degenerate bands near the Fermi level are plotted in the insets. The energy at the Fermi level was set to zero. (b) Top and side view of electron density profile of the wavefunction for the two bands near the Fermi level and the isosurface value of spin-polarized electron density was set to 0.001 Å⁻³.

The effective masses are about 91.9 (electron) and −17.7 (hole) m_e, where m_e is the mass of a free electron. The large difference between the effective masses of electrons and holes facilitates the selective injection or emission of electrons or holes which are crucial for spintronics devices. However, one should notice that the absolute value of effective masses is relatively large due to localization of the two bands which may limit the relevant applications.

The density profiles of the electron wavefunctions for the two bands nearest to the Fermi level (denoted as band1 and band2 marked in Fig. 4(a)) are plotted in Fig. 4(b). Obviously, band1 is mainly contributed by the p_z orbitals of the C atoms in C₃O₃ unit and the N atoms in s-triazine units, while band2 arises mainly from the p_z orbitals of C atoms in C₃O₃ unit. The electron wavefunction of band2 is rather localized compared with that of band1, in good consistent with the energy dispersion of the two bands.

These features are more obvious in the electron density of states (PDOS) projected onto different atoms. In g-C₂NO, there are two types of carbon atoms. One is at the s-triazine unit (denoted as C₁), another is at the C₃O₃ unit (denoted as C₂), as marked in Fig. 1. Fig. 5 gives the PDOS projected onto C₁, C₂, N, and O atoms. Clearly, the valence states near the Fermi level come from C₂ and N atoms, whereas the contributions of O and C₁ atoms are very small. Orbital-resolved PDOS shown in Fig. 5(b–e) confirm that these states originate from the p_z orbitals of these atoms. This differs significantly from the case of g-CN where the electron states near the Fermi level are mainly contributed by the p_xy orbital of N atoms.¹⁵ Since oxygen has one more valence electron than nitrogen, substituting nitrogen with oxygen moves the Fermi level upward to the conduction band region of g-CN where the contribution from p_z atomic orbitals is dominating.

Fig. 5 (a) The electron density of states (PDOS) projected onto the four different atoms of two-dimensional g-C₂NO ternary compound. (b–e) The electron density of states projected onto the s, p_x, p_y, p_z orbital of the four different atoms. The energy at the Fermi level is set to zero.

We also considered the g-C₂NO lattices with other substitution patterns. It is found that the energetically most favorable structure has O atoms distributed in the both rings of the unit cell, as shown Fig. 6(a). This configuration is more stable than that with the O atom in a single ring by about 88 meV per atom. Electron spin-polarization also occurs in this configuration, yielding magnetic moments of 1.0 μ_B in one unit cell. From the spin-resolved band structures shown in Fig. 6(b), one can see that this g-C₂NO lattice is a spin-polarized semiconductor with band gaps of about 54 meV in both spin channels. The FM ordering shown in Fig. 6(b) is energetically preferable. The diversity in electronic structures of 2D oxidized carbon nitrides is crucial for tuning their electronic properties to meet requirements of practical applications.

Fig. 6 (a) Another honeycomb lattice of two-dimensional CON ternary compound. The different atoms (C, O, N) are indicated by the balls in different colors. (b) Spin-resolved band structure line along the high symmetric points in the BZ. (c) Spin-polarized electron density profiles of the FM ordering. The isosurface value of spin-polarized electron density was set to 0.005 Å⁻³.

Finally, we should point out that although there are no experimental evidence of the existence of this 2D material so far, the oxygen-doped graphitic carbon nitrides have been achieved via H₂O₂ hydrothermal procedure.^41,42 Based on these experimental progresses, we deduce that the g-C₂NO lattices may be realized by oxidizing the g-CN²⁷ via similar procedure. First-principles calculations have revealed that the valence band maximum (VBM) and the conduction band minimum (CBM) of g-CN are mainly contributed from the p_xy orbital of N atoms. Therefore, the oxidization may prefer to take place at the N site, leading to substitution reaction of N with O atoms. Our calculations have showed that this reaction is exothermic. By carefully controlling the oxidization process, one may have the possibility to obtain the framework containing s-triazine and C₃O₃ units. It is noteworthy that if all the g-CN is completely oxidized, the resulted g-CO lattice becomes unstable compared with CO gas molecules.

Conclusions

Based on first-principles calculations, we proposed a stable two-dimensional metal-free SGS (g-C₂NO) composing of C, N and O atoms. We demonstrated that it has a spin-polarized ground state with magnetic moments of 1.0 μ_B in one primitive cell which prefers to interact in a ferromagnetic way. The electronic bands of one spin channel exhibits gapless features, while another spin channel has a band gap of 1.15 eV. The valence band and the conduction band nearest to the Fermi level have parabolic energy-momentum dispersion relations with different effective masses. The spin-polarized electronic states near the Fermi level are mainly contributed by the p_z atomic orbitals of the C atoms in C₃O₃ units and the N atoms in s-triazine units. These results offer an effective approach in design of metal-free SGSs which are promising for applications in environmentally-friendly spintronics devices.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 21433006), the 111 project (No. B13029), the Natural Science Foundation of Shandong Province, China (No. ZR2014AQ018), Scientific Research in Universities of Shandong Province (No. J16LJ06) and the National Super Computing Centre in Jinan.

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