Prediction of the two-dimensional cobalt carbonitride compounds ${\mathrm{CoN}}_4{\mathrm{C}}_{10}$, ${\mathrm{Co}}_2{\mathrm{N}}_8{\mathrm{C}}_6$, and ${\mathrm{Co}}_2{\mathrm{N}}_6{\mathrm{C}}_6$

Single-atom-thick two-dimensional material containing $3d$ transition metal was rarely reported in the past. Based on the first principles method, we predict that the cobalt carbonitrides ${\mathrm{CoN}}_4{\mathrm{C}}_{10}$, ${\mathrm{Co}}_2{\mathrm{N}}_8{\mathrm{C}}_6$, and ${\mathrm{Co}}_2{\mathrm{N}}_6{\mathrm{C}}_6$ are a new class of two-dimensional (2D) materials, which are made up of two components: the ${\mathrm{CoN}}_4$ unit and the graphene fragment unit, arranged in a planar pattern. The stability of the ${\mathrm{CoN}}_4{\mathrm{C}}_{10}$, ${\mathrm{Co}}_2{\mathrm{N}}_8{\mathrm{C}}_6$, and ${\mathrm{Co}}_2{\mathrm{N}}_6{\mathrm{C}}_6$ monolayers is demonstrated by the formation energy and phonon spectra calculations, as well as the molecular dynamics simulations. The spin-polarized calculations reveal that all three compounds are magnetic metals, and the electronic states near Fermi energy are dominated by Co $3d$ electronic states. Moreover, there exist a few sharp peaks of density of state in the vicinity of Fermi energy, deriving from the $d_{z^2}$ orbitals of Co atom. Thus, the graphenelike transition-metal carbonitrides are not only a new class of 2D materials with single-atom-thickness but also have rich electronic properties due to the incorporation of transition metal.

Figure 1

Atomic structures of (a) ${\mathrm{CoN}}_4{\mathrm{C}}_{10}$, (b) ${\mathrm{Co}}_2{\mathrm{N}}_8{\mathrm{C}}_6$, and (c) ${\mathrm{Co}}_2{\mathrm{N}}_6{\mathrm{C}}_6$ with the $2\times 1$ supercell. The conventional crystal cell is marked as a rectangle with the solid black line, and the dash line rhombus is the primitive cell. Each of the Co-N-C compounds is composed of two building blocks, which are shown in the right part of the panel. The nonequivalent N or C atom according to the group symmetry is named ${\mathrm{N}}_1$, ${\mathrm{N}}_2$, ${\mathrm{C}}_1$, ${\mathrm{C}}_2$, or ${\mathrm{C}}_3$.

Figure 2

Phonon spectra of (a) ${\mathrm{CoN}}_4{\mathrm{C}}_{10}$, (b) ${\mathrm{Co}}_2{\mathrm{N}}_8{\mathrm{C}}_6$, and (c) ${\mathrm{Co}}_2{\mathrm{N}}_6{\mathrm{C}}_6$ in ferromagnetic ordering phase. The $k$ path along high symmetry axes in reciprocal space is same to that in energy band calculations, see the following Fig. 5.

Figure 3

(a) 2D charge density in atomic plane of ${\mathrm{CoN}}_4{\mathrm{C}}_{10}$. (b) charge density difference of ${\mathrm{CoN}}_4{\mathrm{C}}_{10}$ relative to the superposition of atomic charge density. In the left panel, charge density increases with color varying from blue to red. In the right panel, yellow and blue surfaces show charge accumulation and depletion, respectively.

Figure 4

The projected DOS on the atomic orbitals of (a) ${\mathrm{CoN}}_4{\mathrm{C}}_{10}$, (b) ${\mathrm{Co}}_2{\mathrm{N}}_8{\mathrm{C}}_6$, and (c) ${\mathrm{Co}}_2{\mathrm{N}}_6{\mathrm{C}}_6$. The vertical axis of top panel in (a), (b), or (c) has a much larger range of density of states than two panels below. It is noted that the sharp DOS peaks of Co $3d$ states are much higher than the ones of N and C $2p$ states in the three kinds of cobalt carbonitrides. The Fermi energy is set to zero.

Figure 5

Band structures of (a) ${\mathrm{CoN}}_4{\mathrm{C}}_{10}$, (b) ${\mathrm{Co}}_2{\mathrm{N}}_8{\mathrm{C}}_6$, and (c) ${\mathrm{Co}}_2{\mathrm{N}}_6{\mathrm{C}}_6$ in ferromagnetic phase. The blue lines are spin-up electronic bands and the red lines correspond to spin-down electronic bands. (d) the Brillouin zones and high-symmetric $k$ points.

Figure 6

The projected DOS on $d$ orbitals of Co atom are shown for (a) ${\mathrm{CoN}}_4{\mathrm{C}}_{10}$, (b) ${\mathrm{Co}}_2{\mathrm{N}}_8{\mathrm{C}}_6$, and (c) ${\mathrm{Co}}_2{\mathrm{N}}_6{\mathrm{C}}_6$ in the ferromagnetic phase. The Hubbard U values of 2, 4, and 6 eV are used in the $\mathrm{GGA}+$ U calculations, and the corresponding projected DOS of Co $d$ orbitals are displayed with the blue, red, and black lines in the top, middle, and bottom panels for each of the three cobalt carbonitride compounds. The Fermi energy is set to zero and is marked as a vertical dashed line.

Figure 7

Band structures of (a) ${\mathrm{CoN}}_4{\mathrm{C}}_{10}$, (b) ${\mathrm{Co}}_2{\mathrm{N}}_8{\mathrm{C}}_6$, and (c) ${\mathrm{Co}}_2{\mathrm{N}}_6{\mathrm{C}}_6$ are from the $\mathrm{GGA}+\mathrm{U}$ calculation with $U=4$ eV. The blue lines are spin-up electronic bands and the red lines correspond to spin-down electronic bands. The Brillouin zones and high symmetric $k$ points are shown in Fig. 5.