## 3 Results and Discussion  
### Structure, Electronic Properties and Magnetism of Ti\({}_{4}\)N\({}_{3}\) Nanosheet  
Ti\({}_{4}\)N\({}_{3}\) nanosheet is experimentally prepared as the first N-based series MXene nanosheet [15] by melting fluoride salt in argon gas environment and the temperature was 550 \({}^{\circ}\)C. The nanosheet was etched away from Ti\({}_{4}\)AlN\({}_{3}\) precursor powder layer. Figure 1 shows the construction processing of the Ti\({}_{4}\)N\({}_{3}\) MXene nanosheet by etching off the Al atomic layer from the Ti\({}_{4}\)AlN\({}_{3}\) bulk. The Ti\({}_{4}\)N\({}_{3}\) nanosheet had a hexagonal structure with sandwich layers. The N atomic layer was sandwiched between the upper and lower Ti atomic layers. Each N atom was bonded with six nearest Ti atoms. Three Ti atoms were located on the upper layer and the other three Ti atoms were on the lower layer. The whole Ti\({}_{4}\)N\({}_{3}\) nanosheet was composed of seven alternating layers of Ti and N layers. The structure was more complex than those of M\({}_{3}\)X\({}_{2}\) and M\({}_{2}\)X. Therefore, we deduced that M\({}_{4}\)X\({}_{3}\) had better physical and chemical properties than M\({}_{3}\)X\({}_{2}\) and M\({}_{2}\)X. In our work, the spin polarization was set for the structure optimization of Ti\({}_{4}\)N\({}_{3}\) nanosheet. The optimized lattice constants \(a\) and \(c\), bond length (\(d_{\text{Tix-Nx}}\)) and atomic layer thickness \(L\) are listed in Table 1 for comparing them with the structural parameters of the precursor Ti\({}_{4}\)AlN\({}_{3}\)[44]. The structure parameters difference between Ti\({}_{4}\)N\({}_{3}\) and Ti\({}_{4}\)AlN\({}_{3}\) was relatively small. For the lattice constants, the error did not exceed 2%. This indicates that the Ti\({}_{4}\)N\({}_{3}\) nanosheet was stable. There was no significant change between bonds due to etching, which also proves that the bond length of M-X is stronger than that of M-A [45]. Table 2 shows some structural parameters of Ti\({}_{4}\)N\({}_{3}\) nanosheet. For simplicity, the surface Ti atom, the subsurface N atom, the next subsurface Ti atom and the central layer N atom are marked as Ti1, N2, Ti3 and N4, respectively. In Table 1, the bond lengths \(d_{\text{Ti1-N2}}\) and \(d_{\text{N2-Ti3}}\) were different, which shows that N atoms were located in a distorted octahedron. This structure was similar to the Ti\({}_{2}\)NT\({}_{x}\) calculated by [PERSON] et al. [40], but it is different from the single-layer Ti\({}_{4}\)C\({}_{3}\) nanosheet, which is a regular octahedral structure [46]. In order to discuss electronic and magnetic properties of the Ti\({}_{4}\)N\({}_{3}\) nanosheet, the total magnetic moment of Ti\({}_{4}\)N\({}_{3}\) nanosheet is calculated as 1.173 \(\upmu_{\text{B}}\), which may be weakened, even eliminated by the action of the functional groups. This result accords with the conclusion that the magnetism may be removed by functionalization [47]. The atomic magnetic moment of Ti atoms on the surface and the next subsurface was 0.924 and 0.212 \(\upmu_{\text{B}}\), respectively, whereas the atomic magnetic moment of the N atom on the subsurface and central layers were 0.030 and 0.010 \(\upmu_{\text{B}}\), respectively. Therefore, the total magnetic moment was mainly contributed by the spin-polarized \(d\)-electrons of Ti atoms in the surface \begin{table}
\begin{tabular}{c c c c c c} \hline
**System** & \(a\) (Å) & \(c\) (Å) & \(L\) (Å) & \(d_{\text{Ti1-N2}}\) (Å) & \(d_{\text{N2-Ti3}}\) (Å) \\ \hline Ti\({}_{4}\)AlN\({}_{3}\)[44] & 2.991 & 23.396 & 7.239 & 2.082 & 2.096 \\ Ti\({}_{4}\)N\({}_{3}\) & 2.993 & 23.439 & 7.235 & 2.062 & 2.119 \\ \hline \end{tabular}
\end{table} 
Table 1: Calculated lattice constants \(a\) and \(c\), atomic layer thickness \(L\), bond lengths between the N2 atom at subsurface and its neighbor Ti1 atom (\(d_{\text{Ti1-N2}}\)) or Ti3 atom (\(d_{\text{N2-Ti3}}\)) at the surface or the next subsurface, respectively.