# Electronic and Magnetic Properties of Bulk and Monolayer CrSi\({}_{2}\): A First-Principle Study
## 3 Results and Discussion
### Electronic Structure  
We calculated the magnetic moment of unit cell, local magnetic moment of Cr and Si atom, total energy, band length between Cr and Si atoms, band gap and lattice parameters, listed in Table 1. The results were satisfying, compared with those values calculated in References [9; 24; 25; 29; 30]. One can see that bulk CrSi\({}_{2}\) is an indirect gap semiconductor, whereas, monolayer CrSi\({}_{2}\) has metallic character. It can also be seen that there is a big difference between bulk and monolayer compounds in the magnetic moment, i.e., monolayer CrSi\({}_{2}\) unit cell has an obvious magnetic moment\(\sim\)3.68 \(\upmu_{\text{B}}\), and the local magnetic moment of every Cr and Si atom were 4.11 and \(-\)0.21 \(\upmu_{\text{B}}\), respectively. In contrast, for the bulk CrSi\({}_{2}\) system, every Cr and Si atom hardly had any magnetic moment. These results indicated that whilst bulk CrSi\({}_{2}\) was diamagnetic, monolayer CrSi\({}_{2}\) system was ferromagnetic (FM), consistent with the conclusions of References [9; 10; 11; 29]. However, it conflicts with the results of Reference [30]. Unfortunately, until now, there is no available experimental evidence to validate the contradicting theoretical results. Potentially, this research may inspire more experimenters to study these two-dimensional systems. To reveal the origin of metallicity and magnetism, band structure and total and partial density of states (DOS) were systematically studied. As shown in Figure 3, the band structures with up and down spin of bulk and monolayer CrSi\({}_{2}\) are calculated. The results show that bulk CrSi\({}_{2}\) is an indirect gap semiconductor with a band gap of 0.376 eV, which is in good accordance with Ref. [24; 25], and monolayer CrSi\({}_{2}\) is metallic being in good agreement with our previous results [10; 11]. In the bulk CrSi\({}_{2}\) system, the spin-up and spin-down states were completely symmetric, which indicated that bulk CrSi\({}_{2}\) was a nonmagnetic semiconductor. However, for the monolayer CrSi\({}_{2}\) system, the spin-up and spin-down states were in complete asymmetry and both spin-up and spin-down states go across the Fermi level, which manifested that monolayer CrSi\({}_{2}\) was both magnetic and metallic. All these results were in good agreement with the analysis of Table 1. It has been confirmed that the energy band \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **Magnetic** & **Local Magnetic** & **Local Magnetic** & **Total Energy** & **Band Length of** & **Band Gap** & **Lattice** \\  & **Monent of** & **Moment of Cr** & **Moment of Si** & **of System** & **cr-si of Intralayer** & **(eV)** & **(eV)** & **Parameter (Å)** \\  & **Unit Cell** (\(\upmu_{\text{B}}\)) & **Atom** (\(\upmu_{\text{B}}\)) & **Atom** (\(\upmu_{\text{B}}\)) & **(eV)** & **(a)** & **(a)** & **(a)** \\ \hline  & \(4\times 10^{-4}\) & 0 & 0 & \(-\)8050.32 & 2.47, 2.52, 2.55 & 0.376 & \begin{tabular}{c} a = 4.4276 \\ c c c c c c c} \hline \hline bulk CrSi\({}_{2}\) & 0\({}^{\circ}\) & 0\({}^{\circ}\) & 0\({}^{\circ}\) & 0\({}^{\circ}\) & – & 2.47\({}^{\circ}\) * 2.55\({}^{\circ}\) * 3.06 * & 0.35\({}^{\circ}\) * 0.21 \({}^{d}\) & \begin{tabular}{c} a = 4.42\({}^{\circ}\) * 4.43 \\ d \\ c c c c c c} \hline \hline monolayer & 3.68 & 4.11 & \(-\)0.21 & \(-\)24118.24 & 2.55 & 0 & \
\begin{tabular}{c} a = 4.4276 \\ c c c c c c c c} \hline \hline  & 3.6 b & 4.15 c & – & – & – & 2.56 b & 0\({}^{\circ}\) &
\begin{tabular}{c} a = 3.99368 * \\ c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{\({}^{\text{a}}\) Reference [25]. b  Reference [29]. c  Reference [30]. d  Reference [24]. e  Reference [9].} & \multicolumn{3}{c}{\({}^{\text{b}}\) Reference [29].} & \multicolumn{3}{c}{\({}^{\text{c}}\) Reference [30]. d  Reference [24]. e  Reference [9].} \\ \end{tabular}
\end{table} 
Table 1: Magnetic moment and structure of bulk and monolayer CrSi\({}_{2}\).