# Electronic and Magnetic Properties of Bulk and Monolayer CrSi\({}_{2}\): A First-Principle Study
## 3 Results and Discussion
### Magnetic Properties  
To understand the origin of magnetism, which may be dependent on the dimension of the material, we further investigated the spin density of bulk and monolayer CrSi\({}_{2}\) systems. As shown in Figure 5, the spin density isosurface plots of bulk and monolayer CrSi\({}_{2}\) on top view (001) are particularly calculated. For the bulk CrSi\({}_{2}\) system, spin density near Cr and Si atoms was close to zero, which agreed with the calculations of local magnetism moment of Cr and Si atoms (0 \(\mu_{\rm B}\)) in Table 1. Nevertheless, for the monolayer CrSi\({}_{2}\) system, the numerical values of spin density near Cr atoms were very noticeable, which was much larger than those of spin density near Si atoms. It indicated that the behavior of magnetism in the monolayer was mainly contributed by the magnetic property of Cr atoms. Through careful analysis, we found that electron transfer from one Cr atom to one Si was equal in both the bulk and monolayer CrSi\({}_{2}\) systems. The magnetic behavior has discrepancy in different dimension structures, which can be interpreted considering the charge transfer model [43] and [PERSON]'s rules. The valence electron configurations of Cr and Si atoms are 3d\({}^{5}\)4s\({}^{1}\) and 3s\({}^{2}\)3p\({}^{2}\), respectively. In the bulk structure, every Cr (3d\({}^{5}\)4s\({}^{1}\)) atom transfers one 4s electron and one 3d electron to adjacent two Si (3s\({}^{2}\)3p\({}^{2}\)) atoms. Then, the Si atom whose electron configuration is 3s\({}^{2}\)3p\({}^{3}\) captures one electron to form a stable close-shell electronic structure, and thus has zero spin. The electron configuration of Cr atom is 3d\({}^{4}\), which is an unstable electronic structure according to the octet rule. Owing to the van der Waals (vdW) force and chemical bonds energy between layers, valence electrons of Cr atom are antiparallel, as depicted in Figure 6a, leaving neither unpaired electrons nor net spin, which demonstrates that the Cr atom has no magnetic moment in the bulk CrSi\({}_{2}\) system. This is slightly different from spin density, as depicted in Figure 5a, because it does not consider crystal field splitting. In the monolayer structure, valence electrons of Cr atom are parallel, as depicted in Figure 6b, which has the lowest energy due to the absence of the van der Waals (vdW) force and chemical bonds between layers, as well as the decline of chemical bonds energy in intralayer (i.e., the bond lengths increase, see Table 1),  
Figure 4: Total and partial density of states (DOS) varies from the energy for (**a**) bulk and (**b**) monolayer CrSi\({}_{2}\). leaving unpaired electrons and net spin. This demonstrates that the Cr atom has magnetic moment in the monolayer CrSi\({}_{2}\) system. Compared with the bulk material, electrons in the monolayer case favored occupying different orbits and having parallel spins, resulting in the monolayer case having less unfavorable Coulomb repulsion and lower energy. It was consistent with the [PERSON]'s rules, that electrons always take precedence of different orbits and have the same spin direction occupying the equivalent orbital. Owing to quantum size and surface effects, two-dimensional (2D) materials may present extensive novel physical and chemical properties, when downsizing from three dimensions to two dimensions or one dimension [20; 21; 22; 23; 44; 45; 46; 47]. To further investigate the interrelationship between thickness and magnetism in CrSi\({}_{2}\), we also calculated magnetic moment of unit cell of 2D multilayer nanosheets with different layers. The results depicted in Figure 7 show that the magnetic moment sharply decreases with the increase in the numbers of layers (especially, the magnetic moment decreases greatest when the number of layers increases from one layer to two layers). As the layers increase, the decrease of magnetic moments occurs in CrSi\({}_{2}\) nanosheets.