# Electronic and Magnetic Properties of Bulk and Monolayer CrSi\({}_{2}\): A First-Principle Study
## 1 Introduction  
Since graphene [1], which is widely used in the fields of materials, electronics, physics, chemistry, energy resources, biomolecules, etc., was discovered by [PERSON] and [PERSON], two-dimensional (2D) layered materials have triggered extensive interest owing to their unique physical properties [2]. In the past decades, two-dimensional (2D) materials such as silicene, h-BN, layered transition metal dichalcogenides (TMD), and monolayer transition metal silicides (TMSi\({}_{2}\)) have been widely studied [3; 4; 5; 6; 7; 8; 9; 10; 11]. Contrasting with bulk materials, low-dimensional materials with unusual physical properties are important for potential applications in spintronics [12; 13; 14; 15], magnetic storage [16; 17], and molecular scale electronic devices [18; 19], etc. Two-dimensional (2D) materials present extensive novel properties due to quantum size effects [20; 21; 22; 23]. The properties of materials strongly depend on the crystal structure. Thus, we can change structure phases to tune the properties of materials. Previous investigations have proved that controlling the crystal structure and thickness of materials can tune magnetic moment [20], transform metal to semimetal or semiconductor transition [21], and phase segregation [22], as well as alter electronic properties [23]. Among transition metal silicide, CrSi\({}_{2}\) received numerous attention due to important applications in Si-based device technology [24; 25; 26]. Previous literature concludes that bulk CrSi\({}_{2}\) is an indirect semiconductor. Nevertheless, to the best of our knowledge, few studies [27; 28] on their magnetic properties have been reported. In recent years, studies have demonstrated that depending on thecompositions, 2D monolayer transition metal silicides (TMSi\({}_{2}\)) are found to be either magnetic or nonmagnetic [9; 10; 11]. Among TMSi\({}_{2}\) monolayers, CrSi\({}_{2}\) sheet is found to be ferromagnetic [9; 10; 11; 29], thus it may become an important magnetic nanomaterial in spintronics. Theoretically, both [PERSON] et al. [29] and [PERSON] et al. [30] have employed the quantum ESPRESSO package to investigate silicene and transition metal-based materials. Interestingly, they get different even conflicting results, i.e., [PERSON] deduced that two-dimensional CrSi\({}_{2}\) is ferromagnetic, whilst [PERSON] deduced that planar CrSi\({}_{2}\) favors anti-ferromagnetism.  
The development of spintronics and magnetic storage urgently needs synthesized novel 2D magnetic materials. Recently, functionalization of nonmagnetic monolayer materials has been a major way to induce magnetism [31; 32; 33]. Inspired by the synthesis of silicon, both theoretical [29; 30] and experimental [34] researchers have studied the properties of transition metal silicides layers. There is a big obstacle in synthesizing truly two-dimensional nanomaterials and it is because its structural stability depends on temperature sensitively. Naturally, more 2D magnetic materials are required to meet the demand for the rapid development of spintronics and magnetic storage. In this paper, first-principle calculations are employed to probe how dimension and size affect the electronic structure and magnetism of both bulk and monolayer CrSi\({}_{2}\). The phonon dispersion curve, band structures with spin state, total and partial density of states (DOS), spin density of bulk and monolayer CrSi\({}_{2}\) system, and magnetic moment of per unit cell of multilayer CrSi\({}_{2}\) nanosheets varying with different layers, are systematically investigated. These results suggest monolayer CrSi\({}_{2}\) may have potential applications in exploiting molecular scale electronic devices.