Electronic and Magnetic Properties of Bulk and Monolayer CrSi₂: A First-Principle Study

Abstract

We investigated the electronic and magnetic properties of bulk and monolayer CrSi₂ using first-principle methods based on spin-polarized density functional theory. The phonon dispersion, electronic structures, and magnetism of bulk and monolayer CrSi₂ were scientifically studied. Calculated phonon dispersion curves indicated that both bulk and monolayer CrSi₂ were structurally stable. Our calculations revealed that bulk CrSi₂ was an indirect gap nonmagnetic semiconductor, with 0.376 eV band gap. However, monolayer CrSi₂ had metallic and ferromagnetic (FM) characters. Both surface and confinement effects played an important role in the metallic behavior of monolayer CrSi₂. In addition, we also calculated the magnetic moment of unit cell of 2D multilayer CrSi₂ nanosheets with different layers. The results showed that magnetism of CrSi₂ nanosheets was attributed to band energy between layers, quantum size, and surface effects.

1. Introduction

Since graphene [1], which is widely used in the fields of materials, electronics, physics, chemistry, energy resources, biomedicines, etc., was discovered by Andre Geim and Konstantin Novoselov, 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 (TMSi₂) 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, CrSi₂ received numerous attention due to important applications in Si-based device technology [24,25,26]. Previous literature concludes that bulk CrSi₂ 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 the compositions, 2D monolayer transition metal silicides (TMSi₂) are found to be either magnetic or nonmagnetic [9,10,11]. Among TMSi₂ monolayers, CrSi₂ sheet is found to be ferromagnetic [9,10,11,29], thus it may become an important magnetic nanomaterial in spintronics. Theoretically, both Dzade et al. [29] and Bui 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., Dzade deduced that two-dimensional CrSi₂ is ferromagnetic, whilst Bui deduced that planar CrSi₂ 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 CrSi₂. The phonon dispersion curve, band structures with spin state, total and partial density of states (DOS), spin density of bulk and monolayer CrSi₂ system, and magnetic moment of per unit cell of multilayer CrSi₂ nanosheets varying with different layers, are systematically investigated. These results suggest monolayer CrSi₂ may have potential applications in exploiting molecular scale electronic devices.

2. Material and Methods

Our calculations were performed using spin-polarized density functional theory (DFT) in the generalized gradient approximation (GGA) [35,36], with the Pedew-Burke-Ernzerhof (PBE) function for exchange-correlation potential, which were implemented in the Cambridge Sequential Total Energy Package (CASTEP) [37]. Projector augmented-wave (PAW) potentials [38] were employed to illustrate electron–ion interactions. The convergence criterion of total energy was set to be 10⁻⁶ eV, and energy cutoff of 310 eV was adopted for the expansion of plane waves after our test. The Monkhorst-Pack [39] k-point grids of 6 × 6 × 6, 6 × 6 × 1 were applied for the Brillouin-zone (BZ) integration in bulk, and monolayer CrSi₂ computation, respectively. For monolayer CrSi₂, vacuum-slabs of 15Å were used to avoid interactions between adjacent atom layers. CrSi₂ has a hexagonal structure (C40) with nonsymmorphic space group ${\mathrm{D}}_6^4$-P6₂22 [24,25], containing no primitive translations which interchange individual CrSi₂ layers. The lattice constants were a = 4.431 and c = 6.364 Å [24,25]. The lattice constants and atomic positions were fully relaxed until the force on each atom was less than 0.03 eV/Å. Monolayer CrSi₂ has a graphene-like honeycomb structure, which can be formed by a micromechanical cleavage technique due to weak van der Waals (vdW) forces between those layers and strong covalent bonding intralayer [40]. Top and side views of monolayer CrSi₂ after geometry optimization are depicted in Figure 1. According to chemical formula, per unit cell is constructed by one Cr atom and two Si atoms because in every intralayer, one Cr atom is in the center of each hexagonal hole of silicene lattice, leading to a 1:2 ratio between Cr and Si.

3. Results and Discussion

3.1. Phonon Dispersion Curve

It is necessary to check the structural stability of materials before calculation. Although the structures of bulk and monolayer CrSi₂ have been optimized, the phase stability of these structures remains uncertain. Phonon dispersion spectrum analysis is a valid tool to confirm the structural stability. If all the phonon frequencies on the k-points in the Brillouin zone are positive, the structure is stable at absolute zero of temperature. Otherwise, the structure is unstable at absolute zero of temperature [41]. To check the structural stability of bulk and monolayer CrSi₂, we accurately calculated phonon dispersion curves along the high symmetry directions in the Brillouin zone. As shown in Figure 2a for bulk CrSi₂, and b for monolayer CrSi₂, no imaginary vibration frequency appears for bulk and monolayer CrSi₂, indicating that both structures of bulk and monolayer CrSi₂ are stable at ground state in accordance with-Ref. [41].

3.2. 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. Magnetic moment and structure of bulk and monolayer CrSi₂.

	$\mathbf{Magnetic}\mathbf{Moment}\mathbf{of}\mathbf{Unit}\mathbf{Cell}\left({\mathsf{\mu }}_{\mathbf{B}}\right)$	$\mathbf{Local}\mathbf{Magnetic}\mathbf{Moment}\mathbf{of}\mathbf{Cr}\mathbf{Atom}\left({\mathsf{\mu }}_{\mathbf{B}}\right)$	$\mathbf{Local}\mathbf{Magnetic}\mathbf{Moment}\mathbf{of}\mathbf{Si}\mathbf{Atom}\left({\mathsf{\mu }}_{\mathbf{B}}\right)$	Total Energy of System (ev)	Band Length of cr-si of Intralayer (å)	Band Gap (eV)	Lattice Parameter (Å)
bulk CrSi2	4 × 10−4	0	0	−8050.32	2.47, 2.52,2.55	0.376	a = 4.4276 c = 6.3681
	0 c	0 c	0 c	--	2.47 a, 2.55 a, 3.06 a	0.35 a, 0.21 d	a = 4.42 a, 4.43 d c = 6.349 a, 6.36 d
monolayer CrSi2	3.68	4.11	−0.21	−24118.24	2.55	0	a = 4.4276 c = 15
	3.6 b	4.15 c	--	--	2.56 b	0 c	a = 3.93968 e c = 16.49899 e

^a Reference [25]. ^b Reference [29]. ^c Reference [30]. ^d Reference [24]. ^e Reference [9].

. The results were satisfying, compared with those values calculated in References [9,24,25,29,30]. One can see that bulk CrSi₂ is an indirect gap semiconductor, whereas, monolayer CrSi₂ 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 CrSi₂ unit cell has an obvious magnetic moment~3.68 ${\mathsf{\mu }}_{\mathrm{B}}$, and the local magnetic moment of every Cr and Si atom were 4.11 and −0.21 ${\mathsf{\mu }}_{\mathrm{B}}$, respectively. In contrast, for the bulk CrSi₂ system, every Cr and Si atom hardly had any magnetic moment. These results indicated that whilst bulk CrSi₂ was diamagnetic, monolayer CrSi₂ 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 CrSi₂ are calculated. The results show that bulk CrSi₂ is an indirect gap semiconductor with a band gap of 0.376 eV, which is in good accordance with Ref. [24,25], and monolayer CrSi₂ is metallic being in good agreement with our previous results [10,11]. In the bulk CrSi₂ system, the spin-up and spin-down states were completely symmetric, which indicated that bulk CrSi₂ was a nonmagnetic semiconductor. However, for the monolayer CrSi₂ 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 CrSi₂ 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 structure of TMDs are greatly affected by the crystal structure [20]. Huang et al. [42] have explored the origin of the high metallicity on MoSi₂ nanofilms in detail. We can elucidate the physics mechanism of why bulk CrSi₂ is a semiconductor, whilst monolayer CrSi₂ is metallic using Huang’s theory. Both surface and confinement effects contribute to the high sensitivity of the metallicity on nanofilms type, explaining the reason why monolayer has a metallic character.

To further investigate the physical mechanism of magnetism, which may be dependent on the dimension of materials, we calculated the total density of states (DOS) and partial density of states (PDOS) of bulk and monolayer CrSi₂ systems, as depicted in Figure 4. Total DOS and PDOS of the bulk CrSi₂ system were fully symmetric, indicating that bulk CrSi₂ system cannot have a magnetic characteristic, in accordance with Figure 3a. In contrast, for the monolayer CrSi₂ system, both total DOS and PDOS of monolayer CrSi₂ system were asymmetric, manifesting that monolayer CrSi₂ system possesses a magnetic characteristic, in good agreement with Figure 3b. The degree of dissymmetry in PDOS of the Cr atom in monolayer CrSi₂ system was greater than the Si atom’s, which is the reason why the Cr atom has a larger local magnetic moment as depicted in Table 1. In addition, the total density of state near Fermi level of the bulk CrSi₂ system mainly consists of Cr-3d orbital electron. The total density of state near Fermi level of the monolayer CrSi₂ system is mainly made up of Cr-3d orbital electron, with Cr-3p and Si-3p orbital electrons making limited contribution to the total density of state of the system. Moreover, the results also indicated that total magnetic moment (3.68 μB) arose mainly from the spin-up Cr-3d states. Han [9] has investigated the origin of magnetic behavior in monolayer FeSi₂ and CoSi₂ by orbital coupling of atoms. The stronger orbital coupling between atoms may account for the quench of magnetism of the atom. It can be seen from Figure 4b that no noticeable coupling between p orbital of Si atom and d orbital of Cr atom is found around the Fermi level, which indicates that monolayer CrSi₂ has magnetic behavior.

3.3. 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 CrSi₂ systems. As shown in Figure 5, the spin density isosurface plots of bulk and monolayer CrSi₂ on top view (001) are particularly calculated. For the bulk CrSi₂ 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 ${\mathsf{\mu }}_{\mathrm{B}})$ in Table 1. Nevertheless, for the monolayer CrSi₂ 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 CrSi₂ systems. The magnetic behavior has discrepancy in different dimension structures, which can be interpreted considering the charge transfer model [43] and Hund’s rules. The valence electron configurations of Cr and Si atoms are 3d⁵4s¹ and 3s²3p², respectively. In the bulk structure, every Cr (3d⁵4s¹) atom transfers one 4s electron and one 3d electron to adjacent two Si (3s²3p²) atoms. Then, the Si atom whose electron configuration is 3s²3p³ captures one electron to form a stable close-shell electronic structure, and thus has zero spin. The electron configuration of Cr atom is 3d⁴, 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 CrSi₂ 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), leaving unpaired electrons and net spin. This demonstrates that the Cr atom has magnetic moment in the monolayer CrSi₂ 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 Hund’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 CrSi₂, 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 CrSi₂ nanosheets. Considering weak van der Waals force and strong chemical bonds between layers, quantum size [20,21,22,23,46] and surface effects [44] occur when downsizing from bilayers to monolayer in CrSi₂ nanosheets. We deduced that the band energy between layers, as well as quantum size and surface effects play an important role in magnetism of materials. Magnetic response of 2D materials can be tuned by controlling the thinness of thin films, which is an advantageous application in magnetic materials.

4. Conclusions

Electronic and magnetic properties of CrSi₂ were calculated using the first-principle methods based on density functional theory. The phonon dispersion curve, band structures with spin state, total and partial density of states (DOS), and spin density of bulk and monolayer CrSi₂ systems were systematically investigated. Both bulk and monolayer CrSi₂ were structurally stable at ground state. The results showed that the bulk CrSi₂ system is an indirect gap non-magnetic semiconductor with a band gap of 0.376 eV, whilst the monolayer CrSi₂ sheets were metallic and ferromagnetic (FM). Compared with previous literature, our results were consistent with Dzade’s results (ferromagnetism) and inconsistent with Bui’s results (anti-ferromagnetism). We explain the reason why monolayer CrSi₂ had metallic behavior using Huang’s theory, where surface and confinement effects play an important role in the metallic behavior of monolayer CrSi₂. Further analysis showed that total DOS and PDOS of the bulk CrSi₂ system were fully symmetric, and those of the monolayer CrSi₂ system were asymmetric, which may reveal the physical mechanism of magnetism for bulk and CrSi₂ nanosheets. In addition, we also elucidated the origin of magnetism considering the charge transfer model and Hund’s rules, where magnetic moment of unit cell of 2D multilayer nanosheets with different layers was calculated. The results showed that the magnetism of materials is attributed to band energy between layers, as well as quantum size and surface effects. We also expect that our calculations may provide some helpful insight into further experimental investigations, and they show promise in device applications based on 2D CrSi₂ nanosheets.