Electrical and magnetic properties of antiferromagnetic semiconductor MnSi2N4 monolayer

Introduction

In 2004, the successfully prepared graphene opened a new era of two-dimensional materials (Novoselov et al., 2004). Subsequently, numerous new systems have already been discovered, greatly promoting the development of the two-dimensional material family. Two-dimensional materials have a wide variety of electronic properties, including metallic, semi-metallic, semiconducting and insulating properties. For example, 1H-MoS₂ is a semiconductor with a direct band gap, 1T phase MoS₂ is a metal, while 1T’ phase MoS₂ is semimetal (Hung et al., 2018). In addition, hexagonal boron nitride (h-BN) shows insulating properties (Liu et al., 2003), and graphene is semimetal (Sheng et al., 2019). However, many 2D materials lack intrinsic magnetism, such as graphene and MoS₂, which motivates researchers to induce magnetism through defect engineering, adsorption or insertion of magnetic atoms. However, these schemes are difficult to construct stable long-range magnetic order. Therefore, two-dimensional intrinsic ferromagnetic materials have aroused tremendous attention.

According to Mermin-Wagner theory, the long-range magnetic order is predicted to be unstable in 2D material and can be easily destroyed by thermal fluctuations (Mermin and Wagner, 1966). Until 2017, the magnetism in the two-dimensional material CrI₃ at the monolayer limit was observed experimentally (Gong et al., 2017; Huang et al., 2017). Hereafter, more 2D magnetic materials have been found, such as Fe₃GeTe₂ (Xian et al., 2022), FePS₃ (Lee et al., 2016) and VSe₂ (Bonilla et al., 2018). Two-dimensional magnetic materials possess a wide variety of excellent physical properties. For instance, monolayer magnetic metal materials have been widely used as electrodes in electronic devices, such as Fe₃GeTe₂ based van der Waals tunnel junctions (O’Hara et al., 2018). Furthermore, magnetic tunnel junction with antimagnetic semiconductor CrI₃ tunnel barrier has been reported to possess a giant magnetoresistance effect due to the significant difference of energy band in the ferromagnetic and antiferromagnetic states (Song et al., 2018), which has achieved a huge breakthrough in spintronic devices. Hence antiferromagnetic semiconductor materials have become a hot research topic because of their novel band characteristics. However, such materials are very rare, the prediction of new antiferromagnetic semiconductor materials becomes the key to the development of spintronic devices.

In this paper, the electronic structure and magnetic properties of monolayer MnSi₂N₄ are explored based on first-principles calculations. The results demonstrate that 2D MnSi₂N₄ is a stable antiferromagnetic semiconductor in which the ground state is an antiferromagnetic state. The large magnetic exchange parameter indicates a strong antiferromagnetic coupling between the magnetic Mn atoms. When an external magnetic field is applied, the MnSi₂N₄ monolayer turns into a half-metal with a magnetic state transition from an antiferromagnetic state to a ferromagnetic state. In which the spin-up electronic state displays a metallic nature, while the spin-down electronic state exhibits a semiconducting feature. Therefore, the MnSi₂N₄ monolayer has great application prospects in spintronics and nanosensors.

Computational details

All calculations were conducted using the Vienna ab initio simulation package (VASP) (Kresse and Furthmuller, 1996; Kresse and Joubert, 1999). The projection plane wave (PAW) method was adopted to describe the interaction between ions and electrons (Blöchl, 1994). The cutoff energy is set as 500 eV. The generalized gradient approximation (GGA) of the form Perdew–Burke–Ernzerhof (PBE) was employed to describe the exchange correlation (Perdew et al., 1996). The convergence criteria for electronic iteration and ionic relaxation were 10^–6 eV and 0.001 eV/Å, respectively. An 18 Å vacuum layer was added in the out plane direction of the monolayer MnSi₂N₄ to eliminate interlayer interactions. The Brillouin zone was sampled with a 13 × 13 × 1 k-point mesh. Due to the strong correlation effect of Mn atoms, the DFT + U method proposed by Dudarev et al. (Dudarev et al., 1998) was adopted, and the effective parameter U_eff was set to 3.9 eV (Wang et al., 2006; Jain et al., 2011; Ling and Mizuno, 2012; Togo and Tanaka, 2015). The phonon spectrum of monolayer MnSi₂N₄ was calculated by the PHONONPY software (Togoet al., 2015) using a 5 × 5 supercell.

Results and discussion

Similar to the two-dimensional MoSi₂N₄, the monolayer MnSi₂N₄ is a two-dimensional material with a hexagonal lattice structure and D_3h point group as shown in Figure 1. MnSi₂N₄ monolayer consists of seven atomic layers stacked with the order N-Si-N-Mn-N-Si-N, which can be regarded as a 1H-phase MnN₂ triple-layer sandwiched between two buckled N-Si layers. The lattice constant of unit cell is 2.88Å, the bond length between Mn and N atoms is 2.02 Å and the bond length between Si and N atoms is 1.74 Å.

FIGURE 1

FIGURE 1. Top (A) and side (B) views of MnSi₂N₄. The balls are highlighted with blue (Si atom), purple (Mn atom) and silvery (N atom). The rhombic unit cells are marked with black dashed lines.

The cohesive energy of the monolayer MnSi₂N₄ was evaluated to confirm the stability of monolayer MnSi₂N₄ using the equation:

${\mathrm{E}}_{\mathrm{c}\mathrm{o}\mathrm{h}}=\left({\mathrm{E}}_{Mn{Si}_2{N}_4}-{\mathrm{E}}_{Mn}-2{\mathrm{E}}_{Si}-4{\mathrm{E}}_N\right)/7(1)$

Where ${\mathrm{E}}_{Mn{Si}_2{N}_4}$ represents the energy of MnSi₂N_4, ${\mathrm{E}}_{Mn}$ , ${\mathrm{E}}_{Si}$ and ${\mathrm{E}}_N$ represent the energy of isolated single Mn, Si and N atoms, respectively. The calculated results show that the cohesive energy of MnSi₂N₄ is -5.03 eV/atom which is comparable to the value of MoS₂ monolayer (−5.12 eV/atom) (Canton-Vitoria et al., 2020) and MoSi₂N₄ (−8.46 eV/atom) (Bafekry et al., 2021). We also calculated the phonon spectrum to check the stability, and there is no imaginary phonon frequency throughout the Brillouin zone, indicating that the structure is dynamically stable. Consequently, the MnSi₂N₄ monolayer has excellent stability and thus may be experimentally prepared in Figure 2.

FIGURE 2

FIGURE 2. Phonon spectrum of monolayer MnSi₂N_4.

The magnetic properties of monolayer MnSi₂N₄ were investigated. We first determined the ground-state magnetic ordering with two possible magnetic order ferromagnetic (FM) and antiferromagnetic (AFM) states. The total energies of the AFM and FM phases of MnSi₂N₄ are -218.650eV and -217.658 eV, respectively. The energy of the AFM state is lower than that of the FM state, hence MnSi₂N₄ has an AFM ground state. The AFM order in monolayer MnSi₂N₄ sourced from the superexchange interactions between two magnetic atoms bridged by nonmetal atoms, following the Goodenough-Kanamori rules (Goodenough, 1955; Kanamori, 1959). In this case, the net magnetic moment is zero and the four Mn atoms in the supercell have an antiparallel magnetic state along with the same value of magnetic moments (3.05 μ_B). The spin-polarized charge density and the schematic diagram for FM and AFM order are plotted in Figure 3. The spin-polarized charge density map shows that Mn atoms possess an high spin-polarized charge density, while spin-polariztion of N atoms is tiny with small magnetic moments (0.05 μ_B).

FIGURE 3

FIGURE 3. (A,B) spin-polarized charge densities of the FM and AFM case for MnSi₂N₄. The yellow and light blue isosurface with an isosurface value of 0.05 e/Bohr³ represent the spin-up and spin-down charge densities, respectively. (C,D) The scheme represents spin orientation of Mn atoms in FM and AFM case.

The electronic properties of AFM states are investigated to further explore potential applications of MnSi₂N_4. The electronic band structure and density of states (TDOS) are calculated as illustrated in Figure 4. It is clear that MnSi₂N₄ exhibits indirect semiconducting property without band cross Fermi level, which is different from nonmagnetic direct bandgap semiconductor MoSi₂N₄ monolayer (Yuan et al., 2022). The conduction band minimum (CBM) and the valence band maximum (VBM) are located at K point and M point, respectively. The band gap is small (0.26 eV). The bands are degenerate and the TDOS is symmetrical for spin-up and spin-down states. Furthermore, no states exist near the Fermi level along with a small energy gap.

FIGURE 4

FIGURE 4. (A) The band structures and (B) total density of states (TDOS) of MnSi₂N₄ monolayer in the AFM states, the spin-up states and spin-down states are represented by the black lines and red dotted lines, respectively.

The projected density of states (PDOS) for Mn atom and the nearest neighbor N atom are depicted in Figure 5 to better analyze orbit contribution for electron structure and magnetic properties. One can notice that the density of states for the five 3d orbitals are all asymmetric as shown in Figure 5A, indicating the large spin splitting for an isolated Mn atom. The magnetic moment (3.04 μ_B/Mn) is mainly dominated by the spin-up (majority-spin) states of d orbitals which is much more than the spin-down electron. For the N atom, the difference in PDOS between the spin-up and spin-down states is not obvious, resulting in a smaller magnetic moment. In addition, the DOS mainly comes from Mn-d and N-p in the energy range from 0.5 to 1.5 eV indicating that the hybridizations between the N-p and Mn-d orbitals are strong.

FIGURE 5

FIGURE 5. Projected density of states (PDOS) for (A) Mn-d orbital and (B) N-p orbital.

Furthermore, the ground antiferromagnetic states will transition to ferromagnetic states under an external magnetic field. The band structure and density of states for FM state are depicted in Figure 6. It is clear that the spin-up and spin-down energy bands are not degenerate. The spin-polarized states can be noticed around the Fermi level. In the spin-up channel, several flat bands near the Fermi level existe and the others band display dispersion along Γ–M and K–Γ, which behave as a metal. But for the spin-down channel, a direct bandgap of 2.07 eV is observed with the VBM and CBM located at Γ point. Hence, MnSi₂N₄ monolayer behaves half-metallic properties in the FM case. The spin polarization is obvious with an asymmetric density of states distribution for spin-up and spin-down states as depicted in Figure 6B. One can find that a peak of spin-up states can be seen near the Fermi level and a large bandgap exists in the spin-down states, which further confirms the metallic behavior for the spin-up states and semiconducting property for spin-down states, respectively. Therefore, the 2D MnSi₂N₄ in FM state is a half-metal with 100% spin polarization.

FIGURE 6

FIGURE 6. (A) The band structures and (B) total density of states (TDOS) of MnSi₂N₄ in the FM states, the spin-up states and spin-down states are represented by the black lines and red dotted lines, respectively.

Strain is an effective means of manipulating electronic structure and magnetic properties which is widely utilized to modulate the electronic structure and magnetic properties of monolayer system. In this paper, the strain is defined as ε = (a − a₀)/a_0, where a₀ is the relaxed lattice constant in the equilibrium state. The magnetic moment of the Mn atom remains about 3 μ_B per unit cell under strain. The effective spin Hamiltonian based on the Heisenberg model can be expressed as

$H=-{\displaystyle \sum }_{<i,j>}{J}_{ij}{\mu }_i{\mu }_j(2)$

where $J_{ij}$ is the magnetic exchange parameter, and ${\mu }_i/{\mu }_j$ is the magnetic moment at nearest neighbor sites i and j, respectively (Kan et al., 2013). The magnetic exchange parameter J is a significant parameter, which can be evaluated by calculating the total energy of the system in different magnetic states. For the FM case, the total energy can be written as E_FM = E₀ − 3 J | $\mu$ |², where E₀ represents the total energy without spin polarization. For the AFM case, the total energy can be expressed as E_AFM = E₀ + J | $\mu$ |². Thus, the exchange parameter can be extracted by J = (E_AFM − E_FM)/4 | $\mu$ |². According to Figure 7A, although the value of J increases nearly linearly with biaxial strain, the energy difference between AFM case and FM case remains positive over the range of applied biaxial strain, indicating that MnSi₂N₄ behaves as AFM phase and no transition from AFM to FM phase is observed. Furthermore, the magnetic exchange parameter J increases with tensile strain and decreases with compressive strain. According to this trend, an extremely large tensile strain may be needed to turn the AFM to the FM ordering.

FIGURE 7

FIGURE 7. (A) Magnetic exchange parameter J and (B) magnetocrystalline anisotropy energy E_MAE as a function of strain.

To identify the easy axis of MnSi₂N₄, we computed the magnetic anisotropy energy (MAE). The MAE of the magnetic crystal is defined as E_MAE = E_in-E_out (Webster and Yan, 2018), that is, the energy difference between the in-plane (E_in) and out-of-plane (E_out) of MnSi₂N₄. For the strain-free monolayer MnSi₂N₄, the MAE is −345 μeV/Mn atom, indicating that the easy axis of MnSi₂N₄ prefers in-plane and the spin of the Mn atoms is arranged parallel to the basal plane. The MAE of monolayer MnSi₂N₄ is mainly derived from Mn atoms since Mn atoms have relatively stronger spin-orbit coupling than other atoms. The MAE is depicted as a function of strain in Figure 7B. When the structure is compressed, this value fluctuates around −350 μeV/Mn, hence the effect of compressive strain on MAE is not obvious. While MAE increases significantly with increasing tensile strain. MAE changes from -345 μeV/Mn to −290 μeV/Mn under the 5% tensile strain.

Conclusion

The electronic and magnetic properties of monolayer MnSi₂N₄ are explored based on first-principles calculations. Monolayer MnSi₂N₄ is an intrinsic antiferromagnetic semiconductor with a small indirect band gap (0.26 eV). The MnSi₂N₄ has strong antiferromagnetic coupling along with strong in-plane magnetocrystalline anisotropy energy (−345 μeV/Mn). Furthermore, the MnSi₂N₄ monolayer exhibits half-metallic properties with a metallic spin-up state and a semiconducting spin-down state. The effect of biaxial strain on magnetism is also investigated. The magnetic exchange parameter J and MAE increase with biaxial tensile strain. The tunable magnetic properties may enrich the 2D antiferromagnets community and stimulate potential applications in spintronic devices.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

Author contributions

DC and ZJ: Conceptualization, methodology, software; JY and J-JH: Investigation, Formal analysis, Visualization; JZ and YG: Formal analysis, Data Curation; DC and YT: Writing—original draft preparation; JY: Supervision, Writing—review and editing.

Funding

Financial support was received from the National Natural Science Foundation of China (NSFC12004142 and NSFC12264026), and Natural Science Funds for Colleges and Universities in Jiangsu Province (20KJB140017).

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

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