First principles study in two-dimensional antiferromagnetic Mn2Cl8 with strain-controllable and hydrogenation

With the rapid development of spintronics, two-dimensional antiferromagnetic materials have attracted much attention because of their unique physical properties. Here, the monolayer Mn2Cl8 is discovered to be an intrinsically antiferromagnetic semiconductor in current work. The results show that monolayer Mn2Cl8 and Mn2Cl4X4 (X = F, Br) are stable semiconductors with indirect bandgaps of 0.34eV, 0.95eV, and 0.55eV, respectively, and Mn2Cl8 has a Néel temperature (TN) of 245 K. In the systematic study of strain effects, TN changes significantly under strains from −4% to 4% when the antiferromagnetic ground state is not affected. And the compression strain can increase TN to 469 K due to the enhancement of antiferromagnetic coupling of the nearest adjacent magnetic atoms. Moreover, the bandgap and TN of monolayer Mn2Cl8 can be tuned by hydrogenation. This work finds that elemental substitution, strains, and hydrogen passivation is efficient routes to tune the electronic properties of monolayer antiferromagnetic semiconductor Mn2Cl8.


Introduction
Since the discovery of graphene, two-dimensional (2D) materials have attracted much attention due to their excellent properties and potential applications in nanoscale devices [1][2][3][4][5][6]. Many unusual 2D materials, including black phosphorus, transition metal disulfide, transition metal dihalide, etc, have been synthesized and characterized in experiments [7][8][9][10][11][12][13][14][15][16]. Moreover, the existence of magnetism in 2D materials extends its applications to spintronic devices, which require magnetic semiconductors to manipulate both the spin and charge freedom of electrons, doubling the amount of information stored in a limited space [17][18][19][20]. In particular, antiferromagnetic (AFM) materials have obtained a lot of interest recently [21,22] because the total magnetization of AFM is zero and is largely insensitive to the influence of external magnetic fields. When FM materials produce parasitic magnetic fields that may interfere with one another, AFM does not generate such redundant magnetic fields [23]. And AFM nanostructures also encode and store information through spinpolarized tunneling currents [24,25]. Therefore, the first-principle calculations have predicted the possible existence of 2D AFM materials [26][27][28][29], and revealed the correlation between magnetic coupling and AFM ground states. Importantly, in the recent experiments of 2D AFM materials, it is found that few to monolayers of FePS 3 can be mechanically exfoliated from the bulk counterpart, which can be grown using chemical vapor transport and the flux method [30]. Additionally, 2D FeOCl is manufactured using a universal temperatureoscillation chemical vapor transfer [31]. But, because of the low Néel temperatures (T N ), 2D AFM materials currently found in experiments have limited use in spintronic devices. Therefore, it is necessary to theoretically predict new materials and techniques to enhance T N .
An external field can influence and stimulate magnetic properties, including T N , in an ultrathin 2D magnet since it is sensitive to the external environment [32]. Electric field and coupling have proved to be powerful tools for magnetic modulation, but they are limited to certain materials or complex techniques [33][34][35][36]. In contrast, strain field can cause significant deformation in the lattice structure of 2D materials, altering their inherent properties significantly. Thus, strain is a typical technique for modifying the physical properties of 2D materials [37][38][39], as 2D materials can withstand large strains because of the high Young's modulus [40]. For example, Miao et al reported that the Curie temperature of 2D CrOCl can be enhanced by appropriate strain [41]. Zhang et al found that tensile strain can enhance the in-plane magnetic anisotropy of TaTe 2 structures [42]. In addition, a lot of work has been done to study the effect of hydrogenation on the physical properties of 2D materials. Since graphene can now be hydrogenated, spintronics holds great promise for the ferromagnetism caused by the hydrogen adsorption of graphene [43,44]. The on-plane chemical modification with hydrogen has been reported to achieve long-range ferromagnetism without transition-metal doping [45,46]. Houssa et al have explored the direct band gap of hydrogenated silicene and germanene is three orders of magnitude higher than the prototype structures [47]. With a band gap of 0.95 eV, half-hydrogenation silicene exhibits ferromagnetic semiconducting activity and leaves the electrons in the unsaturated Si atoms isolated and unpaired [48]. When hydrogenation is relatively low, the CrSe 2 monolayer exhibits strong dynamical and thermal stability, and the magnetic ground state switch from antiferromagnetic to ferromagnetic. After hydrogenation, the magnetic anisotropy energy and Curie temperature of the monolayer CrSe 2 are much higher, which is attributable to the hydrogen's redistribution of interatomic charge [49]. Therefore, strain and hydrogenation are expected to become efficient methods to control the physical properties of 2D AFM materials.
Inspired by the new 2D structure in the previous work [29], here we predicted the monolayer Mn 2 Cl 8 was dynamically and thermally stable and was a 2D intrinsic AFM semiconductor, which also existed in the Mn 2 Cl 4 X 4 (X = F, Br). Additionally, by applying compressive strains, T N in the Ising model's Monte Carlo simulation could be raised from 245 K to 469 K while the structure maintained stability. This phenomenon occurred because the direct exchange interaction enhanced, leading to AFM domination and T N increase. Finally, our results showed that the bandgap of Mn 2 Cl 8 could be tuned by hydrogenation, and the T N of Mn 2 Cl 8 H 4 was 817 K.

Methods
Device Studio [50] program provides several functions for performing visualization, modeling, simulations, and first-principles calculations by using DS-PAW software [51] integrated into the program. The exchangecorrelation interaction is described by generalized gradient approximation (GGA) in the form of Perdew, Burke, and Ernzerhof (PBE) functional [52]. In this paper, a supercell size of 2 × 2 × 1 unit cell was used to study the magnetic structures in the calculations. The plane-wave cut-off energy, width of smearing, and the number of k points in reciprocal space were set to 600 eV, 0.05 eV, and 15 × 15 × 1, respectively. A 20 Å vacuum layer was applied between the two nearest slabs to avoid interlayer interactions. The conjugate gradient algorithm was employed for geometry optimization using a convergence criterion of 10 −6 eV for the total energy and 0.01 eV/ Å for Hellmann-Feynman force components. The phonon spectrum was calculated using the density functional perturbation theory (DFPT), with a convergence criterion of 10 -10 eV for the total energy and 10 -5 eV/Å for the Hellmann-Feynman force components [53].

Results and discussion
As shown in figures 1(a) and (b), the lattice structure of 2D monolayer Mn 2 Cl 8 consists of [Mn 1 Cl 6 ] octahedral with space group symmetry P21/c. The lattice parameters after highly precise structural optimization are determined to be a 0 = 6.56 Å and b 0 = 5.61 Å. To identify the preferred magnetic ground state [54], we constructed a ferromagnetic (FM) and two AFM configurations (see Supplementary material). For monolayer Mn 2 Cl 8 , the AFM 1 configuration has the lowest energy. More than those on Cl (0.1 μ B ) or X (0.03 μ B ) atoms, the magnetic moments are primarily focused on the magnetic centers of Mn atoms (3 μ B ). The thermal stability of monolayer Mn 2 Cl 8 at room temperature is validated using molecular dynamics (MD) simulations, as illustrated in figure 1(e). The results show that the independent monolayer Mn 2 Cl 8 can be maintained at room temperature. We exploited the phonon spectrum, as shown in figure 1(f), to further confirm the dynamical stability of the monolayer Mn 2 Cl 8 . The absence of an imaginary frequency shows that Mn 2 Cl 8 is dynamically stable [55]. Additionally, the calculated elastic constants for 2D Mn 2 Cl 8 are C 11 = 50.3 N m −1 , C 22 = 23.6 N m −1 , C 12 = 13.6 N m −1 , and C 66 = 0.13 N m −1 , respectively. The Born mechanical stability criteria for 2D monolayer Mn 2 Cl 8 is fully fulfilled, as C 11 , C 66 > 0 and > C C C . . It can also be observed that the t 2g orbital of the Mn atom and the p z orbital of the Cl atom contribute to CBM, and the p x orbital of the Cl atom contributes to VBM. For one Mn 4+ with three d-orbital electrons, lower-energy t 2g orbitals are occupied with spin up and empty with spin down when the high-energy e .g. orbital is empty. This results in three local magnetic moments for the Mn atom in Mn 2 Cl 8 .
The competition between two different exchange interactions helps to explain the mechanism of the AFM ground state. On the one hand, the electrons at the t 2g orbital of the nearest-neighbour Mn atoms directly interact, resulting in the AFM arrangement and the antiparallel spin configuration of the valence electrons. On  FM to AFM should exist. As a result, the AFM configuration originates from the interaction of super-exchanges. Additional computation demonstrates that the AFM ground state of Mn 2 Cl 8 is supported by both negative direct and indirect interactions.
To examine how the properties of monolayers of Mn 2 Cl 8 change, a series of in-plane biaxial and uniaxial strains were used. The value of strains applied was described by the change of the lattice parameter ε = 100% × (a−a 0 )/a 0 = 100% × (b−b 0 )/b 0, where a 0 (b 0 ) and a (b) are the lattice constants of unstrained and strained monolayer Mn 2 Cl 8 , respectively. The range of strains is from −4% to 4%, with the positive value signifying tensile strain and the negative value denoting compressive strain. The longer atomic distance with tensile strain reduces the energy difference between the bonding and antibonding states of the in-plane orbitals of Cl atom, so that the Cl-p x orbitals near VBM decrease [Supplementary material]. For the three types of strains taken into consideration in this work, the bandgap grows monotonically as the lattice constant rises. As demonstrated in figure 3, the biaxial strain has a bigger impact on bandgap than two uniaxial stresses, yet band gaps in all cases still fall within a narrow range of 0.20 ∼ 0.50 eV.
Then, using the element substitution [figure1(c)], we examined the phonon spectra and projected band structure of Mn 2 Cl 4 X 4 (X = F, Br), depicted in figures 4 and 5. Due to the change of the lattice constant, the energy difference between the bonding and antibonding states of the in-plane Mn-d orbitals and the energy band structure change significantly. For example, short lattice constants (a 0 = 6.06 Å and b 0 = 5.41 Å) of Mn 2 Cl 4 F 4 make this energy difference larger, leading to more t 2g orbitals around VBM. The longer lattice constants (a 0 = 6.97 Å and b 0 = 5.86 Å) of Mn 2 Cl 4 Br 4 make this energy difference smaller, that is, t 2g orbitals mainly appear around 1.5 eV. In both cases, CBM becomes contributed by e .g. orbitals. The band gaps of Mn 2 Cl 4 F 4 of Mn 2 Cl 4 Br 4 are 0.95 eV and 0.54 eV, respectively. The VBM of Mn 2 Cl 4 F 4 is placed at the S point, in contrast to previous cases where CBMs are still found at the Y point, which is the most visible modification of the band structure surrounding the bandgap. In addition, Mn atoms have the largest contribution to VBM in Mn 2 Cl 4 F 4 , which is different from Mn 2 Cl 8 and Mn 2 Cl 4 Br 4 . Additionally, the impact of hydrogen passivation [figure1(d)] is investigated by placing an additional H atom right above the outermost Cl atom in Mn 2 Cl 8 . Figure 6 depicts the expected electronic band structure following hydrogen passivation. The magnetic ground state switches from the AFM 1 to the AFM 2 configuration, and the band gap (2.08 eV) of Mn 2 Cl 8 H 4 is significantly bigger than that of Mn 2 Cl 8 . It's important to note that hydrogen passivation results in the Mn atom's valence state changing. The magnetic moment after hydrogen passivation is 5 μB per Mn atom because one Mn 2+ has five spin-parallel electrons that each occupy one of five d orbitals.
To realize the practical application of monolayer Mn 2 Cl 8 in spintronic devices, we examinate the variation trend of local magnetic moment with temperature and predict T N using Monte-Carlo (MC) simulation. The Ising model, characterizing the magnetic coupling in monolayer Mn 2 Cl 8 , can be written as, where J ij is the exchange coupling parameter of Mn-Mn pairs. Here, we only considered the interaction between the nearest neighbor Mn atoms (J 1 ) and the next nearest neighbor Mn atoms (J 2 ), respectively. S i represents the spin of an atom I and is half of the magnetic moment. Here we took |S| = 1.5 for Mn 2 Cl 8 and Mn 2 Cl 4 X 4 (X = F, Br), and |S| = 2.5 for Mn 2 Cl 8 H 4 . As summarized in table 1, monolayer strain-free Mn 2 Cl 8 has a critical temperature of about 245 K [Supplementary material]. The strain-dependent T N mainly originated from the obvious strain effects on the exchange interactions. It is found that the d Mn−Mn changes from 4.1Å to 4.5Å between −4% and +4% cases, while d Mn−Cl is almost unchanged. This indicates that the changes in AFM strength in strains mainly come from the direct interaction between Mn atoms. The direct exchange connection is strengthened by the much shorter distance between the Mn atoms under compressive strains. J 1 and T N values for the compressive strain that was deemed to be the highest (ε = −4%) were −80.54 K and 469 K, respectively, while the corresponding J and T N values decrease when d Mn−Mn increases under tensile strains because of the weaker direct exchange interaction. For Mn 2 Cl 4 X 4 (X = F, Br), the critical temperature increases gradually as the nonmetallic elements move from F to Br. We employ the crystal orbital Hamiltonian population (COHP) analysis to quantify the strength of atomto-atom interactions. The exchange effect is indicated by the COHP integral's negative sign (-ICOHP) and the less negative the value, the weaker the interaction between the two atoms. For Mn 2 Cl 8 , the -ICOHP of Mn-Mn is 0.89, much higher than Mn-Cl (0.2). For Mn 2 Cl 4 X 4 (X = F, Br), nonmetallic elements from F to Br, the -ICOHP between Mn-Mn changes from 0.72 to 1.1. Therefore, we can roughly deduce that the direct exchange interaction increases (the exchange interaction J 1 changes from −18.83 K to −41.43 K), causing T N to rise (297 K of Mn 2 Cl 4 Br 4 ). Furthermore, the significant increase in T N for the structure after hydrogen passivation, which    has -ICOHP is comparable to Mn 2 Cl 8 , is brought on by the increased magnetic moment after hydrogen passivation.

Conclusion
In summary, we predicted the monolayers Mn 2 Cl 8 and Mn 2 Cl 4 X 4 (X = F, Br) were stable 2D intrinsic AFM semiconductor materials. By elemental substitution, T N s of Mn 2 Cl 8 , Mn 2 Cl 4 F 4, and Mn 2 Cl 4 Br 4 were predicted as 245 K, 198 K, and 297 K. In addition, T N of Mn 2 Cl 8 was sensitive to strains. When the compression strain was 4%, T N could be further increased to 469 K, and the phonon spectrum remained stable. The research demonstrated that both direct and indirect exchange interaction resulted in the magnetic ground state of the AFM and that the rise in T N caused by the compression strain was primarily due to the enhancement of direct exchange interaction. It was discovered that T N significantly increased upon hydrogen passivation, which might be due to the Mn atom's strong magnetic moment. As a novel 2D antiferromagnetic semiconductor, our findings indicated that the monolayer Mn 2 Cl 8 was a promising option for the development of ultrafast and ultrahigh-density spintronic and storage devices.