Conversation from antiferromagnetic MnBr2 to ferromagnetic Mn3Br8 monolayer with large MAE

A pressing need in low energy spintronics is two-dimensional (2D) ferromagnets with Curie temperature above the liquid-nitrogen temperature (77 K), and sizeable magnetic anisotropy. We studied Mn3Br8 monolayer which is obtained via inducing Mn vacancy at 1/4 population in MnBr2 monolayer. Such defective configuration is designed to change the coordination structure of the Mn-d5 and achieve ferromagnetism with sizeable magnetic anisotropy energy (MAE). Our calculations show that Mn3Br8 monolayer is a ferromagnetic (FM) half-metal with Curie temperature of 130 K, large MAE of − 2.33 meV per formula unit, and atomic magnetic moment of 13/3μB for the Mn atom. Additionally, Mn3Br8 monolayer maintains to be FM under small biaxial strain, whose Curie temperature under 5% compressive strain is 160 K. Additionally, both biaxial strain and carrier doping make the MAE increases, which mainly contributed by the magneto-crystalline anisotropy energy (MCE). Our designed defective structure of MnBr2 monolayer provides a simple but effective way to achieve ferromagnetism with large MAE in 2D materials. Supplementary information The online version contains supplementary material available at 10.1186/s11671-021-03523-0.


Introduction
Spintronics, exploiting the electron spin and the associated magnetic moment, has attracted extensive attention during the past few decades [1], because of its unique advantages over charge-based devices. The recent realization of two-dimensional (2D) ferromagnets with longrange magnetic ordering at finite temperature [2,3] is of great significance for nanoscale spintronics and related applications and inspires tremendous efforts in investigations and fabrications of 2D ferromagnets [4][5][6][7][8][9].
The first two 2D ferromagnets with atomic-thickness was achieved in 2017, that is monolayer CrI 3 [2] and bilayer Cr 2 Ge 2 Te 6 [3]. Unfortunately, both their Curie temperatures are lower than the liquid-nitrogen temperature (77 K), which limits their realistic applications. Besides the Curie temperature, sizeable magnetic anisotropy and magnetic moment are also indispensable for practical application. Large magnetic anisotropy energy (MAE) implies the benefit for the magnetic ordering against the heat fluctuation, and the possibility to reduce the grain size per bit of information; small MAE may results in super-paramagnetic rather than ferromagnetic. Large magnetic moment provides higher sensitivity, higher efficiency, and higher density for spintronics. Heavy elements are more likely to bring in large MAE due to their strong spin-orbital coupling (SOC) effect [10]. A series of 2D FM materials composed of heavy elements have been predicted having large MAE, such as CrI 3 [11], CrAs [12], CrSeI [13], CrSiTe 3 [14], CrWI 6 [15], FeBr 2 and FeI 2 monolayers [16]. Additionally, the local magnetic moment on Mn atom of MXenes Mn 2 NF 2 and Open Access *Correspondence: xlfan@nwpu.edu.cn 1 State Key Laboratory of Solidification Processing, Center for Advanced Lubrication and Seal Materials, School of Material Science and Engineering, Northwestern Polytechnical University, 127 YouYi Western Road, Xi'an 710072, Shaanxi, China Full list of author information is available at the end of the article Mn 2 N(OH) 2 is 4.5μ B per Mn atom [17], which is the largest among the reported FM 2D materials.
Significant density of Mn vacancy was observed experimentally in LaMnO 3 thin films [28], and the concentration of defects can be controlled by regulating the synthesis process deliberately via irradiation of high energy particles, or chemical etching [29]. In this context, we designed the Mn 3 Br 8 monolayer by inducing single Mn vacancy to MnBr 2 monolayer. The vacancy changes the coordination structure of the Mn atom and breaks the d 5 configuration, which may convert the antiferromagnetic coupling into ferromagnetic coupling and bring in large MAE due to the heavy Br atom. As we expect, Mn 3 Br 8 monolayer is FM and has large MAE of − 2.33 meV per formula unit, the magnetic moment for each Mn atom is 13/3μ B . Considering the easy introducing of strain via bending flexible substrates [30][31][32][33], elongating elastic substrate [33][34][35], exploiting the thermal expansion mismatch [33,36], and so on [33], and the effective control of spin polarization via electrostatic doping [37,38], we also studied the Mn 3 Br 8 monolayer under biaxial strain and carrier doping. Our results show that Mn 3 Br 8 monolayer maintains to be FM with Curie temperature increasing under small biaxial strain. Plus, both biaxial strain and carrier doping can make the MAE increases.

Computational methods
All the calculations in the present study were performed by adopting the spin-polarized density function theory (DFT) method as implemented in the Vienna ab-initio simulation package (VASP) [39]. Interactions between electrons and nuclei were described by the projector augmented wave (PAW) method [40,41], and the electronic exchange-correlation interactions were described by the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) method [42]. The Hubbard U terms were adopted to calculate the strong-correlated interaction [43]; an effective onsite coulomb interaction parameter (U) of 4 eV and an exchange energy (J) of 1 eV which was adopted for studying Mn-incorporated 2D materials were used for the Mn-d electrons [44]. The Brillouin zone integration was carried out by adopting the 9 × 9 × 1 k-mesh based on the Monkhorst-Pack scheme [45]. The phonon spectrums were calculated using the Phonopy code [46] which is implemented within the VASP package. A vacuum space of 20 Å was added along the direction perpendicular to the surface of the monolayer to avoid the interaction between the adjacent layers. The cutoff energy for the plane wave basis set was set as 500 eV. The convergence criterion for the total energy and force was set as 1 × 10 -6 eV and 0.01 eV/Å, respectively.

Results and discussions
Cleavage energy, ground state, and stability of the MnBr 2 monolayer The optimized lattice constants of bulk MnBr 2 are a = b = 3.95 Å, consistent with the previous experimental result (a = b = 3.87 Å) [25]. We firstly explored the feasibility of exfoliating MnBr 2 monolayer from the bulk MnBr 2 . Figure 1a presents the well-known, effective, and widely approved method of calculating the cleavage energy [47][48][49]. Specifically, the cleavage energy was obtained by calculating the variation of the total energy of the ground state with respect to the separation distance d between the two fracture parts as shown in Fig. 1b, the lattice constants of a and b are fixed as the values at the equilibrium state of bulk MnBr 2 . The interlayer longrange vdW interactions was described by the Grimme's DFT-D2 scheme [50,51]. The total energy increases with separation distance and then slowly converges as shown in Fig. 1b. The calculated cleavage energy is 0.10 J/m 2 , which is smaller compared with the cleavage energy between the two fracture parts of graphite (0.35 J/m 2 ) [52], demonstrating the feasibility of obtaining MnBr 2 monolayer via micro-mechanical exfoliating method.
MnBr 2 monolayer has the C 3v symmetry as shown in Fig. 1c; each Mn atom is surrounded by 6 neighboring Br atoms, forming an octahedral [MnBr 6 ] 4− unit. As shown in Fig. 2a and b, three possible magnetic configurations, namely non-magnetic (NM), ferromagnetic (FM), and antiferromagnetic (AFM) states are considered. Both high-spin and low-spin states of the Mn ion are considered. Our results show that the Mn ions of FM state are in low-spin with d 1 configuration, while the Mn ions in AFM state are in high-spin with d 5 configuration. The ground state of MnBr 2 monolayer is the AFM state, which is more stable than the NM and FM states by 3.91 eV and 0.72 eV per formula unit, respectively (Additional file 1: Table. S1). The MAE is 0.25 meV, the positive value indicating that the easy magnetization axis is along the out-of-plane directions, agreeing with the previous result [16]. The optimized lattice constants are a = b = 3.95 Å, same with the lattice constants of the bulk MnBr 2 . The Mn-Br bond length is 2.73 Å, and the vertical distance between the two halide planes is 3.03 Å.
The stability of the MnBr 2 monolayer was further investigated by calculating the formation energy, phonon spectrum, and elastic constants. The formation energy is calculated as: where E MnBr 2 represents the energy of MnBr 2 monolayer, E Mn and E Br are the energies of Mn and Br atoms in their bulk structures, respectively. The calculated E form is − 1.87 eV per atom; the negative value means that the formation is exothermic and MnBr 2 monolayer is energetical favorable. Plus, our calculated phonon spectrum ( Fig. 1d) for MnBr 2 monolayer shows no negative frequency in the whole Brillouin zone, indicating dynamically stable. Additionally, the calculated elastic constants Fig. 1 a Bulk model of MnBr 2 used to calculate the cleavage energy and b the cleavage energy as a function of the separation distance d between two fractured parts (the equilibrium interlayer distance is set as 0). c Top and side views, d phonon spectrum, e electronic band structure for both spin channels and f projected density of states (PDOS) of Mn-d orbitals and Br-p orbitals for MnBr 2 monolayer. Δh represents the vertical distance between two halide planes. The primitive cell is circulated in black dash lines. The Fermi level for band structure and DOS is set as 0 eV  Table S2) comply with the Born-Huang criteria [53] of C 11 > 0 , C 11 C 22 − C 2 12 > 0 and C 66 > 0 , confirming that MnBr 2 monolayer is mechanically stable. The calculated in-plane stiffness is 26.98 J/m 2 , about 75% of the MnPSe 3 (36 J/m 2 ) [49], and 15% of MoS 2 monolayer (180 J/m 2 ) [54]. Plus, MnBr 2 monolayer demonstrates higher flexibility, and the ability of sustaining larger tensile strain comparing with MoS 2 monolayer (11%) [54]. This may attributes to ionic bonds for MnBr 2 monolayer against the covalent bonds of MoS 2 monolayer. The analysis of the deformation related to elastic constants indicates it can withstand its weight (See details in the SI).
The electronic band structure of MnBr 2 monolayer is shown in Fig. 1e, it indicates that MnBr 2 monolayer is a semiconductor with a direct band gap of 3.35 eV. Both valence band maximum (VBM) and conduction band minimum (CBM) are located at the Ŵ point. To gain insight of the electronic structures, projected density of states (DOS) for the Mn-d and Br-p orbital are presented in Fig. 1f. The five d orbitals of Mn ion split into a(d z 2 ) , e 1 (d xz + d yz ) , and e 2 (d xy + d x 2 −y 2 ) groups according to the C 3v symmetry. The bader charge analysis suggests that each Mn atom donates two electrons to the two neighboring Br atoms. Thus, the five d-orbitals in one spin-channel are fully occupied by the five d-electrons of the Mn 2+ ions. Correspondingly, the two Mn 2+ ions in the unit cell are in the d 5 high-spin state with the magnetic moment of 5μ B /− 5μ B , the Br 1− ions are in the lowspin state of 4p 6 with neglectable magnetic moment of − 0.02μ B (Additional file 1: Fig. S1(a)). According to the Goodenough-Kanamori-Anderson (GKA) rule, such configuration always provides antiferromagnetic coupling [55].

Stability, electronic, and magnetic properties of Mn 3 Br 8 monolayer
Mn vacancy was introduced to break the d 5 configuration of the Mn 2+ ions. Single Mn vacancy is introduced in the 2 × 2 × 1 supercell of MnBr 2 monolayer, which gives out the Mn 3 Br 8 monolayer. As shown in Fig. 3a, each Mn atom has four nearest neighboring Mn atoms and binds to six Br atoms, forming a distorted octahedral [MnBr 6 ] unit. Five magnetic states (NM, FM, FIM, AFM-1, and AFM-2) shown in Fig. 4 were considered. Our results indicate that the FM state is the ground state, which is more stable than the other four by 9.84 eV, 32.90 meV, 129.85 meV, and 97.65 meV per formula unit, respectively. The optimized lattice constant is still 3.95 Å. Different from MnBr 2 monolayer, Mn 3 Br 8 monolayer has 2 types of Mn-Br bonds (Fig. 3b)   The vertical distance between the two halide planes is 3.33 Å.
To verify the feasibility of inducing Mn vacancy, we firstly calculated the vacancy formation energies under Mn-rich and Br-rich environments via following equations, where E Mn 3 Br 8 and E MnBr 2 represent the total energies of the Mn 3 Br 8 and MnBr 2 monolayers, µ Mn-max is the chemical potential of Mn under Mn-rich environment, which is calculated as the energy of Mn atom in its bulk structure, µ Mn-min is the chemical potential of Mn under the Br-rich environment, which is calculated as: where µ Br-max is the chemical potential of Br and calculated as the energy of Br atom in gas phase. As shown in Fig. 3c, the formation energies under Mn-rich/Br-rich µ Mn-min = E MnBr 2 − 2 × µ Br-max environment are 6.30/0.71 eV per Mn vacancy, indicating that the formation of Mn vacancy is energetically more favorable under the Br-rich environment. Indeed, the S vacancy has been experimentally achieved in MoS 2 monolayer [56], and the predicted formation energy of S vacancy under the S-rich environment is 2.35 eV [57]. Moreover, structuring porous nano-architecture like β-FeOOH/PNGNs (porous nitrogen-doped graphene networks) can induce significant Fe-vacancy [58], and the Bridgman method was adopted to induce ordering Fe vacancy. We also hope that these methods are applicable for inducing Mn vacancy [59]. Plus, there is no negative frequency found in the phonon spectrum of Mn 3 Br 8 monolayer shown in Fig. 5a, proving the dynamical stability. These results approve our design of introducing Mn vacancy to bring in ferromagnetism.
The ferromagnetism of Mn 3 Br 8 monolayer attributes to the FM super-exchange interaction. According to the Goodenough-Kanamori-Anderson (GKA) rule [55], super-exchange interaction between the Mn ions is FM when the Mn-Br-Mn angle is around 90°. In such configuration (Additional file 1: Fig. S2), the Mn-d orbital tends  Fig. S1(b)). Inducing ferromagnetism by vacancy can also be observed for the d 0 systems, like ZnS and ZnO [61,62], single vacancy can induce magnetic moment as large as 2μ B [61] . For each Mn ion, 2/3 d-orbital is unoccupied; the spin-up channel of both e 1 and e 2 orbitals are partially occupied and crossing the Fermi level, resulting in half-metallicity. The half-metallic character also can be observed from the spin-resolved electronic band structure shown in Fig. 5b. The spin-up channel is metallic, while the spindown channel is semiconducting with the indirect band gap of 2.97 eV; the VBM/CBM locates at the M/Ŵ point. The value of the band gap is close to those of the MnP (2.86 eV) [63], MnAs (2.92 eV) [63], and Ni 2 NO 2 (2.98 eV) [64], which is large enough to prevent the thermally excited spin-flip. Comparing with the MnBr 2 monolayer, both the VBM and CBM of the semiconducting channel get more closer to the Fermi level. The CBM is still dominated by the Mn atoms, while the VBM is dominated by the new Br1,2 atoms. Meanwhile, the semiconducting channel converts from direct to indirect, and the band gap reduces. The similar phenomenon was observed in MnCl 2 monolayer with H functionalization [60].
The magnetization directions are determined by the magnetic anisotropy energy (MAE). The MAE of solids arises from two contributors, namely the magneto-crystalline energy (MCE) related to the spinorbit coupling (SOC) and the magnetic dipolar anisotropy energy (MDE) attributed by the magneto-static dipole-dipole interaction. The MDE in the 3D isotropic materials, such as bcc Fe and fcc Ni, is very small. But for low-dimensional materials composed of transition metal atoms with large magnetic moment, the MDE should not be ignored [65][66][67]. The MCE is defined as the difference between the magnetization energy along the in-plane (100 or 010) and out-of-plane (001) directions by taking the SOC into account. The MDE is obtained as the difference of E d between the in-plane and out-of-plane magnetizations. E d in atomic Rydberg units is given by [65,66] where the speed of light, c = 274.072 , i/j are the atomic position vectors in the unit cell, and m i /m j is the atomic magnetic moment (μ B ) on site i/j . The magnetic dipolar Madelung constant M ij is calculated via where R are the lattice vectors. In a 2D material, since all the R and i are in-plane, the second term would be zero for the out-of-plane magnetization, resulting in the positive M ij , while M ij is negative for an in-plane magnetization [67]. Therefore, the MDE relates to the magnetic moment of transition metal and always prefers the inplane magnetization.
The calculated MCE for Mn 3 Br 8 monolayer is − 1.90 meV per formula unit (Fig. 6a), much larger than those of bulk Fe (0.001 meV per atom), and Ni (0.003 meV per atom) [68], and larger than that of the Fe monolayer on Rh (111) (0.08 meV per atom) [69], suggesting that the magnetization of the Mn 3 Br 8 monolayer is thermal stable. The relationship between the MCE and the azimuthal angle can be described by the following equation [70]: where A and B are the anisotropy constants and θ is the azimuthal angle. The fitting result is shown in Additional file 1: Figs. S3. Additionally, the evolution of MCE with the spin axis rotating through the whole space is illustrated in Fig. 6b. MCE within the xy plane shows no difference, but reaches the maximum value along the direction perpendicular to the xy plane, confirming the strong magnetic anisotropy. The MDE is − 0.43 meV per formula unit, and MAE (MCE + MDE) is − 2.33 meV per formula unit. The negative value indicates that the easy magnetization axis is along the in-plane directions. The MDE does not change the magnetization direction, but enhances it. Additionally, the MAE of Mn 3 Br 8 monolayer is much larger than that of MnBr 2 monolayer, proving again the effectiveness of our design. We further calculated the T c for FM Mn 3 Br 8 monolayer by performing the Monte Carlo (MC) simulations based on the Heisenberg model, which has been proven to be the effective method for predicting T c for 2D materials [11,15,48,58,[71][72][73][74][75][76]. Our estimated T c of CrI 3 monolayer is 42 K (Additional file 1: Fig. S4) [76], agreeing well with the experimental measured value [2] and previous calculation results [15,58,71,72,74,76], which proves the accuracy of our adopted method. The spin-Hamiltonian including the nearest neighboring (NN) magnetic interaction is described as where J is the NN magnetic exchange parameter, M i/j is the magnetic moment of Mn ions and integral close to the number of the spin polarized electrons based on Monte Carlo method [71,77,78], i and j stand for the NN pair of Mn ions. The magnetic coupling parameter J is calculated via the energy difference between the FM and AFM states as The calculated J of NN Mn ions is 1.01 meV; the positive value indicates the preferring of FM coupling.
The calculated J of the NN Mn ions and the 100 × 100 × 1 supercell containing 20,000 magnetic moment vectors were adopted to perform the MC simulations. The simulations at each temperature lasts for 10 5 steps. Each magnetic moment vector rotates randomly in all directions. Figure 5d shows the evolution of specific heat defined as C V = E 2 − �E� 2 K B T 2 with temperature, from which we obtained the T c of 130 K for Mn 3 Br 8 monolayer by locating the peak position of C v , higher than the liquid-nitrogen temperature (77 K), and T c of CrI 3 (45 K) [2] and Cr 2 Ge 2 Te 6 (28 K) [3], CrX 3 (X = F, Cl, Br) (36 ~ 51 K) [11], CrXTe 3 (X = Si, Ge) (35.7 K, 57,2 K) [48]. Our calculations demonstrate that the FM Mn 3 Br 8 monolayer has the large MAE and Curie temperature higher than the liquid-nitrogen temperature.

Mn 3 Br 8 monolayer under biaxial strain and carrier doping
Strain engineering has been proven applicable for many 2D materials, and effective to alter the structural parameters, such as the bond lengths and angles, and tune the electronic and magnetic properties. In this context, we investigated Mn 3 Br 8 monolayer under the biaxial strain ranging from − 5% to 5%. It turns out that Mn 3 Br 8 monolayer under biaxial strain from − 5 to 5% maintains to be FM and the atomic magnetic moment hardly changes. As shown in Figs. 7a and c, the angles between two Mn atoms and Br1,2 atoms (θ Mn-Br1,2-Mn ) are 84°-90°, which increases as the strain and gradually approaches 90°. The Mn-Br-Mn angles involving Br3,4,5,6 atoms (θ Mn-Br3,4,5,6-Mn ) gradually deviate from 90°, ranging from 90° to 100°. Thus, super-exchange interactions between the Mn ions mediated via different orthogonal Br-p orbitals are still FM. Both the Mn-Mn and Mn-Br distances increase monotonically as the strain changing from -5% to 5%. Correspondingly, the exchange parameter under the biaxial strain presented in Fig. 8a decreases with the biaxial strain changing from -5% to 5% and reach the largest value (1.18 meV) under -5% biaxial strain. The Curie Fig. 6 Variation of magneto-crystalline anisotropy energy (MCE) a with respect to azimuthal angle and b in the space for Mn 3 Br 8 monolayer temperature of Mn 3 Br 8 monolayer under -5% biaxial strain is 160 K (Fig. 9a). Particularly, the Mn-Br bonds under the increasing tensile strain become longer, and the angles of Mn-Br3,4,5,6-Mn deviate from 90°, which are the main reason why the FM super-exchange interaction becomes weaker. Consequently, the Curie temperature decreases. It is similar with CrPTe 3 and FePS 3 monolayers [79]. Additionally, the MDE decreases with the increasing strain (Additional file 1: Fig. S5(b)); the MAE under -1% biaxial strain is the largest (-3.04 meV). The -5-5% strain does not cause large structural deformation for Mn 3 Br 8 monolayer, and the morphology of its band structures hardly changes. Mn 3 Br 8 monolayer keeps to be half-metallic. Both VBM and CBM in the semiconducting spin-channel move upward slightly to the higher energy as shown in Figs. 8c and 10; the band gap increases slowly with the increasing biaxial strain to 3.12 eV under 5% biaxial strain.
Electron/hole doping always leads to VBM/ CBM moving away from the Fermi level. Our calculations show that Mn 3 Br 8 monolayer with -1-1e (~ 1.7 × 10 14 cm −2 ) carrier doping per formula unit is still FM; the atomic magnetic moment of each Mn ion is still 13/3μ B. As shown in Fig. 7b and d, with carrier doping from -1e to 1e per formula unit, the Mn-Br-Mn angles involving Br3,4,5,6 atoms are about 90° ~ 98°; the Mn-Br1,2-Mn angles are about 88° ~ 90°. The Mn-Mn and Mn-Br1,2 distances increase with the increasing electron doping. Mn 3 Br 8 monolayer with 0.2e and 0.4e carrier doping has larger magnetic exchange parameter (Fig. 8a). The Curie temperature at 0.2e electron doping is largest of 140 K (Fig. 9b). Additionally, with -1e ~ 0.2e doping, the MAE is along in-plane directions; the MDE decreases with the increasing electron doping. Under 0.4e doping, the MCE turns to be positive with the value of 0.41 meV per formula unit; the MAE is only 0.01 meV per formula unit with taking the MDE into account (Additional file 1: Figs. S5(a) and (b)). With 0.6e, 0.8e and 1e doping, the PMA (perpendicular magnetic anisotropy energy) is 1.70, 2.42, and 5.13 meV, respectively, large enough for spintronic applications (Fig. 8b). Additionally, Mn 3 Br 8 monolayer with carrier doping of -1e ~ 1e per formula unit maintains to be half-metallic. Its band gap in the semiconducting spin-channel increases/decreases slightly with the increasing electron/ hole doping as shown in Fig. 8d; the positions of the VBM and CBM do not change. Exceptional, Mn 3 Br 8 monolayer turns to be FM spin-gapless semiconductors (SGS) with the metallic spin-channel opening up a very small energy gap (0.07 eV) under -0.6e and -0.8e hole doping; its Fermi level locates in the band gap region (Fig. 11b and c, more clearly figures are presented in Additional file 1: Figs. S6(a) and (b)). Correspondingly, electrons may be easily excited from the valence band to the conduction band with a small input of energy, which simultaneously produces 100% spin polarized electron and hole carriers. The Curie temperature at -0.6e and -0.8e hole doping is 110 K (Fig. 9c and d), higher than liquid-nitrogen temperature (77 K). Considering with that the charge density modulation of 10 13 ∼ 10 15 cm −2 was already achieved experimentally [80][81][82], our predicted properties of Mn 3 Br 8 monolayer with carrier doping are also experimentally approachable.

Conclusions
In summary, the stability, electronic, and magnetic properties of Mn 3 Br 8 monolayer have been carefully investigated. Our results show that Mn 3 Br 8 monolayer is FM half-metal with 130 K Curie temperature and with 2.97 eV band gap for the semiconducting spinchannel. Plus, the magnetic moment of each Mn ion is 13/3μ B ; the MAE is -2.33 meV per formula unit. The Mn 3 Br 8 monolayer is designed by inducing single Mn vacancy in the 2 × 2 × 1 supercell of MnBr 2 monolayer to break the AFM coupling d 5 configuration. The feasibility of forming the Mn vacancy and the dynamical, mechanical stability of Mn 3 Br 8 monolayer have been comprehensively confirmed. Additionally, Mn 3 Br 8 monolayer under biaxial strain -5% ~ 5% is still FM half-metal with 2.71 ~ 3.12 eV band gap for the semiconducting spin-channel, whose Curie temperature   under -5% biaxial strain is 160 K. Both biaxial strain and carrier doping make the MAE increase, which turns to be perpendicular to the plane under electron doping. With 0.8e and 0.6e hole doping, Mn 3 Br 8 monolayer turns to be spin-gapless semiconductor (SGS) with band gap of 0.07 eV. Our calculations demonstrate Mn 3 Br 8 monolayer as FM half-metal with high Curie temperature, and having large MAE and large magnetic moment, and tunable electronic and magnetic properties under the applied biaxial strain and carrier doping.
Additional file 1. Revised supporting information.