 Nano Express
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Conversation from antiferromagnetic MnBr_{2} to ferromagnetic Mn_{3}Br_{8} monolayer with large MAE
Nanoscale Research Letters volume 16, Article number: 72 (2021)
Abstract
A pressing need in low energy spintronics is twodimensional (2D) ferromagnets with Curie temperature above the liquidnitrogen temperature (77 K), and sizeable magnetic anisotropy. We studied Mn_{3}Br_{8} monolayer which is obtained via inducing Mn vacancy at 1/4 population in MnBr_{2} monolayer. Such defective configuration is designed to change the coordination structure of the Mnd^{5} and achieve ferromagnetism with sizeable magnetic anisotropy energy (MAE). Our calculations show that Mn_{3}Br_{8} monolayer is a ferromagnetic (FM) halfmetal with Curie temperature of 130 K, large MAE of − 2.33 meV per formula unit, and atomic magnetic moment of 13/3μ_{B} for the Mn atom_{.} Additionally, Mn_{3}Br_{8} 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 magnetocrystalline anisotropy energy (MCE). Our designed defective structure of MnBr_{2} monolayer provides a simple but effective way to achieve ferromagnetism with large MAE in 2D materials.
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 chargebased devices. The recent realization of twodimensional (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 atomicthickness 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 liquidnitrogen 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 superparamagnetic 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 spinorbital 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 Mn_{2}N(OH)_{2} is 4.5μ_{B} per Mn atom [17], which is the largest among the reported FM 2D materials.
Since CrI_{3} monolayer has been successfully synthesized, transitionmetal halides have attracted much attentions [18,19,20,21,22,23,24,25,26,27]. Spin Seeback effect has been observed in bilayer MnF_{2} [20]; few layers of CrI_{3} has been implemented into the magnetic tunneling junctions (MTJ) [21]; NiCl_{3} monolayer has been predicted to be a novel Dirac spingapless semiconductor (SGS) [22]. Particularly, MnBr_{2} monolayer is antiferromagnetic with 0.25 meV MAE along the perpendicular direction to the plane based on the firstprinciples calculations [16]; Mn^{2+} ions are in the d^{5} highspin state with magnetic moment of 5μ_{B} [16, 26]. These results imply the potentials of MnBr_{2} as monolayer ferromagnet with large magnetic moment. The key problem is how to convert the AFM coupling between Mn ions into FM coupling.
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 spinpolarized density function theory (DFT) method as implemented in the Vienna abinitio 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 strongcorrelated 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 Mnincorporated 2D materials were used for the Mnd electrons [44]. The Brillouin zone integration was carried out by adopting the 9 × 9 × 1 kmesh 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 wellknown, 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 DFTD2 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 micromechanical exfoliating method.
MnBr_{2} monolayer has the \(C_{{{3}v}}\) 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 nonmagnetic (NM), ferromagnetic (FM), and antiferromagnetic (AFM) states are considered. Both highspin and lowspin states of the Mn ion are considered. Our results show that the Mn ions of FM state are in lowspin with d^{1} configuration, while the Mn ions in AFM state are in highspin 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 outofplane 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 MnBr 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 \(E_{{{\text{MnBr}}_{{2}} }}\) represents the energy of MnBr_{2} monolayer, \(E_{{{\text{Mn}}}}\) and \(E_{{{\text{Br}}}}\) are the energies of Mn and Br atoms in their bulk structures, respectively. The calculated \(E_{{{\text{form}}}}\) 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 (Additional file 1: Table S2) comply with the BornHuang criteria [53] of \(C_{11} > 0\), \(C_{11} C_{22}  C_{12}^{2} > 0\) and \(C_{66} > 0\), confirming that MnBr_{2} monolayer is mechanically stable. The calculated inplane 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 \(\Gamma\) point. To gain insight of the electronic structures, projected density of states (DOS) for the Mnd and Brp 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 \(C_{{{3}v}}\) symmetry. The bader charge analysis suggests that each Mn atom donates two electrons to the two neighboring Br atoms. Thus, the five dorbitals in one spinchannel are fully occupied by the five delectrons of the Mn^{2+} ions. Correspondingly, the two Mn^{2+} ions in the unit cell are in the d^{5} highspin 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 \(2 \times 2 \times 1\) 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, AFM1, and AFM2) 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 MnBr bonds (Fig. 3b). The bonds between Mn atom and the two central Br atoms (\(d_{{\text{MnBr1,2}}}\)) are 2.76 Å, while the other Mn–Br bonds (\(d_{{\text{MnBr3,4,5,6}}}\)) are 2.59 Å. 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 Mnrich and Brrich environments via following equations,
where \(E_{{{\text{Mn}}_{{3}} {\text{Br}}_{{8}} }}\) and \(E_{{{\text{MnBr}}_{{2}} }}\) represent the total energies of the Mn_{3}Br_{8} and MnBr_{2} monolayers, \(\mu_{{\text{Mnmax}}}\) is the chemical potential of Mn under Mnrich environment, which is calculated as the energy of Mn atom in its bulk structure, \(\mu_{{\text{Mnmin}}}\) is the chemical potential of Mn under the Brrich environment, which is calculated as:
where \(\mu_{{\text{Brmax}}}\) 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 Mnrich/Brrich environment are 6.30/0.71 eV per Mn vacancy, indicating that the formation of Mn vacancy is energetically more favorable under the Brrich environment. Indeed, the S vacancy has been experimentally achieved in MoS_{2} monolayer [56], and the predicted formation energy of S vacancy under the Srich environment is 2.35 eV [57]. Moreover, structuring porous nanoarchitecture like βFeOOH/PNGNs (porous nitrogendoped graphene networks) can induce significant Fevacancy [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 superexchange interaction. According to the Goodenough–Kanamori–Anderson (GKA) rule [55], superexchange interaction between the Mn ions is FM when the MnBrMn angle is around 90°. In such configuration (Additional file 1: Fig. S2), the Mnd orbital tends to AFM couples with different orthogonal Brp orbitals, and thus the indirect Mn–Mn magnetic coupling is expected to be FM. But if each Mn ion has 5 unpaired electrons like MnBr_{2} monolayer, superexchange is AFM although the MnBrMn angle is close to 90° because there are no empty spinup Mnd orbitals left in MnBr_{2} monolayer and spinup delectrons cannot hop between the neighboring Mn site [60]. There are existing two different superexchange interaction paths in Mn_{3}Br_{8} (Fig. 3a), and both are FM. One involves central Br1,2 atoms with MnBr bond lengths of 2.76 Å and MnBrMn angles of 87.5°; the other one involves Br3,4,5,6 atoms with MnBr bond length of 2.59 Å and MnBrMn angles of 95°. The hybridized interactions between p orbitals of Br3,4,5,6 atoms and Mnd orbitals are stronger than that of pd hybridization involving Br1,2 atoms, as shown in Fig. 5c, particularly from − 2 eV to − 1.4 eV. While from 1.4 to − 0.9 eV, the pd hybridization involving Br1,2 atoms are dominated.
The bader charge analysis suggests that each Mn atom donates 8/3 electrons to the neighboring Br atoms. Thus, the Mn ions are in the Mn^{8/3+} state. As shown in Fig. 5c, the 13/3 electrons of each Mn ion all fill in the spinup channel of the dorbital, while the Br^{1−} ions are in the lowspin state of 4p^{6}. Thus, the magnetic moment of each Mn^{8/3+} ion is 13/3μ_{B}; the magnetic moment of Br^{1−} ions are neglectable (Additional file 1: 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 dorbital is unoccupied; the spinup channel of both \(e_{1}\) and \(e_{{2}}\) orbitals are partially occupied and crossing the Fermi level, resulting in halfmetallicity. The halfmetallic character also can be observed from the spinresolved electronic band structure shown in Fig. 5b. The spinup channel is metallic, while the spindown channel is semiconducting with the indirect band gap of 2.97 eV; the VBM/CBM locates at the \({\text{M}}\)/\(\Gamma\) 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 spinflip. 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 magnetocrystalline energy (MCE) related to the spin–orbit coupling (SOC) and the magnetic dipolar anisotropy energy (MDE) attributed by the magnetostatic dipole–dipole interaction. The MDE in the 3D isotropic materials, such as bcc Fe and fcc Ni, is very small. But for lowdimensional 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 inplane (100 or 010) and outofplane (001) directions by taking the SOC into account. The MDE is obtained as the difference of \(E_{d}\) between the inplane and outofplane 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 inplane, the second term would be zero for the outofplane magnetization, resulting in the positive \(M_{ij}\), while \(M_{ij}\) is negative for an inplane 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 \(\theta\) 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 inplane 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 spinHamiltonian 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 \(100 \times 100 \times 1\) 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 \(C_{{_{V} }} = {{\left( {\left\langle {E^{2} } \right\rangle  \left\langle E \right\rangle^{2} } \right)} \mathord{\left/ {\vphantom {{\left( {\left\langle {E^{2} } \right\rangle  \left\langle E \right\rangle^{2} } \right)} {K_{B} T^{2} }}} \right. \kern\nulldelimiterspace} {K_{B} T^{2} }}\) 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 liquidnitrogen 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 liquidnitrogen 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_{MnBr1,2Mn}) are 84°–90°, which increases as the strain and gradually approaches 90°. The Mn–Br–Mn angles involving Br3,4,5,6 atoms (θ_{MnBr3,4,5,6Mn}) gradually deviate from 90°, ranging from 90° to 100°. Thus, superexchange interactions between the Mn ions mediated via different orthogonal Brp orbitals are still FM.
Both the Mn–Mn and MnBr 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 temperature of Mn_{3}Br_{8} monolayer under –5% biaxial strain is 160 K (Fig. 9a). Particularly, the MnBr bonds under the increasing tensile strain become longer, and the angles of MnBr3,4,5,6Mn deviate from 90°, which are the main reason why the FM superexchange 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 halfmetallic. Both VBM and CBM in the semiconducting spinchannel 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 (~ \(1.7 \times 10^{14} {\text{cm}}^{{  2}}\)) 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 MnBrMn angles involving Br3,4,5,6 atoms are about 90° ~ 98°; the MnBr1,2Mn angles are about 88° ~ 90°. The Mn–Mn and MnBr1,2 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 inplane 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 halfmetallic. Its band gap in the semiconducting spinchannel 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 spingapless semiconductors (SGS) with the metallic spinchannel 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 liquidnitrogen temperature (77 K). Considering with that the charge density modulation of \(10^{13} \sim10^{15} {\text{cm}}^{  2}\) 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 halfmetal 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 \({2} \times {2} \times {1}\) 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 halfmetal with 2.71 ~ 3.12 eV band gap for the semiconducting spinchannel, 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 spingapless semiconductor (SGS) with band gap of 0.07 eV. Our calculations demonstrate Mn_{3}Br_{8} monolayer as FM halfmetal 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.
Availability of data and materials
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
Abbreviations
 2D:

Twodimensional
 AFM:

Antiferromagnetic
 CBM:

Conduction band minimum
 DFT:

Density functional theory
 DOS:

Density of states
 FIM:

Ferrimagnetic
 FM:

Ferromagnetic
 GGA:

Generalized gradient approximation
 GKA:

Goodenough–Kanamori–Anderson
 MAE:

Magnetic anisotropy energy
 MCE:

Magnetocrystalline anisotropy energy
 MC:

Monte Carlo
 MDE:

Magnetic dipolar anisotropy energy
 MTJ:

Magnetic tunneling junctions
 NM:

Nonmagnetic
 NN:

Nearest neighboring
 PAW:

Projector augmented wave
 PBE:

Perdew–Burke–Ernzerhof
 PMA:

Perpendicular magnetic anisotropy energy
 PNGN:

Porous nitrogendoped graphene networks
 SGS:

Spingapless semiconductor
 SOC:

Spin–orbit coupling
 VASP:

Vienna abinitio simulation package
 VBM:

Valence band maximum
 VDW:

Van der Waals
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This work was supported by the National key R&D Program of China (2018YFB0703800), the Natural Science Fund of Shaanxi Province for distinguished Young Scholars (2019JC10) and Key Project (2021JZ07), the Polymer Electromagnetic Functional Materials Innovation Team of Shaanxi Sanqin Scholars, and sponsored by the seed Foundation of Innovation and Creation for Graduate Students (CX2020083) in Northwestern Polytechnical University.
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YH designed the study, performed the research and drafted the original manuscript, SJ, ZFL, HHZ, and JHW participated in part of research, XLF supervised the study, and revised the original and revised manuscript. All authors read and approved the final manuscript.
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Hu, Y., Jin, S., Luo, Z.F. et al. Conversation from antiferromagnetic MnBr_{2} to ferromagnetic Mn_{3}Br_{8} monolayer with large MAE. Nanoscale Res Lett 16, 72 (2021). https://doi.org/10.1186/s11671021035230
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DOI: https://doi.org/10.1186/s11671021035230
Keywords
 Firstprinciples calculations
 Ferromagnetism
 Twodimensional (2D) materials
 Magnetic anisotropy energy (MAE)