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Tuning the electronic and magnetic properties of MgO monolayer by nonmetal doping: A first-principles investigation

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Tuning the electronic and magnetic properties of MgO monolayer by nonmetal doping: A first-principles investigation suggests an effective approach to tune the electronic and magnetic properties of the pristine and doped MgO monolayer by simply controlling the dopant concentration and distance between dopants, which may be helpful for the applications in optoelectronic and spintronic nanodevices.

Tuning the electronic and magnetic properties of MgO monolayer by nonmetal doping: A first-principles investigation Duy Khanh Nguyen1, Vo Van On1, J Guerrero-Sanchez2 and D M Hoat3,4,* Group of Computational Physics and Simulation of Advanced Materials, Institute of Applied Technology, Thu Dau Mot University, Binh Duong Province, Vietnam Universidad Nacional Autónoma de México, Centro de Nanociencias y Nanotecnología, Apartado Postal 14, Ensenada, Baja California, C´odigo Postal 22800, Mexico Institute of Theoretical and Applied Research, Duy Tan University, Ha Noi 100000, Viet Nam Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Viet Nam *Corresponding author: dominhhoat@duytan.edu.vn ABSTRACTS Significant magnetization of two-dimensional (2D) materials has been achieved by doping with nonmetal species due to s − p and p − p interactions In this work, we have studied the structural, electronic, and magnetic properties of the pristine, N-, C-, and B-doped graphene-like MgO monolayer using first-principles calculations 2D MgO is a paramagnetic semiconductor with an energy gap of 3.373 eV Doping induces new electronic states in the forbidden energy region of MgO monolayer, which in turns regulate the electronic and magnetic properties This layer becomes a 2D ferromagnetic (FM) semiconductor when substituting one O atom by one N, C, or B atom Upon increasing the dopant number to two atoms per supercell, the electronic structure and magnetic properties show a strong dependence on the separation of dopants The 2N doped systems exhibit the antiferromagnetic (AFM) coupling While the C2 and B2 dimers are formed when replacing two neighboring O atoms, giving place to a non-magnetic semiconductor behavior However, when these are further apart, significant magnetism is induced due to the long-term effects Specifically, the 2C-doped structure undergoes a FM-AFM-FM-AFM state transition, whereas the AFM state is found to be energetically stable for the 2B-doped systems In all cases, the magnetic properties are produced mainly by the dopants, while the contribution from remaining constituent atoms is quite small Our study suggests an effective approach to tune the electronic and magnetic properties of the pristine and doped MgO monolayer by simply controlling the dopant concentration and distance between dopants, which may be helpful for the applications in optoelectronic and spintronic nanodevices Keywords: 2D materials, MgO monolayer, band structure, magnetic configuration, and DFT calculations Điều khiển tính chất điện tử từ tính đơn lớp MgO thông qua doping nguyên tố phi kim: Nghiên cứu nguyên lý ban đầu Duy Khanh Nguyen1, Vo Van On1, J Guerrero-Sanchez2 and D M Hoat3,4,* Group of Computational Physics and Simulation of Advanced Materials, Institute of Applied Technology, Thu Dau Mot University, Binh Duong Province, Vietnam Universidad Nacional Autónoma de México, Centro de Nanociencias y Nanotecnología, Apartado Postal 14, Ensenada, Baja California, C´odigo Postal 22800, Mexico Institute of Theoretical and Applied Research, Duy Tan University, Ha Noi 100000, Viet Nam Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Viet Nam TÓM TẮT Do tương tác s-s p-p nên từ tính đáng kể vật liệu hai chiều (2D) sinh doping nguyên tố phi kim Trong nghiên cứu này, chúng tơi nghiên cứu tính chất cấu trúc, điện tử từ tính vật liệu đơn lớp MgO nguyên sơ bị dope với nguyên tử N, C B thông qua tính tốn ngun lý ban đầu Đơn lớp MgO 2D chất bán dẫn khơng từ tính với độ rộng vùng cấm 3.37 eV Khi đơn lớp bị dope với nguyên tố phi kim sinh trạng thái điện tử vùng lượng bị cấm đơn lớp MgO Điều làm đa dạng tính chất điện tử từ tính Đơn lớp MgO nguyên sơ trở thành chất bán dẫn sắt từ 2D thay với đơn nguyên tử O với đơn nguyên tử N, C B Khi nồng độ nguyên tử dope tăng lên cấu trúc điện tử tính chất từ cho thấy phụ thuộc mạnh vào tách biệt nguyên tử dope Đơn lớp bị dope với 2N biểu thị bắt cập phản sắt từ (AFM), C2 and B2 hình thành thay 2O, điều dẫn đến vận động bán dẫn khơng từ tính Khi đơn lớp MgO dope với 2C tạo chuyển trạng thái FM-AFM-FM-AFM, trạng thái AFM ổn định đơn lớp MgO bị dope với 2B Trong tất trường hợp, tính chất từ sinh chủ yếu nguyên tử dope, 10 đóng góp từ nguyên tử cấu thành nhỏ Nghiên cứu đề xuất phương pháp hiệu để điều chỉnh tính chất điện tử từ tính đơn lớp MgO thông qua dope nguyên tử Các kết từ nghiên cứu hữu ích cho ứng dụng thiết bị nano quang điện tử điện tử spin Từ khóa: Vật liệu 2D, đơn lớp MgO, cấu trúc vùng điện tử, cấu hình từ tính tính tốn DFT Introduction The successful exfoliation of graphene has marked the beginning of two-dimensional (2D) materials era in developing diminutive high-performance devices for a broad range of applications [1, 2] Despite its unprecedented intriguing properties as excellent mechanical resistance [3], high thermal conductivity and carrier mobility [4, 5], quantum Hall effect at room temperature [6], and ambipolar field effect [7], its zero gap has restricted considerably the incorporation of graphene in devices In this regard, extensive investigations have been carried out in order to open the graphene band gap So far, two main approaches have been applied: (1) formation of nanoribbons [8, 9], and (2) chemical modification [10, 11] Due to the challenge of an effective control of width, the first method is less practical than the second Besides, the development of sophisticated equipment has made possible the scalable production of a great number of 2D materials including graphene-like elemental [12–14] and compound [15–18] 2D materials Interestingly, most of them are semiconductor with tunable properties induced by their flexible chemical modification and sensitivity to external factors as stress and strain, and electric and magnetic fields On the other hand, tailoring the fundamental properties of 2D materials via doping has been extensively investigated In this respect, transition metals (TMs) have been employed to induce intriguing magnetic properties For example, Juan et al [19] have explored the geometries, electronic and magnetic properties of ZnO monolayer doped with TM atoms Results indicate that Cr, Mn, Fe, Co, Ni, and Cu doping induces significant magnetization, while the Sc, Ti, and V-doped systems are nonmagnetic BeO monolayer doped with Sc-, V-, Mn-, and Ni- results in diluted antiferromagnetic semiconductors, when doping it with Ti-, Cr-, Fe-, Co-, and Cu- a halfmetal effect emerges [20] Such control in the magnetic properties makes these systems suitable for spintronic applications Undoubtedly the magnetic properties of these systems are generated by TM atoms with the unpaired 3d orbital Interestingly, the magnetism appears also in the 2D 11 materials doped non-metal atoms, which is a result of the p − p interaction Recently, we have found that the magnetic semiconductor nature can be induced in the BeO monolayer by N doping, where the spin-up and spin-down energy gaps exhibit an important dependence on the dopants concentration and their separation distance [21] Magnetic behavior is also induced in the buckled MgO monolayer doped with B, C, and N atoms Doping it with F atom generates a non-magnetic response [22] Along with other I I-VI group monolayers, a stable planar graphene-like MgO has been predicted by Zheng et al [23] First-principles calculations yield a large indirect K − Γ band gap of 3.60 eV Later, various theoretical investigations have been performed to explore the electronic and optical properties of this single layer [24, 25] In addition, we have investigated the change in the structure, electronic and magnetic properties of 2D MgO through chemical functionalization [26] We found that the metallization is achieved by nitrogenation, while the fluorination induces an indirect-direct gap transition with a considerable energy gap reduction To the best of our knowledge, non-metal doping effects on the physical properties of planar MgO monolayer have not been investigated well, so far Therefore, we consider necessary to carry out a detailed study in order to fill this lack of knowledge as well as recommend novel multifunctional 2D materials for practical applications In this work, we carry out a comprehensive investigation on the structural, electronic, and magnetic properties of the pristine and X-doped (X = N, C, and B) MgO monolayer The effects of substituting one O atom in the supercell by one X atom, corresponding to a concentration of 6.25%, are analyzed via spin-polarized band structure, density of states, magnetic moments and spin density distribution Then, we increase the concentration to 12.5% to investigate the magnetic coupling Regardless of the N-N distance, the N-doped MgO is an antiferromagnetic 2D material In contrast, the C-doped and B-doped layers undergoes a NM-FM-AFM-FM-AFM and NM-AFM state transition upon varying the C-C and B-B distance Results reported herein may be useful to search for new multifunctional 2D materials for nano-optoelectronic and spintronic applications 12 Computational detials The density functional theory (DFT) [27] calculations have been performed, using the planewave basis projector augmented wave (PAW) approach as implemented in the Vienne ab-initio Simulation Package (VASP) [28, 29], to investigate the structural, electronic, and magnetic properties of the pristine, N-, C-, and B-doped MgO monolayer The Perdew-Burke-Ernzerhof functional within the generalized gradient approximation (GGA-PBE) [30] is employed to describe the exchange correlation potential The plane-wave expansion is realized with a cut-off energy of 500 eV The convergence criteria for energy and atomic forces are set to 10-6 eV and 0.01 eV/Å The k-mesh sizes of 20 × 20 × and × × are generated for the Brillouin zone sampling of the pristine MgO and supercells, respectively, using the Monkhorst-Pack scheme [31] In all cases, a vacuum width larger than 14 (Å) is generated, which guarantees null interlayer interaction along the direction perpendicular to the monolayer (z-axis) Results and discussions 3.1 Pristine MgO monolayer Recently, Hui et al [17] have carried out successfully the epitaxial synthesis of a single atomic sheet of honeycomb BeO structure using the Molecular Beam Epitaxy (MB) method, confirming the previous theoretical predictions [23, 32] Such mentioned work may also open the feasibility of synthesizing other IIA-oxides Therefore, in this work, we consider the MgO monolayer in a planar graphene-like hexagonal structure, in which the interatomic angle is 1200 In an unit cell, there is one Mg atom and one O atom, Fig.1a shows a × × supercell As a first step, the geometry and electronic structure are studied for further analysis of doping effects According to our simulations, the optimized lattice parameter is 3.299 (Å), which corresponds to a chemical bond length dMg-O of 1.905 (Å) These results are in good agreement with previous theoretical calculations [23, 26] In addition, the phonon spectra suggest good dynamical stability of the MgO single layer since no imaginary phonon frequencies are noted (See Fig.1b) 13 Figure (a) Optimized × × atomic structure (Orange ball: Mg; Red ball: O) and (b) Phonon dispersion curves The band structure of MgO monolayer has been calculated along the Γ − M − K − Γ high symmetry direction Results in Fig.2a shows that the valence band maximum (VBM) and conduction band minimum (CBM) take place at the K and Γ point, respectively Accordingly, an indirect band gap of 3.373 eV is obtained, which is consistent with the results reported previously [23, 26] Note that in the considered energy range from -3.0 to 9.0 eV, the dense valence band is originated mainly from O atom, while both constituent atoms contribute to the less dense conduction band This is also reflected in the images of the VBM and CBM charge density The density of states (DOS) spectra will provide more information about the band structure formation Fig.2b indicates that the valence band is formed mainly by the pz and px + py states, while the contribution of electronic states belonging to Mg atom is quite small In contrast, the Mg-s is main contributor to the lower part of the conduction band, at higher energies it shows nearly equal contribution along with the Mg-pz, O-pz, and O-px + py To analyze the chemical bond, we have calculated the charge density difference, which is defined by: ∆ρ = ρ(m) − ρ(Mg) − ρ(O), herein the last terms refer to the charge density of the monolayer, Mg atom, and O atom, respectively From Fig.2c, one can see that the charge is accumulated at the O-site On the contrary, a significant depletion is noted at the Mg atom These results suggest that the chemical bonds are predominantly ionic, which may be a result of charge transfer from Mg to O atom due to their large electronegativity difference 14 Figure (a) Band structure with VBM and CBM charge density (Red color: Mg; Green color: O), (b) Density of states, and (c) Charge density difference (Yellow surface: accumulation; Blue surface: depletion) of MgO monolayer Table 1: Formation energy Ef (eV/Å2) and band gap Eg (eV) of the doped MgO monolayer, and atomic magnetic moments of the dopants (FM/AFM - µB) 15 In order investigate the N, C, and B doping effects on the MgO monolayer structural, electronic, and magnetic properties, one O atom at 0-site is substituted by one dopant atom (See Fig.1a), forming the Mg16 O15X (X = N, C, and B) monolayer with a doping concentration of 6.25%, which will be denoted as 1X systems To further study the magnetic coupling between dopant atoms, the concentration is increased to 12.5% (Mg16O14X2) Note that if seen from 0-site, there are five inequivalent O atoms Therefore, all five possible configurations will be considered, being termed as 2X-1, 2X-2, 2X-3, 2X-4, and 2X-5 with the second dopant located at the 1-, 2-, 3-, 4-, and 5-site, respectively We have calculated the formation energy Ef of the doped systems using the following formula: 𝐸𝐹 = 𝐸𝑡 − 𝐸𝑀𝑔𝑂 + 𝑛𝑂 µ𝑂 − 𝑛𝑋 µ𝑋 𝑆 (1) herein Et and EMgO denote the total energy of the doped and pristine MgO monolayer, respectively; nO = nX refer to the number of substituted(incorporated) O(X) atoms; µ(O) and µ(X) are chemical potential of the O and X atoms, respectively S is the cell area Our calculations demonstrated that the doping is energetically favorable under Mg-rich condition Results are given in Table.1 Smaller formation energy, easier will be the doping realization in experiments Note that Ef increase in the following order: B < C < N, indicating that the synthesis difficulty decreases in this direction, while may be a result of the smaller extra valence electron Note that the 2C-1 and 2B-1 systems exhibit smaller formation energy as compared to the corresponding 2C-n and 2B-n structures, which is a result of the formation of the C2 and B2 dimers as will be analyzed below Our results are in good agreement with other II-oxide monolayers doped with nonmetal such as buckled MgO monolayer [22] or ZnO monolayer [33, 34] It it expected that the doping of MgO monolayer could be experimentally carried out using the chemical vapor deposition (CVD) [35, 36], low-energy ion irradiation [37, 38], and molecular beam epitaxy (MBE) [39, 40] 3.2 N-doped MgO monolayer Fig.3a shows the relaxed atomic structure of the Mg16O15N monolayer Our calculations yield the interatomic distance dMg-N = 1.989 (Å), which is slightly larger than dMg-O in the pristine layer (of the order of 4.41%), while the interatomic angle retains its original value These results indicate that the N incorporation causes negligible structural changes in the MgO monolayer, 16 which is due to the similar atomic size of the O and N atoms The spin density distribution illustrated in Fig.3b suggest significant magnetization of the 1N system induced by N doping, where the magnetism is originated mainly by the dopant spin-up state with a magnetic moment of 0.540 µB Now, we analyze the electronic properties including band structure and density of states, which are closely related to the magnetic properties One can note the appearance of four flat bands (two in the spin-up channel with similar energy and two in the spin-down channel) in the forbidden energy region of MgO monolayer (See Fig.3c) The band structure profile implies magnetic semiconductor nature of the Mg16O15N monolayer, where both spin-up and spin-down states are semiconductor exhibiting energy gaps of 3.152 and 1.244 eV, respectively These values correspond to a reduction of the order of 6.55% and 63.12% as compared with those of MgO, respectively From the partial density of state (PDOS) spectra in Fig.3d, it can be noted that the quite symmetric subbands at energies lower than -0.85 eV and higher than 2.55 eV are derived mainly by the electronic states of Mg and O atoms In contrast, the flat energy curves in the spin-up configuration is formed mainly by the N-px + py states These are also the main contributors to the lower flat band in the spin-down state, while the higher one is originated mainly from the N-pz state It is worth mentioning that the N(p)-Mg(p) coupling causes slight spin symmetry breaking of Mg-p states at the vicinity of the Fermi level, however its contribution to magnetic properties is quite small in comparison with that of N-p electrons (as reflected in Fig.3b) 17 Figure (a) Optimized atomic structure, (b) Spin density (Yellow surface: spin-up; iso-value: 0.004), (c) Spin-polarized band structure (Black line: spin-up; Red line: spin-down), and (d) Density of states of the 1N system The relaxed structures of the Mg16O14N2 monolayer with varying N-N distance are illustrated in Fig.4 Structurally, the most important effects are noted in the case of 2N-1 systems, where the interatomic distance dMg-N and angle ∠NMgN take values of 1.976 (Å) and 108.130, respectively These correspond to the increase and reduction of the order of 3.73% and 9.89%, respectively As the N atoms are further apart, the doping induces quite small local structural modification The spin charge density maps of the 2N-n are displayed in Fig.5, which suggest significant magnetization induced by doping Note that in all cases, the dopants are main contributors to the magnetism For the 2N-1 system, the antiferromagnetic (AFM) coupling is quite stable as compared to the ferromagnetic (FM) ordering exhibiting smaller energy (198.3 meV) Similar feature is observed in the remaining cases, however the difference in energy between AFM and FM states is small (0.2 to 0.3 meV) These results suggest the AFM state stability favored by the short-term interactions of dopants According to our simulations, the local magnetic moments generated by the dopant spin-up and spin-down states are between [0.534 and 0.540] and [-0.534 and -0.539] µB, respectively Moreover, the electronic properties 18 show important dependence on the separation of dopants, which are regulated mainly by the Ninduced flat bands Specifically, the 2N-1, 2N-3, and 2N-5 systems show spin-symmetric band structures (See Fig.6a,c,e), suggesting a semiconductor nature The energy gap increases according to increase the N-N distance, taking values of 0.826, 1.103, and 1.103 eV, respectively Unlikely, the difference in energy of the flat electronic states in their respective spin channels gives place to the magnetic semiconductor behavior of the 2N-2 and 2N-4 systems considering that both spin states are semiconductor, however with slightly different separation between the VBM and CBM points Specifically, energy gap values of 1.210 and 1.241 eV are obtained for the spin-up and spin-down configurations, respectively Figure Optimized atomic structure of 2N-n, 2C-n, and 2B-n (n = 1, 2, 3, 4, and 5) 19 Figure Spin density (Yellow surface: spin-up; Cyan surface: spin-down; iso-value: 0.004) of 2N-n (n = 1, 2, 3, 4, and 5) systems and transition energy Figure Spin-resolved band structure (Black line: spin-up; Red line: spin-down) of (a) 2N-1, (b) 2N-2, (c) 2N-3, (d) 2N-4, and (e) 2N-5 systems 3.3 C-doped MgO monolayer Next, the MgO monolayer doped with one C atom is studied, whose relaxed atomic structure is given in Fig.7a After relaxation, the neighbor Mg atoms move away from C site, giving a bond length dMg-C = 2.096 (Å), that is an increase of the order of 10.03% in comparison with the equilibrium dMg-C While the angle ∠MgCMg exhibits negligible change However, around the dopant site it is noted an increase of interatomic angle ∠MgOMg and ∠OMgO to 121.530 and 127.860, respectively In Fig.7b, the spin density illustration suggests that the MgO monolayer has been magnetized by substituting one O atom by one C atom, and the magnetic properties are produced mainly by the dopant The local magnetic moment of C atom is 0.739 µ B, while that of 20 nearest O atoms is quite small (0.02 µB) The electronic band structure profile indicates that the Mg16O15C monolayer is a half-metallic 2D material generated by the semiconductor spin-up state and metallic spin-down state (See Fig.7c Specifically, with three flat bands in the energy range from -1.122 to -0.960, the spin-up energy gap decreases from 3.373 (pristine) to 2.537 eV, presenting a reduction of 24.76% In contrast, two of the three spin-up flat energy curves spread in the energy range from -0.022 to 0.017 eV, crossing the Fermi level, giving the metallic behavior The PDOS spectra displayed in Fig.7d indicate that the band structure is formed mainly by the electronic states belonging to Mg and O atoms unless the flat bands in the forbidden energy region of the pristine layer, which are created by the dopant To precise, those in the spin-up channel are derived by the C-px + py and C-pz states, where the latter is found at slightly larger energies In the case of spin-down configuration, the metallic nature is induced mainly by the C-px + py, and the remaining dopant state is due to the C-pz orbital The PDOS also suggest the p-p and s-p coupling between constituent atoms of the 1C system, consequently slight spin asymmetry is also noted for the Mg and O atoms at the vicinity of the Fermi level, however their magnetic contribution is negligible Figure (a) Optimized atomic structure, (b) Spin density (Yellow surface: spin-up; iso-value: 0.004), (c) Spin-p olarized band structure (Black line: spin-up; Red line: spin-down), and (d) Density of states of the 1C system 21 The structural, electronic, and magnetic properties of the Mg16O14C2 monolayer show strong dependence upon varying the doping sites As seen in Fig.4, the C atoms leave their original sites to form a C2 dimer with a length of 1.410 (Å) when they replacing two neighboring O atoms, such that the 2C-1 system structure suffer a strongest effect of doping The atomic rings around doping sites exhibit notable deformation, which is reflected in the interatomic distance dMg-C (between 2.050 and 2.105 (Å) and angle ∠MgCMg (84.940) In the contrary, when separating the C atoms from each other, the dopants tend to occupy the original position, and their nearest atoms perform a re-accommodation due to the difference in atomic size and modification of electronic interactions However, the changes are quite small in comparison with the 2C-1 system The optimized C-C distances in the 2C-2, 2C-3, 2C-4, and 2C -5 systems are 5.560, 6.598, 8.830, and 11.428 (Å), respectively Fig.8 indicates that the C2 dimer-doped MgO monolayer retains the paramagnetic nature When the C atoms are further apart, the doping leads to the formation of magnetic materials that undergoes a FM-AFM-FM-AFM state transition Specifically, the FM coupling is energetically stable in the 2C-2 and 2C-4 structures exhibiting lower energy (14.9 and 15.0 meV) than the AFM coupling In contrast, the ground state 2C-3 and 2C-4 structures are antiferromagnetic, which possess lower energy than the FM state (23.8 meV) These results indicate that the magnetic coupling of the Mg16O14C2 monolayer can be effectively tuned by simply controlling the doping sites In these cases, the C atomic magnetic moments vary between [0.718 and 0.752] and [-0.731 and -0.734] µB, which are the main contributor to the material magnetism In addition, the calculated band structures indicate either semiconductor or magnetic semiconductor of the Mg16O14C2 monolayer upon C-C distance variation, as indicated in Fig.9 To precise, the C2 dimer decreases considerably the spin-symmetric energy gap to 0.189 eV Unlikely, the magnetic nature induces strong spin asymmetry in the remaining cases, especially around the Fermi level with the appearance of dopant states The calculated spin-up energy gaps of the 2C-n structures are 2.244, 0.800, 2.244, 0.790 eV when the ”n” index is 2, 3, 4, and 5, respectively Whereas the band gaps of 0.396, 0.800, 0.395, and 0.790 eV, respectively, are obtained in the spin-down state 22 Figure Spin density (Yellow surface: spin-up; Cyan surface: spin-down; iso-value: 0.004) of 2C-n (n = 1, 2, 3, 4, and 5) systems and transition energy Figure Spin-resolved band structure (Black line: spin-up; Red line: spin-down) of (a) 2C-1, (b) 2C-2, (c) 2C-3, (d) 2C-4, and (e) 2C-5 systems 3.4 B-doped MgO monolayer After relaxation, a slight local atomic re-arrangement is carried out in the B-doped MgO monolayer with one B atom per supercell, where the chemical bond d Mg-B is larger than the pristine dMg-O (2.209 compared to 1.905 Å), indicating a Mg atom movement away from the doping site (See Fig.10a) Consequently, the interatomic angles ∠MgOMg and ∠OMgO increase to 123.020 and 133.050, respectively In the contrary, ∠OMgB value is reduced to 113.470, suggesting the atomic ring domains nearest to the dopant As shown in the Fig.10b, the MgO monolayer becomes a magnetic 2D material when it is doped with B atom, where the magnetism is generated mainly by the magnetization of the dopant, little contribution is also noted from the closest O atoms Specifically, the atomic magnetic moments of 0.888 and 0.03 µB are obtained 23 for the B and O atoms, respectively It can be noted in Fig.10c that both of the spin states are semiconductors, where the flat bands appeared in the spin-up valence band cause a considerable energy gap reduction to 1.387 eV (that is, 58.88%) Unlikely, three flat energy curves take place in the spin-down conduction band, where two of them are found below the VBM of host MgO and the other is inserted into the host conduction band Consequently, the band gap decreases slight to 3.025 eV corresponding to a reduction of 10.32% The s-p and p-p interactions cause the spin symmetry breaking around the Fermi level of the constituent atoms, however the PDOS values suggest that the spin asymmetry degree of Mg and O atoms is negligible in comparison to that of B atom (See Fig.10d) The flat bands in both spin channels are formed mainly by the B-px + py and B-pz states, where the former states are found at smaller energies Figure 10 (a) Optimized atomic structure, (b) Spin density (Yellow surface: spin-up; iso-value: 0.004), (c) Spin-polarized band structure (Black line: spin-up; Red line: spin-down), and (d) Density of states of the 1B system Similar to the case of 2C doping, in the Mg16O14B2 the B atoms form a dimer when they substitute two neighboring O atoms, and they return to their original sites when moving away 24 from each other as shown in Fig.4 In the 2B-1 structure, the calculated dimer length is 1.520 (Å), and the bond length dMg−B and angle ∠MgBMg increase to 2.209 (Å) and 123.020, respectively To characterize the deformation of the atomic rings closest to the dimer, we have determined the bond length dMg−O and angle ∠MgOMg These parameters vary between [1.800 and 1.940] (Å) and [104.170 and 133.050], which present significant deviation from their original values in the pristine layer Note that the O-Mg-O atoms between B atoms are nearly aligned in the 2B-2 monolayer with an interatomic angle of 177.850 Undoubtedly, the doping effects on the structural properties become weaker when increasing the B-B distance Fig.11 indicates that the B2 dimer doping results in the paramagnetic 2D material Whereas the 2B-2, 2B-3, 2B-4, and 2B-5 systems prefer an AFM coupling over the FM state with energy difference of -328.8, -59.7, -268.1, and -59.7 meV, respectively Similar to previous cases, the dopant magnetization plays a main role on the magnetic properties of the doped monolayer According to our calculations, the B atoms magnetic moments are found between [0.795 and 0.889] and [-0.771 and -0.889] µB The appearance of flat energy bands of dopant decreases considerably the Mg 16O14B2 monolayer band gap (See Fig.12) Specifically, gap values vary between 0.188 to 1.994 eV in the spin-up state and 0.735 to 1.194 eV in the spin-down state, where largest energy gaps are found in the semiconductor B2 dimer-doped MgO single layer Figure 11 Spin density (Yellow surface: spin-up; Cyan surface: spin-down; iso-value: 0.004) of 2B-n (n = 1, 2, 3, 4, and 5) systems and transition energy 25 Figure 12 Spin-resolved band structure (Black line: spin-up; Red line: spin-down) of (a) 2B-1, (b) 2B-2, (c) 2B-3, (d) 2B-4, and (e) 2B-5 systems Conclusions In summary, the structural, electronic, and magnetic properties of the pristine, and N-, C-, and B-doped MgO monolayer have been comprehensively investigated using first-principles calculations based on the projector augmented wave method MgO is a wide gap semiconductor, whose band structure is mainly formed by the O-p, Mgs, and Mg-p states The chemical bond is predominantly ionic that is generated by a charge transference from Mg to O atom MgO single layer doped with single N, C, and B atom generates FM semiconductors, where the electronic and magnetic properties are regulated mainly by the dopant p states appeared in the host forbidden energy range When two N atoms are incorporated into the structure by substitution, the final material prefers the AFM state over FM state independent of the separation between N atoms In the contrary, the no magnetization is induced when substituting two neighboring O atoms with two C or B atoms because the dopants prefer to move closer each other to form C2 or B2 dimer However, the doped structures become magnetic when increasing the C-C and B-B distance Consequently, the 2C-n and 2B-n undergoes magnetic state transitions Our study may pave a solid way to effectively tune the electronic and magnetic properties of 2D materials through a controllable doping with nonmetal atoms, which will make possible the formation of novel multifunctional 2D materials Acknowledgment: Calculations were performed in the high-performance computing cluster (HPCC) of Thu Dau Mot University (TDMU) and DGCTIC-UNAM Supercomputing Center (projects LANCAD-UNAM-DGTIC-368 and LANCADUNAM-DGTIC-390) 26 REFERENCES [1] K S Novoselov, A K Geim, S V Morozov, D.-e Jiang, Y Zhang, S V 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[0.795 and 0.889] and [-0.771 and -0.889] µB The appearance of flat energy bands of dopant decreases considerably the Mg 16O14B2 monolayer band gap (See Fig.12) Specifically, gap values vary between... Universidad Nacional Autónoma de México, Centro de Nanociencias y Nanotecnolog? ?a, Apartado Postal 14, Ensenada, Baja California, C´odigo Postal 22800, Mexico Institute of Theoretical and Applied Research,

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