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

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,*

1Group of Computational Physics and Simulation of Advanced Materials,

Institute of Applied Technology, Thu Dau Mot University, Binh Duong Province, Vietnam

2Universidad Nacional Autónoma de México, Centro de Nanociencias y Nanotecnología, Apartado Postal 14, Ensenada, Baja California, C´odigo Postal 22800, Mexico

3Institute of Theoretical and Applied Research, Duy Tan University, Ha Noi 100000, Viet Nam

4Faculty 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 các tính chất điện tử và từ tính của 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,*

1Group of Computational Physics and Simulation of Advanced Materials,

Institute of Applied Technology, Thu Dau Mot University, Binh Duong Province, Vietnam

2Universidad Nacional Autónoma de México, Centro de Nanociencias y Nanotecnología, Apartado Postal 14, Ensenada, Baja California, C´odigo Postal 22800, Mexico

3Institute of Theoretical and Applied Research, Duy Tan University, Ha Noi 100000, Viet Nam

4Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Viet Nam

TÓM TẮT

Do các tương tác s-s và p-p nên từ tính đáng kể trong các vật liệu hai chiều (2D) có thể được sinh

ra khi doping các nguyên tố phi kim Trong nghiên cứu này, chúng tôi nghiên cứu các tính chất cấu trúc, điện tử và từ tính của các vật liệu đơn lớp MgO nguyên sơ và khi bị dope với các nguyên tử N, C và B thông qua các tính toán nguyên lý ban đầu Đơn lớp MgO 2D là chất bán dẫn không từ tính với độ rộng vùng cấm là 3.37 eV Khi đơn lớp này bị dope với các nguyên tố phi kim sẽ sinh ra các trạng thái điện tử mới trong vùng năng lượng bị cấm của đơn lớp MgO Điều này sẽ làm đa dạng các tính chất điện tử và từ tính Đơn lớp MgO nguyên sơ sẽ trở thành chất bán dẫn sắt từ 2D khi thay thế với đơn nguyên tử O với đơn nguyên tử N, C hoặc B Khi nồng độ nguyên tử dope tăng lên thì các cấu trúc điện tử và tính chất từ cho thấy sự phụ thuộc mạnh vào sự tách biệt của các nguyên tử dope Đơn lớp bị dope với 2N biểu thị sự bắt cập phản sắt từ (AFM), trong khi đó C2 and B2 là được hình thành khi thay thế 2O, điều này dẫn đến các vận động bán dẫn không từ tính Khi đơn lớp MgO dope với 2C sẽ tạo ra sự chuyển trạng thái FM-AFM-FM-AFM, trong đó trạng thái AFM là được ổn định đối với đơn lớp MgO bị dope với 2B Trong tất cả các trường hợp, các tính chất từ được sinh ra chủ yếu do nguyên tử dope, trong

khi đó sự đóng góp từ các nguyên tử cấu thành là khá nhỏ Nghiên cứu của chúng tôi đề xuất một phương pháp hiệu quả để điều chỉnh các tính chất điện tử và từ tính của các đơn lớp MgO thông qua dope nguyên tử Các kết quả từ nghiên cứu này sẽ rất hữu ích cho các ứng dụng trong các thiết bị nano quang điện tử và điện tử spin

Từ khóa: Vật liệu 2D, đơn lớp MgO, cấu trúc vùng điện tử, cấu hình từ tính và tính toán DFT

1 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 half-metal 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

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

2 Computational detials

The density functional theory (DFT) [27] calculations have been performed, using the wave 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 × 1 and 4 × 4 × 1 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)

plane-3 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 4 × 4 × 1 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)

Figure 1 (a) Optimized 4 × 4 × 1 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

Figure 2 (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 E f (eV/Å 2 ) and band gap E g (eV) of the doped MgO monolayer, and atomic

magnetic moments of the dopants (FM/AFM - µ B )

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+ 𝑛𝑂µ𝑂− 𝑛𝑋µ𝑋

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,

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)

Figure 3 (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