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,*
1

Group of Computational Physics and Simulation of Advanced Materials,

Institute of Applied Technology, Thu Dau Mot University, Binh Duong Province, Vietnam
2

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

3

Institute of Theoretical and Applied Research, Duy Tan University, Ha Noi 100000, Viet Nam
4

Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Viet Nam
*Corresponding author:

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
9


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,*
1

Group of Computational Physics and Simulation of Advanced Materials,

Institute of Applied Technology, Thu Dau Mot University, Binh Duong Province, Vietnam
2

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

3


Institute of Theoretical and Applied Research, Duy Tan University, Ha Noi 100000, Viet Nam
4

Faculty 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 tơi 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 thơng qua các tính tốn ngun 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
10


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 tốn 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 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


2. 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 × 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).

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).

13



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.

14


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 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 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
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 4. Optimized atomic structure of 2N-n, 2C-n, and 2B-n (n = 1, 2, 3, 4, and 5).

19


Figure 5. 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 6. 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 7. (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 8. 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 9. 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.

4. 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. Dubonos, I. V. Grigorieva,
A. A. Firsov, Electric field effect in atomically thin carbon films, science 306 (5696) (2004) 666–669.
[2] A. K. Geim, K. S. Novoselov, The rise of graphene, in: Nanoscience and technology: a collection of
reviews from nature journals, World Scientific, 2010, pp. 11–19.
[3] D. G. Papageorgiou, I. A. Kinloch, R. J. Young, Mechanical properties of graphene and graphenebased nanocomposites, Progress in Materials Science 90 (2017) 75–127.
[4] D. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L. Nika, A. A. Balandin, W. Bao, F. Miao,
C. N. Lau, Extremely high thermal conductivity of graphene: Prospects for thermal management
applications in nanoelectronic circuits, Applied Physics Letters 92 (15) (2008) 151911.
[5] M. D. Stoller, S. Park, Y. Zhu, J. An, R. S. Ruoff, Graphene-based ultracapacitors, Nano letters 8 (10)
(2008) 3498–3502.
[6] K. Nomura, A. H. MacDonald, Quantum Hall ferromagnetism in graphene, Physical review letters 96
(25) (2006) 256602.
[7] B. K. Sharma, J.-H. Ahn, Graphene based field effect transistors: Efforts made towards flexible
electronics, Solid-State Electronics 89 (2013) 177–188.
[8] Y.-C. Chen, D. G. De Oteyza, Z. Pedramrazi, C. Chen, F. R. Fischer, M. F. Crommie, Tuning the
band gap of graphene nanoribbons synthesized from molecular precursors, ACS nano 7 (7) (2013) 6123–
6128.
[9] J. Liu, B.-W. Li, Y.-Z. Tan, A. Giannakopoulos, C. Sanchez-Sanchez, D. Beljonne, P. Ruffieux, R.
Fasel, X. Feng, K. Muullen, Toward cove-edged low band gap graphene nanoribbons, Journal of the
American Chemical Society 137 (18) (2015) 6097–6103.
[10] A. Hunt, E. Kurmaev, A. Moewes, Band gap engineering of graphene oxide by chemical
modification, Carbon 75 (2014) 366–371.
[11] K.-J. Jeon, Z. Lee, E. Pollak, L. Moreschini, A. Bostwick, C.-M. Park, R. Mendelsberg, V.
Radmilovic, R. Kostecki, T. J. Richardson, et al., Fluorographene: a wide bandgap semiconductor with
ultraviolet luminescence, Acs Nano 5 (2) (2011) 1042–1046.
[12] L. Tao, E. Cinquanta, D. Chiappe, C. Grazianetti, M. Fanciulli, M. Dubey, A. Molle, D. Akinwande,
Silicene field-effect transistors operating at room temperature, Nature nanotechnology 10 (3) (2015) 227–
231.

[13] J. Gou, Q. Zhong, S. Sheng, W. Li, P. Cheng, H. Li, L. Chen, K. Wu, Strained monolayer germanene
with 1 × 1 lattice on Sb (111), 2D Materials 3 (4) (2016) 045005.
[14] H.-S. Tsai, S.-W. Wang, C.-H. Hsiao, C.-W. Chen, H. Ouyang, Y.-L. Chueh, H.-C. Kuo, J.-H. Liang,
Direct synthesis and practical bandgap estimation of multilayer arsenene nanoribbons, Chemistry of
Materials 28 (2) (2016) 425–429.
[15] K. M. McCreary, A. T. Hanbicki, J. T. Robinson, E. Cobas, J. C. Culbertson, A. L. Friedman, G. G.
Jernigan, B. T. Jonker, Large-area synthesis of continuous and uniform MoS 2 monolayer films on
graphene, Advanced Functional Materials 24 (41) (2014) 6449–6454.
27


[16] J.-K. Huang, J. Pu, C.-L. Hsu, M.-H. Chiu, Z.-Y. Juang, Y.-H. Chang, W.-H. Chang, Y. Iwasa, T.
Takenobu, L.-J. Li, Large-area synthesis of highly crystalline WSe2 monolayers and device applications,
ACS nano 8 (1) (2014) 923–930.
[17] H. Zhang, M. Holbrook, F. Cheng, H. Nam, M. Liu, C.- R. Pan, D. West, S. Zhang, M.-Y. Chou, C.K. Shih, Epitaxial growth of two-dimensional insulator monolayer honeycomb BeO, ACS nano 15 (2)
(2021) 2497–2505.
[18] Y.-L. Hong, Z. Liu, L. Wang, T. Zhou, W. Ma, C. Xu, S. Feng, L. Chen, M.-L. Chen, D.-M. Sun, et
al., Chemical vapor deposition of layered two-dimensional MoSi2N4 materials, Science 369 (6504)
(2020) 670–674.
[19] J. Ren, H. Zhang, X. Cheng, Electronic and magnetic properties of all 3d transition-metal-doped ZnO
monolayers, International Journal of Quantum Chemistry 113 (19) (2013) 2243–2250.
[20] N. H. Song, Y. S. Wang, L. Y. Zhang, Y. Y. Yang, Y. Jia, Density functional theory study of tunable
electronic and magnetic properties of monolayer BeO with intrinsic vacancy and transition metal
substitutional doping, Journal of Magnetism and Magnetic Materials 468 (2018) 252–258.
[21] D. M. Hoat, D. K. Nguyen, J. Guerrero-Sanchez, R. Ponce-Pérez, J. Rivas-Silva, V. Van On, G. H.
Cocoletzi, Nitrogen doping and oxygen vacancy effects on the fundamental properties of BeO monolayer:
a DFT study, Journal of Physics: Condensed Matter 33 (32) (2021) 325305.
[22] P. Wu, M. Huang, W. Cheng, F. Tang, First-principles study of B, C, N and F doped graphene-like
MgO monolayer, Physica E: Low-dimensional Systems and Nanostructures 81 (2016) 7–13.
[23] H. Zheng, X.-B. Li, N.-K. Chen, S.-Y. Xie, W. Q. Tian, Y. Chen, H. Xia, S. Zhang, H.-B. Sun,

Monolayer IIVI semiconductors: A first-principles prediction, Physical Review B 92 (11) (2015) 115307.
[24] B. Luo, Y. Yao, E. Tian, H. Song, X. Wang, G. Li, K. Xi, B. Li, H. Song, L. Li, Graphene-like
monolayer monoxides and monochlorides, Proceedings of the National Academy of Sciences 116 (35)
(2019) 17213–17218.
[25] B. Nourozi, A. Aminian, N. Fili, Y. Zangeneh, A. Boochani, P. Darabi, The electronic and optical
properties of MgO mono-layer: Based on GGA-mBJ, Results in Physics 12 (2019) 2038–2043.
[26] D. Hoat, V. Van On, D. K. Nguyen, M. Naseri, R. Ponce Pérez, T. V. Vu, J. Rivas-Silva, N. N. Hieu,
G. H. Cocoletzi, Structural, electronic and optical properties of pristine and functionalized MgO
monolayers: a first principles study, RSC Advances 10 (66) (2020) 40411–40420.
[27] W. Kohn, L. J. Sham, Self-consistent equations including exchange and correlation effects, Physical
review 140 (4A) (1965) A1133.
[28] G. Kresse, J. Furthmăuller, Efficient iterative schemes for ab initio total-energy calculations using a
plane-wave basis set, Physical review B 54 (16) (1996) 11169.
[29] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method,
Physical review b 59 (3) (1999) 1758.
[30] J. P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Physical
review letters 77 (18) (1996) 3865.

28


[31] H. J. Monkhorst, J. D. Pack, Special points for Brillouin zone integrations, Physical review B 13 (12)
(1976) 5188.
[32] V. Van On, D. Hoat, D. K. Nguyen, R. Ponce-Pérez, T. V. Vu, J. Rivas-Silva, G. H. Cocoletzi,
Fluorinating the graphene-like BeO monolayer: A spin-polarized first principles study of the electronic,
magnetic and optical properties, Physica Scripta 95 (10) (2020) 105806.
[33] S. Y. Wakhare, M. D. Deshpande, Structural, electronic and optical properties of metalloid element
(B, Si, Ge, As, Sb, and Te) doped g-ZnO monolayer: A DFT study, Journal of Molecular Graphics and
Modelling 101 (2020) 107753.
[34] J.-Q. Wen, X. Tong, Y.-T. Lei, P.-H. Tian, H. Wu, W.-L. He, J.-M. Zhang, Ferromagnetism induced

by C doped graphene-like ZnO films with different concentrations,
Solid State Communications 299 (2019) 113663.
[35] H. Wang, Y. Zhou, D. Wu, L. Liao, S. Zhao, H. Peng, Z. Liu, Synthesis of boron-doped graphene
monolayers using the sole solid feedstock by chemical vapor deposition, small 9 (8) (2013) 1316–1320.
[36] D. Wei, Y. Liu, Y. Wang, H. Zhang, L. Huang, G. Yu, Synthesis of N-doped graphene by chemical
vapor deposition and its electrical properties, Nano letters 9 (5) (2009) 1752–1758.
[37] E. H. ˚Ahlgren, J. Kotakoski, A. Krasheninnikov, Atomistic simulations of the implantation of lowenergy boron and nitrogen ions into graphene, Physical Review B 83 (11) (2011) 115424.
[38] P. Willke, J. A. Amani, A. Sinterhauf, S. Thakur, T. Kotzott, T. Druga, S. Weikert, K. Maiti, H.
Hofsaass, M. Wenderoth, Doping of graphene by low-energy ion beam implantation: structural,
electronic, and transport properties, Nano letters 15 (8) (2015) 5110–5115.
[39] G. V. Soares, S. Nakhaie, M. Heilmann, H. Riechert, J. M. J. Lopes, Growth of boron-doped fewlayer graphene by molecular beam epitaxy, Applied Physics Letters 112 (16) (2018) 163103.
[40] A. Khosravi, R. Addou, C. M. Smyth, R. Yue, C. R. Cormier, J. Kim, C. L. Hinkle, R. M. Wallace,
Covalent nitrogen doping in molecular beam epitaxy-grown and bulk WSe 2, APL Materials 6 (2) (2018)
026603.

29