BIBECHANA Vol. 21, No. 2, August 2024, 129-141 ISSN 2091-0762 (Print), 2382-5340 (Online) Journal homepage: http://nepjol.info/index.php/BIBECHANA Publisher:Dept. of Phys., Mahendra Morang A. M. Campus (Tribhuvan University)Biratnagar Adsorption of water on vacancy defected h-BN bilayer at B and N sites Madhav Nepal1, Ganesh Paudel1, Santosh Aryal1 Arun Devkota2, Hari Krishna Neupane1∗ 1Amrit Campus, Tribhuvan University, Kathmandu, Nepal 2Central Department of Physics, Tribhuvan University, Kathmandu, Nepal ∗Corresponding author. Email: hari.neupane@ac.tu.edu.np Abstract Two dimensional (2D) materials are used to manufacture the various gadgets. Their proper- ties are therefore appealing. In the present work, we have studied the structural, electronic, and magnetic properties of 2D bilayer hexagonal-Boron Nitride (h-BN), single B vacancy de- fect on h-BN (B-hBN), single N vacancy defect on h-BN (N-hBN), water adsorption; on B-hBN (w-B-hBN) and on N-hBN (w-N-hBN), materials by spin-polarized density func- tional theory (DFT) methods employing Quantum ESPRESSO (QE) computational tools. The structural stability of the h-BN, B-hBN, N-hBN, w-B-hBN, & w-N-hBN materials has been investigated by determining their minimum ground state energy and binding energy, and found that they are stable materials. The pristine h-BN bilayer supercell structure is also found to be more compact than other defective configurations. By analyzing the band struc- tures and density of states (DoS) plots of these materials, we have examined their electronic properties, and found that pristine h-BN has a broad bandgap, whereas B-hBN, N-hBN, w- B-hBN, & w-N-hBN exhibit semiconducting nature. The DoS and partial density of states (PDoS) computations of the considered materials are used to study their magnetic properties. It is found that pristine h-BN is a non-magnetic, and B-hBN, N-hBN, w-B-hBN & w-N-BN are magnetic materials. Therefore, vacancy defects on pristine h-BN, and water adsorption on vacancy defected h-BN materials cause it to change from non-magnetic to magnetic. They could find use in the domain of device Keywords Adsorption, bilayer, defect, spin states. Article information Manuscript received: February 7, 2024; Revised: April 4, 2024; Accepted: April 5, 2024 DOI https://doi.org/10.3126/bibechana.v21i2.62607 This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons. org/licenses/by-nc/4.0/ 1 Introduction Boron Nitride (BN) stands out as the most lightweight chemical compound within the group III- V in periodic table, having an equal distribution of Boron and Nitrogen atoms [1–6]. It’s structure is similar of graphene’s structure [7]. Two dimen- sional (2D) hexagonal Boron Nitride (h-BN) was 129 http://nepjol.info/index.php/BIBECHANA hari.neupane@ac.tu.edu.np https://doi.org/10.3126/bibechana.v21i2.62607 https://creativecommons.org/licenses/by-nc/4.0/ https://creativecommons.org/licenses/by-nc/4.0/ Madhav Nepal et al./ BIBECHANA 21 (2024) 129-141 130 constructed by numerous methods including liquid and micromechanical exfoliation, chemical vapor deposition (CVD), and other novel synthetic ap- proaches [8–10]. At room temperature and under ambient pressure, the hexagonal structure stands out as the stable phase among these various struc- tures [11]. h-BN is originally an electrical insulator due to its wide bandgap energy of values in the range of (3.5-6.0) eV obtained from DFT and GW calculations [12, 13]. h-BN is used in various fields such as tunneling devices, chemical sensors, tran- sistors, lubricants due to their wide bandgap en- ergy and various structural characteristics [13–17]. Additionally, it exhibits a high degree of inertness towards a wide range of gas molecules, and it also be easily adjusted using various methods to attain different properties and functions [17–19] This tun- ing can be achieved through strategies like doping and introducing vacancy defect in the stable struc- ture [19, 20]. The presence of vacancy defect in 2D h-BN material develops the spontaneous magneti- zation due to the distribution of unequal spin states of electrons in the orbitals of atoms present in the material [15, 21–23]. Boron (B) and Nitrogen (N) atoms in h-BN are strongly covalently bound due to their electronega- tivity [24]. In the meantime, nearby layers interact with one another by a weak van der Waals (vdWs) force [25]. h-BN is formed a sp2-hybridization be- tween B & N atoms [26–28]. Furthermore, com- pared to graphene, h-BN’s structure is thermally and chemically stable. It works well as a lubricant because of its lower coefficient of friction [29, 30]. h-BN has a unique set of characteristics, includ- ing atomic flatness, incredibly low roughness, and no dangling bonds on its surface [31]. Young's modulus (270 Nm-1) and thermal conductivity (400 Wm-1K-1) of 2D h-BN are significantly higher than those of the majority of metals and ceramic mate- rials [32–36]. h-BN bilayer is created by vertically staking two monolayers. Its properties are changed when it placed in a humid environment. Thus, adsorbed water molecules modify its electronic, magnetic, op- tical, and thermal properties [37–42]. Many inves- tigations have been conducted recently on the ad- sorption of water molecules on the surface of differ- ent other 2D materials. It is found that structural, electronic, and magnetic properties of defected ma- terials are changed due to the adsorption of water molecules [14, 42]. After a thorough analysis of the literature, we found that no studies have been done on the structural, electronic, and magnetic charac- teristics of water adsorbed on pristine h-BN, and B & N vacancy defected h-BN bilayer materials. In the present work, we have investigated the struc- tural, electronic, and magnetic properties of B & N sites vacancy defected bilayer of h-BN supercell structures (i.e., B-hBN & N-hBN), and water ad- sorption on these supercell structures (i.e., w-B- hBN & w-N-hBN) respectively, by spin-polarized density functional theory (DFT) methods using the computational tools’ Quantum ESPRESSO (QE) codes. Below is an arrangement of the remaining por- tions of this manuscript: In the methods and ma- terials section, the procedures and supplies utilized in this investigation are detailed. In the results and discussion section, we present our findings and their interpretations, and in the conclusions section, we express our final thoughts. 2 Material and Methods The investigation of structural, electronic, and magnetic properties of single B atom vacancy de- fect on (4×4) bilayer supercell structure of h-BN (B-hBN), single N atom vacancy defect on (4×4) bi- layer supercell structure of h-BN (N-hBN), and wa- ter molecules adsorbed on B-hBN (w-B-hBN) and N-hBN (w-N-hBN) materials was done using first- principles calculations based on the spin-polarized density functional theory (DFT) method [42]. The Generalized Gradient Approximation (GGA) was utilized using Perdew-Burke-Ernzerhof (PBE) ex- change correlations in order to incorporate the elec- tronic exchange and correlation effects in the DFT theory [43]. PBE functional cannot adequately de- scribe the weak van der Waals (vdWs) force present in bilayer supercell structures. Therefore, to de- termine the type of vdWs interaction between the interlayers of bilayer structures, semi-empirical dis- persion correlated density functional theory (DFT- D2) technique is utilized. An effective potential for each atom in a system is used to substitute the com- plex effects of the motion of an atom's core elec- trons and its nucleus using Grimme's Rappe-Rabe- Kaxiras-Joannopoulos (RRJK) model of ultrasoft pseudopotentials. So, we have used RRJK model of ultrasoft pseudopotentials and plane wave basis set in the convergence test. A (4×4) supercell bilayer structure of h-BN is constructed by incorporating 64 atoms, where sin- gle layer of h-BN contains 16 B atoms, and 16 N atoms. Single B & N sites vacancy defected h-BN are created by randomly removing 1B & 1N atoms respectively from the upper surface of h-BN super- cell structure. In single layer h-BN, B or N va- cancy defect of 3.13% is formed, whereas in bilayer h-BN, B or N vacancy defect of 1.56% is produced (i.e., 1B or 1N atom out of 32 BN atoms in sin- gle layer). Then, these supercell structures are op- timized by calculating their kinetic energy cutoff (ecutoff), lattice parameter (a), and k-points (k- cutoff), through the convergence test. They are found to be 35 Ry, 4.65 Å, and (22×22×1) re- Madhav Nepal et al./ BIBECHANA 21 (2024) 129-141 131 spectively. These optimized values are taken in the input file for relax calculations. The relax calculations of considered materials have done by using Broyden-Fletcher-Goldfrab-Shanno (BFGS) scheme [44] until the force and total energy change between two successive scf iterations are less than 10-3 Ry/Bohrs and less than 10-4 Ry, respectively. The optimized and relaxed structures of pristine h- BN, and B & N sites vacancy defected bilayer h-BN are shown in figures-1(a-c) respectively. Furthermore, water molecule is adsorbed on the defected structures of B-hBN & N-hBN, re- spectively. Then relax calculations are carried out with the Broyden-Fletcher-Goldfrab-Shanno (BFGS) scheme [43] until the force and total en- ergy minimum values vary between two consecu- tive scf iterations. These values are likewise found to be less than 10-4 Ry and 10-3 Ry/Bohrs, respec- tively. Figures-1(d-e) displays the relax structures of water adsorbed on B-hBN (i.e., w-B-hBN) and on N-hBN (i.e., w-N-hBN) materials, respectively. To assure the accuracy of the results, the Marzarri- Vanderbilt (M-V) smearing method is utilized in the calculations, with a small broadening width of 0.001 Ry [43–47]. For self-consistency, the "David" diagonalization approach with a 0.6 mixing factor is selected. In order to do the band calculations, 200 k-points are chosen along the reciprocal lattice's high symmetry points. The sample locations in the reciprocal lattice's first Brillouin Zone are these k- points. Density of states (DoS) and partial density of states (PDoS) computations are carried out to investigate magnetic properties of materials. 3 Results and Discussion 3.1 Structural Properties The structural properties of bilayer h-BN material with single B atom vacancy defect, and single N atom vacancy defect; have been examined, along with the effects of water adsorption on these mate- rials. This analysis is conducted by computing the bond length between B-N atoms, binding energy of the systems, interlayer distance of bilayers, and de- fect generation energies. First, a unit cell of bilayer h-BN material has been created by taking the op- timized values of lattice parameter (a) = 4.65 Å, kinetic energy cutoff = 35 Ry, and k-points = 22 in the input file. Then relax calculations are done to get optimized and relaxed unit cell structure of bilayer h-BN. The prepared relaxed unit cell of h- BN is stretched along x-and y-directions (axes) by repeating its four times, which is called (4×4) su- percell structure of h-BN bilayer is illustrated in figure-1(a). We have estimated the bond length be- tween B-N atoms, interlayer distance between bi- layer’s atoms, binding energy, and ground state en- ergy of bilayer h-BN supercell structure, they are found to be 1.43 Å, 3.72 Å, -707.36 meV & -874.39 Ry respectively. These values are comparable with other reported values of 2D materials [28,48]. They reflect that bilayer h-BN supercell structure is a sta- ble material. The binding energy of bilayer h-BN is calculated by using equation-(1), [49]; (Eb)d = Eg(h−BN−bi)d −(Eg(h−BN−mono)d + Eg(h−BN−mono)p) (1) where, Eb, Eg(h-BN-bi) & Eg(h-BN-monolayer) rep- resent the binding energy of h-BN system, ground state energy of h-BN bilayer supercell, and ground state energy of monolayer h-BN supercell structure respectively. Furthermore, we have created the B atom va- cancy defected h-BN (B-hBN), and N atom vacancy defected h-BN (N-hBN) materials by randomly re- moving single B atom, and single N atom from the upper surface of bilayer material respectively. Then calculate the minimum ground state, and binding energies of them. It is found that our considered materials (are shown in figures-1(b-c)) have mini- mum value of ground state energy, and maximum value of binding energy. The ground state energy, binding energy, defect formation energy, interlayer distance of bilayers, and bond length between B- N atoms of B-hBN are found to be -845.39 Ry, - 515.36 meV, 0.21 eV, 3.72 Å & 1.46 Å respectively, and of N-hBN are found to be -831.69 Ry, -643.36 meV, 0.16 eV, 3.72 Å & 1.44 Å respectively. These calculated values are comparable with the reported values of others 2D materials [28, 48]. The binding energy of defected bilayer h-BN systems (B-hBN & N-hBN) are obtained by using equation-(2), [49]; Eb = Eg(h−BN−bi)d − ( Eg(w−hBN−mono)d +Eg(h−BN−mono)p + EH2O ) (2) where, (Eb)d, Eg(h-BN-bi)d, Eg(h-BN-mono)d & Eg(h-BN-mono)p are represented by binding energy of defected system, minimum ground state energy of B or N sites vacancy defected system, minimum ground state energy of B or N sites vacancy defected monolayer h-BN and minimum ground state energy of pristine h-BN monolayer respectively. The defect formation energy of defected bilayer h-BN systems (B-hBN & N-hBN) are obtained by using equation- (3), [14, 28,41]; (Ed)f = Ed − (Ep + nBµB + nNµN ) (3) where, (Ed)f, Ed, Ep, nB or nN & µB or µN represent the defect formation energy, ground state energy of defected monolayer of h-BN, ground state Madhav Nepal et al./ BIBECHANA 21 (2024) 129-141 132 energy of pristine monolayer of h-BN, number of de- fected atom and chemical potential of defected atom respectively. The calculations of above parameters implies that B-hBN & N-hBN are stable materi- als. From above estimated values of bond length between B-N atoms in structures, it is confirmed that pristine system is more compact than defected systems. In addition, we have constructed water adsorp- tion on B-hBN (w-B-hBN) and N-hBN (w-N-hBN) materials by adsorbing water molecule at different position (orientation) above the surface of defected layer of h-BN bilayer, and then relax calculation are done. It is found that adsorbed water molecule is appeared at 2.34 Å distance above from the up- per surface of defected h-BN bilayer. The water molecules were then positioned on the left, middle, and right at constant 2.34 distances in various ori- entations above the upper surface of the defected h-BN bilayer. Their minimum ground state en- ergy, binding energy, water adsorption energy, in- terlayer distance between the bilayers, and bond length between B-N atoms were then estimated. The calculated binding energies of the adsorbed wa- ter molecule at the left and right positions on the defective h-BN bilayer are found to be smaller than those of the middle location, while the ground state energy is found to be larger. Higher binding ener- gies and lower ground state energies are known to indicate that a material is more stable. Thus, we have chosen w-B-hBN and w-N-hBN materials by adsorbing water molecule on the middle position at 2.34 Å distance above the surface of defected layer of h-BN bilayer for further calculations. The op- timized and relax structures of water molecule ad- sorbed on the middle position at 2.34 Å distance above from the upper surface of defected h-BN bi- layer (w-B-hBN & w-N-hBN) are shown in figures- 1(d-e). The minimum ground state energy, binding energy, water adsorption energy, interlayer distance between the bilayers, and bond length between B- N atoms of w-B-hBN are found to be -880.04 Ry, -515.36 meV, -0.24 eV, 3.72 Å, and 1.46 Å respec- tively, and of w-N-hBN are found to be -867.393 Ry, -643.36 meV, -0.32 eV, 3.72 Å, and 1.44 Å re- spectively. These estimated values are agreed with the reported values of 2D materials [14, 28, 41, 50]. They reveal that these materials are stable materi- als. The binding energy of w-B-hBN & w-N-hBN are estimated by using equation-(4), [28, 41] Eb = Eg(w−hBN−bi)d − ( Eg(w−hBN−mono)d +Eg(h−BN−mono)p + EH2O ) (4) where, Eb, Eg(w-hBN-bi)d, Eg(w-hBN-mono)d, Eg(h-BN-mono)p & EH2O are represented by bind- ing energy w-B-hBN or w-N-hBN system, minimum ground state energy w-B-hBN or w-N-hBN, mini- mum ground state energy of water adsorbed on B or N sites h-BN monolayer, minimum ground state energy of pristine h-BN monolayer and ground state energy of water molecule respectively. We also have compared the estimated parameters of considered systems and found that pristine h-BN bilayer su- percell structure is more compact and stable than defected, and water adsorption on defected mate- rials. Pristine bilayer h-BN, B-hBN, N-hBN, w-B- hBN & w-N-hBN bilayer supercell structures are shown in figures-1(a-e) respectively. 3.2 Electronic Properties Electronic properties of pristine h-BN, single B atom vacancy defect on h-BN (B-hBN), single N atom vacancy defect on h-BN (N-hBN), water ad- sorption on B-hBN (w-B-hBN) & water adsorption on N-hBN (w-N-hBN) bilayer supercell materials are studied by the analysis of their band structures and density of states (DoS) plots. The band struc- ture plots of these materials are shown in figures- 2(a-e) respectively. In the band plots, highly symmetric points (Γ−M−K−Γ) within the irreducible Brillion zone (BZ) are plotted along the x-axis, and its corre- sponding energy levels are plotted along the y-axis. The horizontal blue dot line represents the Fermi energy level which separates the electronic bands. The region below the Fermi energy level is called valence band, and above the Fermi energy level is called conduction band. To obtain the fine band structure, we have taken 200 k-points in the irre- ducible BZ. Bandgap energy is the distance between the material's lowest level of conduction band and topmost level of valence band. The pristine bilayer h-BN supercell structure's bandgap energy 4.56 eV is calculated, which indicates that material has a broad bandgap. This number is somewhat consis- tent with the monolayer h-BN supercell structure value that has been reported [15, 28]. Figure-1(a) depicts the pristine bilayer h-BN supercell struc- ture's electronic band states that we have obtained. Compared to conduction band states, valence band states are found to be more closely spaced with the Fermi energy level in band structure. Consequently, we have p-type Schottky barrier of pristine bilayer h-BN supercell structure. Madhav Nepal et al./ BIBECHANA 21 (2024) 129-141 133 (a) (b) (c) (d) (e) Figure 1: (Color online) Optimized and relax structures of B N sites vacancy defected bilayer h- BN supercell material: (a) pristine bilayer h-BN supercell structure, (b) single Boron atom vacancy defected bilayer h-BN supercell (B-hBN) material, (c) single Nitrogen atom vacancy defected h-BN bilayer supercell (N-hBN) material, (d) water adsorption on B-hBN (i.e., w-B-hBN) material, and (e ) water adsorption on N-hBN (i.e., w-N-hBN) material. Madhav Nepal et al./ BIBECHANA 21 (2024) 129-141 134 (a) (b) (c) (d) (e) Figure 2: (Colour online) band structure plots of pristine and defected bilayer h-BN materials: (a) band structure of pristine h-BN bilayer supercell material, (b) band structure of B-hBN bilayer supercell material, (c) band structure of N-hBN bilayer supercell material, (d) band structure of w-B-hBN bilayer supercell material, and (e) band structure of w-N-hBN bilayer supercell material. Figures-2(b-c) display the band structures that we have created of B-hBN & N-hBN materials, re- spectively. It is calculated that the bandgap en- ergies of B-hBN & N-hBN are 1.25 eV & 1.49 eV, respectively. The energy gaps between the Fermi energy level and the lowest level of band states in the conduction band, and the Fermi level and higher level of band states in the valence band are added up to get these values. Electronic band states of va- lence band are observed near the Fermi energy level in both materials. Thus, they are known as p-type semiconducting materials. The unpaired arrange- ment of electronic spin-states in the atoms' orbitals within the structures is what causes the flat bands to form in the valence band of N-hBN and the con- duction band of B-hBN. Moreover, we have analyzed the band structures of w-B-hBN & w-N-hBN materials, which are il- Madhav Nepal et al./ BIBECHANA 21 (2024) 129-141 135 lustrated in figures-2(d-e) respectively. From these plots, we have estimated the bandgap energy of w- B-hBN & w-N-hBN are found to be 0.97 eV & 1.24 eV respectively. It means, adsorbed water molecule affects the electronic states of defected systems. This is because, water molecule like to be adsorbed on the region of vacancy sites, as a result, more numbers of flat bands are appeared in the conduc- tion band of w-B-hBN & in the valence band of w-N-hBN materials. In both materials, electronic band states of valence band are presented closely with the Fermi energy level, and hence, they are p- type semiconducting materials. The estimated val- ues of total minimum ground state energy, Fermi energy, bandgap energy, binding energy, defect for- mation energy of studied materials are presented in Table-1. Table 1: Estimated values of total energy (Et), Fermi energy (Ef ), band gap energy (Eg), binding energy (Eb), and defect formation energy (Ed) of pristine h-BN, B-hBN, N-hBN, w-B-hBN & w-N-hBN bilayer supercell materials. Bilayer materials Et (Ry) Ef (eV) Eg (eV) Eb (meV) Ed (eV) Nature of material h-BN -852.38 -2.27 4.56 -707.36 - Wide bandgap B-hBN -845.39 -2.93 1.25 -515.36 0.21 Semiconductor N-hBN -831.69 -0.38 1.49 -643.36 0.16 Semiconductor w-B-hBN -880.04 -3.07 0.97 -515.36 - Semiconductor w-N-hBN -867.39 -0.60 1.24 -643.36 - Semiconductor In addition, we have analyzed the DoS plots of pristine h-BN, B-hBN, N-hBN, w-B-hBN & w-N- hBN bilayer supercell materials for the investiga- tion of their electronic properties. The DoS plots of these materials are shown in figures-3(a-e) re- spectively, where DoS states are plotted along y- axis and corresponding it energies are taken along x-axis. The vertical dot line separates the valence band and conduction band. The region toward LHS represents valence band, and region toward RHS represents conduction band. The horizontal dot line distinguishes the DoS states of up-spins and down-spins. Black and red colours of spin states are respectively, indicate the distributed up and down spin-states of electrons in the orbitals of atoms present in the materials. It is found that bandgap energies of pristine h-BN, B-hBN, N-hBN, w-B-hBN & w-N-hBN bilayer supercell materials have values 4.56 eV, 1.30 eV, 1.47 eV, 1.27 eV & 1.12 eV respectively. These calculated values are fairly agreed with the computed values obtained from band structure calculations [5, 28]. Thus, it is also confirmed that pristine h-BN bilayer super- cell is a wide bandgap material, and B-hBN, N- hBN, w-B-hBN & w-N-hBN bilayer supercell struc- tures have semiconducting nature. Semiconducting materials can find usage in a variety of technolo- gies, including memory devices, photocatalysts, in- tegrated logic circuits, transistors, signal amplifiers, photodetectors, flexible optoelectronic devices, so- lar cells [9, 13,17]. 3.3 Magnetic Properties Magnetic properties of pristine h-BN, B-hBN, N- hBN, w-B-hBN & w-N-hBN bilayer supercell ma- terials are investigated by the analysis of their den- sity of states (DoS) and partial density of states (PDoS) calculations. DoS gives an idea of num- ber of electronic states per unit energy range, and PDoS gives an idea of distribution of spin states of electrons in the orbital of atom present in the material [15, 23, 26]. DoS & PDoS plots of pristine h-BN, B-hBN, N-hBN, w-B-hBN & w-N-hBN ma- terials are presented in the figures-3(a-e) & figures- 4(a-e) respectively. In DoS & PDoS plots, vertical dot line represents the Fermi energy level which sep- arates the electronic bands. The horizontal dot line separates the distributed up-and down-spin states. Madhav Nepal et al./ BIBECHANA 21 (2024) 129-141 136 (a) (b) (c) (d) (e) Figure 3: Colour online) density of states (DoS) plots of pristine and defected bilayer h-BN materials: (a) DoS plot of pristine h-BN bilayer supercell material, (b) DoS plot of B-hBN bilayer supercell material, (c) DoS plot of N-hBN bilayer supercell material, (d) DoS plot of w-B-hBN bilayer supercell material, and (e) DoS plot of w-N-hBN bilayer supercell material. Insets represent the zoom scale of DoS plots. The DoS & PDoS plots of pristine h-BN bi- layer supercell structure are shown in figure-3(a) & figure-4(a) respectively. In both plots, up and down spin states are symmetrically distributed around the Fermi energy level. It indicates that magnetic moment has not yet developed. It is therefore a non-magnetic substance. We have examined the DoS & PDoS plots of B-hBN & N-hBN materials, which are depicted in figures-3(b-c) & figures-4(b- c) respectively. Asymmetric distribution of up and down spin states of electrons in atom orbitals in materials around the Fermi energy level results in magnetic moments of -1.71 µB/cell in B-hBN & 1.00 µB/cell in N-hBN. As a result, both materials pos- sess magnetic properties. The negative sign signi- fied that down spin states of electrons contribute more than up spin states of electrons to the forma- tion of magnetic moment in the materials. Based Madhav Nepal et al./ BIBECHANA 21 (2024) 129-141 137 on the calculations, we found that the magnetic moment values of B atom's 2s & 2p orbitals are 0.01 µB/cell & -0.06 µB/cell, whereas N atom's 2s & 2p orbitals have 0.14 µB/cell & -1.52 µB/cell in B-hBN. It has been demonstrated that the N atom's 2p orbital plays a major role in the mag- netic moment produced in B-hBN material. In the same way, we calculated the magnetic moment of N-hBN material and found that it is 0.04 µB/cell & 0.30 µB/cell of B atoms' 2s & 2p orbitals, and 0.08 µB/cell & 0.58 µB/cell of N atoms' 2s & 2p or- bitals, respectively. Positive magnetic moment val- ues show that up spin states are mostly responsible for the material's magnetic moment production. 2 (a) (b) (c) (d) (e) Figure 4: (Colour online) Partial density of states (PDoS) plots of pristine and defected bilayer h-BN materials: (a) PDoS plot of pristine h-BN bilayer supercell material, (b) PDoS plot of B-hBN bilayer supercell material, (c) PDoS plot of N-hBN bilayer supercell material, (d) PDoS plot of w-B-hBN bilayer supercell material, and (e) PDoS plot of w-N-hBN bilayer supercell material. Insets represent the zoom Madhav Nepal et al./ BIBECHANA 21 (2024) 129-141 138 scale of PDoS plots. Furthermore, we have examined the DoS & PDoS computations of w-B-hBN & w-N-hBN bi- layer supercell materials to learn more about their magnetic characteristics. Figures-3(d-e) and figures-4(d-e) respectively depict the asymmetric distribution of up and down spin states of elec- tron in the orbitals of atoms found in the materials near the Fermi energy level. It indicates that they possess magnetic properties. We have estimated the magnetic moment created by the unpaired spin states of electrons in the orbitals of atoms present in the materials. In w-B-hBN, the spins in the 2s & 2p orbitals of B atoms and the 2s & 2p orbitals of N atoms have values of 0.01 µB/cell & 0.57 µB/cell, and -0.24 µB/cell & -1.69 µB/cell, respectively. Ad- ditionally, the magnetic moments of the 1s of H atoms and 2s & 2p of O atom in w-B-hBN material are found to be -0.02 µB/cell, and 0.00 µB/cell & 0.37 µB/cell respectively. The total magnetic mo- ment generated in w-B-hBN is therefore equal to -1.00 µB/cell. Likewise, we computed the magnetic moment given by unpaired spin states in the 2s & 2p orbitals of B atoms, and 2s & 2p orbitals of N atoms are found to be 0.04 µB/cell & 0.00 µB/cell, and 0.00 µB/cell & -0.42 µB/cell in w-N-hBN martial respec- tively. Also, magnetic moment given by spin states of electrons in the 1s orbital of H atoms and 2s & 2p orbitals of O atom in w-N-hBN material are found to be 0.00 µB/cell, and 0.00 µB/cell & 1.38 µB/cell values respectively. This indicates that the forma- tion of magnetic moment in the material is primar- ily attributed to the 2p orbital of N & O atoms. Consequently, total magnetic moment of w-N-hBN material have value -1.00 µB/cell. The estimated magnetic moment of B-hBN, N-hBN, w-B-hBN & w-N-hBN materials are illustrated in Table-2. Table 2: Magnetic moment (µT in µB/cell) is produced by unpaired spin states of electrons in the 2s & 2p orbitals of Boron, Nitrogen, and Oxygen atoms and 1s orbital of Hydrogen atom in the pristine, defected, and water adsorbed on defected h-BN bilayer supercell structures. Orbitals Materials B-hBN w-B-hBN N-hBN w-N-hBN 2s of B atoms 0.01 0.01 0.04 0.04 2p of B atoms -0.06 0.57 0.30 -0.00 2s of N atoms -0.14 -0.24 0.08 -0.00 2p of N atoms -1.52 -1.69 0.58 -0.42 1s of H atoms - -0.02 - 0.00 2s of O atom - 0.00 - 0.00 2p of O atom - 0.37 - 1.38 Total magnetic moment (µT ) -1.71 -1.00 1.00 1.00 It can be observed from the calculations above that B & N vacancy defected atoms turn non- magnetic pure h-BN bilayer supercell structures into magnetic ones. This is because the electrons in the remaining atoms in the structures have re- arranged their unpaired spin states. However, be- cause the unpaired electron spins around the B va- cancy position in the h-BN structure are rearranged together with the adsorbed water molecule, the presence of adsorbed water on B sites h-BN weakens the magnetic moment. Furthermore, the values of the magnetic moment of N vacancy defected h-BN, and water adsorbed on the vacancy defective h-BN of N sites are comparable. These values are pro- duced in the materials as a result of the electronic spin states' unpaired configuration. We determined the magnetic moment values in h-BN materials with vacancy defects at sites B and N. These materials appear to be promising for use in a variety of de- vices requiring magnetic characteristics because of the appearance of magnetism. Magnetism and mag- netic materials are essential to many of the modern electronic equipment we use. Biomedicine, molecu- lar biology, biochemistry, diagnostics, catalysis, and nanoelectronics devices are just a few of the indus- trial applications for novel nanomagnetic materi- als that could be used. Other applications include magnetic seals in motors, magnetic sensors, bank check ink, electrical power generators and trans- formers, magnetic recording media, computers, and more [51, 52]. Therefore, key frameworks for the material to device applications may be provided by our understanding of unique electrical and magnetic phenomena on defective materials. 4 Conclusion In the present work, we have studied the impact of adsorbed water molecule on single B atom va- cancy defect on h-BN, single N atom vacancy de- Madhav Nepal et al./ BIBECHANA 21 (2024) 129-141 139 fect on h-BN by first-principles calculation based on spin-polarized DFT methods through Quantum ESPRESSO (QE) computational tools. Firstly, we have investigated the structural properties of 2D bilayer hexagonal-Boron Nitride (h-BN), single B atom vacancy defect on h-BN (B-hBN), single N atom vacancy defect on h-BN (N-hBN), water ad- sorption; on B-hBN (w-B-hBN) and on N-hBN (w-N-hBN), materials by estimating their ground states energy and binding energy. They are found to be structurally stable materials. Additionally, we have measured the interlayer distances and bond length between any two nearest B-N atoms, and found that defective materials are also shown to be less compact than perfect h-BN bilayer material. Secondly, we have studied the electronic properties of considered materials by developing their band structures and DoS plots. It is found that pristine h-BN has wide bandgap energy of value 4.56 eV, so is called wide bandgap material. On the other hands, B-hBN, N-hBN, w-B-hBN & w-N-hBN ma- terials have small bandgap energy of values 1.25 eV, 1.49 eV, 0.97 eV & 1.24 eV respectively. Hence, they have semiconducting properties. Thirdly, we have examined the magnetic properties of pristine h-BN, B-hBN, N-hBN, w-B-hBN & w-N-hBN bi- layer supercell materials, by the analysis of their DoS and PDoS calculations. Electronic spin-states of up and down spins are symmetrically distributed around the Fermi energy level in pristine h-BN, and hence it has zero value of magnetic moment. So, it is a non-magnetic material. The distribution of up and down spins is asymmetrically distributed around the Fermi energy level in B-hBN, N-hBN, w-B-hBN & w-N-hBN materials. As a results, mag- netic moment are developed of values -1.71 µB/cell, 1.00 µB/cell, -1.00 µB/cell & 1.00 µB/cell respec- tively. Thus, B & N sites vacancy defected h-BN, and water adsorption on these defected materials are magnetic materials. Thus, water adsorption on vacancy defected h-BN materials, and vacancy de- fects on pristine h-BN materials cause it to become magnetic instead of non-magnetic. They might be useful in the field of applications for devices. Authorship Contribution Statement M. Nepal: Gathering information, analyzing and interpreting it, making figures and graphs, and writing the manuscript. G. Poudel: Gathering information, assisting with data analysis. S. Aryal & A. Devkota: Gathering data and contributing to its analysis. H. K. Neupane: Developed the idea, oversaw its analysis, interpreted the findings, and thoroughly revised the manuscript. Data Availability If you have any questions about data reproduction, you can get the data that were used to create the figures, tables, and graphs in this paper directly from the corresponding author. Declaration of Competing Interest The authors declare that none of the work reported in this study could have been influenced by any known competing financial interests or personal re- lationships. 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