Coexistence of magnetism and ferroelectricity in (PbTiO3)m∕(BaTiO3)n superlattices

Journal Pre-proof Coexistence of magnetism and ferroelectricity in (𝑃 𝑏𝑇 𝑖𝑂3 )𝑚 ∕(𝐵𝑎𝑇 𝑖𝑂3 )𝑛 superlattices Fariba Ahmadi, Houshang Araghi

PII: DOI: Reference:

S0749-6036(19)32036-1 https://doi.org/10.1016/j.spmi.2020.106427 YSPMI 106427

To appear in:

Superlattices and Microstructures

Received date : 28 November 2019 Revised date : 26 January 2020 Accepted date : 2 February 2020 Please cite this article as: F. Ahmadi and H. Araghi, Coexistence of magnetism and ferroelectricity in (𝑃 𝑏𝑇 𝑖𝑂3 )𝑚 ∕(𝐵𝑎𝑇 𝑖𝑂3 )𝑛 superlattices, Superlattices and Microstructures (2020), doi: https://doi.org/10.1016/j.spmi.2020.106427. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

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Coexistence of magnetism and ferroelectricity in (P bT iO3 )m /(BaT iO3 )n superlattices Fariba Ahmadia , Houshang Araghia,∗ a Departmenet

of energy engineering and physics, Amirkabir University of Technology (Tehran Polytechnic), Iran.

Abstract

In the present study, the electronic and multiferroic i.e. coexisting ferroelectric and ferromagnetic features of metal-doped (P bT iO3 )m /(BaT iO3 )n ferroelectric

superlattices are investigated using first-principles calculations. The generalized

gradient approximation is implemented in the numerical computations. Our re-

sults are verified with less than 1% error compared to the experimental and theoretical works. Taking into account intrinsic vacancy defect, the density of states and electron charge density along the [001] axis are computed. Our find-

ings report that the strong hybridization between T i−3d and O −2p contributes to the ferromagnetic order. In addition, we found out that substituting T i with 3d transition metals (F e, Co and N i) as well as F e impurity leads to ferro-

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magnetic configuration with the maximum magnetic moment. Our theoretical calculations provide physical insights into the design of multiferroic features in conventional ferroelectrics.

Keywords: First-principles calculation, Metal doped P bT iO3 /BaT iO3 ,

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Superlattice, Multiferroic materials, Formation energy, Density of states.

1. Introduction

Perovskite oxides (ABO3 ) because of their unique structure and properties

have been extensively studied. In perovskite structures, A element is a large ∗ Corresponding

author Email address: [email protected] (Houshang Araghi)

Preprint submitted to Journal of LATEX Templates

January 25, 2020

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cation at the corners of the unit cell, while the B element is a smaller cation

located at the body center. On the other hand, oxygen atoms are positioned

at the face centers. Lead titanate (P bT iO3 ) and barium titanate (BaT iO3 ) are

the most popular examples of these substances. Ferroelectric BaT iO3 (BT O) and P bT iO3 (P T O) are suitable for a wide range of technological applications including ultrasonic actuators, pyroelectric detectors, multilayer ceramic ca10

pacitors, temperature sensors [1, 2, 3, 4, 5, 6, 7], controllers, transducers and

electromechanical devices [8, 9]. Designing perovskite heterostructures, such as

superlattices have attracted a great deal of scientific interest during the past decade, to tailor their physical properties.

conventional ferroelectrics, such as BaT iO3 and P bT iO3 , are well-known as non15

magnetic materials because the formal d0 electron configuration (e.g. T i4+ ) in these ferroelectrics contradicts with the partially filled d states required for fer-

romagnetism [8, 9, 10, 11, 12]. In BaT iO3 and P bT iO3 , Ba − 6s and P b − 6s

lead to a chemical mechanism for stabilization of ferroelectricity, respectively. This mechanism occurs if the ionic site of cation does not have inversion sym20

metry. The second mechanism that causes polarization in ferroelectrics is the

off-center displacement of small cation in perovskite ferroelectrics. However,

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this mechanism requires the d0 -ness scale in the small transition metal.

Multiferroic materials possess coupled magnetic, electric and structural order parameters [13, 14]. BaT iO3 and P bT iO3 are capable of coupling the electric 25

and magnetic polarizations [15, 16, 17, 18], which makes them suitable for utilization in a variety of devices, particularly for spintronic applications, such as multiple state memories [10], data-storage media [19], etc. BaT iO3 and P bT iO3

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exhibit ferroelectric and ferromagnetism features at room temperature, which are related to their tetragonal phase. The structural characteristics of these ma-

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terials make them possible to dope them with 3d transition metals to enhance their properties [4, 20, 21, 22, 23, 24]. Oxide superlattices are composed of periodic repetitions of two or more different oxide layers with coherent interfaces between the layers. They may exhibit properties that are not simply the volumetric averaged properties of oxide 2

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layers. Ferroelectric superlattices are associated with enhanced polarization,

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permittivity and switching properties [25, 26], due to the complex phase interactions at their layer interfaces [25, 27]. The presence of interfaces between dissimilar oxide layers in oxide superlattices, can change the defect properties, compared to those bulk oxides. However, the majority of previous studies 40

have been focused on superlattices containing ferroelectric and paraelectric layers, such as BaT iO3 /SrT iO3 [28, 29, 30, 31, 32, 33, 34] and P bT iO3 /SrT iO3 [35, 36, 37, 38, 39].

(P T O)m /(BT O)n superlattices (m=n=2, m=n=3) exhibit ferroelectric feature,

corresponding to their tetragonal phase [40]. Spatial configuration of oxygen va45

cancy causes magnetic configuration in tetragonal structures [41]. In the present

study, we consider a specific example of (P T O)m /(BT O)n superlattices which m and n denote the thickness (in unit cell) of the (001)-oriented P bT iO3 and BaT iO3 layers, respectively. We focused on superlattices with both ferroelec-

tric layers and performed first-principles calculations to investigate the effects 50

of vacancy and transition metal doping in P bT iO3 /BaT iO3 (001) superlattices with tetragonal structure and explore the possibility of magnetism in these fer-

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roelectric substances.

2. Computational method

In the present research, all calculations are performed using Quantum Espresso 55

package [42], which is based on the density functional theory (DFT). The projector-augmented wave function (PAW) method accompanied by the PerdewBurke-Ernzerhof (PBE) [43] of generalized gradient approximation (GGA) for

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the exchange-correlation functional are adopted for ferroelectric superlattices. We utilize 40 Ry wave-function and 360 Ry electron density plane-wave cutoffs

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in the calculations. Also, the Brillouin zone (BZ) is sampled using 6 × 6 × 1 Monkhorest-Pack [44] k meshes. The structure is fully relaxed to ensure the well-converged total energy and geometrical configuration. The energies and forces on each ion are converged to 0.01 Ry/atom and 0.5 × 10−3 Ry/Bohr, 3

respectively. 65

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It should be pointed out that doping metals are selected based on the metal ion radius, electronegativy, and experimental feasibility. First, the ion radius of

doping metal approaches T i4+ radius. Second, the closer the electronegativity of doping metals to the oxygen, the stronger the covalent bond and the smaller

the band gap. Third, experimental feasibility, is evaluated based on the acces70

sibility of doping metals [45].

The (P bT iO3 )m /(BaT iO3 )n superlattices within the P 4mm space group with

1 periodicity are considered in which each unit cell consists of m P T O and n BT O unit cellsalong the thickness direction. Fig.1 and Fig.2 show the period-

icity repeating unit of P T O and BT O layers in the superlattice for m = n = 2 75

and m = n = 3, respectively. In Fig.1, one T i atom in P bT iO3 is substituted with transition metals and an oxygen atom is removed from the supercell, while

in Fig.2, two T i atoms in P bT iO3 are substituted in the presence of oxygen

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vacancy.

Figure 1: Schematic crystal structure of (P bT iO3 )m /(BaT iO3 )n ferroelectric superlattices for m = n = 2: (a) pure P bT iO3 /BaT iO3 superlattice; (b) F e doped P bT iO3 /BaT iO3 + VO ; (c) Co doped P bT iO3 /BaT iO3 + VO ; and (d) N i doped P bT iO3 /BaT iO3 + VO . These pictures are drawn using VESTA.

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Figure 2: Schematic crystal structure of (P bT iO3 )m /(BaT iO3 )n ferroelectric superlattices for m = n = 3: (a) pure P bT iO3 /BaT iO3 superlattice; (b) F e doped P bT iO3 /BaT iO3 + VO ; (c)

Co doped P bT iO3 /BaT iO3 + VO ; and (d) N i doped P bT iO3 /BaT iO3 + VO . These pictures are drawn using VESTA.

3. Results and discussion

As usual, first, the bulk lattice constants of tetragonal P 4mm five atom unit

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cells of P bT iO3 and BaT iO3 are optimized, leading to the lattice constants of tetragonal BaT iO3 unit cell a = 3.992 A◦ and c = 4.036 A◦ , while those of

the tetragonal P bT iO3 unit cell are equaled to a = 3.905 A◦ and c = 4.152 A◦ . These results are in reasonable agreement with the outcomes of previous experimental studies and theoretical analyses [46, 47, 48, 49, 50, 51, 52]. The obtaines theoretical constants are used in the following calculations. The in-plane lattice

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constant for all superlattice calculations are set to the optimized value of bulk SrT iO3 (i.e. 3.9045 A◦ ) to minimize the effects of superlattices on the SrT iO3 substrate [53, 54, 55]. The z-coordinate of each layer N are defined as Eq.1, Me O where ZN −1 and ZN −1 are z-coordinates of the cation and anion of the previous

atomic layer, respectively [56]. On the other hand, due to symmetry, the c lattice parameter is fully relaxed in the z direction. Fully optimized lattice parameters

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with the lowest energy are obtained for (P bT iO3 )m /(BaT iO3 )n superlattices,

based on the first-principles calculations. In-plane lattice parameters, c/a and tetragonality (c/(m + n)a) values have been listed in table.1. The obtained data

are consistent with the results of previous theoretical and experimental studies [40].

ref Me O ZN = 1/2 (ZN −1 + ZN −1 )

(1)

Table 1: Relaxed lattice parameters of (P bT iO3 )m /(BaT iO3 )n for m = n = 2 and m = n = 3.

Lattice parameters a=b(A◦ ) c(A◦ ) c/a tetragonality

(P bT iO3 )2 /(BaT iO3 )2

(P bT iO3 )3 /(BaT iO3 )3

3.9045

3.9045

16.2970

24.9144

4.1739

6.3809

1.0434

1.0634

To study the effect of doping on superlattices, the T i host atom is replaced with F e, Co and N i. It is necessary to mention that we focus here on a situation

in which the T i ion located close to the layer interface is substituted by a defect corresponding to an inclusion atom (3d transition metals) across the

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interface. Due to the presence of different defects and lattice imperfections,

natural crystals are not perfect materials. In oxide materials, oxygen vacancy is an intrinsic defect. In this study, oxygen vacancy (VO ) is generated through removing a natural oxygen atom from the simulation system. This generates VO , due to charge imbalance in defective superlattices. For all relevant combinations of defect and oxygen vacancy positions, We have computed the defect formation

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energy, and have provided a physical understanding of the results across the interface.

Four and nine different configurations are chosen for the doping atom and oxygen vacancy positions in P T O for m = n = 2 and m = n = 3, respectively, and the defect formation energy is calculated easily. These configurations are generated through changing the positions and distances between the dopants and the VO

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site. The defect formation energy is calculated based on the following equation:

(2)

Ef ormation = E(pure) − E(doped) 80

Where, E(pure) and E(doped) are the energies of pure and doped superlattices, respectively [57]. the Defect formation energy is obtained when impurity is

placed in P T O, BT O, or in both P T O and BT O. According to the obtained results, the lowest energy is observed for the case of defect presence in P T O. It 85

is notable that a smaller total energy is related to a more stable structure.

Table.2 lists the nonzero total magnetic moments for defective (P bT iO3 )m /(BaT iO3 )n superlattices. The findings show that F e, Co and N i impurities cause maximum

to minimum magnetic moments, respectively. Moreover, increasing thickness and impurity percentage enhance the magnetic moment.

Table 2: Total magnetic moment of defective superlattices (in µB ).

Magnetic moment (µB )

F e doped (P bT iO3 )2 /(BaT iO3 )2 + VO

3.09

Co doped (P bT iO3 )2 /(BaT iO3 )2 + VO

1.76

N i doped (P bT iO3 )2 /(BaT iO3 )2 + VO

0.83

F e doped (P bT iO3 )3 /(BaT iO3 )3 + VO

6.67

Co doped (P bT iO3 )3 /(BaT iO3 )3 + VO

5.67

N i doped (P bT iO3 )3 /(BaT iO3 )3 + VO

1.44

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Superlattices

Density of states is studied to gain a deep understanding of the origin of

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ferromagnetism in doped perovskite superlattices. The total density of states (TDOS) and projected density of states (PDOS) of pure and doped superlattices have been shown in Fig.3 to 10. Up-spin and down spin states are shown in the upper and lower portions of the panels, respectively. A small portion of down-

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spin states appears above the Fermi level, indicating that the area under the DOS curve for down-spin state is smaller than that for up-spin states. As shown

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in Fig.3 and Fig.7, there is a positive spin splitting and thus a positive magnetic

moment would occur for doped superlattices. These spin polarized channels cause ferromagnetism. Due to the reduced crystal symmetry in doped super100

lattices compared to the pure ones, the TDOS distribution of transition metal

doped superlattices is broader than that of the pure superlattice, revealing that

the electronic nonlocality feature is more noticeable in doped superlattices. The strong hybridization between T i − 3d and O − 2p orbitals leads to the stabilizing ferroelectric off-centering behavior. Transition metal d state contributes to the 105

hybridization with O − 2p and T i − 3d states and results in impurity energy

levels. As a result of such hybridization, the band gaps of doped superlattices

are reduced. It can be seen that the doped superlattices exhibit conductivity, as both spin states across the Fermi level Ef .

T i atom tends to form the T i4+ oxidation state, that can be accepted by DOS 110

for T i shown in Fig.3 and Fig.7. the majority and minority spin states of T i−3d

are nearly unoccupied in the conduction bands, being indicative of the T i4+ oxidation state. The T i − 3d orbital exhibits a quite little broadening under the Fermi level, implying a smaller deviation of the T i4+ oxidation state. In doped

superlattices, the defective atoms tend to form T M 3+ oxidation state. Fig.4 to 6 and Fig.8 to 10 illustrate the DOS of sub-orbitals. The up spin states in dxy ,

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dyz and dzx orbitals are partly occupied. Occupied orbitals indicate the orientation of bonding. After doping transition metals, T i − 3d states are broadened

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and pushed towards the Fermi level.

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Figure 3:

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Total DOS of (a) pure; (b) F e doped; (c) Co doped and (d) N i doped

(P bT iO3 )2 /(BaT iO3 )2 +VO and projected DOS for T i and defective atoms of (e) pure; (f) F e doped (g) Co doped and (h) N i doped (P bT iO3 )2 /(BaT iO3 )2 + VO . Up-spin and down-spin states are shown in the upper portions and lower portions in the panels, respectively. The

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solid vertical line indicates the Fermi level.

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Figure 4: Projected DOS for (a) dxy ; (b) dyz ; (c) dzx ; (d) dx2 −y2 and (e) dz2 for F e doping in

(P bT iO3 )2 /(BaT iO3 )2 + VO . Up-spin and down-spin states are shown in the upper portions

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and lower portions in the panels, respectively. The solid vertical line indicates the Fermi level.

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Figure 5: Projected DOS for (a) dxy ; (b) dyz ; (c) dzx ; (d) dx2 −y2 and (e) dz2 for Co doping in

(P bT iO3 )2 /(BaT iO3 )2 + VO . Up-spin and down-spin states are shown in the upper portions

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and lower portions in the panels, respectively. The solid vertical line indicates the Fermi level.

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Figure 6: Projected DOS for (a) dxy ; (b) dyz ; (c) dzx ; (d) dx2 −y2 and (e) dz2 for N i doping in

(P bT iO3 )2 /(BaT iO3 )2 + VO . Up-spin and down-spin states are shown in the upper portions

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and lower portions in the panels, respectively. The solid vertical line indicates the Fermi level.

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Figure 7:

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Total DOS of (a) pure; (b) F e doped; (c) Co doped and (d) N i doped

(P bT iO3 )3 /(BaT iO3 )3 +VO and projected DOS for T i and defective atoms of (e) pure; (f) F e doped (g) Co doped and (h) N i doped (P bT iO3 )3 /(BaT iO3 )3 + VO . Up-spin and down-spin states are shown in the upper portions and lower portions in the panels, respectively. The

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solid vertical line indicates the Fermi level.

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Figure 8: Projected DOS for (a) dxy ; (b) dyz ; (c) dzx ; (d) dx2 −y2 and (e) dz2 for F e doping in

(P bT iO3 )3 /(BaT iO3 )3 + VO . Up-spin and down-spin states are shown in the upper portions

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and lower portions in the panels, respectively. The solid vertical line indicates the Fermi level.

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Figure 9: Projected DOS for (a) dxy ; (b) dyz ; (c) dzx ; (d) dx2 −y2 and (e) dz2 for Co doping in

(P bT iO3 )3 /(BaT iO3 )3 + VO . Up-spin and down-spin states are shown in the upper portions

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and lower portions in the panels, respectively. The solid vertical line indicates the Fermi level.

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Figure 10: Projected DOS for (a) dxy ; (b) dyz ; (c) dzx ; (d) dx2 −y2 and (e) dz2 for N i doping in

(P bT iO3 )3 /(BaT iO3 )3 + VO . Up-spin and down-spin states are shown in the upper portions and lower portions in the panels, respectively. The solid vertical line indicates the Fermi level.

To examine the changes in hybridization and chemical bonding after doping, the electron charge density of superlattices is calculated along the [001] axis in

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the (110) plane. The obtained results are shown in Fig.11 and Fig.12. The charge distribution around T i and transition metal sites tells us the T i − O, F e − O, Co − O and N i − O are smaller than the P b − O and Ba − O interatomic distances, which upholds the covalent nature of T i − O, F e − O, Co − O and

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N i − O bonding. Charge density results for doped and pure superlattices show

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that after doping F e, Co and N i, the T i − O bonding strength is reduced compared to the pure superlattice.

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Figure 11: Charge density distribution for (a) pure (P bT iO3 )2 /(BaT iO3 )2 superlattice; (b)

F e doped (P bT iO3 )2 /(BaT iO3 )2 + VO ; (c) Co doped (P bT iO3 )2 /(BaT iO3 )2 + VO ; (d) N i doped (P bT iO3 )2 /(BaT iO3 )2 + VO along the [001] axis in the (110) plane. Pictures have

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been drawn using VESTA.

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Figure 12: Charge density distribution for (a) pure (P bT iO3 )3 /(BaT iO3 )3 superlattice; (b)

F e doped (P bT iO3 )3 /(BaT iO3 )3 + VO ; (c) Co doped (P bT iO3 )3 /(BaT iO3 )3 + VO ; (d) N i

doped (P bT iO3 )3 /(BaT iO3 )3 + VO along the [001] axis in the (110) plane. Pictures have been drawn using VESTA.

Ferroelectricity arises from a balance of short-range covalent interactions

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and long-range Coulomb interactions. Defects break the balance between short-

range and long-range interactions. Hybridization between O − 2p and T i − 3d orbitals has given insight into the origin of ferroelectricity and its relation to the long-range interactions. Transition metal d state contributes to the hybridization with O − 2p and T i − 3d states and reduces the off-centering T i atom in

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octahedral cavity. The electronegativity of transition metals is larger than T i, 135

which indicates that T M − O bond length is smaller than T i − O. F e has the lowest electronegativity in comparison with Co and N i, so F e doping causes lowest reduction of polarization in (P bT iO3 )m /(BaT iO3 )n superlattices. According to the crystal field in the perovskite, a 5-fold degenerate transition metal 3d state in octahedral symmetry splits into eg and t2g states. If the

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octahedral symmetry is Oh point group (M L6 ), the 3d orbital splits into eg 18

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(including dx2 −y2 and dz2 orbital) and t2g (including dxy , dyz and dxz orbital) energy levels [14], while in the case the octahedral symmetry is D4h (M L4 ), the 3d state splits into eg , b2g , a1g and b1g . the local point group symmetry of tran-

sition metals in ABO3 perovskite is 4/mmm, corresponding to D4h symmetry 145

in Schonflies’ notation. In an ionic picture, T M 3+ has the following electronic structure: F e3+ with d5 , Co3+ with d6 , and N i3+ with d7 . The valence states of

these T M s are confirmed by the partial magnetic moment analysis: as 2.2µB for

F e, 1.7µB for Co and 0.6µB for N i, where µB is the Bohr magneton. According to the following spin configuration of T M 3+ , the eg state for the cells is partly 150

or fully electron-occupied. Given that F e is octahedrally coordinated with six

oxygen atoms and is displaced in Oh symmetry, F e3+ (d5 ) has a configuration

of t32g e2g in the high spin state (Fig.13(a)). In the ferroelectric state with oxygen vacancy, the degeneracy of eg is lifted, as dx2 −y2 and dz2 components are filled with electrons. For T M = Co, the electronic configuration of Co3+ (d6 ) in Oh 155

symmetry is expressed as t42g e2g in the high spin state (Fig.13(b)). The occupied

DOS of Co − 3d in the majority spin state is spread in the valance band, indi-

cating that one electron is present in the bonding state of eg . The electronic

configuration of N i3+ (d7 ) in Oh symmetry is described as t52g e2g (Fig.13(c)).

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In the minority spin component, the unoccupied dx2 −y2 state is present in the

gap, while the dz2 state is stabilized and appears at the valence band minimum level, because of the strong hybridization with adjacent O − 2p, which leads to a relatively small magnetic moment. In classical physics, ferroelectricity is described as a consequence of some constituent ions leading to the instability of the nonpolar state and thus, creation of ferroelectricity. Establishment of a strong covalent bond between the transition metal ion (T i, F e, Co, N i) with

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surrounding oxygen ions is the microscopic explanation of the appearance of ferroelectricity and magnetism in the perovskite transition metal oxides. Ferroelectricity in pure (P bT iO3 )m /(BaT iO3 )n superlattices is practically observed in perovskite with transition metal B-ions with empty d-shell, i.e. with d0 occu-

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pation. On the other hand, magnetism requires partial occupation of d states in defective superlattices. Several physical factors have been proposed to explain 19

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this feature. For instance, one explanation is that ions with empty d shells are

usually smaller than those with dn (n ̸= 0) configurations. Thus, such small

ions can easily shift from the center of octahedral cavity. Another factor could 175

be related to the fact that formation of a strong covalent bond with oxygen leads to a decrease in electron energy. The formation of transition metal and oxygen covalent bonds results in ferroelectricity. Covalent bond is a typical singlet chemical bond. In the presence of another localized d electron, the Hund’s

rule exchange would destabilize the singlet covalent bond. These factors can lead to the coexistence of magnetism and ferroelectricity in these systems.

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Figure 13: Schematic view of the transition metal impurity in the octahedral surrounding of

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(a) F e, (b) Co and (c) N i at high spin state.

conclusions

In summary, first-principles calculations are carried out to study the elec-

tronic and magnetic properties of metal-doped tetragonal (P bT iO3 )m /(BaT iO3 )n superlattices. In doing so, oxygen vacancy is taken into account as an intrinsic

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ubiquitous point defect. Based on defect formation energy values, we found that

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oxygen vacancy and transition metal impurities are likely formed at the interface of P T O and BT O layers. The preceding analysis indicates that F e impurity

doping leads to introduce the maximum local magnetic moment. Moreover, interpretation of hybridization between T M − 3d and O − 2p atomic orbitals 190

is responsible for the magnetic moment appearance. Eventually, increasing

the thickness of layers and impurity percentage results in the enhancement of magnetic moment value. We believe that reported results provide funda-

mental insights for future design of multiferroic materials using conventional ferroelectrics.

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Highlights

• Employing the first-principles calculation to invetigate the electronic structure and magnetic properties of (P bT iO3 )m /(BaT iO3 )n superlattices constructed by the tetragonal ferroelectric P bT iO3 and BaT iO3 growing along (001) direction, alternatively. • Substituting T i with 3d transition metals (F e, Co and N i) in the presence of oxygen vacancy as an intrinsic ubiquitous point defect, induces ferromagnetic phase.

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• F e impurity leads to ferromagnetic configuration with the maximum magnetic moment in ferroelectric (P bT iO3 )m /(BaT iO3 )n superlattices and results multiferroic feature.

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Declaration of interests

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☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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Houshang Araghi: Corresponding author, Supervision, Idea of manuscript Fariba Ahmadi: Methodology, Software, Visualization

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Houshang Araghi and fariba Ahmadi: Writing-Reviewing and editing, Analysis of data, revision of manuscript.