Physical properties of half-metallic AMnO3 (A = Mg, Ca) oxides via ab initio calculations

Computational Materials Science 146 (2018) 248–254

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Physical properties of half-metallic AMnO3 (A = Mg, Ca) oxides via ab initio calculations B. Amin a, Farzana Majid b, M. Bilal Saddique c, Bakhtiar Ul Haq d,⇑, A. Laref e, Tahani A. Alrebdi f, Muhammad Rashid g,⇑ a

Department of Physics, Hazara University, Mansehra, Pakistan Department of Physics, University of the Punjab, Quaid-e-Azam Campus, 54590 Lahore, Pakistan Physics Department, School of Science, University of Management and Technology, 54590 Lahore, Pakistan d Advanced Functional Materials & Optoelectronics Laboratory (AFMOL), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia e Department of Physics and Astronomy, College of Science, King Saud University, Riyadh 11451, Saudi Arabia f Department of Physics, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia g Department of Physics, COMSATS Institute of Information Technology, 44000 Islamabad, Pakistan b c

a r t i c l e

i n f o

Article history: Received 20 October 2017 Received in revised form 6 December 2017 Accepted 15 January 2018

Keywords: Half-metallic oxides Modified becke and Johnson potential (mBJ) Exchange mechanism John Teller distortion (JTD) Thermal efficiency

a b s t r a c t In this paper, the physical properties of AMnO3(A = Mg, Ca) have been explored by means of density functional theory based computational approaches. The calculations for structural, electronic, magnetic and thermoelectric properties have been performed by adopting the full-potential linearized-augmented-pl us-local-orbital (FP-LAPW+lo) method employed in WIEN2k code, whereas the thermoelectric properties have been determined by applying Boltzmann transport theory in BoltzTraP code. The half-metallic ferromagnetism has been enquired by the analysis of spin polarized band structures and density of states. The nature and origin of ferromagnetism has been illustrated in terms of crystal field energies, exchange energies and concerned exchange constants. Additionally, the diminution of magnetic moment from Mn sites and occurrence of small magnetic moments on Mg/Ca and oxygen and interstitials sites yields to negative values of indirect exchange energy Dx(pd) and strong hybridization. Lastly, the thermoelectric behavior of AMnO3 has been elucidated by the explanation of electrical conductivity, thermal conductivity, Seebeck coefficient, power factor and thermal efficiency. The assessment of magnetic and thermoelectric properties of AMnO3 suggests that these compounds are greatly appropriate for spintronic and thermoelectric applications. Ó 2018 Elsevier B.V. All rights reserved.

1. Introduction Perovskite oxides are well-known as pragmatic broad materials for industrial purposes owing to their special physical properties, as piezoelectricity, ferro-electricity, ferromagnetism and semiconductor technology [1–4]. Consequently, perovskite materials have been substantiated as potential candidates for applications in new devices, such as, micro electro-mechanical systems, nonvolatile memories, like catalysts and magneto resistance [5,6]. Half metallicity has been perceived in maximum figure of perovskites materials, which is owed to origin of their special electronic performance. This character clues them like an auspicious material to accelerate information in various devices with less energy utiliza-

⇑ Corresponding authors. E-mail addresses: [email protected] (B. Ul Haq), muhammad.rashid@comsats. edu.pk (M. Rashid). https://doi.org/10.1016/j.commatsci.2018.01.033 0927-0256/Ó 2018 Elsevier B.V. All rights reserved.

tion and producing circuit integration density. So, the spintronic field is the admirable place to utilize such type of materials in the technological applications similar to magnetic sensors with concentrated feasible proficiency and single-spin electron source [7,8]. In this concern, transition metal (TM) perovskites are further promising to explore the ferromagnetic retort in various forms of magnetic materials. From the time when strong pd hybridization begins for the cause of TM with p states of anions owing to splitting of d states. Owing to this tempting role, quick growth on the purview of theoretical works has been promoted to describe halfmetallic ferromagnetism (HMF) [9–11]. In supplement, the key purpose to investigate magnetic properties in oxide materials is to create small energy utilization devices [12,13]. Lately, due to their prospective application, transitional metal perovskites have received devotion from researchers [14–16]. Among these oxides, near room temperature MgMnO3 shows semiconducting behavior and displays favorably insulating

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behavior at low temperature [17]. Recently, Thota et al. [18], have described the chance of stability of MgMnO3 compounds in cubic phase when manufactured by low temperature sol–gel procedure. On the hand, CaMnO3 manganese oxide crystal structure has attracted much attention in the earlier era with perovskite type owed to its structural [16], topological [19], physical [20], magnetic [21] and thermoelectric (TE) properties [16,22,23]. However, for the TE properties, the aristocratic manganite reveals comparatively larger thermo-power and smaller thermal conductivity at room temperature [16]. Besides, it has additional interesting features such as high temperature stability, non-noxious gas emission, inexpensive raw materials and simple fabrication associating with predictable TE alloys. CaMnO3 perovskite is appropriate for long time utilization in air for energy exchange at high temperature and by doping TE properties could be foster improved [16,22–24]. Earlier consideration of manganite CaMnO3 perovskite for TE characteristics has been paid on its crystal structure, magnetic properties, temperature change induced phase transition and doping properties [16,19,20,25]. As discussed above most of the experimental work is devoted to the investigations of electrical, magnetic and optical properties of AMnO3 (A = Mg, Ca) perovskites, which can be evaluated with the density functional theory (DFT) supported exertion and supplementary theoretical exploration can sustain establish experimental confirmation. The increasing energy demands have initiated research for thermoelectric properties of such materials, which are comparatively cheaper and more efficient to design clean energy devices [26,27]. The thermoelectric behavior is analyzed in terms of figure of merit (ZT) or the power-factor (PF) rS2 parameters. In order to shift the figure of merit toward the unity value, the See-beck co-efficient and electrical conductivity is enhanced while the thermal conductivity is reduced [28]. Therefore, these parameters are quite important to be discussed as well. For many of the materials, these characteristics have been analyzed but our detailed literature survey reveals that our compounds have not been approached for thermoelectric trends. For this purpose, we

demonstrate explanation to see evolution in structural, electronic, magnetic and thermoelectric properties of AMnO3 (A = Mg, Ca). Their technological importance motivated us to work out and investigate their magnetic and thermoelectric aspects in this research work for useful applications in advanced technology. 2. Method of calculations To explore electronic and magnetic properties of AMnO3(A = Mg, Ca), we used FP-L(APW+lo) density functional technique as accomplished in all-electron WIEN2k code [29] for the elucidation of single particle Kohn-Sham equations [30]. The class of AMnO3(A = Mg, Ca) is perovskite-type oxides ABO3. To performed ferromagnetic (FM) calculations, we used ideal cubic perovskite structure, where A cations at the cubic corner, cation Mn at center and the O at the center of cubic faces form a regular octahedron. Further, the calculations for the anti-ferromagnetic (AFM) case were performed using a 1
1
2 supercell of the perovskite structure such that each of two atoms in the supercell had opposite spin orientation. The exchange and correlation energy have been treated by employing generalized gradient approximations (GGA-PBEsol) [31] has been utilized for the optimization of structural parameters. In addition, Trans and Balaha modified Becke Johnson potential (TB-mBJ) is used to obtain more accurate results for electronic, magnetic and thermo-electric properties as the selection of proper

Table 1 The calculated values of lattice constant a0 (Å), bulk modulus B0 (GPa), enthalpy of formation DH (eV) for AMnO3 (A = Mg, Ca) compounds using GGA PBEsol compared to other theoretical calculations and experiment. Parameters a0 (Å) B0 (GPa) DH (eV) a b c

Fig. 1. The volume optimization for (a) MgMnO3 and (b) CaMnO3 compounds in FM, AFM and NM phases.

MgMnO3 3.68 197.26 1.68

Other Cal. b

3.73 , 3.71 218c

Exp. c

3.807

a

CaMnO3

Other Cal.

3.74 177.73 2.32

3.81b

[46], [47], [48].

Fig. 2. The band structures plots of cubic AMnO3 (A = Mg, Ca) compounds for up spin (") channel and down spin (;) channel by using mBJ potential.

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exchange–correlation functional has significant consequences in DFT computations [32]. The performance of TB-mBJ potential for sp semiconductors and simple transition metal oxides was first confirmed by Trans and Balaha. However, later studies revealed that this potential can be effectively used for an accurate prediction of electronic properties like band gap owing to its better performance as compared to the semi-local exchange–correlation functional [33–35]. Therefore, we have used mBJ potential for electronic properties and provide evidence of its suitability for large band gap complex oxides like perovskite structure. In the recent calculations, designated parameters which establish the size of the secular matrix is RMT
Kmax = 8, where the RMT is the MuffinTin sphere radii and Kmax is the cut-off wave-vector in the first Brillion zone (BZ). Gaussian factor Gmax = 18 and angular momentum vector lmax = 10. Furthermore, k-mesh of 1000 k-points has been considered for preeminent convergence and energy drop of the stability of 0.1 mRyd. The RMT values have been used as Mg = 2.5, Ca = 1.9, Mn = 1.8 and O = 1.7. Finally, the results of electronic structure calculations have been used thermoelectric properties

such as electrical conductivity, thermal conductivity, See-beck coefficient, power factor and thermal efficiency are determined by using BoltzTrap code [36].

3. Result and discussion 3.1. Structural and electronic properties The cubic perovskites, AMnO3(A = Mg, Ca) are optimized within ferromagnetic (FM), Anti-ferromagnetic (AFM) as well as nonmagnetic (NM) phases. From Fig. 1, it is noted that FM-phases exhibit lower energies, hence both compounds can be characterized as stable in FM-phase. Further, confirmation for stability of FM-phase is examined by applying enthalpy of formation method [37]. The method of enthalpy (DH) for both compounds are measured by following relations; tetra 3 DHAMnO3 ¼ EAMnO  EAt cubic  EMn  3=2EOt 2 t t

Fig. 3. The TDOS and PDOS plots of cubic MgMnO3 compound for up spin (") channel and down spin (;) channel by using mBJ potential.

ð1Þ

B. Amin et al. / Computational Materials Science 146 (2018) 248–254 3 where EAMnO , EAt , EMn and EOt 2 are expressed for least total energies of t t AMnO3(A = Mg, Ca), cubic A (solid), tetragonal Mn (solid) and O2 (molecule), respectively. Our calculated values of DH are negative (see Table 1), that further confirm the stability of both compounds FM-phase. The optimized volume against total energy plots are shown in Fig. 1, where total energy-volume statistics are fitted with equation of state to assess structural pattern and some other properties for both compounds in FM-phase. Table 1 enlists the lattice constant and bulk modulus of our compounds. While moving down the groups in periodic table (from Mg toward Ca), the lattice constant is increased but the bulk modulus is decreased that can be attributed to increasing of ionic radii. Beside it, the spin polarized electronic band structure (BS) and density of states (DOS) plots for our compounds are shown in Fig. 2 and Fig. 3, 4 respectively. It can be observed from electronic BS plotting that spin-up (") and spin-down (;) channels display metallic and semiconducting behavior respectively, hence our compounds are half-metallic ferromagnetic (HMF). Similar trend can be noted from total density of states (TDOS) plots as well. It has been established that the HMF compounds are completely spin

251

polarized. The equation P ¼ N#N"
100 (where N;/N" represent N#þN" the electrons at the Fermi level (EF) in up spin (")/down spin (;) respectively) is applied to evaluate spin polarization, which present the electron density values at Fermi-level 1 and 0 for spinup (") and spin-down (;) channel respectively with 100% spin polarized [38]. Further, analysis of the splitting of energy states in spin-down (;) channel shift the indirect bandgap (M-C) to higher values as listed in Table 2. Generally, the growing number of electrons in a shell enhances the columbic repulsion, which in turn shifts away the electronic states from Fermi-level and enlarges the band width. The electronic contribution to magnetism can be understood from spin polarized partial density of states (PDOS) plots in Figs. 3 and 4. It is noted that Mn 3d-states hybridize with O 2p-states (from 1.9 eV to Fermi level (EF) for spin-up (") channel and 1.2 eV to 2.4 eV for spin-down (;) channel) and Mg/Ca s-states. The John-Teller effect causes Mn states to form five degenerated states. This degeneracy is split with the formation of doublet states, eg(dx2-y2 and dz2) and triplet states t2g (dxy, dxz and dyz), where eg states lies at comparatively higher energy than the t2g states.

Fig. 4. The TDOS and PDOS plots of cubic CaMnO3 compound for up spin (") channel and down spin (;) channel by using mBJ potential.

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Table 2 The calculated values of spin down gap (;Eg (eV)), half-metallic gap (gh (eV)), crystal field energy (DEcrystal), direct exchange Dx(d), John-Teller DJT(eV) and indirect exchange Dx(pd) energies, total and the local magnetic moments (in Bohr magneton) and the exchange constants (Noa and Nob) for AMnO3 (A = Mg, Ca) using TB-mBJ potential.

c

Parameters

MgMnO3

Eg (eV) GHM (DEcrystal) Dx(d) DJT(eV) Dx(pd) Total (mB) A (mB) Mn (mB) O (mB) Interstitial (mB) Noa Nob

0.44 0.20 1.48 2.42 2.14 0.12 3.000 0.025 2.443 0.093 0.249 0.30 0.098

Other Cal.

CaMnO3

2.36c

0.47 0.15 1.17 2.34 2.05 0.08 3.000 0.018 2.483 0.089 0.090 0.34 0.064

Other Cal.

[48].

Further, splitting shifts the d2z state to higher value (comparative to dx2-y2 state) and dxy state to higher value (comparative to dxz and dyz states) [39,40]. The retrogressive way of John Teller distortion, constructs the contest between Mn at octahedral situation of oxygen atoms but involvement to hybridization with oxygen 2p-states (pxy, pyz, pzx) mostly originates owing to the linear states of Mn atoms. The energies are enumerated in Table 2, included in structures of considered compounds owing to crystal field strain. Furthermore, the direct exchange energy DX ðdÞ have been derived that shows greater energy values than the John-Teller effect ðDJT ¼# DCF  " DCF Þ and indicate that dominancy of exchange mechanism over all other mechanisms for electron spins [41].

Moreover, the valence band edge splitting (also called indirect exchange energy) is calculated from O 2p-states maxima in spin-down channel. Table 2 shows their negative values for both compounds and verifies the existence of exchange mechanism in electronic spin and makes such compounds favorable for spintronic and ferroelectric appliances. 3.2. Magnetic properties Magnetism in compounds is caused due to both the constituent atoms and crystal fields of neighboring atoms. The main contributions to the magnetic moment are of partially filled Mn d-states and of interstitial sites [42]. A deep analysis of ferromagnetism is discussed by listing local as well as total magnetic moments in Table 2. It is evident that the major contribution to the observed FM is from Mn-atom and minor contribution of Mg, Ca, O atoms along from interstitial sites. Further, the hybridization mechanism not only reduces the local magnetic moment of Mn-atom but also shift a part of it to non-magnetic and interstitial sites. The electronic spin is anti-parallel, since the magnetic moments come out negative for O and positive for cations (Mg, Ca). It is also noticed that the total magnetic moment of both compounds are integer 3 mB, which is again an identification of their half-metallic character. The exchange constants Noa and Nob are used to estimate the coupling strength of s-d and p-d respectively and are calculated using following equations

No a ¼ DEC =xS and No b ¼ DEV =xS E#C

E"C

E#V

ð2Þ E"V

where DEc ¼  and DEV ¼  are conduction and valence band edge splitting energies respectively [43] and hSi, x are for average magnetic moment of both compounds and Mn concentration. The values come out for exchange constants, Noa and Nob are

Fig. 5. Temperature verses (a) electrical conductivity, (b) Seebeck coefficient, (c) thermal conductivity and (d) power factor plots for cubic MgMnO3 and CaMnO3 compounds.

B. Amin et al. / Computational Materials Science 146 (2018) 248–254

positive and negative (see Table 2) respectively, that reveals HMF [38,44]. Also, negative values of Nob support to exchange mechanism. 3.3. Thermoelectric properties Recently, some compounds are being used to convert useless heat energy to electrical energy for the purpose of green and sustainable production. In this regard, the thermoelectric oxides have been proved favorable due to their ability of efficient energy conversion, abundant availability, lesser manufacturing price and non-toxic nature. To our knowledge, the thermoelectric efficiency for AMnO3 (A = Mg, Ca) has not been explored to date. Therefore, recent work may provide new horizon to use these compounds for energy conversion in thermoelectric devices. The thermoelectric behavior of AMnO3 (A = Mg, Ca) is analyzed in terms of their electrical conductivity r/s (Oms)1, thermal conductivity k/s (W/mKs), See-beck coefficient S(mV/K), power factor S2r (W/mK2s) and thermoelectric efficiency. Fig. 5(a) displays that r/s (Oms)1 for both compounds that increases linearly with temperature range from 300 to 800 K. Though, CaMnO3 indicates distinct increases in r/s, owing to rise in temperature, as likened with MgMnO3. At 800 K, the maximum computed value for CaMnO3 compound is 8.56
1019 (Oms)1. The highest computed value r/s for MgMnO3 is 7.64
1019 (Oms)1 at 800 K. Similar trend for S can also be seen from Fig. 5(b) for both compounds. From Fig. 5(b), it is evident that S is increases with temperature in the considered compounds. At room temperature, the computed values of S are 23.13 lV/K and 3.79 mV/K for MgMnO3 and CaMnO3 respectively. Therefore, S linearly increases with the rise of temperature up to 800 K. The highest computed values of S for both compounds are 36.18 lV/K and 41.82 lV/K at 800 K respectively. The thermal conductivity is also a significant consideration to discourse thermoelectric materials applications. The k/s of studied compounds are schemed in range of temperature from 300 K to 800 K in Fig. 5c. The k/s of MgMnO3 rises linearly from 5.72
1014 (W/mKs) to 25.40
1014 (W/m Ks) with increase of temperature from 300 K to 800 K. The power factor (PF = S2r/s) is a prominent parameter of thermoelectric calculations that explains the association between S and r/s [45]. At room temperature, the calculated value of PF is 0.25
1012 (W/mK2s) for MgMnO3. As the temperature increase up to 400 K, its value is decreased to 0.184
1012 (W/mK2s) and after 450 K its value increase linearly and become maximum 1.0
1012 (W/mK2s) at 800 K. For CaMnO3, the value of PF increases linearly with rise in temperature

Fig. 6. Temperature verses thermal efficiency plots for cubic MgMnO3 and CaMnO3 compounds.

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and achieve maximum value of 1.5
1012 (W/mK2s) at 800 K. Finally, thermoelectric efficiency is discussed with temperature for AMnO3 (A = Mg, Ca) in Fig. 6, whose maximum values 5.5% at 700 K for CaMnO3 and 3.5% at 800 K for MgMnO3. The thermoelectric properties of these compounds favor their usage for thermoelectric devices. 4. Conclusion In summary, the negative values for enthalpy of formation gives the confirmation of stability in the cubic phase of perovskite compounds AMnO3 (A = Mg, Ca). Their half-metallic ferromagnetism with 100% spin polarization has been divulged by density of states and band structures at Fermi level. The superior value of direct exchange energy than crystal field energy/John-Teller distortion and negative value of indirect exchange energy endorse that spin of electron play vital character to produce ferromagnetism sooner than any extra effect. Furthermore, the sturdy hybridization between Mn ions at octahedral site and oxygen, decreases the magnetic moment of magnetic ions and creates diminutive magnetic moments on nonmagnetic and interstitial sites. Latterly, the electrical conductivity and thermal efficiency raises with the increase in temperature of AMnO3 (A = Mg, Ca) to formulate them as appropriate compound for spin based and renewable energy device applications. Acknowledgment The author A. Laref acknowledges the financial support by a grant from the ‘‘Research Center of the Female Scientific and Medical Colleges”, Deanship of Scientific Research, King Saud University. The author (Bakhtiar Ul Haq) extends his appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under grant number R.G.P. 2/3/38. References [1] J.G. Bednorz, K.A. Muller, Phys. Rev. Lett. 52 (1984) 2289. [2] P. Baettig, C.F. Schelle, R. Lesar, U.V. Waghmare, N.A. Spaldin, Chem. Mater. 17 (2005) 1376. [3] H. Wang, B. Wang, Q. Li, Z. Zhu, R. Wang, C.H. Woo, Phys. Rev. B 75 (2007) 245209. [4] H.P.R. Frederikse, W.R. Thurber, W.R. Hosler, Phys. Rev. 134 (1964) A442. [5] Y. Moritomo, A. Asamitsu, H. Kuwahara, Y. Tokura, Nature 380 (1996) 141. [6] J.M. De Teresa, M.R. Ibarra, P.A. Alagarabel, C. Ritter, C. Marquina, J. Blasco, J. Garcia, A.D. Moral, Z. Arnold, Nature 386 (1997) 256. [7] S. Chattopadhyay, T.K. Nath, Current Appl. Phys. 11 (2011) 1153–1158. [8] J.G. Banach, W.M. Temmerman, Phys. Rev. B 69 (2004) 054427. [9] Z. Ali, I. Ahmad, I. Khan, B. Amin, Intermetallic 31 (2012) 287. [10] M. Rashid, Z. Abbas, M. Yaseen, Q. Afzal, Asif Mahmood, Shahid M. Ramay, J. Supercond. Nov. Magn. 30 (2017) 3129. [11] B. Sabir, G. Murtaza, Q. Mahmood, R. Ahmad, K.C. Bhamu, Curr. Appl. Phys. 17 (2017) 1539–1546. [12] Hideo Hosono, Thin Solid Films 515 (2007) 6000. [13] C.Z. Wu, Feng Feng, Yi Xie, Chem. Soc. Rev. 42 (2013) 5157–5183. [14] M. Karppinen, H. Fjellvag, T. Konno, Y. Morita, T. Motohashi, H. Yamauchi, Chem. Mater. 16 (2004) 2790. [15] K. Fujita, T. Mochida, K. Nakamura, Jpn. J. Appl. Phys. 40 (2001) 4644. [16] L. Bocher, M.H. Aguirre, R. Robert, D. Logvinovich, S. Bakardjieva, J. Hejtmanek, A. Weidenkaff, Acta Mater. 57 (2009) 5667. [17] B.L. Chamberland, A.W. Sleight, J.F. Weiher, J. Solid State Chem. 1 (1970) 512. [18] S. Thota, K. Singh, B. Prasad, J. Kumar, Ch. Simon, W. Prellier, AIP Adv. 2 (2012) 032140. [19] K.R. Poeppelmeier, M.E. Leonowicz, J.C. Scanlon, J. Solid State Chem. 45 (1982) 71. [20] D. Sousa, M.R. Nunes, C. Silveira, I. Matos, A.B. Lopes, M.E.M. Jorge, Mater. Chem. Phys. 109 (2008) 311. [21] X.J. Fan, H. Koinuma, T. Hasegawa, Physica B 329–333 (2003) 723. [22] N. Kumar, H. Kishan, A. Rao, V.P.S. Awana, J. Alloys Compd. 502 (2010) 283. [23] Y. Wang, Y. Sui, P. Ren, L. Wang, X. Wang, W. Su, H. Fan, Inorg. Chem. 49 (2010) 3216. [24] J.W. Park, D.H. Kwak, S.H. Yoon, S.C. Choi, J. Alloys Compd. 487 (2009) 550. [25] Q. Zhou, B.J. Kennedy, J. Phys. Chem. Solids 67 (2006) 1598.

254

B. Amin et al. / Computational Materials Science 146 (2018) 248–254

[26] C. Hadjistassou, E. Kyriakides, J. Georgiou, Energy Convers. Manage. 66 (2013) 165. [27] M. Chen, H. Lund, L.A. Rosendahl, T.J. Condra, Appl. Energy 87 (2010) 1231– 1238. [28] N.A. Noor, S.M. Alay-e-Abbas, M. Hassan, I. Mahmood, Z.A. Alahmed, A.H. Reshak, Philosop. Mag. 97 (2017) 1884. [29] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2K, an Augmented-plane-waveþLocal Orbitals Program for Calculating Crystal Properties, Karlheinz Schwarz, Techn. Wien, Austria, 2001. [30] Walter Kohn, Lu Jeu Sham, Phys. Rev. 140 (1965) A1133–A1138. [31] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, K. Burke, Phys. Rev. Lett. 100 (2008) 136406. [32] F. Tran, P. Blaha, Phys. Rev. Lett. 102 (2009) 226401. [33] Muhammad Rashid, N.A. Noor, Bushra Sabir, S. Ali, M. Sajjad, F. Hussain, N.U. Khan, B. Amin, R. Khenata, Comput. Mat. Sci. 91 (2014) 285. [34] W. Tanveer, M.A. Faridi, N.A. Noor, A. Mahmood, B. Amin, Current Appl. Phys. 15 (2015) 1324. [35] N.A. Noor, S. Ali, G. Murtaza, M. Sajjad, S.M. Alay-e-Abbas, A. Shaukat, Z.A. Alahmed, A.H. Reshak, Comput. Mat. Sci. 93 (2014) 151. [36] G.K.H. Madsen, K. Schwarz, D.J. Singh, Comput. Phys. Commun. 175 (2006) 67.

[37] J. Bai, J.M. Raulot, Y.D. Zhang, C. Esling, X. Zhao, L. Zuo, J. Appl. Phys. 109 (2011) 014908. [38] Q. Mahmood, M. Hassan, N.A. Noor, J. Phys.: Condens. Matter 28 (2016) 506001. [39] J.A. Alonso, M.J. Martınez-Lope, M.T. Casais, M.T. Fernandez-Dıaz, Inorg. Chem. 39 (2000) 917–923. [40] H.T. Jeng, S.H. Lin, C.H. Hsue, Phys. Rev. Lett. 97 (2006) 067002. [41] H. Keller, A.B. Holder, K.A. Müller, Mater. Today 11 (2008) 38–46. [42] N.A. Noor, S. Ali, W. Tahir, A. Shaukat, A.H. Reshak, J. Alloys. Compds. 509 (2011) 8137–8143. [43] Q. Mahmood, S.M. Alay-e-Abbas, M. Hassan, N.A. Noor, J. Alloys. Compds. 688 (2016) 899–907. [44] N.A. Noor, S. Ali, A. Shaukat, J. Phys. Chem. Solid 72 (2011) 836–841. [45] H. Hashimoto, T. Kusunose, T. Sekino, J. Ceramic. Proc. Res. 12 (2011) 223–227. [46] L. Rormark, K. Wiik, S. Stolen, T. Grande, J. Matter Chem. 13 (2001) 4005. [47] J. Saal, S. Kirklin, M. Aykol, B. Meredig, C. Wolverton, Materials design and discovery with high-throughput density functional theory: the open quantum materials database (oqmd), JOM 65 (11) (2013) 1501–1509. [48] N. Hamdad, B. Bouhaf, Physica B 405 (2010) 4595–4606.