Study of Structural, Electronic, and Magnetic

0 downloads 0 Views 668KB Size Report
Nov 8, 2018 - Lanthanide Based on Oxide Perovskite-Type NdGaO3. Mohammed El ... and chalcogenides in zinc-blend structure Mn-doped GaAs,. Cr- and ...
Journal of Superconductivity and Novel Magnetism https://doi.org/10.1007/s10948-018-4938-7

ORIGINAL PAPER

Study of Structural, Electronic, and Magnetic Properties of Cubic Lanthanide Based on Oxide Perovskite-Type NdGaO3 Mohammed El Amine Monir 1

&

Hadj Baltach 1 & Fouad El Haj Hassan 2 & Aicha Bahnes 3 & Zohra Bahnes 4

Received: 2 September 2018 / Accepted: 8 November 2018 # Springer Science+Business Media, LLC, part of Springer Nature 2018

Abstract Based on the density functional theory (DFT), the full-potential linearized augmented plane wave with local orbital (FP-L/APW+ lo) technique is now employed in this approach to understand the structural, electronic, and magnetic properties of simple cubic oxide perovskite NdGaO3 compound. In all this investigation, the exchange-correlation (XC) energy is selected in the framework of spin-polarized generalized gradient approximation (spin-GGA). The structural analysis unveils that the ferromagnetic (FM) phase is the stable ground state of the cubic NdGaO3 compound, where the equilibrium lattice parameters (lattice constant (a0), bulk modulus (B0), and its first pressure derivative (B′)) are determined in both FM and paramagnetic (PM) phases. The spinpolarized electronic properties (band structure and density of states) of the cubic NdGaO3 oxide perovskite are studied under the platform of equilibrium lattice parameters; this investigation demonstrates the half-metallic behavior of the studied cubic NdGaO3 compound because the spin-up case displays the metallic nature, whereas the semiconducting character is observed in spin-down case. The magnetic properties reveal that the total magnetic moment of the cubic NdGaO3 compound is equal to 3 μB and its contribution is mostly generated by Nd atoms, whereas feeble local magnetic moments are installed in non-magnetic Ga and O sites. Through the electronic and magnetic results, we conclude that the cubic perovskite NdGaO3 compound is classified as a half-metallic ferromagnetic material. Keywords Cubic oxide perovskite NdGaO3 . Electronic properties . Magnetic properties . Half-metallic behavior . FP-L/APW+lo

1 Introduction Half-metallic ferromagnetic (HMF) materials are the most attractive materials in this decade because their applications are extensively promising in spintronic devices [1]. The electronic behavior of half-metallic (HM) materials is described in two spin channels: the first has a metallic nature and the other is a semiconductor, leading to 100% spin polarization at the Fermi

* Mohammed El Amine Monir [email protected] 1

Faculté des Sciences Exactes, Université Mustapha Stambouli de Mascara, B.P. 305, 29000 Mascara, Algeria

2

Université Libanaise, EDST- PRASE, Beirut, El-Hadath, Lebanon

3

Laboratoire d’Elaboration et Caractérisation Physico Mécanique et Métallurgique des Matériaux (ECP3M), Département de Physique, Faculté des Sciences Exactes et Informatique, Université Abdelhamid Ibn Badis de Mostaganem, 27000 Mostaganem, Algeria

4

SEA2M Laboratery, Abdelhamid Ibn Badis University of Mostaganem, 27000 Mostaganem, Algeria

level (EF). The epistemology of this field shows that the first prediction of the half-metallic ferromagnetism is performed on the electronic structure of half-Heusler alloys NiMnSb and PtMnSb [2]; this prediction has been published in 1983 by de Groot et al. [2]. Due to this initiative, many theoretical and experimental works have been done in different types of materials, such as perovskite alloys La0.7Sr0.3MnO3 [3] and La1-xSrxO3 [4]; double-perovskite Sr2FeMoO6 [5]; metal oxides Fe3O4 [6] and CrO2 [7]; transition metal-doped pnictides and chalcogenides in zinc-blend structure Mn-doped GaAs, Cr- and Mn-doped AlN, V- and Cr-doped GeTe, and Mnand Cr-doped ZnTe [8–15]; and full-Heusler compounds Co2MnSi [16] and Co2FeSi [17]. The aim of this prediction is focused on the study of structural, electronic, and magnetic properties of cubic perovskite NdGaO3 compound, using the accurate first-principles fullpotential linearized augmented plane waves plus local orbitals (FP-L/APW+lo) method within the generalized gradient approximation (GGA). In the literature, many studies on the orthorhombic NdGaO3 compound have been realized, like the work of Marti et al. [18] that analyze the crystal structures

J Supercond Nov Magn

and phase transitions of the orthorhombic NdGaO3, and Reshak et al. [19] have studied the effect of U on the electronic properties by both theoretical and experimental techniques. The rest of the present paper is organized as follows: Computational method and detail of calculations are described in Section 2. Results and discussions of structural, electronic, and magnetic properties are detailed in Section 3. The important conclusions of this study are summarized in Section 4. The half-metallic results of this prediction are novel because the NdGaO3 perovskite compound is taken in cubic structure comparing to the other previous studies which describe the NdGaO3 compound in orthorhombic structure.

2 Model and Computational Method Fig. 1 Ideal cubic perovskite structure illustrated for NdGaO3 compound

3 Results and Discussion 3.1 Structural Properties In this prediction, the NdGaO3 perovskite compound has been studied in the cubic structure of ideal perovskite (ABO3) under Pm3m (no. 221) space group. Figure 1 shows the schematic cubic crystal of NdGaO3 compound. 3.1.1 Equilibrium Lattice Parameters The empirical Birch-Murnaghan’s equation of states (EOS) [30, 31] has been adopted to fit the calculated total energy versus lattice constant curve (E-a); it is presented under the following formula: E ðV Þ ¼ a þ bV −2=3 þ cV −4=3 þ dV −6=3

ð1Þ

NdGaO3 compound

Energy (Ry)

The ab initio full-potential linearized augmented plane wave with local orbital (FP-L/APW+lo) [20, 21] method within the framework of density functional theory (DFT) [22] has been adopted in this approach to treat different physical properties of the cubic perovskite NdGaO3 compound. Based on the fundamentals of FP-L/APW+lo method, the WIEN2k [23] computer package is now used in this study as a computer tool for achievement primordial goals of this prediction. The exchange and correlation (XC) energy is selected under the parameterization of generalized gradient approximation of Perdew-Burk-Ernzerhof (GGA-PBE) [24]. The muffin-tin sphere radii (RMT) of Nd, Ga, and O atoms are considered about 2.50, 1.82, and 1.64 Bohr, respectively. The value of the plane wave cutoff parameter is taken as RMT × Kmax = 8 to assure the expansion of wave functions in the interstitial zone, where RMT is the smallest muffin-tin sphere radius and Kmax is the maximum modulus of the reciprocal lattice vector in the first Brillouin zone (BZ). The Brillouin zone integrations were performed with 56 k-points which are distributed on the Monkhorst-Pack grid of 11 × 11 × 11 mesh in the irreducible first Brillouin zone. In these calculations, the Nd (6s24f4), Ga (4s23d104p1), and O (2s22p4) were treated as valence orbitals. The process of self-consistent iterations stops when the change in the absolute value of total energy convergence is less than 10−4 Ry per formula unit. The structure of cubic perovskite is a perfect structure that is defined in ABX3 stoichiometry, where A is the bigger cation, B is the smallest cation, and X is an anion [25–27]. In this structure, the A and B cation atoms occupy (0, 0, 0) and (1/2, 1/2, 1/2) positions, respectively, while X atoms are localized at (1/2, 1/2, 0) positions with the space group Pm3m (no. 221) [25]. The perovskite NdGaO3 compound crystallizes in orthorhombic structure under the space group Pbnm (no. 62) and their experimental lattice parameters are a = 5.4276 Å, b = 5.4979 Å [28], and c = 7.7078 Å [29].

-23600,12 -23600,14 -23600,16 -23600,18 -23600,20 -23600,22 -23600,24 -23600,26 -23600,28 -23600,30 -23600,32 -23600,34 -23600,36 3,6

Paramagnetic Phase Ferromagnetic Phase

3,7

3,8

3,9

4,0

4,1

4,2

Lattice constant (Å)

Fig. 2 Optimized total energy as a function of unit cell volume for the NdGaO3 cubic perovskite compound which is taken in both paramagnetic (PM) and ferromagnetic (FM) states

J Supercond Nov Magn Table 1 Calculated equilibrium lattice constants a0 (in Å), bulk modulus B0 (in GPa), its pressure derivative B′, and minimum total energy E0 (in Ry) for paramagnetic (PM) and ferromagnetic (FM) NdGaO3 cubic perovskite, employing PBE-GGA approximation Compound

Calculations

NdGaO3

PM state FM state Previous

Lattice parameter a0 (Å)

Bulk modulus B0 (GPa)

3.8773 3.9169 –

179.7069 173.7568 –

10

10

10

8

8

8

6

6

4

− 23,600.227638 − 23,600.363559 –

4.5101 4.5372 –

The formation energy (Ef) is a physical parameter which reviews the possibility of allowing stability for crystal compounds at the zero temperature (T = 0 K); in fact, the negative value of this quantity (Ef) proves that there exists a stronger bonding between the constituent atoms and the favorable allowing stability of the crystal [32–34]. Therefore, the energy of formation (Ef) of NdGaO3 cubic perovskite compound is a discard between the total energy (E0) and the addition of all pure energies of the constituent atoms at their favorable crystal structure; it is translated in the following relation [35, 36]: E f ¼ E0 −ðENd þ E Ga þ 3EO Þ

ð2Þ

where E0 is the total energy of the cubic NdGaO3 system and

NdGaO3 compound (b)

(c)

10

10

8

8

8

6

6

6

6

4

4

4

4

4

2

2

2

2

2

2

0

0 E 0 F

0 E 0 F

0

-2

-2

-2

-2

-2

-2

-4

-4

-4

-4

-4

-4

-6

-6

-6

-6

-6

-6

-8

-8

-8

-8

-8

-8

Spin Dn Spin Up

Spin Dn

Energy (eV)

Equilibrium total energy E0 (Ry)

3.1.2 Formation Energy

Here, a, b, c, and d are the fitting parameters at the equilibrium and V is the unit cell volume. Figure 2 displays the analysis of optimization that are done in both paramagnetic (PM) and ferromagnetic (FM) states of the cubic NdGaO3 compound; consequently, the results prove that the ferromagnetic state is energetically more favorable than the paramagnetic state, so the stable ground state of the cubic NdGaO3 compound is reported in the ferromagnetic phase. The ground state lattice parameters of the equilibrium lattice constant (a0), bulk modulus (B0), its first pressure derivative (B′), and minimum total energy (E0) are calculated for both PM and FM phases, where their obtained results are listed in Table 1. The previous experimental and theoretical works of NdGaO3 cubic perovskite have not been done until now; therefore, it is impossible to make comparison.

(a)

B′

Spin Up

10

-10

-10 -10

-10 -10

-10

-12

-12 -12

-12 -12

-12

-14

R

X Z M

-14 -14

-6

-4

-2

0

2

4

Total Density Of States (States/eV)

6

-14 -14

R

X Z M

-14

Fig. 3 Spin-polarized electronic band structure and total density of states (TDOS) of NdGaO3 cubic perovskite compound at its equilibrium lattice parameters, using GGA-PBE approximation

J Supercond Nov Magn

ENd, EGa, and EO are the atomic energies of separable Nd, Ga, and O atoms, respectively. The calculated Ef values of the cubic NdGaO3 compound in both paramagnetic and ferromagnetic phases are about − 1.994 Ry and − 2.130 Ry, respectively; therefore, the negative sign affirms the allowing stability of this compound.

3.2 Electronic Properties 3.2.1 Electronic Band Structures

3.2.2 Electronic Density of States The electronic density of states is a tool for describing the electronic structure and the bonding of materials in detail. The TDOS curves of the equilibrium cubic NdGaO3 compound is shown in Fig. 3(b), where it is a direct projection of electronic structure; also, it translates the perfect halfmetallic behavior that has been confirmed earlier by the electronic structure analysis. The spin-polarized partial density of states (PDOS) of the cubic NdGaO3 system is also predicted at their equilibrium lattice parameters of ferromagnetic state by employing the GGA-PBE parameterization; the illustration is presented in Fig. 4; we can see a large exchange splitting between majority-spin and minority-spin states around the Fermi level (EF); the 4f-Nd states of the two majority-spin and minorityspin states are full-filled, whereas the 2p-O states are partialfilled in both majority-spin and minority-spin directions. Furthermore, the energy range from − 4.50 to − 0.50 eV is mainly occupied by 2p-O electrons for both spin-up and spindown channels with a feeble participation of 4d-Nd and 3d-Ga electrons; the states of majority-spin case which cut the Fermi level are belonging to 4f-Nd electrons, while their corresponding minority-spin states are completely located in the region between + 2 and + 3 eV, where these 4f-Nd states are important to understand the ferromagnetism, because their curves in DOS are responsible for the producing of the half-metallic character. Thus, the majority-spin and minority-spin states between + 4 and + 6 eV arise from 4d-Nd electrons. NdGaO3 with GGA approximation

4

EF

3

Nd-Tot Ga-Tot O-Tot

2 1 0 -1 -2 -3 -4 -6

-5

-4

-3

-2

-1

4

Partial Density Of States (States/eV)

Fig. 4 Spin-dependent partial density of states (PDOS) of the equilibrium NdGaO3 cubic perovskite compound, by employing GGA-PBE parameterization

Partial Density Of States (States/eV)

The spin-polarized electronic structure (band structures and density of states) of NdGaO3 cubic compound is determined at their equilibrium lattice parameters by using the GGA-PBE scheme; the computed results of band structures and the depended total density of states (TDOS) are together depicted in Fig. 3. The (a) and (c) panels of Fig. 3 show respectively spin-polarized (spin-up and spin-down channels) electronic band structures of NdGaO3 cubic compound along the high symmetry directions in the first Brillouin zone; we can observe from these illustrations that the majority-spin (spin-up) case is electronically metal, this phenomenon is due to the overlapping between valence and conduction energy bands at the Fermi level (EF), while the minority-spin (spin-down) case has a semiconductor behavior, because EF is spotted within the band gap that is created in this electronic spin channel; therefore, both behaviors of spin-up and spin-down states for the cubic NdGaO3 compound confirm its complete halfmetallic character. The half-metallic gap (EHM) is defined as the minimum between the lowest energy of majority-spin and minority-spin conduction bands with respect to the Fermi level, and the absolute values of the highest energy of majorityspin and minority-spin valence bands [37, 38]. The predicted

values of half-metallic gap (EHM) and spin-down gap (Eg) for NdGaO3 cubic compound are about 2.653 eV and 1.921 eV, respectively.

0

Energy (eV)

1

2

EF

3

3

4

5

6

4

5

6

Nd (4d) Nd (4f) Ga (4p) Ga (3d) O (2s) O (2p)

2 1 0 -1 -2 -3 -4 -6

-5

-4

-3

-2

-1

0

Energy (eV)

1

2

3

J Supercond Nov Magn Table 2 Calculated total magnetic moments (MTot in μB), magnetic moments in the interstitial zone, and local magnetic moments of each site in ferromagnetic NdGaO3 cubic perovskite compound obtained by GGA-PBE approximation Compound

NdGaO3

Magnetic moment (μB) Nd

Ga

O

Interstitial

Total

3.0489

0.0015

− 0.0408

0.0741

3.0021

The Δ( f ) spin-exchange splitting of the effective 4f-Nd states is defined as an energical discard between the corresponding majority-spin and minority-spin peaks; the corresponding Δ( f ) value of the cubic perovskite NdGaO3 compound is found about + 2.37 eV.

3.3 Magnetic Properties The total magnetic moment (MTot), interstitial magnetic moment, and atomic magnetic moments of each site of the cubic perovskite NdGaO3 compound were computed by using the GGA-PBE framework; the obtained results of these entities are collected in Table 2. The MTot value of the cubic NdGaO3 compound is very close to 3 μB, confirming the half-metallic ferromagnetic character which is consistent with the integer value of MTot (3 μB). In the other hand, the total magnetic moment (MTot) is strongly originated from the Nd site, where the weak hybridization between 3d-Ga and 2p-O states (see Fig. 4) is responsible for the bringing of little local magnetic moments on the non-magnetic Ga and O sites. Moreover, the atomic magnetic moments of Nd and O sites are in opposite sign, indicating that the valence band spins of Nd and O atoms interact in anti-ferromagnetic manner. So, we conclude from both electronic and magnetic studies that the cubic perovskite of NdGaO3 compound is half-metallic ferromagnetic material.

4 Conclusions In this approach, we have studied the structural and the magneto-electronic properties of the cubic perovskite NdGaO3 compound by applying the ab initio method of FPL/APW+lo within the framework of GGA-PBE scheme; the main results are summarized according to the following points: i. The investigations on the structural properties of NdGaO3 cubic compound demonstrate that its ferromagnetic phase is energetically more favorable than the non-magnetic (paramagnetic) phase. ii. Through this prediction, the obtained values of the equilibrium structural parameters for the cubic NdGaO3 compound are given for the first time.

iii. The spin-polarized electronic analyses of the cubic perovskite NdGaO3 compound prove its half-metallic feature at their equilibrium lattice parameters. iv. The total magnetic moment of the cubic NdGaO3 compound is found in integral value which confirms the halfmetallic character. v. The Nd site contributes mostly the total magnetic moment of this studied compound. vi. In all these investigations, we conclude that the cubic perovskite NdGaO3 compound is classified in the row of half-metallic ferromagnetic materials. Furthermore, the electronic and magnetic properties of the cubic NdGaO3 compound are performed only by using the GGA approximation because the goal of proving the halfmetallic property is now accomplished. For further researches on this axis, it is necessary to improve the magneto-electronic properties of the cubic NdGaO3 compound by the DFT+U (LDA+U or GGA+U) approximations because the Nd element presents important correlations due to its f orbitals. Acknowledgements The author Mohammed El Amine Monir acknowledges the help of Professor Hadj Baltach from the Mustapha Stambouli University of Mascara and the help of Professor Fouad El Haj Hassan from the Lebanese University of Beirut. Funding information This work is supported by the Mustapha Stambouli University of Mascara-Algeria and Lebanese University of El-Hadath, Beirut, Lebanon.

References 1.

Wolf, S.A., Awschalom, D.D., Buhrman, R.A., Daughton, J.M., von Molnar, S., Roukes, M.L., Chtchelkanova, A.Y., Treger, D.M.: Spintronics: a spin-based electronics vision for the future. Science. 294, 1488–1495 (2001) 2. de Groot, R.A., Mueller, F.M., van Engen, P.G., Buschow, K.H.J.: New class of materials: half-metallic ferromagnets. Phys. Rev. Lett. 50, 2024–2027 (1983) 3. Soulen Jr., R.J., Byers, J.M., Osofsky, M.S., Nadgorny, B., Ambrose, T., Barry, A., Coey, J.M.D.: Measuring the spin polarization of a metal with a superconducting point contact. Science. 282, 85–88 (1998) 4. Park, J.H., Vescovo, E., Kim, H.-J., Kwon, C., Ramesh, R., Venkatesan, T.: Direct evidence for a half-metallic ferromagnet. Nature (Lond). 392, 794–796 (1998) 5. Kobayashi, K.L., Kimura, T., Sawada, H., Terakuraand, K., Tokura, Y.: Room-temperature magnetoresistance in an oxide material with an ordered double-perovskite structure. Nature. 395, 677–680 (1998) 6. Jedema, F.J., Filip, A.T., Wees, B.V.: Electrical spin injection and accumulation at room temperature in an all-metal mesoscopic spin valve. Nature. 410, 345–348 (2001) 7. Lewis, S.P., Allen, P.B., Sasaki, T.: Band structure and transport properties ofCrO2. Phys. Rev. B. 55, 10253–10260 (1997) 8. Jungwirth, T., Sinova, J., Mašek, J., Kučera, J., MacDonald, A.H.: Theory of ferromagnetic (III,Mn)V semiconductors. Rev. Mod. Phys. 78, 809–864 (2006)

J Supercond Nov Magn 9.

10. 11.

12.

13. 14.

15. 16. 17. 18. 19.

20. 21. 22. 23. 24. 25.

Shi, L.-J., Liu, B.-G.: Half-metallic ferromagnetism in hexagonalMAl7N8and cubicMAl3N4(M=Crand Mn) from first principles. Phys. Rev. B. 76, 115201 (2007) Zhao, Y.-H., Xie, W.-H., Zhu, L.-F., Liu, B.-G.: J. Phys.: Condens. Matter. 18, 10259 (2006) Xie, W.-H., Liu, B.-G.: Half-metallic ferromagnetism in ternary transition-metal compounds based on ZnTe and CdTe semiconductors. J. Appl. Phys. 96, 3559–3561 (2004) Liu, Y., Liu, B.-G.: First-principles study of half-metallic ferromagnetism and structural stability of CrxZn1−xTe. J. Phys. D. Appl. Phys. 40, 6791–6796 (2007) Giebultowicz, T.M., et al.: Phys. Rev. B. 48, 12817 (1993) Saito, H., Zayets, V., Yamagata, S., Ando, K.: Room-temperature ferromagnetism in a II-VI diluted magnetic semiconductorZn1 −xCrxTe. Phys. Rev. Lett. 90, 207202 (2003) Sreenivasan, M.G., Bi, J.F., Teo, K.L., Liew, T.: J. Appl. Phys. 103, 043908 (2008) Galanakis, I.: Phys. Rev. B. 71, 012413 (2005) Wurmehl, S., Fecher, G.H., Kandpal, H.C., Ksenofontov, V., Felser, C., Ji Lin, H.: Appl. Phys. Lett. 88, 032503 (2006) Mart, W., Fischer, P., Altorfer, F., Scheel, H.J., Tadin, M.: J. Phys.: Condens. Matter. 6, 127–135 (1994) Reshak, A.H., Piasecki, M., Auluck, S., Kityk, I.V., Khenata, R., Andriyevsky, B., Cobet, C., Esser, N., Majchrowski, A., Swirkowicz, M., Diduszko, R., Szyrski, W.: Effect of U on the electronic properties of neodymium gallate (NdGaO3): theoretical and experimental studies. J. Phys. Chem. B. 113, 15237–15242 (2009) Wong, K.M., Alay-e-Abbas, S.M., Shaukat, A., Fang, Y., Lei, Y.: J. Appl. Phys. 113, 014304 (2013) Wong, K.M., Alay-e-Abbas, S.M., Fang, Y., Shaukat, A., Lei, Y.: J. Appl. Phys. 114, 034901 (2013) Hohenberg, P., Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964) Blaha, P., Schwarz, K., Sorantin, P., Trickey, S.K.: Comput. Phys. Commun. 59, 339 (1990) Perdew, J.P., Burke, S., Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996) Galasso, F.S.: Perovskites and High Tc Superconductors. Gordon and Breach, New York (1990)

26.

Wang, Z.L., Kang, Z.C.: Functional and smart materials: structural evolution and structure analysis. Plenum Press, New York (1998) 27. Chen, H.C.: Crystal Chemistry. Shandong Education Press, Jinan (1985) (In Chinese) 28. Geller, S., Wood, E.A.: Crystallographic studies of perovskite-like compounds. I. Rare earth orthoferrites and YFeO3, YCrO3, YAlO3. Acta Cryst. 9, 563–568 (1956) 29. Geller, S.: Crystallographic studies of perovskite-like compounds. IV. Rare earth scandates, vanadites, galliates, orthochromites. Acta Cryst. 10, 243–248 (1957) 30. Murnaghan, F.D.: The compressibility of media under extreme pressures. Proc. Natl. Acad. Sci. U. S. A. 30, 244–247 (1944) 31. Shang, S.L., Wang, Y., Kim, D., Liu, Z.-K.: First-principles thermodynamics from phonon and Debye model: application to Ni and Ni3Al. Comput. Mater. Sci. 47, 1040–1048 (2010) 32. Wang, J., Zhou, Y.: Dependence of elastic stiffness on electronic band structure of nanolaminateM2AlC(M=Ti,V,Nb, andCr) ceramics. Phys. Rev. B. 69(21), 214111 (2004) 33. Chen, G., Wang, X.Q., Fu, K., Rong, X., Hashimoto, H., Zhang, B.S., Xu, F.J., Tang, N., Yoshikawa, A., Ge, W.K., Shen, B.: Multibands photoconductive response in AlGaN/GaN multiple quantum wells. Appl. Phys. Lett. 104(17), 172108 (2014) 34. Gunnarsson, O., Andersen, O.K., Jepsen, O., Zaanen, J.: Densityfunctional calculation of the parameters in the Anderson model: Application to Mn in CdTe. Phys. Rev. B. 39, 1708–1722 (1989) 35. Zeng, Z.H., Calle-Vallejo, F., Mogensen, M.B., Rossmeisl, J.: Generalized trends in the formation energies of perovskite oxides. Phys. Chem. Chem. Phys. 15, 7526 (2013) 36. Rai, D.P., Shankar, A., Sandeep, Ghimire, M.P., Khenata, R., Thapa, R.K.: Study of the enhanced electronic and thermoelectric (TE) properties of ZrxHf1−x−yTayNiSn: a first principles study. RSC Adv. 5, 95353–95359 (2015) 37. Yao, K.L., Gao, G.Y., Liu, Z.L., Zhu, L.: Half-metallic ferromagnetism of zinc-blende CrS and CrP: a first-principles pseudopotential study. Solid State Commun. 133, 301–304 (2005) 38. Gao, G.Y., Yao, K.L., Sasioglu, E., Sandratskii, L.M., Liu, Z.L., Jiang, J.L.: Half-metallic ferromagnetism in zinc-blendeCaC,SrC, andBaCfrom first principles. Phys. Rev. B. 75, 174442 (2007)