The role of the Mn, Fe and La dopants on magnetic properties and electronic structures of strontium titanate quinary compounds

Net magnetic moment (NM) per unit cell, spin magnetic moment (SM) of Mn atom and energy difference ( D E) between the FM and SG states with Curie temperature (T C ) of (Sr 1-y La y )(Ti [r]

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Original Article

The role of the Mn, Fe and La dopants on magnetic properties and electronic structures of strontium titanate quinary compounds M.J Sadiquea, M Shahjahana,b,*

aDepartment of Physics, University of Dhaka, Dhaka 1000, Bangladesh

bSchool of Advanced Materials Science and Engineering, Sungkyunkwan University, Suwon 16419, Republic of Korea

a r t i c l e i n f o

Article history: Received 23 May 2018 Received in revised form August 2018 Accepted August 2018 Available online 28 August 2018 Keywords:

Quinary compounds KKR-CPA

Curie temperature Density of states Strontium titanate Band shifting

a b s t r a c t

Magnetic properties and electronic structures of the quinary compounds (Sr1yLay)(Ti0.90D0.10)O3have

been calculated using the Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) method, where y represents La concentration (y¼ 0e0.15) and D indicates the magnetic cations (Mn, Fe) The stability of the magnetic states changes in the opposite manner for the (La, Mn) and (La, Fe) pairs doped into the strontium titanate The Sr(Ti0.90Fe0.10)O3(y¼ 0) shows stable ferromagnetic (FM) state with a

high Curie temperature (TC) and a large magnetic moment (MM), whereas the spin glass (SG) state is

found for Sr(Ti0.90Mn0.10)O3(y¼ 0) A variation of the magnetic properties of (Sr1-yLay)(Ti0.90Fe0.10)O3

(SLTFO) and (Sr1-yLay)(Ti0.90Mn0.10)O3(SLTMO) is found for different La concentrations The TCand MM

for SLTFO decrease with increasing La concentration Interestingly, SLTMO compounds exhibit a phase transition from SG to FM states upon introducing La at the Sr site The density of states (DOS) for La concentrations (y¼ 0.01, 0.05, 0.10, and 0.15) in SLTFO and SLTMO are calculated to understand the mechanism of the FM stability The bands shaping and shifting are found in the DOS of SLTFO and SLTMO around the Fermi level The band manipulations are explained in terms of the orbital hybridization and exchange mechanisms

© 2018 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

1 Introduction

Spintronics is an attractingﬁeld of current research, where the spin degrees of freedom are exploited along with the electronic charge for microelectronic applications[1] Spintronic devices carry information encoded in their spin states They utilize semi-conductors with the ferromagnetic (FM) property, which are familiar as dilute magnetic semiconductors (DMS)[2] A promising DMS can be formed by doping suitable transition metals (TM) into a hosting semiconductor material The induced magnetic properties and the interaction between the electrons in the valence and the conduction bands affect the positions of the energy band and the band-gap in DMS[3] The growth technology of DMS is quite so-phisticated and the magnetic properties mainly depend on the impurity concentrations of the properly grown multicomponent compounds

Currently, oxide perovskites have drawn much attention pref-erably for their fascinating properties of multifunctional applica-tions Among the oxides, strontium titanate SrTiO3 (STO) is an

excellent substrate for epitaxial growth of thin ﬁlms At room temperature (RT), STO is a non-magnetic semiconductor with a model ABO3type perovskite structure, here A and B indicate the Sr

and Ti cation sites, respectively The STO semiconductor is changed into a magnetic material by introducing TM atoms at either of the cation sites Numerical design of the STO-based FM semiconductors is challenging with the suitable control doping of magnetic ions

Recently, Kim et al have studied the magnetic and magneto-optical properties and found a high Faraday rotation with low optical loss for 40% Fe doping at the Ti site of STOﬁlms[4] Egilmez group has measured the magnetic properties of LaySr1-yTi0.9

Fe0.1O3-d ﬁlms for compositions y ¼ 0, 0.2, 0.5, and 0.7, which exhibit RT ferromagnetism with magnetic moments ranging from 0.7mB=Fe to 0.2mB=Fe[5] The variant pattern of magnetic moments

per Fe atom and TCagree well with their measured values Zhang's

team has reported the magnetic and electrical properties of (Mn, La) Co-doped STO thinﬁlms and observed FM behavior at RT for magnetic coupling between the induced electrons and the Mn 3d spins[6] Modak and Ghosh have explained the role of La and Ru

* Corresponding author Department of Physics, University of Dhaka, Dhaka 1000, Bangladesh

E-mail address:mjahan@du.ac.bd(M Shahjahan)

Peer review under responsibility of Vietnam National University, Hanoi

Contents lists available atScienceDirect

Journal of Science: Advanced Materials and Devices j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / j s a m d

https://doi.org/10.1016/j.jsamd.2018.08.001

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codoped at STO for enhanced hydrogen evolution using the band structure calculations[7] Again, Jiang-Ni group has investigated the electronic structures and optical properties of La-doped STO, where they found broadened optical band gaps for the La substi-tution[8] Besides, Guo group has argued that the band structure of Nb doping at the Ti site of STO exhibits metallic behavior for 12.5% Nb concentration[9] An extensive spectroscopic analysis has been carried out by Higuchi et al on the electronic structures of STO with 2% Sc or Nb doping at the Ti site, where the band gap was found to increase by increasing the dopant concentrations [10] Further-more, Matsushima group has analyzed the electronic structures of pure and La-doped STO using X-ray photoemission spectroscopy and reported the improvement of electrical conductivity by La doping[11] Yahyaoui and Diep have investigated the magnetic properties of (La0.56Ce0.14)Sr0.30MnO3using Monte Carlo simulation

and found a very sharp FM-paramagnetic transition at 357 K[12] In addition, Berri group has performed theﬁrst-principle calculations of the structural, electronic and magnetic properties of CeMnO3and

found half-metallic FM ground state in the GGAỵ U treatment[13] In this article, magnetic properties and electronic structures of the quinary compounds (Sr1-yLay)(Ti0.90D0.10)O3 are investigated

using the Korringa-Kohn-Rostoker (KKR)-Green's function method, where D indicates the TM atoms (Mn, Fe) and y repre-sents the fractional concentration of La atom We focus on the substitution of the two cation sites (Sr and Ti) of STO with metallic ions The Curie temperature (TC) is estimated using the

meanﬁeld approximation (MFA) In our previous paper[14], Mn doped STO was found instable in the FM state We have been motivated to search for its stability in the FM phase by tuning concentrations or by some suitable double doping approaches Therefore, substitution of La at the Sr site and Mn at the Ti site as (Sr1-yLay)(Ti0.90Mn0.10)O3(SLTMO) shows a phase transition from

the spin glass (SG) to the FM states, where La concentrations are taken in the range y¼ 0.01e0.15 By contrast, 10% Fe substitution at the Ti site of STO exhibits a stable FM state, whereas inclusion of La at the Sr site and Fe at the Ti site as (Sr1-yLay)(Ti0.90Fe0.10)O3

(SLTFO) shows a variation of the magnetic moments and TCwith

the La concentrations The net magnetic moment (NM) and TC

decrease with the increase of La concentrations in SLTFO To un-derstand the effect of La and the magnetic ions in the STO-based DMS, the density of states (DOS) are calculated for different La concentrations Total and component DOS exhibit the induced magnetic properties of SLTFO and SLTMO by varying La concen-trations The shaping and shifting of the energy bands occur due to the orbital hybridization in SLTFO and SLTMO The magnetic properties of the quinary compounds are calculated and the role of dopants on magnetic states is discussed

The article is organized in the following way: in section2, the computational details are described brieﬂy The magnetic phase

stability, NM, spin magnetic moment (SM), TC, total and component

DOS of perovskite STO type DMS are presented and the underlying mechanisms are explained in section3 Graphical presentations of the calculated results are also shown and discussed in this section The results are brieﬂy summarized in section4

2 Computational details

Electronic structures and magnetic properties of the quinary compounds (Sr1-yLay)(Ti0.90D0.10)O3(D¼ Mn, Fe) have been

calcu-lated using the KKR-coherent potential approximation (CPA) method[15e19] In the CPA scheme, one can simulate arbitrary the concentrations of impurities at any constituent sites of the host semiconductor [20] The CPA is the procedure of averaging over random impurity configurations in terms of the coherent t-matrix of the muffin-tin potential, which describes the average atom The generalized gradient approximation (GGA) is used to estimate the exchange correlation (XC) energy functional of the inhomogenous systems[21,22] In the GGA, the XC energy functional is approxi-mated as a function of the electron density and the gradient of the electron density of inhomogenous systems, where the electron density changes rapidly The muffin-tin (MT) potential approxi-mation is used to describe the shape of the potential, which as-sumes that the potential is spherically symmetric inside the atomic spheres and constant in the interstitial areas of many body systems The MT potentials are restricted by the condition that they may not overlap each other, but there is no restriction on the depth of the potential The scalar relativistic approximation was used to account the relativistic effects of the calculation

At RT, pure STO crystallizes into the cubic perovskite structure of the space group Pm-3m (group number 221)[23] The experi-mental indirect band gap of STO is 3.25 eV and the direct one is 3.75 eV[24] We use the lattice constant a¼ 0.3905 nm for the numerical calculations [25] The unit cell of the perovskite STO with the schematic substitution of La and D atoms are shown in Fig 1(a) Calculated total and partial DOS of Sr d, Ti d, and O p states of the basic STO semiconductor are shown inFig 1(b) The band gap, as an evidence of a semiconductor, was found around the Fermi level, which is set at zero Ry energy Although, the basic material is a non magnetic semiconductor, we have performed spin polarized calculations and plotted DOS exhibiting up spin and down spin states as identical (see Fig 1(b)) The local lattice distortion was ignored in the dilute limit of impurity concentra-tions (y¼ 0.01e0.15) The experimental lattice constant of the pure STO was used to calculate the electronic structures and magnetic properties of the quinary compounds In the calculation, the assigned angular momenta to identify the spherical harmonics were considered up to l¼ for the electronic wave functions The Brillouin zone integration was carried out with 286 k sampling

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points of the ﬁrst Brillouin zone The calculations were imple-mented by KKR-CPA program package“Machikaneyama” devel-oped by Akai[26]

3 Results and discussion

In the perspective of electron-spin polarization, the effect of dopants on magnetic properties and electronic structures of (Sr1-yLay)(Ti0.90D0.10)O3(D¼ Mn, Fe) was investigated for a range of

La concentrations y¼ 0e0.15

We calculated the fascinating properties of the quinary DMS such as, NM per unit cell, SM per magnetic ions, DOS and the Fermi energies of the compounds The compound (Sr1-yLay)ðTi0:90D[0:10Þ

O3indicates the FM conﬁguration, where up arrow denotes the spin

in a particular orientation with nonzero net magnetization On the other hand, the compound (Sr1-yLay)ðTi0:90D[0:05DY0:05ÞO3seems a

good choice to consider as SG conﬁguration, where the bidirectional arrows denote the random orientation of spins with zero net magnetization There is a controversy of using the term SG state in the literature In this article, the SG phase is simply meant a simu-lating paramagnetic phase, where the net moment is zero by cancelling of local moments in the spin disordered system In order to design the DMS materials, total energies (TE) per unit cell for FM and SG states were calculated and the stability of magnetic state was ﬁxed out from the lower energy state Then, the energy deference (DE) between FM and SG states was calculated as

DE¼ TESGeTEFM Subsequently, T

C is estimated using DE in the

framework of MFA The expression,kBTC¼3z2DE was used to

esti-mate TC in the present calculation, wherekB is the Boltzmann

constant and zẳ (y ỵ 0.10) is the total concentration of dopants[27] The NM per unit cell, SM per atom,DE in mRy, and estimated TC

in Kelvin are tabulated inTable 1andTable 2for SLTMO and SLTFO, respectively The positiveDE indicates the stable FM state, whereas negativeDE denotes the relatively lower energy case of the SG state The SLTMO (y¼ 0) exhibits lower energy situation in the SG state, whereas the SLTFO (y¼ 0) shows a stable FM state with TChigher

than RT Interestingly, when the Sr site of SLTMO was doped with La, a change in phase was found from SG to FM states The SM per Mn atom is ascending with the increasing of La concentrations, whereas NM per unit cell gradually rises to a top value and then slowly decreases in SLTMO compounds On the other hand, in SLTFO compounds, NM per cell spans from 0.384ðmB=cellÞ to 0.056

ðmB=cellÞ for the speciﬁc concentrations y ¼ 0e0.15, as shown in

Table At y¼ 0, the largest numerical value of NM, SM, and TCwas

found The calculated magnetic properties over the two cases oppositely rise or lower (fall) with La concentrations The (La, Mn) based systems (see Table 1) might have a disadvantage for the conventional electronics, because of their low operational TC Very

recently, Yahyaoui et al have reported the magnetic properties due to the Ti substitution with Mn in the compounds La0.7Sr0.3Mn

1-xTixO3 (x ¼ 0.1, 0.2, 0.25) and analyzed the effect of

nearest-neighbor interactions in the FM ordering [28] The calculated magnetic moments concur well with their reported values

The La dependence of TCand NM per unit cell in the quinary

compounds SLTMO and SLTFO are shown inFig 2(aed), respec-tively The tiny solid squares indicate the data points and the con-necting line indicates the overall trend of the TCand moments In

SLTMO compounds, TCand NM are rising at low concentrations,

peaked at around 7% and onwards decreasing with the La con-centrations, as shown inFig 2(a, c), respectively On the contrary, Fig 2(b, d) indicates that in the SLTFO compounds, TC and NM

gradually decrease and it seems that the FM behavior will be ceased at some higher La concentrations In the Mn doped cases, NM and TCslowly decrease due to the weakening of the double-exchange

mechanism Beyond 7% La concentration, super exchange mecha-nism dominates over double exchange mechamecha-nism Additional electrons are introduced to the system by substituting Sr with La Therefore, at concentrations of over 7% La, NM and TC slowly

decrease through the disappearing of ferromagnetism in (La, Mn) doped STO due to the dominating super-exchange mechanism[29] In order to elucidate the origin of magnetism, electronic struc-tures of the quinary compounds SLTMO and SLTFO were calculated The physical origin is the mixed valence magnetism between the orbitals as well as the p-d orbital hybridization, which dominate the main electronic properties of the system As a result, the system becomes stable in the FM state and hence produces magnetic moments The La doping enhances the spin band coupling and shifting towards the lower energy state and therefore stabilizes the FM state The total DOS per unit cell and local DOS of Mn and La d states in the SLTMO compounds are shown inFig 3(aed) The variation of DOS is found for 10% Mn and different La concentra-tions of y¼ 0.01, 0.05, 0.10, and 0.15 The DOS data show impurity bands around the Fermi level in both spin directions The partial spin polarization at the Fermi level indicates the FM situation and produces NM The spin band changes signiﬁcantly around the Fermi level for the varying concentrations of La The SG state previously shown of SLTMO (y¼ 0) changes into the stable FM state even for a low doping concentration of La at the Sr site[14] Noticeable band shifting is seen in the DOS of the majority and minority spin states The La3ỵions fully act as electron donors in the compound system [8] Clearly, the spin polarization at the Fermi level is increasing with the rising of the electron density due to the La substitution The domination of La 5d states induces delocalized electrons near the Fermi level Therefore, the delocalized electrons can be exited to the conduction band (CB) as free carriers for electrical conduction by the thermal ionization or carrier diffusion[8]

The total and component DOS of SLTFO for various La concen-trations y¼ 0.01, 0.05, 0.10, and 0.15 are shown inFig 4(aed), respectively The spin polarized DOS are found at the Fermi level for the compounds The plotted DOS explore a band shifting around

Table

Net magnetic moment (NM) per unit cell, spin magnetic moment (SM) of Mn atom and energy difference (DE) between the FM and SG states with Curie temperature (TC) of (Sr1-yLay)(Ti0.90Mn0.10)O3 compounds with a range of La concentrations

yẳ 0e0.15

La conc NMmB=cellị SMmB=Mnị DE (mRy) Tcalc:C (K)

y¼ 0.302 2.786 0.029 e y¼ 0.01 0.310 2.834 0.036 34 y¼ 0.03 0.325 2.915 0.156 126 y¼ 0.05 0.338 2.982 0.261 183 y¼ 0.07 0.345 3.029 0.349 216 y¼ 0.10 0.332 3.031 0.409 215 y¼ 0.13 0.325 3.033 0.435 199 y¼ 0.15 0.323 3.036 0.441 186

Table

Net magnetic moment (NM) per unit cell, spin magnetic moment (SM) of Fe atom and energy difference (DE) between the FM and SG states with Curie temperature (TC) of (Sr1-yLay)(Ti0.90Fe0.10)O3 compounds with a range of La concentrations

yẳ 0e0.15

La conc NMmB=cellị SMmB=Feị DE (mRy) Tcalc:C (K)

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the Fermi level as well as the La 5d states modify the electronic structures of the SLTFO compounds The Fe 3d states (sharp peak) are responsible for the ferromagnetism in the SLTFO compounds, whereas the La impurity attempts to slowly diminish the FM sta-bility[29] The DOS of the Fe 3d states are shifted oppositely in both spin directions for the band coupling with the La 5d states How-ever, the introduction of n-type carriers (La atom) into the SLTFO

shifts the Fermi level towards the conduction band CB, which is a good agreement with previously reported results[8,30] Therefore, the rigid band shifting at the Fermi level is ensured by the electron doping At the same time, the SLTFO compounds show half metallic behavior for 5%, 10%, and 15% La impurity concentrations The half metallicity in the SLTFO type of DMS can be manifested signi ﬁ-cantly by n-type carrier doping at Sr site

Fig Curie temperature TCin Kelvin (K) of (a) Mn, (b) Fe doped STO and net magnetic moment (NM) in Bohr magneton of (c) Mn, and (d) Fe doped STO as a function of the La

concentrations

Fig Total density of states per unit cell (red solid line) of (Sr1-yLay)(Ti0.90Mn0.10)O3compounds for different La concentrations at (a) y¼ 0.01, (b) y ¼ 0.05, (c) y ¼ 0.10, and

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4 Conclusion

The electronic structures and magnetic properties of the pro-posed quinary compounds SLTMO and SLTFO type DMS are re-ported by ab-initio calculations Estimated TC was obtained by

tuning the controlled doping at the Sr and Ti sites The signiﬁcance of tunable La doping has been found to play a reverse role of La in the SLTMO and SLTFO compounds The SLTMO (y¼ 0) exhibits an SG state, whereas the FM stability is found in SLTMO compounds with La concentrations y¼ 0.01e0.15 The low TCof 216 K and a

high NM of 0.345 mB=cell were found for 7% y concentration in

SLTMO On the other hand, high TCof 382 K and NM of 0.384mB=cell

have been found in SLTFO (y¼ 0) with slowly decreasing trend of TC

and NM at higher y concentrations The magnetic properties are induced by incorporating Mn and Fe at the Ti site and are manip-ulated by the La doping The plotted DOS data reveal the band shifting in both the compounds around the Fermi level The carrier induced FM behavior is hindered due to excess amount of La doping Moreover, FM half metallicity has been found for 5%, 10%, and 15% La concentrations at the Sr site of SLTFO The fully spin polarized results offer the possibility to magnetically store infor-mation for spintronic applications, where spins are the key con-trolling factor

Acknowledgments

The authors are thankful to the authority of the center for advanced research in sciences (CARS), University of Dhaka, Dhaka 1000 for providing advanced computing facilities to perform the numerical computation

References

[1] S.A Wolf, D.D Awschalom, R.A Buhrman, J.M Daughton, S von Molnar,

M.L Roukes, A.Y Chtchelkanova, D.M Treger, Spintronics: a spin-based electronics vision for the future, Science 294 (2001) 1488e1495

[2] H Ohno, Making nonmagnetic semiconductors ferromagnetic, Science 281 (1998) 951e956

[3] H.-F Lin, W.-M Lau, J Zhao, Magnetism in the p-type monolayer IIeVI semiconductors SrS and SrSe, Sci Rep (2017) 45869e45878

[4] H.-S Kim, L Bi, G.F Dionne, C.A Ross, Magnetic and magneto-optical prop-erties of Fe-doped SrTiO3ﬁlms, Appl Phys Lett 93 (2008) 0925061e0925063

[5] M Egilmez, G.W Leung, A.M.H.R Hakimi, M.G Blamire, Origin of magnetism in La and Fe doped SrTiO3-dﬁlms, J Appl Phys 108 (2010) 1239121e1239126

[6] S.Y Zhang, Y.H Lin, C.W Nan, R Zhao, J He, Magnetic and electrical properties of (Mn, La) codoped SrTiO3thinﬁlms, J Am Ceram Soc 91 (2008) 3263e3266

[7] B Modak, S.K Ghosh, Exploring the role of La codoping beyond charge compensation for enhanced hydrogen evolution by RhSrTiO3, J Phys Chem B 119 (2015) 11089e11098

[8] Y.J Ni, Z.Z.- Yong, Y.J.- Feng, Z Wu, Electronic structure and optical properties of La-doped SrTiO3and Sr2TiO4by density function theory, Chin Phys Lett 26 (2009) 0171071e0171074

[9] X.G Gou, X.S Chen, Y.L Sun, W Lu, Electronic band structure of Nb doped SrTiO3fromﬁrst principles calculation, Phys Lett A 317 (2003) 501e506

[10] T Higuchi, T Tsukamoto, N Sata, M Ishigame, Y Tezuka, S Shin, Electronic structure of p-type SrTiO3by photoemission spectroscopy, Phys Rev B 57 (1998) 6978

[11] S Matsushima, S Kohiki, M Oku, Effect of La doping on the electronic structure of SrTiO3, J Ceram Soc Jpn 108 (2000) 518e520

[12] S Yahyaoui, H.T Diep, Magnetic properties of (La0.56Ce0.14)Sr0.30MnO3 perovskite, Phys Lett A 380 (2016) 3212e3216

[13] S Berri, D Maouche, M Ibrir, B Bakri, Electronic structure and magnetic properties of the perovskite cerium manganese oxide from ab initio calcula-tions, Mater Sci Semicond Process 26 (2014) 199e204

[14] M Shahjahan, M.J Sadique, Stable dilute magnetic semiconductor and Curie temperature of 3d transition metal doped strontium titanate perovskite ma-terial, Comput Condens Matter 14 (2018) 89e93

[15] J Korringa, On the calculation of the energy of a bloch wave in a metal, Physica 13 (1947) 392e400

[16] W Kohn, N Rostoker, Solution of the Schr€odinger equation in periodic lattices

with an application to metallic lithium, Phys Rev 94 (1954) 1111e1120 [17] M Schr€oter, H Ebert, H Akai, P Entel, E Hoffmann, G.G Reddy,

First-prin-ciples investigations of atomic disorder effects on magnetic and structural instabilities in transition-metal alloys, Phys Rev B 52 (1995) 188e209 [18] H Akai, Fast Korringa-Kohn-Rostoker coherent potential approximation and its

application to FCC Ni-Fe systems, J Phys Condens Matter (1989) 8045e8064 [19] N Papanikolaou, R Zeller, P.H Dederichs, Conceptual improvements of the

KKR method, J Phys Condens Matter 14 (2002) 2799e2824

[20] H Shiba, A reformulation of the coherent potential approximation and its applications, Prog Theor Phys 46 (1971) 77e94

[21] J.P Perdew, K Burke, M Ernzerhof, Generalized gradient approximation made simple, Phys Rev Lett 77 (1996) 3865e3868

Fig Total density of states per unit cell (red solid line) of (Sr1-yLay)(Ti0.90Fe0.10)O3compounds for different La concentrations at (a) y¼ 0.01, (b) y ¼ 0.05, (c) y ¼ 0.10, and

(6)

[22] J.P Perdew, K Burke, Y Wang, Generalized gradient approximation for the exchange-correlation hole of a many-electron system, Phys Rev B 54 (1996) 16533e16539

[23] R.W.G Wyckoff, Crystal Structures, second ed., John Wiley, New York, 1963, p

[24] K van Benthem, C Els€asser, R.H French, Bulk electronic structure of SrTiO3: experiment and theory, J Appl Phys 90 (2001) 6156e6164

[25] A.S Verma, V.K Jindala, Lattice constant of cubic perovskites, J Alloy Comp 485 (2009) 514e518

[26] H Akai,<http://kkr.issp.u-tokyo.ac.jp/>

[27] M Shahjahan, M Toyoda, T Oguchi, Ferromagnetic half metallicity in doped chalcopyrite semiconductors Cu(Al1-xAx)Se2(A¼ 3d transition-metal atoms), J Phys Soc Jpn 83 (2014) 094702e094706

[28] S Yahyaoui, S Kallel, H.T Diep, Magnetic properties of perovskites La0.7Sr0.3Mn0.74ỵMn0.3-x2ỵ TixO3: Monte Carlo simulation versus experiments, J Magn Magn Mater 416 (2016) 441e448

[29] K Sato, L Bergqvist, J Kudrnovský, P.H Dederichs, O Eriksson, I Turek, B Sanyal, G Bouzerar, H Katayama-Yoshida, V.A Dinh, T Fukushima, H Kizaki, R Zeller, First-principles theory of dilute magnetic semiconductors, Rev Mod Phys 82 (2010) 1633e1690