The electronic, half-metallic, and magnetic properties of Ca1-xCrxS ternary alloys: Insights from the first-principle calculations

The electronic, half-metallic, and magnetic properties of Ca1-xCrxS ternary alloys: Insights from the first-principle calculations

Accepted Manuscript The electronic, half-metallic, and magnetic properties of Ca1-xCrxS ternary alloys: Insights from the first-principle calculations...

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Accepted Manuscript The electronic, half-metallic, and magnetic properties of Ca1-xCrxS ternary alloys: Insights from the first-principle calculations Mohammed M. Obeid, Hamad Rahman Jappor, Shaker J. Edrees, Majid M. Shukur, Rabah Khenata, Y. Mogulkoc PII:

S1093-3263(19)30015-4

DOI:

https://doi.org/10.1016/j.jmgm.2019.02.004

Reference:

JMG 7320

To appear in:

Journal of Molecular Graphics and Modelling

Received Date: 7 January 2019 Revised Date:

5 February 2019

Accepted Date: 6 February 2019

Please cite this article as: M.M. Obeid, H.R. Jappor, S.J. Edrees, M.M. Shukur, R. Khenata, Y. Mogulkoc, The electronic, half-metallic, and magnetic properties of Ca1-xCrxS ternary alloys: Insights from the first-principle calculations, Journal of Molecular Graphics and Modelling (2019), doi: https:// doi.org/10.1016/j.jmgm.2019.02.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.

Graphical Abstract

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ACCEPTED MANUSCRIPT The Electronic, Half-Metallic, and Magnetic Properties of Ca1-xCrxS Ternary Alloys: Insights from the First-Principle Calculations Mohammed M. Obeida,*, Hamad Rahman Japporb, Shaker J. Edreesa, Majid M. Shukura, Rabah Khenatac, Y. Mogulkocd Department of Non-metallic Materials, College of Materials Engineering, University of Babylon, Hilla, Iraq b

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a

Department of Physics, College of Education for Pure Sciences, University of Babylon, Hilla, Iraq c

Laboratoire de Physique Quantique, de La Matie`re et de La Modélisation Mathématique (LPQ3M), Université de Mascara, Mascara, 29000, Algeria

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Department of Physics Engineering, Faculty of Engineering, Ankara University, 06100, Ankara, Turkey

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Keywords: DFT; electronic structure; HMF; structural properties; magnetic materials Abstract

The electronic, structural, and magnetic characteristics of Cr atom substituting Ca

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atom in rocksalt CaS have been investigated within the formalism of (GGA+PBE) and PBE with Hubbard correction (GGA+U). Our findings point out that the ternary alloys are dynamically stable depending on the obtained results of elastic constants.

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For structural properties, it is clear that the lattice constants decrease and bulk modulus increases with increasing concentration of chromium impurity. Interestingly, the perceived total magnetic moments increase with the Cr concentration and reaches

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the maximum for Ca0.25Cr0.75S, which is mainly composed of Cr atoms. Besides, it is found from PBE and PBE+U calculations that the Cr-substituted CaS gives halfmetallic ferromagnetism (HMF). Finally, the deduced results of minority-spin bands demonstrate a half-metallic ferromagnetic gap and half-metallic (HM) gap. The predicted results confirmed that Ca1-xCrxS could be considered as a promising candidate material for spintronics applications.

*Corresponding author. Tel: +9647812307281 E-mail address: [email protected] (Mohammed. M. Obeid) 1

ACCEPTED MANUSCRIPT 1. Introduction Spintronics is a newly advanced branch of microelectronics, that utilizes the spin of charge carriers in the developing field of favorable crystalline solids for spinbased multiuse devices [1]. Diluted magnetic semiconductors (DMSs) are basically related to spin transport electrons technology owing to the high Curie temperatures [2]

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besides, the ferromagnetic half-metallic behavior [3]. These materials act as semiconductors with respect to the spin of electrons in the first spin direction and similar to metals in the spin of the opposite direction [3,4].

To discover the magnetic features and utilizing these properties in spintronics

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applications, the DMSs relied on II-VI and III-V groups substituted with 3d metals were exhaustively investigated in several theoretical [5-9] and experimental [10-13]

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studies. Among the members of the group II-VI alkaline earth sulfides, calcium sulfide (CaS) is extensively studied to be an excellent phosphor host solid [14]. CaS crystalizes in the cubic crystal structure at ambient conditions with space group Fm 3 m (no. 225) [15]. CaS can be doped with numerous activators, such as lanthanide ions Bi3+, Ce3+, Sm3+, Eu2+ [16-19], and transition metals Ag and Pb [20]. These activators are able to create an assortment of large bandgap semiconductors to

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improve the luminescence features. Recently, the half-metallic ferromagnetism has been found in, Cr doped rocksalt SrX (X=S, Se, Te) [2], Sr1-x(Mn, Cr)xO alloys [4], Cr2+ doped MgO [21], Cr-substituted BaTe [3], Sn1-xMnxTe [22], and C-substituted alkaline-earth chalcogenides [23]. More importantly, the ferromagnetic behaviors

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have been confirmed experimentally in the Fe2+ doped CaS nanoparticles [14,24]. Despite the aforementioned efforts, the investigations on Cr based wide bandgap

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semiconductors for spintronics applications are limited. Thus, this study important not only to cover the lack of information for these materials but also to improve our understanding of their essential characteristics. Nowadays, the density functional theory (DFT) derived from first principle

calculations represents a powerful tool for examining the structural, optical, magnetic and electronic properties of crystalline solids at the atomic level [25]. In the present study, the first-principles calculations have been executed to see the effect of stable Cr3+ substitution on the structural, magnetic, and electronic properties for rocksalt CaS structure. Therefore, introducing of Cr3+ to the lattice of CaS is expected to enhance the properties of the material since trivalent Cr is magnetic material where 2

ACCEPTED MANUSCRIPT the charge and spin might be coupled together to improve them substantially. We anticipate that our study will embolden more experimental and theoretical efforts. The results revealed that Ca1-xCrxS (x = 0.25, 0.5, 0.75) are half-metallic ferromagnets and they are potential candidates for spintronics uses.

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2. Computational details The ab-initio calculations were performed by applying the ultrasoft pseudopotential plane-waves scheme [26] based on DFT as executed in the CASTEP code [27]. The spin-polarized generalized gradient approximation of Wu and Cohen

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(GGA-WC) [28] were employed to estimate the ground state structural properties. This is owing to its improved presentation for structural optimization [3], consequent

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from the fourth-order extension of exchange-correlation efficient [29]. The halfmetallic and magnetic features of the pristine and ternary compounds were assessed by means of the spin GGA within the formalism of Perdew–Burke–Ernzerhof function (PBE) and PBE with Hubbard correction (GGA + U) [30,31]. The value of Hubbard expression U for Cr atoms has been taken as 2.5 eV. The valence electron arrangements were chosen as following; Ca 3s23p64s2, S 3s23p4, and Cr 3s23p63d54s1.

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Moreover, the non-local hybrid Perdew–Burke–Ernzerhof (PBE0) formalism [32] was also employed for the electronic properties to resolve the deficiencies of the common GGA, such as bandgap underestimation. Plane-wave cutoff energy of 400 eV was applied for all the assessments. Brillouin zone integration of 20 irreducible k-points

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was exploited in the Monkhorst-Pack [33] grid scheme for the conventional unit cell of parent and ternary alloys. The convergence benchmarks in the BFGS minimization

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algorithm [34] were fixed as a fine quality with a maximum force of 3×10-2 eV/Å. The self-consistent valuations were anticipated to converge when the total energy of the crystal is stable within 10-6 eV/atom. In the present calculations, a special quasi-random structure methodology [35]

was utilized to model the computational crystal structure. Supercells were built to change the atomic position of the studied alloys. Zunger et al. [35] suggest employing a quasi-random structure technique to reduce the supercell size. This technique can be used to study various properties of alloys [36-38]. With this method, it is feasible to appropriately simulate the statistics of a solid solution in a relatively small supercell. The CaS semiconductor has NaCl crystal form with space group Fm 3 m (no.225), 3

ACCEPTED MANUSCRIPT where Ca, S atomic positions at (0,0,0) and (1/2, 1/2, 1/2), correspondingly, and the experimental lattice constant equal to 5.6836 Å [39]. For x = 0.25 and 0.75, Cr atoms were positioned at the apex and the face-center locations of the rocksalt crystal with space group Pm 3 m (no.221), correspondingly. Regarding x = 0.5, the Cr atoms located at (0, 0, 0) and (1/2, 1/2, 1/2) Wyckoff positions of the unit cell, therefore, the

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space group is distorted to P4/mmm (no. 123).

3. Results and discussion 3.1.

Structural properties

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The ternary compounds Ca1-xCrxS (x = 0.25, 0.5, 0.75) have been prepared by alloying of the parent binary calcium sulfide. The structural properties of the parent and ternary alloys were predicted by fitting the change of total energy versus the unit

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cell volume using Birch-Murnaghan [40] equation of state. The optimized crystal structures of Ca1-xCrxS (x = 0, 0.25, 0.5, 0.75) in the ferromagnetic ordering are illustrated in Fig. 1. The structural properties like lattice parameters (a), bulk modulus (B0), and its pressure derivative (B') were estimated for the pristine and ternary systems using the spin-polarized GGA-WC formalism. The calculated results

Table 1.

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along with other experimental [39,41] and theoretical [42,43] values are given in

From this table, it is clear for CaS that the lattice constant is found to be 5.6409 Å and the bulk modulus is 61.53 GPa. These values are consistent with the values

[39,41]

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experimental

and

better

than

the

available

theoretical results [44-46]. This is owing to the better presentation of GGA-WC

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approximation for structural characteristics with a percentage error of less than 0.8% [3,47]. Furthermore, the lattice constants of ternary Ca1−xCrxS alloys decreases with augmenting x concentration of Cr3+ impurity. This may be ascribed to smaller atomic radii of Cr (1.28 Å) than that of Ca atom (1.97 Å) [48]. Also, it should be related to the large lattice mismatch of the end compounds. Thus, Ca1-xCrxS becomes harder with the increasing Cr3+ amount. The obtained results are in excellent consistent with a similar report [43]. Very recently, Hamidane et al. [43] confirmed the ferromagnetic phase stability of unstable Cr2+ substituted CaS over the paramagnetic and antiferromagnetic phases.

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ACCEPTED MANUSCRIPT From an experimental point of view, if one considered the phase stability, phase segregation might arise even at the low substitution of Cr impurity. This is due to the large differences of ionic radius between Cr and Ca atoms. The high temperature is the most crucial parameter in this aspect. Rocksalt CaS and rhombohedral Cr2S3 alloys may coexist as stable phases at higher x concentration.

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Further, one may take into account the possible formation of toxic H2S or CS2 gases during the synthesis process.

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3.2. Elastic properties

To unravel the mechanical and dynamical demeanor of crystals, the knowledge of elastic constants is extremely substantial [49]. The elastic constants of the ternary

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alloys have been calculated using the method presented in detail in Ref. [50]. Results of the three independent elastic constants, namely C11, C12, and C44 are tabulated in

Table 2. The latter demonstrates that the studied alloys satisfy Born criteria [51]: C44 > 0, C11 ─ C12 > 0, C11 + 2C12 > 0

(1)

Thus, we can validate the mechanical stability of the studied compounds. To date,

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there are no theoretical or experimental studies on the ternary alloys; at x = 0.25, 0.5 and 0.75 for the elastic constants available in the literature to be compared with our obtained results. Hence, our finding can be considered as a reference for future investigations. Furthermore, the computed elastic constants of the pristine CaS are

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consistent with the previous theoretical report [52]. We observe that the calculated bulk modulus values from elastic parameters B0 = (1/3) (C11+ 2C12) closely have the

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equal values as achieved from fits of Birch Murnaghan equation of state (see Table

2). In order to understand the isotropy of crystal, shear anisotropic A plays a key role. For an isotropic solid, A = 2C44/C11─C12 is equal to unity whereas any deviation from unity is a sign of elastic anisotropy. From Table 2, one can observe that the ternary alloys have a degree of elastic anisotropy as values deviate from unity. The deviation indicates that alloys in the growing process might generate structural defects. Another momentous aspect is the internal strain parameter ξ presented by Kleinman [53]. Its value drops between zero and one for minimizing bend bonding and stretching [49]. In the current investigation, bond bending is dominated over bond stretching (perceive Table 2).

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Electronic behavior

The spin-polarized band structures of the ferromagnetic Ca1-xCrxS (x = 0.25, 0.5, 0.75) were estimated based on their optimized lattice constants within the GGA-PBE and GGA-PBE+U schemes. Figs. 2-4 show both spin-up and spin-down electronic

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band structures of the ternary compounds along the directions of high symmetry in the first Brillouin zone. One can observe that the conduction band minimum (CB) and valence band maximum (VB) found at the Γ point. This gives a direct band gap for all ternary compounds. It's obvious from the Figs. 2-4 that the band is symmetric in the

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spin-down channel across the Fermi level. This is due to splitting of Cr atoms 3d degenerate states without distorting the semiconducting behavior of CaS. On the other

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hand, the spin-up channel of ternary compounds exhibits metallic demeanor. Hence, the total contributions of both majority-spin and minority-spin channels show the half-metallic ferromagnetic behavior in these ternary alloys. Besides, the band structures reveal that the spin-up bands are denser than the spin-down bands because of the strong p-d exchange interaction. This generates the half-metallic ferromagnetic gaps (GHMF) and half-metallic gaps (GHM) in the spin-down channel.

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The projected values of the GHMF and GHM values are tabulated in Table 3. The expected values were achieved by applying the spin-polarized GGA-PBE and GGAPBE+U formalisms. The resulted values in Table 3 reveal a nonlinear decrease in

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GHMF and GHM of Ca1-xCrxS with increasing of Cr impurities caused by the topical electric field and local strain generated by Cr atoms [2,54]. What is more, the values of the studied bandgaps with GGA+U formalism have considerably bettered the

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results based on GGA-PBE owing to the fact the U modification perfectly impacts the Cr-3d states. The deduced results of Ca1-xCrxS alloys are comparable with the previous theoretical reports of Sr0.75Cr0.25S [2] and recent published Ca0.75Cr0.25S [43]. Most importantly, it can be noticed that the ternary alloys possess large GHM shapes, this makes the ternary alloys as a promising material for the practical spintronics applications [47,55]. The spin-polarized bandgap structures of the pristine CaS using GGA-WC, GGAPBE and hybrid PBE0 are represented in Fig. 5, which obviously shows the CBM and VBM for the parent system is positioned at Г point. Consequently, CaS is a direct band gap semiconductor. The estimated band gap of CaS along with the available 6

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[56]

and

experimental

[57]

values

are

stated

in

Table

3.

It can be seen from this table that the experimental result of the band gap is 5.8 eV [57]. Hence, for pristine CaS, the PBE0 method gives a band gap (4.70 eV) close to the experimental values in comparison with the calculations of spin-polarized GGAWC and GGA-PBE schemes. Though, it is acknowledged that the conventional PBE

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calculations will underestimate the energy band gap [58-60]. It is worth mention that the spin-up and spin-down bands in pristine CaS are well overlapped indicating the non-magnetic performance of this system as shown in Fig. 5.

To elucidate the nature of the electronic band structure of the Ca1-xCrxS (x = 0.25,

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0.5, 0.75) crystal systems. The partial and total density of states of the ternary systems for spin-down and spin-up channels were projected by means of GGA-PBE and GGA-PBE+U as shown in Figs. 6 and 7, respectively. One can perceive that the spin-

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up and spin-down channels of the substituted systems are asymmetric, pointing out that magnetic moments carried by Cr atoms are ferromagnetically ordered [50,61]. The spin-down channel exhibits a semiconductor character with a wide bandgap whereas the Fermi level (0 eV) passes through the one spin-up peak originating from Cr-3d state hybridized with 3p state of its six adjacent S atoms presenting a metallic

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demeanor. The results confirm the half-metallicity of stable Cr3+ substituted rocksalt CaS system [13,62]. Our findings agree well with the results of recently published Cr2+ substituted CaS half-metallic system reported by Hamidane et al. [43]. It can be noticed from the partial DOS plots that the conduction band consists

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mainly of Ca-d orbitals. The bands between – 6.75 eV and –1.61 eV for GGA-PB and between – 6.61 eV and –1.04 eV for GGA-PBE+U are attributed to 3p states of S

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atoms with contributions of Cr-3d, Ca-3s, and d-orbitals as shown in Fig. 9. Additionally, for majority-spin states, the peak approach the Fermi level is the source of strong hybridization between S-3p and Cr-3d states. This p-d hybridization might create the ferromagnetic ordering in the Ca1-xCrxS (x = 0.25, 0.5, 0.75) alloys. Owing to the Oh crystal field symmetry, the Cr-d orbital of each spin channel is split into doublet eg and triplet t2g for low and high energies, respectively[21]. In the CaS system, the Cr atom loses two electrons after bonding and becomes Cr2+ [63]. The d electrons progressively take the majority spin t2g+, majority spin eg+, and the minority spin t2g- states. The majority spin fragment between –1.2 eV and – 0.2 eV initiates from Cr-t2g states with the minor influence of Cr-eg state. This is responsible for the strong Cr t2g-S p hybridization and weak Cr eg-S p hybridization [64]. 7

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Magnetic Properties The integrated local and total magnetic moments (MTot) of the ternary compounds

are calculated and presented in Table 4 based on the spin-polarized PBE and PBE+U functions. The magnetism in the Ca1-xCrxS alloys is caused by the 3d states of the transition metal (Cr). Based on the Hund’s rule, the presence of unpaired electrons

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produces a total magnetic moment of 4 µB per Cr atom in the Ca1-xCrxS compounds [65]. Obviously, one can identify that the main contributions of total magnetic moments of Ca1-xCrxS alloys (x = 0.25, 0.5, 0.75) systems are initiated from the local magnetic moments of 3d (Cr) ions and due to strong p-d hybridization

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between S-3p and Cr-3d states. Finally, the calculated magnetic moments for the ternary compounds increase by increasing Cr concentration (Fig. 8). This bear out the

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ferromagnetic nature of the abovementioned compounds. The magnetic moments of the Cr atoms are in agreement with the previous theoretical values [2,3,43].

4. Conclusion

In this paper, the structural, electronic and magnetic features of Ca1-xCrxS alloys (x = 0, 0.25, 0.5, 0.75) have been evaluated by means of spin-polarized DFT and DFT with Hubbard correction. The study evaluates the effect of substitution

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concentration on the lattice constant, bulk modulus, elastic constants, shear anisotropy, Kleinman parameter, band gap, and the density of states. The estimated values of elastic constants satisfy the Born criteria at zero pressure and temperature

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and confirm that ternary alloys are mechanically stable. On the other hand, the electronic structure calculations reported here disclosed that the Ca1-xCrxS systems are half-metallic ferromagnets. The total magnetic moments augment with the increase of

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Cr concentration, which is primarily contributed by the Cr atoms. As a result, these compounds are promising spintronic materials.

Acknowledgements

The corresponding author (M. M. Obeid) acknowledges the constant support and engorgement of the college of Materials Engineering/University of Babylon, Iraq.

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Tables Table 1 Calculate lattice constants a0, bulk modulus B and its pressure derivative B' for Ca1-xCrxS at x = 0.25, 0.5 and 0.75 along with available experimental and theoretical data. Bulk modulus B (GPa)

B'

Present Previous Exp.

Present Exp.

Previous

Present

61.53

77.96

5.6409

a

5.637 , b

5.598 , 5.717

g

5.5030

5.53

0.5

5.3570

5.436

5.1861

57

64

5.280

g g



66.67

61



73.38

69



77.84

4.1

77

5.171 4.1

g g g

─ ─ ─

Ref. [46]

c`

Ref. [39]

d

d

g

Ref. [44]

b

e

f

Exp.

4.12

4.2

3.52

4.3

4.00

a

4.2

d

g

4.1

g



g



g



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a

5.689

d

e

0.25

0.75

c

5.6836 ,

Previous

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0.00

Lattice parameters a0 (Å)

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Composition x

Ref. [41]

Ref. [42]

f

Ref. [45]

g

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Ref. [43]

Table 2 Calculated elastic constants Cij (GPa), Kleinman parameter ξ, bulk modulus B0 (GPa) and shear anisotropy A for Ca1-xCrxS B0

33.5a

0.31

61.39

0.58

32.33



0.30

66.71

0.50

C11

Present

Cal.

Present

Cal.

0.00

138.35 122.1a

22.91

23.9a

33.61

0.25

152.09 ─

24.02



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C12

ξ

Composition x

Cal.

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Present

C44

A

0.5

172.16 ─

24.82



31.32



0.29

73.93

0.42

0.75

176.89 ─

28.76



32.82



0.31

78.13

0.44

a

Ref. [52]

ACCEPTED MANUSCRIPT Table 3 Calculated direct band gap for CaS, half-metallic ferromagnetic gap (GHMF), and half-metallic gap (GHM) of minority-spin bands for Ca1-xCrxS at x = 0.25, 0.5 and 0.75 of Cr atoms. Compound

Method

GHMF(eV)

GHM (eV)

Eg (eV)

Behavior

Present

2.15

GGA-PBE

2.38

PBE0

Ca0.5Cr0.5S

Ca0.25Cr0.75S

1.10 (1.390 )

HMF

GGA+U

2.55

0.85

HMF

GGA-PBE

1.73 (2.832 )

GGA+U

2.74

GGA-PBE

Experimental LDA (Γ−Γ), (Γ−X) GGA-PBE (Γ−Γ), (Γ−X)

b

Ref. [56]

EP

Ref. [43]

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c

c

c

0.41(0.870 )

HMF

0.96

HMF

c

c

1.84 (3.045 )

0.18 (0.290 )

HMF

2.69

1.29

HMF

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GGA-WC (Γ−Γ), (Γ−X)

Ref. [57]

c

2.25 (3.122 )

Other calculations

a

c

GGA-PBE

GGA+U

CaS

4.70

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Ca0.75Cr0.25S

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GGA-WC

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CaS

a

5.343 , 5.8 b

3.9 , 1.9

b

b

4.25 , 2.15 b

4.2 , 2.1

a

b

b

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Ca (µB)

Cr (µB)

S (µB)

Total (µB)

Ca0.75Cr0.25S

GGA-PBE GGA+U

-0.01 -0.01

4.34 4.54

-0.0825 -0.1275

4.45469 4.69766

Ca0.5Cr0.5S

GGA-PBE GGA+U

0.00 -0.01

4.27 4.54

-0.13 -0.275

8.59327 9.30538

Ca0.25Cr0.75S

GGA-PBE GGA+U

0.00 -0.01

4.25 4.49

-0.195 -0.3725

12.675 13.6314

0.001 0.007 0.005 0.003 0.02295

3.996 3.821 3.847 3.921 3.7851

-0.261 -0.171 -0.228 -0.224 -0.01933

4 4.002 4.003 4.002 4

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a

Ref. [3]

b

Ref. [2]

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Ref. [43]

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c

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a

Ba0.75Cr0.25Te b Sr0.75Cr0.25S b Sr0.75Cr0.25Se b Sr0.75Cr0.25Te c Ca0.75Cr0.25S

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Alloys

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Fig. 1. The optimized structures of Ca1-xCrxS (x = 0, 0.25, 0.5, 0.75) in the

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ternary systems.

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ferromagnetic ordering. The insets show the crystal structure of the pristine and

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4

4

0

0

-4

-4

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Energy (eV)

Cr S, Spin GGA-PBE 0.75 0.25

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(a) Ca

8

Spin up -8

X

R

M

Γ

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4

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0

M

Γ

R

8

4

-4

Spin down

Spin up

-8

R

R

0

-4

X

X

R

(b) Ca Cr S, Spin GGA-PBE +U 0.75 0.25 8

Energy (eV)

Spin down

M

Γ

-8

R

X

R

M

Γ

R

Fig. 2. Spin-polarized electronic band structure of 0.25 Cr3+ using (a) GGA-PBE and (b) GGA-PBE+U. The horizontal dashed line represents Fermi level.

ACCEPTED MANUSCRIPT Cr0.5S, Spin GGA-PBE

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

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Energy (eV)

0.5

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(b) Ca

8

-6

Spin up

X

(b) Ca

R

Cr S, Spin GGA-PBE +U 0.5 0.5

EP

4

0

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Energy (eV)

Γ

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8

M

R

Spin down

-8

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-8

M

Γ

R

8

4

-4

Spin up

-8

R

R

0

-4

X

X

M

Γ

Spin down

R

-8

X

R

M

Γ

R

Fig. 3. Spin-polarized electronic band structure of 0.5 Cr using (a) GGA-PBE and (b) GGA-PBE+U. The horizontal dashed line denotes Fermi level.

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4

4

0

0

-4

-4

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(a) Ca Cr S, Spin GGA-PBE 0.25 0.75

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Energy (eV)

8

Spin up

X

Γ

M

R

Spin down

-8

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-8

R

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(b) Ca Cr S, Spin GGA-PBE +U 0.25 0.75 8

EP

0

AC C

Energy (eV)

4

Γ

M

R

8

4

-4

Spin down

Spin up

-8

R

R

0

-4

X

X

M

Γ

-8

R

X

R

M

Γ

R

Fig. 4. Spin-polarized electronic band structure of 0.75 Cr using (a) GGA-PBE and (b) GGA-PBE+U. The horizontal dashed line signifies Fermi level.

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Spin up Spin down

GGA-WC -8

X

8

Γ

R

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Energy (eV)

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R

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Energy (eV)

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GGA-PBE -8

X

R

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R

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hybrid PBE0. The horizontal dashed line signifies Fermi level.

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Fig. 6. Spin-dependent total density of states of the equilibrium Ca1-xCrxS alloys at (a) x = 0.25, (b) x = 0.5 and (c) x = 0.75 using GGA-PBE and GGA-PBE+U. The vertical dashed line designates Fermi level.

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Fig. 7. Spin-dependent partial density of states of the equilibrium Ca1-xCrxS alloys at (a) x = 0.25, (b) x = 0.5 and (c) x = 0.75 using GGA-PBE and GGA-PBE+U. The vertical dashed line indicates Fermi level.

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content x using (a) GGA-PBE, and (b) GGA-PBE+U.

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Highlights

 Spin effect theoretical studies on Cr-substituted CaS have been performed.  The Ca1-xCrxS (x = 0.0, 0.25, 0.5, 0.75) compounds are mechanically stable.

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 Structural and electronic band parameters have been calculated and discussed.

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