Ab Initio Investigation of Structural, Electronic, and ...

Journal of Superconductivity and Novel Magnetism https://doi.org/10.1007/s10948-018-4731-7

ORIGINAL PAPER

Ab Initio Investigation of Structural, Electronic, and Magnetic Properties of Cr-Doped ZnS and ZnSe in Wurtzite Structure O. Cheref1 · M. Merabet1,2 · S. Benalia1,2 · N. Bettaher1 · D. Rached1 · L. Djoudi1,2 Received: 24 March 2018 / Accepted: 9 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018

Abstract Using the first-principles calculations with the full potential linear muffin–tin orbital (FP-LMTO) method, we investigated the structural, electronic, and magnetic properties of Zn1−x Crx (S,Se)-diluted magnetic semiconductors (DMSs) in wurtzite structures with varying concentrations (x = 0.0625, x = 0.125, and x = 0.25) of Cr. The electronic properties indicated that Zn1−x Crx (S,Se), in all concentrations, exhibited half-metallic ferromagnetic (HMF) behavior with spin polarization of 100%. The density of states showed a hybridization between the p(S, Se) and 3d(Cr) states, which created an antibonding state in the gap that stabilized the ferromagnetic ground state linked to the double-exchange mechanism. Therefore, these compounds are highly likely candidates for spintronic applications. Keywords DMS · Electronic properties · Magnetic properties · Spintronics

1 Introduction Currently, one of the major challenges is to develop the microelectronic properties of semiconductors [1, 2] so that the electronic properties can be strongly coupled with the magnetic properties, which would allow for the gathering or alternation of the effects of charge and spin at the same time [3]. This would not only improve performance and add new functionalities to existing devices but also revolutionize electronics and radically change the behavior of the technology in a way that could handle both the transport and storage of information through a single brick element. The recent demonstration of ferromagnetism in diluted magnetic semiconductors (DMSs) has shown that DMSs are a source of spin that is compatible with existing semiconductor technology. They have also attracted much attention as

D. Rached

[email protected] 1

Laboratoire des Matériaux Magnétiques, Faculté des Sciences, Université Djillali Liabès de Sidi-Bel-Abbès, 22000 Sidi Bel Abbès, Algeria

2

Département de Physique, Institue des Sciences et des Technologies, Centre Universitaire de Tissemsilt, 3800 Tissemsilt, Algeria

materials for spintronic applications [4–9] because of their half-metallic ferromagnetic (HMF) behavior at Curie temperatures higher than room temperature [10, 11, 13]. As a result, this material family has led to the discovery of a new generation of high-speed, high-power, and low-energy non-volatile devices [14]. These can be used to develop the transmission and storage of data and fuse the electronics and magnetism into unique technologies for multifunctional devices that exhibit varied and complicated physical phenomena [6, 9, 15]. DMSs from the materials encompassing standard semiconductors, in which a fraction of host atoms are substituted by such elements, produce localized magnetic moments in the semiconductor matrix. The exchange interactions induced by the localized magnetic moment generate a strong spindependent coupling between the band and the localized states, which leads to the remarkable properties of DMSs and gives an order of antiferromagnetic or ferromagnetic spin [16–19]. Several works show that various properties of DMSs can be controlled and modified using doping, either in their semiconductor character, which can be varied between n- or p-type, or in their semi-metallic character by varying the concentration of magnetic dopants, as illustrated in the works of Sun et al. [20–25]. Although the concentration ranges are, in some cases, very limited, the same compound can be used in a large number of applications.

J Supercond Nov Magn

More recently, the development of DMS-based II–VI materials shows magnificent properties, which have a great potential to be used in spintronics [6, 17, 26]. Otherwise, previous works have confirmed that Cr impurities in II–VI compounds produce FM materials, even at room temperature [27–35]. The promising ferromagnetic properties of II–VI DMS types containing Cr were experimentally verified for numerous highly Cr-doped bulk crystals, such as ZnCrSe [32, 35], ZnCrS [33], ZnCrTe [36], and CdCrS [37], even theoretically for Cdx Cr1−x (S, Se, Te) [38] and Znx Cr1−x (S, Se, Te) [39]. Moreover, Cr-doped ZnS is an interesting material that potentially can be used for various spintronic [40, 41] and optoelectronic [42] applications; likewise, it is proposed as an intermediate band (IB) material by ab initio calculations [43] to be used in intermediate band solar cells (IBSCs) [44]. Nowadays, to improve the technology, it is also possible to develop top quality crystals containing a small amount of Cr [14, 15]; for that, we study the structural, electronic, and magnetic properties of Zn1−x Crx S(Se) by varying the chromium concentration for the values x = 0.25, x = 0.125, and x = 0.0625 in the wurtzite phase using the first-principles method calculation “full potential linear muffin–tin orbital” (FP-LMTO).

using the parameterization of Perdew–Wang version [55]. LSDA is a generalization of the local density approximation for magnetic systems where a polarization of the spins is taken into account. The ground-state properties are linked to the population difference of the up and down spin levels. In order to achieve energy eigenvalues convergence, the charge density and potential inside the MTSs are represented by spherical harmonics up to Imax = 6. The self-consistent calculations are considered to be converged when the total energy of the system is stable at 10−6 Ry. The k integration over the Brillouin zone is performed using the tetrahedron method [56]. To avoid the overlap of atomic spheres, the MTS radii for each atomic position are taken differently for each composition. We point out that the use of the full-potential calculation ensures that the calculation is not completely independent of the choice of sphere’s radii. The values of the sphere’s radii (MTSs), the number of plane waves (NPLW), and the plane-wave cutoff (Ecut ), used in our calculation, are summarized in Table 1.

3 Results and Discussion 3.1 Structural Properties

2 Calculation Methodology The calculations in this study are performed based on the density functional theory (DFT) [45, 46], which is a universal quantum mechanical approach for many body problems of electron and nucleus interactions. These problems can be mapped into a system of one-electron equations, also known as Kohn–Sham equations [47, 48]. To solve those equations in order to calculate the structural, electronic, and magnetic properties of Znx Cr1−x (S,Se) alloys, we have employed the FP-LMTO method [49] with atomic plane-wave basis (PLW) representation [50], using the computer code LmtArt. In the FP-LMTO method, the crystalline space is divided into non-overlapping muffin– tin spheres (MTSs), centered at the atomic sites, and an interstitial region (IR). In the IR, the basis set is composed of plane waves where there functions are Hankel functions [50–52]. Inside the MTSs, the basic sets are described by numerical radial solutions of Schrodinger equation for one particle (at fixed energy), and their energy derivatives are multiplied by spherical harmonics [50, 53]. The key point of this method is that the potential inside MTSs (r ≤ RMT ) is assumed to be spherically symmetrically close to the ion core, while in the IR (r > RMT ), it is assumed to be constant, where RMT is the radius of the MTSs and r is the position. The exchange-correlation energy is described in the local spin density approximation (LSDA) technique [54], by

Hexagonal ZnS and ZnSe are the prototype of the wurtzite crystalline structure, which are referred in the Strukturbericht designation by B4 and in the Pearson by hP4. There corresponding space group is No. 186 (in the International Union of Crystallography classification) and P63mc (in Hermann–Mauguin notation). The wurtzite crystalline structure is built up from two interpenetrating hexagonal compact hcp lattices for each atomic species; whereabouts, zinc atoms are occupying the special position 2(b) with coordinates 1/3, 2/3, 0 and 2/3, 1/3, 1/2, and sulfur or selenium atoms are also occupying the special position 2(b) with coordinates 1/3, 2/3, u and 2/3, 1/3, u + 1/2, where u is the dimensionless internal parameter that represents the distance between Zn plane and its nearest-neighbor S(Se) plane, in the unit of c. In addition, a thorough literature search has failed to reveal a precisely determined value for u, and it is often taken to have the ideal value √ 3/8 in the case when the ratio c/a is equivalent to 8/3 [57]. The geometric models for DMS Zn1−x Crx (S,Se) are constructed by replacing S(Se) atoms of wurtzite Zn(S,Se) with transition Cr atoms. For each fraction (x) of Zn1−x Crx (S,Se) composition, a Cr-doped model was developed from unit cell expansion in the direction of a-, b-, and c-axes, resulting from 6.25, 12.5, and 25% Cr doping (Fig. 1, Table 2). The determination of the structural properties is a very important step to know more information on the properties

J Supercond Nov Magn Table 1 Parameters used in the calculations: the number of plane wave (NPW), the energy cutoff (in Rydberg), and the muffin–tin radius (RMT in atomic units) Compound

Concentration

Zn1−x Crx S

0.0625

Zn1−x Crx Se

0.125 0.25 0.0625 0.125 0.25

NPLW (total)

117,028 8 57,296 57,116 117,160 0 57,164 56,840

of the materials to study. To determine the structural groundstate properties of wurtzite Zn1−x Crx (S,Se), we performed a self-consistent calculation of the total energy in terms of three variables: the lattice constant a, the ratio c/a, and the internal parameter u, in a way to calculate the lattice constant a, at ideal values of the ratio c/a, and the internal √ parameter u (such that ideal u = 3/8 and ideal c/a = 8/3). Then, we optimize the ratio c/a at aop and ideal u. After that, we determine u using the ratio (c/a)op and aop . Finally, and for accuracy, we use the optimized values, meaning the lattice constant aop , the internal parameter uop , and the ratio (c/a)op , for recalculating the equilibrium internal parameter u, the ratio c/a, and the lattice constant a of equilibrium cell. The equilibrium lattice constant a, bulk modulus B, and its pressure derivative (B of Zn1−x Crx (S,Se) supercells) are optimized by an adjustment of the total energy obtained

Ecut (Ry)

MTS (u.a.) Zn

S

Se

Cr

140.94351

2.128

2.211

–

2.150

37.1892 134.9912 127.5770

2.142 2.156 2.193

2.221 2.227 –

– – 2.371

2.164 2.178 2.216

124.9163 123.6363

2.198 2.204

– –

2.372 2.370

2.221 2.228

in terms of cell volume (Etotal (V)) using the fitting Birch’s equation of state [58]. However, the ratio c/a and the internal parameter u are optimized by an adjustment of their total energies obtained in terms of c/a and u (Etotal (c/a) and Etotal (u)) using a polynomial fitting. The results for the different structural parameters are grouped in Table 3. The computed lattice constants a = 7163 u.a. of ZnS and a = 7501 u.a. of ZnSe and their c/a ratio stayed in good agreement with experimental ones [59, 62], and they are very close to theoretical values [60, 63]. For the Zn1−x Crx (S,Se), we observed that the lattice constants are directly proportional to the concentration of Cr-doped atoms in a manner that when the Cr concentration is increased, the lattice constants increased evenly, due to the smaller atomic radii of Zn compared to the Cr atom. For x = 0.25, the lattice constant computed and the c/a ratio of Zn1−x Crx S is very close to the theoretical value obtained by the same LDA-PW approximation with the FP-LAPW method [65]. The comparison was not possible for all ternary alloys due to a lack of data in the literature. We can clearly see from Table 3 that the calculated bulk modulus of Zn1−x Crx S and Zn1−x Crx Se alloys increases with the increasing of Cr concentrations, which suggests the same increasing for the compressibility of each compound. These compounds became harder when the Cr concentrations increase. It represents bond strengthening or weakening effects induced by changing the composition [66].

Table 2 Description of the unit cells used for simulating the Cr doping on ZnS and ZnSe materials

Fig. 1 Crystal structure of wurtzite Zn1−x Crx S and Zn1−x Crx Se. a, b The side views of a 2 × 2 × 1 supercell with 0.25 and 0.125 of Cr concentrations, respectively. c The side view of a 2 × 2 × 2 supercell with 0.0625 of Cr concentration

Concentration (x)

Supercell

Number of atoms

Cr-doping atom

0.0625 0.125 0.25

2×2×2 2×2×1 2×2×1

32 16 16

1 1 2

J Supercond Nov Magn ˚ ratio c/a, internal parameter u, bulk modulus B (GPa), and pressure derivative of bulk modulus B for Table 3 Calculated lattice constant a0 (A), Zn1−x Crx (S,Se) at different concentrations (x) Compound

Concentration (x)

a (u.a.)

c/a

u

B (GPa)

B

Zn1−x Crx S

0

7.163 7.214a 7.353b 7.179 7.202 7.233 7.191d 7.501 7.542e 7.542f 7.512 7.523 7.54

1.636 1.638a 1.59b 1.639 1.641 1.645 1.651d 1.64 1.659e 1.659f 1.642 1.644 1.649

0.3839 0.374c

81.6 74.0b 76.4b 82.83 83.72 85.46

3.85

3.72 3.82 4.12

0.3836 0.371g

69.87

3.81

0.3832 0.3827 0.3819

70.26 71.84 73.2

3.52 3.38 3.86

0.0625 0.125 0.25 Zn1−x Crx Se

0

0.0625 0.125 0.25 a Ref

0.3838 0.3835 0.3831

[58], b Ref [59], c Ref [60], d Ref [64], e Ref [61], f Ref [62], g Ref [63]

For the ratio c/a and the internal parameter u, we saw that the first is proportional with the Cr concentrations, and this is due to the large atomic radii of the Cr compared to the Zn; however, the second is inversely proportional with the Cr concentrations, which go well with the linear approximation relationship between the value of u and the c/a ratio in materials with wurtzite structure [57].

Fig. 2 Spin-polarized band structures and total DOS of majority spin (up) and minority spin (down) for Zn0.9375 Cr0.0625 S. The Fermi level is set to zero (horizontal dotted line)

3.2 Electronic Properties 3.2.1 Band Structure with Half-Metallic Gap The spin-polarized band structures along high-symmetry directions and the total densities of states (DOS) of Zn1−x Crx (S,Se) alloys at concentrations x = 0.0625,

J Supercond Nov Magn Fig. 3 Spin-polarized band structures and total DOS of majority spin (up) and minority spin (down) forZn0.875 Cr0.125 S. The Fermi level is set to zero (horizontal dotted line)

x = 0.125, and x = 0.25 are illustrated in Figs. 2, 3, 4, 5, 6, and 7, respectively. They illustrate that the majorityspin band has a semi-metallic nature due to the top of valence band cutting the Fermi level with an existence of a gap between the valence and the conduction bands, Fig. 4 Spin-polarized band structures and total DOS of majority spin (up) and minority spin (down) for Zn0.75 Cr0.25 S. The Fermi level is set to zero (horizontal dotted line)

which clearly decreases as a function of concentration tends towards metallicity. This explains the influence of the doping element Cr. By contrast, the minority-spin bands clarify a band gap in the vicinity of the Fermi level, which is a semiconductor in nature. Consequently, these compounds

J Supercond Nov Magn Fig. 5 Spin-polarized band structures and total DOS of majority spin (up) and minority spin (down) for Zn0.9375 Cr0.0625 Se. The Fermi level is set to zero (horizontal dotted line)

have a half-metallic ferromagnetic behavior. The band structures in Figs. 2, 3, 4, 5, 6, and 7 show that majority-spin bands are more numerous than the minority-spin bands, due to the p-d exchange interaction. This gives the half-metallic ferromagnetic band gaps (Eg ) and half-metallic gaps (GHM ) Fig. 6 Spin-polarized band structures and total DOS of majority spin (up) and minority spin (down) forZn0.875 Cr0.125 Se. The Fermi level is set to zero (horizontal dotted line)

in the minority-spin bands [12, 67, 68]. The calculations of Eg (eV) and GHM (eV) for minority-spin channels are given in Table 4. From Figs. 2, 3, 4, 5, 6, and 7, it is observed that the minority-spin channels have a direct band gap for all

J Supercond Nov Magn Fig. 7 Spin-polarized band structures and total DOS of majority spin (up) and minority spin (down) for Zn0.75 Cr0.25 Se. The Fermi level is set to zero (horizontal dotted line)

compounds because the energy gaps (Eg ) are situated at the point of the Brillouin zone. Their values are 2.39, 2.54, and 2.49 eV for Zn1−x Crx S compounds and 1.42, 1.66, and 1.99 eV for Zn1−x Crx Se compounds at concentrations x = 0.0625, x = 0.125, and x = 0.25, respectively. Again, the energy gaps (Eg ) are decreased for the same concentration from Zn1−x Crx S to Zn1−x Crx Se. For all alloys, the minority-spin band has a HM gap situated between the minimum of the conduction band and the Fermi level (0 eV), which describes the smallest energy (gap) of a spin excitation for generating an electron in the conduction bands [69]. The HM gaps are 0.98, 0.92, and 0.60 eV for Zn1−x Crx S compounds and 0.33, 0.36, and 0.44 eV for Zn1−x Crx Se compounds at concentrations x = 0.0625, x = 0.125, and x = 0.25, respectively. Furthermore, the HM gaps (GHM ) are increased for the same concentration from Zn1−x Crx Se to Zn1−x Crx S. The

Table 4 Calculated halfmetallic ferromagnetic band gap (Eg ) and half-metallic gap (GHM ) of minority-spin bands for Zn1−x Crx (S,Se) at different concentrations (x)

large HM gap has been given to all compounds (terrific halfmetallic ferromagnets) and makes them potential candidates for practical spintronic applications. 3.2.2 Density of States To understand the origin of the spin-polarized concept of the DOS in Figs. 2, 3, 4, 5, 6, and 7, we analyzed their partial DOS for all alloys as shown in Figs. 8, 9, 10, 11, 12, and 13. They presented a similar behavior for all alloys with spin polarization of 100% at the Fermi level. Also, they illustrate that the valence band in the range −6 to −1.7 eV usually comes from the p(S, Se) and 3d(Cr) states, with small contributions of 4s(Zn) states, and being close to the Fermi level, the DOS originates from 3d(Cr) states. Otherwise, the degenerated atomic levels of 3d(Cr) were divided into triply degenerated t2g (dxy , dxz , and dyz ) states

Compound

Concentration (x)

Eg (eV)

GHM (eV)

Zn1−x Crx S

0.0625 0.125 0.25 0.0625 0.125 0.25

2.39 2.54 2.49 1.42 1.66 1.99

0.98 0.92 0.60 0.33 0.36 0.44

Zn1−x Crx Se


Fig. 8 Spin-polarized partial DOS of Zn0.9375 Cr0.0625 S. The Fermi level is set to zero (vertical dotted line)



Fig. 11 Spin-polarized partial DOS of Zn0.9375 Cr0.0625 Se. The Fermi level is set to zero (vertical dotted line)



J Supercond Nov Magn Table 5 Calculated total and local magnetic moments per Cr atom (in Bohr magneton, μB ) within the muffin–tin spheres and in the interstitial sites for Zn1−x Crx (S,Se) at different concentrations (x)

Compound

Concentration (x)

M (μB )

Zn (μB )

Cr (μB )

Interstitial (μB )

Total (μB )

Zn1−x Crx S

0.0625 0.125 0.25 0.0625 0.125 0.25

0.0554 0.0536 0.0445 −0.0199 −0.0269 −0.0658

0.0853 0.0819 0.1368 0.0845 0.0824 0.1392

3.1520 3.1799 3.2447 3.2732 3.2954 3.3293

0.6932 0.6763 1.3131 0.6501 0.6444 1.2563

3.9860 3.9821 7.9840 3.9827 3.9937 7.9395

Zn1−x Crx Se

and doubly degenerated eg (dz2 and dx2 –2y ) states. This division generates from the crystal field of surrounding (S, Se) ligands [70]. In addition, Zn site is substituted by Cr, and two of the six Cr valence electrons replace two Zn electrons. As for the rest four electrons, two have occupied the doubly degenerated eg states and two have occupied the triply degenerated t2g states. The triply degenerated states are filled up to two thirds. Consequently, the 3d(Cr) majorityspin states cutting the Fermi level are partially filled, while the minority-spin states possess a large band gap at the Fermi level. So, the partially filled majority-spin t2g states suggest that the system is a half-metallic ferromagnet. As also shown in Figs. 8, 9, 10, 11, 12, and 13, the top of valence bands of majority spin is principally formed by the strong hybridizations between 3d(Cr) and p(S, Se) band carriers of host semiconductors. This engenders some bands in the host valence bands: the bonding (tb ) states and the non-bonding (e) states in the valence bands, and the antibonding states (ta ) in the band gap. The antibonding states stabilize the ferromagnetic ground state linked to a double-exchange mechanism and confirm that our alloys are predicted to be promising candidates for possible future semiconductor spintronic applications. [10, 71–74].

3.3 Magnetic Properties 3.3.1 Magnetic Moments The calculated total and local magnetic moments of the muffin–tin spheres of Zn, S, Se, and Cr atoms, and of the interstitial sites for all alloys, are listed in Table 5. The

Table 6 Calculated conduction and valence band-edge spin-splitting Ec Ec and Ev Ev and exchange constants N0 αN0 α and N0 βN0 β for Zn1−x Crx (S,Se) at different concentrations (x)

half-metallic feature of these compounds is coherent with the integral value of magnetic moment of the unit cell. From Figs. 8, 9, 10, 11, 12, and 13, we observe that splitting of the DOS is mainly produced by 3d(Cr) and p(S, Se) states, which provides the main magnetic moment. Moreover, for the majority-spin states, there is a strong p-d hybridization between p(S, Se) and 3d(Cr) states in the gap at the top of valence band. Because of this p-d hybridization, the local magnetic moment of Cr decreases from its free space charge value and creates small local magnetic moments on the non-magnetic Zn, S, and Se sites. Alternatively, the pd hybridization minimizes the total energy and stabilizes the ferromagnetic order configuration. The total magnetic moments in all compounds usually come from the Cr site. The negative signs of the magnetic moments of Se atoms revealed the antiferromagnetic interaction between valence band and 3d(Cr) spins, while the ferromagnetic interaction has been known by the positive signs which appeared between Zn, S, and 3d(Cr) magnetic spins. 3.3.2 Exchange Coupling The half-metallic ferromagnetic band structures are used to calculate two essential characteristics that explain the magnetic properties of DMSs: the s-d exchange constant N0 α (conduction band) and the p-d exchange constant N0 β (valence band), where N0 denotes the concentration of cations. Also, the intrinsic vacancies may play some part here. These characteristics indicate precisely how the valence and conduction bands are affected in the exchange and splitting process. The fundamental idea comes from

Compound

Concentration (x)

Ec Ec (eV)

Ev Ev (eV)

N0 αN0 α

N0 βN0 β

Zn1−x Crx S

0.0625 0.125 0.25 0.0625 0.125 0.25

0.0235 0.0528 −0.2114 0.0192 0.0434 −0.1759

−1.6037 −1.8866 −2.4176 −1.3284 −1.6062 −1.9962

0.1886 0.2121 −0.2119 0.1545 0.1737 −0.1772

−12.8750 −7.5805 −2.4224 −10.6731 −6.4351 −2.0115

v Zn1−x Crx Se


mean field theory which is based on the Hamiltonian (H ) given by [75, 76] H = −N0 βs · S where β is the p-d exchange integral, and s and S are the hole spin and Cr spin, respectively. The exchange constants are defined directly by Ec N0 α = xS Ev N0 β = xS ↓ ↑ where Ec = Ec − Ec is the conduction band-edge spin ↓ ↑ splitting, Ev = Ev − Ev is the valence band-edge spin splitting at the symmetry point, (x) is the concentration of Cr, and S is half of the calculated magnetization per Cr ion [76, 77]. The calculated exchange constants N0 α and N0 β for all alloys are listed in Table 6. It indicates that at all concentrations of Cr, the exchange N0 β constants are negative, while the N0 α constants are positive at x = 0.125 and x = 0.0625, and they are negative at x = 0.25. The exchange interaction between the Cr spins and the electron carriers of conduction bands is explained by the N0 α constants, while the N0 β constants describe the exchange interaction between the Cr spins and the holes of valence bands. The negative and positive signs refer to the antiparallel and parallel spins, respectively. So, in the compounds where x = 0.125 and x = 0.0625, the exchange coupling between Cr impurity and the conduction band is ferromagnetic. This confirms the magnetic behavior of the compounds under study.

4 Conclusion This manuscript presents a theoretical investigations of structural, electronic, and magnetic properties of Zn1−x Crx (S,Se) DMSs in wurtzite structure, with concentrations x = 0.0625, x = 0.125, and x = 0.25 of Cr impurities, in its ordered supercells of 32, 16, and 16 atoms, respectively, employing the first-principles calculations with the FP-LMTO method. The different results obtained are summarized in the following points: –

–

–

Based on the optimized geometric structures, the lattice constants and bulk modulus of all ternary Zn1−x Crx (S,Se) alloys are correlated proportionally with increasing Cr concentration. The electronic structures have proved that all alloys possess a half-metallic ferromagnetic behavior with spin polarization of 100% at the Fermi level. All compounds having large HM gap in their electronic structures appear to be leading candidates as

–

–

half-metallic ferromagnetism materials for spintronic applications. The magnetic behavior is proven by the ferromagnetic p-d exchange coupling, where p-d hybridization in all alloys reduces the total magnetic moment of Cr atom from its free space value and induces small local magnetic moments on the non-magnetic (S, Se) sites. The p-d hybridization generates the antibonding states in the gap, which stabilize the ferromagnetic ground state linked to double-exchange mechanism, and confirms that our alloys are predicted to be promising candidates for possible future semiconductor spintronic applications.

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