Half metallic ferromagnetism in (Mn,Cr) codoped ZnS dilute magnetic semiconductor: First principles calculations

Computational Materials Science 101 (2015) 281–286

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Half metallic ferromagnetism in (Mn,Cr) codoped ZnS dilute magnetic semiconductor: First principles calculations S. Fathhoor Rabbani, I.B. Shameem Banu ⇑ Department of Physics, B.S. Abdur Rahman University, Vandalur, Chennai 600048, India

a r t i c l e

i n f o

Article history: Received 29 June 2014 Received in revised form 25 November 2014 Accepted 27 January 2015

Keywords: FP-LAPW + lo Dilute magnetic semiconductors Codoped ZnS Spintronics Ferromagnetism

a b s t r a c t We have investigated the half metallic ferromagnetism in (Mn,Cr) codoped ZnS using first principles calculations. While, Cr doped ZnS (ZnS:Cr) exhibits half-metallic ferromagnetic character, Mn doped ZnS (ZnS:Mn) is not found to be half-metallic. When Cr codoped to ZnS:Mn, it is found to transform into a half-metallic ferromagnetic semiconductor. The effect of occupation of Cr and Mn at two different sites of Zn atoms has brought out conspicuous difference in the band structure and density of states. The positional differences of Cr and Mn give rise to different characteristics, while in one case half-metallic nature is shown, in other case, there is no half-metallic nature. The half-metallic (Mn,Cr) codoped ZnS shows 100% spin polarization. Exchange constants clearly illustrates that all the compounds are in ferromagnetic order and the ferromagnetic coupling is mediated through the direct exchange interaction. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction Half metallic ferromagnets (HMFs) are key ingredients for the future high-performance spintronic devices in which the spin of the electron plays the role of information carrier. Conduction in magnetic materials is due to two types of electron, i.e., electrons with spin up and electrons with spin down. A half-metal is a substance that acts as a conductor to electrons in one spin direction while it acts as an insulator in the opposite spin direction. Dilute magnetic semiconductors (DMSs) have attracted intense interest as they exhibit half-metallic ferromagnetism. DMS materials are alloys of semiconductors in which some cations are substituted by transition metal (TM) ions while the crystal field structure of the host material is maintained. Half-metallic DMS are used for injecting spin polarized carrier into semiconductors and spin valves. The major challenge for commercial applications of these materials is to attain Curie temperature (Tc) at or above room temperature. In this direction, to date, most of the attention on DMSs has been focused on transition metal TM-doped semiconductors, such as GaN and ZnO. Typically, the Curie temperatures of such systems are below room temperature, meaning that they are difficult to use in practice for spintronics applications. Hence, it is important to find magnetic semiconductors which are ferromagnetic at or above room temperature with 100% spin polarization. The possibility of ferromagnetic semiconducting behavior at room ⇑ Corresponding author. E-mail address: [email protected] (I.B.S. Banu). http://dx.doi.org/10.1016/j.commatsci.2015.01.043 0927-0256/Ó 2015 Elsevier B.V. All rights reserved.

temperature introduced by Dietl et al. [1] motivated other researchers to study ferromagnetism above room temperature. The 3d-TMs doped II–VI compound semiconductors with zincblende type have high potential as magneto-optical and semiconductor spintronics materials, because the solubility of the 3d-TMs in II–VI compound semiconductor is extremely higher than that in the III–V compound semiconductors [2–4]. It is, therefore, extremely desirable to explore new half-metallic ferromagnetic materials which are well-suited with significant II–VI semiconductors. Among the most studied II–VI semiconductor host materials, ZnS has a huge band gap (3.7 eV at room temperature). ZnS is one of the great potential materials for device applications. Many experiments have confirmed ZnS as a suitable host semiconductor for obtaining room temperature ferromagnetism with numerous 3d transition-metal ions, such as Cr [5], Mn [6–8], Fe [9,10] and Co [11–13]. Recently, theoretically, McNorton et al. [14] have investigated the electronic structure and magnetic properties of transition metal (TM) doped Zn1xTMxB (B = S, Se, and Te) and showed the half metallic behavior for Cr, Fe, and Ni impurities. There are numerous literature on TM doped ZnO II–VI semiconductor host material for DMS studies both by experiment and theory [15–21] for single doping. Also experimental and theoretical research on dual substitution to ZnO have been reported enormously. [22–24]. However, the investigations on TM doped ZnS are sparse and in particular simultaneous doping of two TMs (dual doping) to ZnS is not reported in the literature theoretically for the magnetic properties to the best of our knowledge. From the literature search, it is found that codoping to ZnS is mostly studied

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trons) and the ionic radius of Mn (0.081 nm) is less than that of Cr (0.087 nm). Since the ionic radius of Zn (0.074 nm) is nearly closer to Cr and Mn, the host lattice accommodates the atom Mn (Cr) in its lattice replacing Zn2+ ion by Mn2+ (Cr2+) ion. The main focus of the present work is to bring out the half metallic character of the Cr and Mn codoped ZnS and to compare with the effects of Cr doped and Mn doped ZnS cases. Effect of position of the two atoms Cr and Mn simultaneously at two Zn sites namely 0, 0, 0 and 0.5, 0, 0 are presented with respect to the magnetic properties. Interchanging their positions have revealed interesting results which have been discussed in detail. For better elucidation and comparison, it is essential to study the cases of singly doped ZnS namely, Cr doped ZnS (Zn1xCrxS at x = 0.125) and Mn doped ZnS (Zn1xMnxS at x = 0.125) and so results of these two have also been illustrated. The results of the present study suggest that Cr and Mn codoped ZnS are potential candidates for spintronics applications.

2. Method of calculation

Fig. 1. Band structure for undoped ZnS.

for the optical properties [25–28]. Reddy et al. have experimentally reported that (Cu, Cr) codoped ZnS nanoparticles [27] show room temperature ferromagnetism. Experimental and theoretical studies have shown that Mn doped ZnS (ZnS:Mn) exhibits ferromagnetism [29,30] and not half metallic (HM) nature and so codoping ZnS:Mn with another TM is an effective route to achieve HM behavior as this codoping is expected to induce room temperature HM character useful for spintronic applications. Therefore, in this paper, first principles studies on the structural, electronic and magnetic properties of Cr and Mn codoped ZnS (Zn1–2xCrxMnxS at x = 0.125) are reported. Theoretical and experimental studies on Mn and Cr codoped ZnS are not reported in the literature when several works have been reported on the Mn doped ZnS and Cr doped ZnS. Among these two atoms, Mn (25 electrons) atom has just one electron more than Cr (24 elec-

The calculations were performed using the full-potential linearized augmented plane wave plus local orbital (FP-LAPW + lo) method as implemented in the Wien2k package [31,32] within the framework of density functional theory (DFT). The exchange and correlation potential was evaluated in the Perdew–Burke– Ernzerhof generalized gradient approximation (PBE-GGA) and Becke–Johnson potential (mBJ-LSDA). In FP-LAPW + lo method, a muffin tin model for the crystal potential is assumed and the unit cell is divided into two regions, within and outside the muffin-tin sphere. Fully relativistic effects were taken into account for core states and scalar relativistic approximation was used for the valence states. As the spin-orbit coupling has a small effect on the ferromagnetism, it was neglected. The spherical harmonic expansion was used, inside the muffin-tin sphere and the plane wave basis set was chosen outside the sphere. For plane wave expansion of the electron wave in the interstitial region, the plane wave cut-off value RKmax = 7.00 was used. The integration on the irreducible Brillouin zone was done on the grid of 64 points. Potential and charge density are treated without shape approximation in this method, with the smooth variation of potential and wave function. The doped ZnS was modeled in 2  2  2 supercell consisting of 16 atoms in zinc blende phase. For the case of single doping, when Cr (Mn) was doped to host lattice to replace Zn at site (0, 0, 0), the supercell of Zn1xCrxS (Zn1xMnxS) was created with the doping level x = 0.125 when the other seven Zn and eight S atoms were left in their respective positions. When Cr and Mn were doped simultaneously in ZnS lattice at x = 0.125 replacing two Zn atoms (at sites 0, 0, 0 and 0.5, 0, 0) the supercells of Zn1–2xCrxMnxS and

Fig. 2. Band structure for ZnCrS in PBE-GGA and in mBJ-LSDA.

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Fig. 3. Band structure for ZnMnS in PBE-GGA and in mBJ-LSDA.

Zn1–2xMnxCrxS are formed. For the codoping case of Zn1–2xCrxMnxS, one Zn atom at (0, 0, 0) was replaced by Cr and another Zn atom at (0.5, 0, 0) was replaced by Mn atom, while other six Zn and eight S atom kept in their sites. Next, the substitution positions of Cr and Mn were interchanged so that the Zn atom at 0, 0, 0 was replaced by Mn while Zn atom at 0.5, 0, 0 was replaced by Cr atom so that supercell of Zn1–2xMnxCrxS is formed. The self-consistency was attained when total energy convergence is less than 105 Ry for the stability of the system. From the spin polarized electronic band structure calculations, the band structure, density of states and the magnetic properties were obtained.

3. Result and discussion The structural optimization was obtained for Zn1xCrxS (ZnCrS), Zn1xMnxS (ZnMnS), Zn1–2xCrxMnxS (ZnCrMnS), and Zn1–2xMnxCrxS (ZnMnCrS) by computing the total energy as a function of unit cell volume for paramagnetic (PM), antiferromagnetic (AFM) and ferromagnetic (FM) states. The energy differences DE = EPM – EFM and EPM – EAFM are positive to indicate the magnetic phase of the compound. The stability of the ferromagnetic structure of these compounds were investigated by the difference between the energies in the antiferromagnetic and ferromagnetic phases (DE = EAFM – EFM). It is found that for every TM concentration, the FM state is lower in energy than the AFM and PM state and also the total energy difference (DE = EAFM – EFM) between FM and AFM are positive, which indicates that the FM state is favorable than the AFM and PM state. The equilibrium values of the optimized lattice parameter ‘a’ was determined in the magnetic state which are 5.45 Å, 5.472 Å, 5.483 Å and 5.492 Å respectively for ZnCrS, ZnMnS, ZnCrMnS and ZnMnCrS showing a gradual increase and this may be due to the radius of Cr and Mn being slightly larger than the Zn atom. The calculated value of ‘a’ for Cr doped ZnS is in agreement with that determined by Nasir et al. [33]. No experimental or theoretical value is available to compare the value of ‘a’ for the case of codoped ZnS and hence, it can be said that in the present work, the same has been predicted. As the value of ‘a’ for ZnCrMnS and ZnMnCrS are different, it is obvious that the positions of Cr and Mn in the ZnS host lattice play a vital role in rendering the property for these two cases. The spin polarized electronic band structures and density of states for the doped ZnS compounds were calculated using the calculated equilibrium lattice constants. To visualize the changes in the band structure during doping, the band structure of ZnS is also plotted and is depicted in Fig. 1. In the band structure of ZnS, the lowest bands around 12 to 13 eV below Fermi level are Sulfur s-like which are well localized. The bands above these are mainly due to Zn d-like states (6 to 7 eV) which are dispersion free.

The highly dispersed broad band lying between 5.5 eV to EF above Zn-d are mainly S p-like states which are below the Fermi level forming the upper part of the valence band. The lower part of the valence band is from Zn-d states which hybridize with S-p states. Above the Fermi level, the Zn s-like states exist and they form the lower part of the conduction band and they are highly dispersed. The band gap is formed between the top of the S-p like valence bands and the bottom of the conduction bands which are Zn-s like. The spin-polarized band structures for ZnCrS in the majority spin channel (MAC) and minority spin channel (MIC) computed based on PBE-GGA and mBJ-LSDA are shown in Fig. 2. When Cr (or Mn) is doped into ZnS lattice replacing Zn, the energy states of Cr (or Mn), particularly, the d-like states of Cr/Mn (t2g and eg) are dominating near the Fermi level in the band gap, changing the position of the valence band and conduction band with respect to the Fermi level. The d states of Cr (Mn) namely t2g and eg have pushed the S-p and Zn-d bands down and occupy the region in the vicinity of the Fermi level EF above the S-p states. Cr (Mn) eg bands are above the t2g bands. In MAS channel of ZnCrS, the Cr t2g bands which are above its eg bands are partially filled whereas the corresponding bands for Mn in ZnMnS are completely filled i.e., well below EF. For the case of ZnCrS, in the majority spin (MAS) channel, the metallic character exists which is evidenced from the crossing over of the Cr t2g bands across the EF at C. In the minority spin (MIS) channel, ZnCrS has an energy gap exhibiting semiconducting character. It is visible from the MIS channel that the Cr t2g and eg have been pushed above the EF and the band

Fig. 4. Binding energy curves for ZnCrMnS and ZnMnCrS.

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Fig. 5. Band structure for ZnMnCrS in PBE-GGA and in mBJ-LSDA.

gap is formed between the bottom of eg bands and top of the S-p bands, which are now just below the EF. This metallic nature in one spin direction and semiconducting in other spin direction for the ZnCrS renders this compound into a half metallic ferromagnet (HMF) and shows 100% spin polarization due to its zero DOS at EF in the MIS channel. The spin polarized band structures of ZnCrS are in good agreement with that of Nazir et al. [33]. Unlike ZnCrS, in the case of ZnMnS (Fig. 3), there is an energy gap in both spin channel and so it does not show half-metallic nature as the DOS is zero in both channels (not shown). However, the Mn doped ZnS is a ferromagnetic semiconductor as shown by experiments [34]. It is to be noted that the spin gap is small in the case of majority spin (1.105 eV) compared to that of minority spin case (2.085 eV) and the position of the bands in majority and minority spin are not unique. In order to understand the influence of Cr in ZnMnS system, Cr was codoped into ZnS lattice replacing one more Zn atom at site 0.5, 0, 0 to form ZnCrMnS and the influence of (Mn,Cr) co-doping in the host lattice of ZnS was investigated. Cr and Mn were substituted to two Zn sites namely, 0, 0, 0 and 0.5, 0, 0 in the host lattice to achieve the doping level of 12.5% for each doped atom. So, first, with Cr at 0, 0, 0 Zn site and Mn at 0.5, 0, 0 Zn site, the supercell of the compound ZnCrMnS was obtained. Then the positions of Cr and Mn were interchanged so that Mn is at 0, 0, 0 and Cr is at 0.5, 0, 0 Zn sites and the supercell of the compound ZnMnCrS was obtained. The spin polarized band structure calculations were carried out to plot the binding energy curve for both these cases which are given in (Fig. 4). It is evident from these binding energy

Fig. 6. Partial density of states (PDOS) for Cr-d and Mn-d states in ZnMnCrS.

curves that the compound ZnMnCrS in which Mn at 0, 0, 0 and Cr at 0.5, 0, 0 is energetically stable compared to ZnCrMnS for which Cr is at 0, 0, 0 Zn site and Mn at 0.5, 0, 0 Zn site. Having optimized the positions of Mn and Cr in the ZnS lattice, the band structure and density of states were calculated for ZnMnCrS and ZnCrMnS. It is important to note that the lattice parameter ‘a’ are different for these two cases which suggests that the tetrahedron coordination may be possibly different. First we discuss the case of ZnMnCrS. As in the case of singly (Mn or Cr) doped ZnS, the band structure of ZnMnCrS shows that the d states of Mn and Cr are above S-p states in the MAS channel (Fig. 5). In order to understand the band structure of ZnMnCrS, the band structures of ZnMnS and ZnMnCrS are compared. In the case of ZnMnS, the d states of Mn are localized well below the Fermi level in both channels. When Cr is introduced to ZnMnS, the d states of Cr lie above the d states of Mn in MAS channel with Cr t2g on top. Also it is seen that the center of the Mn d states have moved up by about 0.2 Ry along C direction. In MAS channel, the Cr t2g state crosses the Fermi level for ZnMnCrS to create the metallic character. In the MIS channel (Fig. 5), a wide gap (2.625 eV) is found to exist depicting the semi conducting nature with EF being located in the energy gap and this is a typical HM character The present study therefore has confirmed that ZnMnCrS is a half metallic ferromagnet. Hence the codoped Cr has induced half metallic character in ZnMnS. Moreover, the zero DOS is clearly seen from its partial density of states (PDOS) plot (Fig. 6) in the MIS channel indicating the best feature of the unambiguous 100% spin polarization for ZnMnCrS and so ZnMnCrS is a promising material for spintronics applications. These PDOS features are in well agreement with the reports of Huawei et al. [22]. The magnetism in simultaneous Cr and Mn doping is also evidently due to the Cr-d and Mn-d hybridization (Fig. 6) in addition to p-d hybridization. Since there are no experimental or theoretical results to compare, we have predicted the HM-FM in Cr doped ZnS:Mn. Next we discuss about ZnCrMnS. Here the band structures and DOS in the MAS and MIS channel are exhibiting a completely different features compared to that of ZnMnCrS. From the MAS channel (Fig. 7) of ZnCrMnS, it is seen that Zn-s states have been pushed down below Fermi level along C direction and this shows that Zn-s states are occupied to contribute to valence band leading to the metallic character in MAS channel of ZnCrMnS. Moreover, the MAS channel shows that Cr-d states are also localized as that for Mn in ZnMnS. In the MIS channel (Fig. 7) of ZnCrMnS, the d bands of two TMs are pushed above Fermi level to form an energy gap (2.525 eV) indicating the pseudo gap character for ZnCrMnS. So the spin polarization is slightly less than 100% for this compound. Moreover, it is also to be noted that in the cases of ZnCrS and ZnMnCrS for the MAS channel, the TM d-t2g bands cross over the

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Fig. 7. Band structure for ZnCrMnS in PBE-GGA and in mBJ-LSDA.

Table 1 Calculated total and local magnetic moment (in Bohr Magneton lB) within the muffin tin spheres and in the interstitial sites. Compound

Method of calculation

Minterstitial (lB)

MCr (lB)

MMn (lB)

MZn (lB)

MS (lB)

MTot (lB)

Zn1xCrxS

PBE-GGA mBJ-LSDA

0.6736 0.62699

3.33867 3.3991

– –

0.01166 0.01035

0.02105 0.02223

4.00216 4.00064

Zn1xMnxS

PBE-GGA mBJ-LSDA

0.66898 0.52967

– –

4.05071 4.30346

0.01459 0.00754

0.00212 0.02952

5.00057 5.00082

Zn1–2xCrxMnxS

PBE-GGA mBJ-LSDA

1.39614 1.2368

3.31614 3.36592

4.07162 4.18855

0.02796 0.02067

0.01160 0.01634

9.00426 9.00174

Zn1–2xMnxCrxS

PBE-GGA mBJ-LSDA

1.3084 1.16788

3.3445 3.41101

4.1284 4.25623

0.0221 0.01843

0.0128 0.02013

8.9978 9.00141

Table 2 Energy of the lowest conduction band and highest valence band for majority and minority spin along with band gaps for minority spin and half metallic band gaps. C–C

Compound

Method of calculation

E"C (eV)

E"V (eV)

Eg-HM (eV)

E;C (eV)

E;V (eV)

Eg

Zn1xCrxS

PBE-GGA mBJ-LSDA

0.395 1.685

0.22 0.142

0.175 1.543

0.56 1.748

1.64 2.064

2.2 3.812

Zn1xMnxS

PBE-GGA mBJ-LSDA

0.265 2.732

0.840 0.282

1.105 3.014

0.40 2.748

1.685 0.843

2.085 3.591

Zn1–2xCrxMnxS

PBE-GGA mBJ-LSDA

0.370 0.084

0.615 0.995

0.245 0.911

0.18 0.112

2.8 3.431

2.62 3.319

Zn1–2xMnxCrxS

PBE-GGA mBJ-LSDA

0.575 1.395

0.21 0.137

0.57 1.258

0.78 1.325

1.95 2.315

2.525 3.640

Fermi level for the metallic character, whereas for ZnCrMnS, Zn-s states move down to cross the Fermi level. The attracting electronic behavior is the semiconducting gap for ZnMnCrS which is significantly more than that of ZnCrMnS and ZnCrS. The present study shows that ZnCrS and ZnMnCrS are found to have 100% spin polarization and ZnCrMnS is not an HM in both GGA mBJ-LSDA. The calculated total magnetic moment per TM atom and the magnetic moments at the site of other atoms are scheduled in Table 1 for both PBE-GGA and mBJ-LSDA. The major magnetic moment in Zn1xCrxS and Zn1xMnxS compounds mainly come from the Cr and Mn site respectively while for dual doped compounds, the major contribution is from Cr and Mn atoms. The magnetic moment values of Zn1xCrxS are in agreement with the results of Nazir et al. [33]. The negative sign in the local magnetic moments of the S site exhibit that the induced magnetic polarization of the S atom is anti-parallel to that of Cr and Mn atoms. The strong ferromagnetic coupling of the local magnetic moments can be explained in terms of strong hybridization between TM-d and S-p states. The total energy is lowered due to this p-d hybridization between TM (d-t2g) atoms and S-p states and negative coupling between TM and S states in these doped semiconductors which stabilizes the ferromagnetic order configuration. Moreover, the

(eV)

p-d hybridization produces local magnetic moments on the sites such as Zn and S and so, the magnetic moment of Cr (Mn) is less than its free charge magnetic moment (4 lB/5 lB). The ferromagnetic coupling is due to the double exchange mechanism. The values of DE = EPM–EFM for all the studied compounds are more than kBT = 30 meV and so all these compounds are room temperature ferromagnets. To gain further insight into the ferromagnetic character of these compounds, two significant parameters, namely the s-p exchange constant N0a (conduction band) and the p-d exchange constant N0b (valence band) were calculated. The band structure of halfmetallic compounds can be used to estimate these two parameters which can be determined by the mean – field theory expressions [34–36]:

N 0a ¼

DE c xðsÞ

N0b ¼

DE v xðsÞ

where DEc is the conduction band-edge spin splitting and DEv is the valence band-edge spin splitting. x is the concentration of the TM

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Table 3 Calculated conduction and valence band edge spin splitting and exchange constant. Compound

Method of calculation

DEc (eV)

Zn1xCrxS

PBE-GGA mBJ-LSDA

0.165 0.063

Zn1xMnxS

PBE-GGA mBJ-LSDA

0.135 0.016

Zn1–2xCrxMnxS

PBE-GGA mBJ-LSDA

Zn1–2xMnxCrxS

PBE-GGA mBJ-LSDA

DEv (eV)

N0b

0.659 0.252

1.86 2.206

7.435 8.822

0.432 0.051

0.845 0.561

2.703 1.795

0.19 0.028

0.338 0.049

2.185 2.436

3.883 4.329

0.205 0.07

0.365 0.124

2.16 2.452

3.841 4.358

atom and (s) is half of the total magnetic moment. In fact, the exchange constants N0a and N0b are helpful in finding the conduction band and valence band contributions in exchange splitting process. The band structures were used to calculate energy of the lowest conduction band for majority and minority spin (E"C and E;C) and the energy of the highest valence band for majority and minority spin (E"V and E;V). The values of E"C, E;C, E"V and E;V along with band gaps for minority spin are presented in Table 2 for all the doped compounds. DEc, the conduction band-edge spin splitting and DEv, the valence band-edge spin splitting were calculated using the following the equations DEc = E;C – E"C and DEv = E;V – E"V. It is clear from the band structures that the minima of the conduction band for the same compound are different in MAS and MIS channels and similar is the case for the valance bands. The difference between the spin-up and spin-down states is due to the hybridization of d bands of TM atoms and S-p states. The band gap Eg calculated on the basis of mBJ-LSDA are more than that calculated with PBE-GGA. The calculated values of DEc, DEv, N0a and N0b are listed in the Table 3 and it is obvious that the values of p-d exchange splitting N0a and p-d exchange constants N0b are consistent with respect to their negative signs. The opposite signs of N0a and N0b indicates the FM character as this reveals that the conduction and valence states are behaving in an opposite mode during the exchange splitting process. N0a and N0b have opposite sign for all the compounds in PBE-GGA while in mBJ-LSDA, N0a and N0b have same sign for ZnMnCrS and ZnCrMnS and opposite sign for ZnCrS and ZnMnS. 4. Conclusions Full-potential linearized augmented plane wave plus local orbital (FP-LAPW + lo) method was employed to investigate halfmetallic ferromagnetic properties of (Mn,Cr) doped ZnS dilute magnetic semiconductor. The calculations were carried out in both PBE-GGA and mBJ-LSDA. Cr doped ZnS:Mn exhibited the half metallic ferromagnetism which was demonstrated by the band structures and density of states. The stability of the Cr doped ZnS:Mn with respect to the occupation of Cr and Mn at Zn sites was found. The FM character of the doped ZnS determined through the respective values of p-d exchange splitting N0a and p-d exchange constants N0b reveals that ZnCrS, ZnMnS, ZnMnCrS and ZnCrMnS are stable in the ferromagnetic phase. ZnCrS and ZnMnCrS are found to have 100% spin polarization and ZnCrMnS

N0a

is not an HM in both GGA mBJ-LSDA. The band gap values calculated by mBJ-LSDA are more than the band gap values obtained by PBE-GGA. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]

[32] [33] [34] [35] [36]

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