Physica B 406 (2011) 4547–4553

Contents lists available at SciVerse ScienceDirect

Physica B

0921-45

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/physb

Ab-initio investigations of structural, electronic, magnetic and opticalproperties of ferromagnetic Cd1–xMnxTe

Sonu Sharma, Nisha Devi, U.P. Verma n, P. RajaRam

School of Studies in Physics, Jiwaji University, Gwalior 474011, India

a r t i c l e i n f o

Article history:

Received 22 April 2011

Received in revised form

2 September 2011

Accepted 3 September 2011Available online 12 September 2011

Keywords:

Ab-initio calculations

II–VI Semiconductors

CdMnTe

Magnetic properties

26/$ - see front matter & 2011 Elsevier B.V. A

016/j.physb.2011.09.007

esponding author. Tel.: þ91 751 2442782.

ail address: upv.udai@gmail.com (U.P. Verma

a b s t r a c t

We report ab-initio calculations of the structural, electronic, magnetic and optical properties of the

alloy Cd1–xMnxTe as a function of the Mn concentration ‘x’. Ab-initio calculations are based on the

density functional theory (DFT) within the generalized gradient approximation (GGA). The calculated

lattice constants of the Cd1–xMnxTe alloys exhibit Vegard’s law downward bowing parameter. For the

minority spin channel the Fermi level shifts toward higher energy with the value of ‘x’ in Cd1–xMnxTe.

The spin-exchange splitting energy Dx(d) increases with increasing ‘x’ in Cd1–xMnxTe and the values of

p–d exchange splitting energy Dx(pd) of Cd1–xMnxTe show that the effective potential for the minority

spin is more attractive than that for the majority spin. The values of exchange constants N0a and N0bobtained for Cd1–xMnxTe are in agreement with the reported data. The magnetic moment per Mn atom

reduces from its free space charge value of 5mB to around 4mB due to p–d hybridization and this results

into an appearance of small local magnetic moments on the non-magnetic Cd and Te sites. The

absorption threshold shifts toward higher energy and the static refractive index decreases with the

increasing value of ‘x’ in Cd1–xMnxTe.

& 2011 Elsevier B.V. All rights reserved.

1. Introduction

The possibility of using the spin degree of freedom as well asthe electronic charge for electronic applications (spintronics) hasreceived great attention in the last few years. The most effectiveway to incorporate both of these effects in a material is to makediluted magnetic semiconductors (DMSs) or semi-magnetic semi-conductors [1]. Controlling the spin state of electrons provides animportant versatility for future nano-electronics [2]. Transitionmetal-doped II–VI diluted magnetic semiconductors haveattracted considerable interest for several years and these com-pounds show novel magneto-optical, magneto-electrical andmagneto-transport properties if the cation is partly substitutedby transition metal atoms with its half-filled 3d shell [3].

Among the 3d transition metals, Mn having electronic config-uration 3d54s2 plays a special role. If one considers the 3d5

electrons as a part of the core, the Mn atom becomes chemicallydivalent, which can be used to replace a cation in a II–VIcompound. In the class of II–VI DMSs of the type AII

1–xMnxBVI,Cd1–xMnxTe is a good candidate for gamma-ray detection, solarcells, lasers and infrared detectors [4] because of its wideband-gap, high resistivity and good electro-transport properties.

ll rights reserved.

).

The ternary nature of AII1–xMnxBVI gives us the possibility of tuning

the lattice and band parameters by varying the composition of thematerial [5].

In the context of spintronics, particularly, ferromagnetic semicon-ductors are very interesting as these materials combine complemen-tary functionalities of ferromagnetic and semiconductor materialsystems. Systematic experimental and theoretical studies of thecarrier-induced ferromagnetism in II–VI semi-magnetic semiconduc-tors have been undertaken by the Grenoble–Warsaw collaboration [6].In agreement with the theoretical model proposed by the team forvarious dimensionality II–VI semi-magnetic semiconductors [6], theferromagnetic order has been observed above temperature 1 K in twodimensional modulation-doped p-type Cd1–xMnxTe/Cd1–y–zMgy

ZnzTe:N heterostructures [7,8]. Tatarenko et al. [9] have demonstratedelectric-field control of ferromagnetism in the Cd0.96Mn0.04Te quan-tum well using the Molecular Beam Epitaxy (MBE) technique. Withthe advent of MBE technique it became possible to fabricate samplesof the Cd1–xMnxTe for most of the concentration range x¼0–x¼1.0except for a small compositional range (x�0.77–0.96), in whichmultiphase structures prevail [10–12].

Early theoretical works for Cd1–xMnxTe have been presentedby Larson et al. [13] using the augmented spherical-wave (ASW)method and Hass et al. [14] using the empirical tight-binding(ETB) method. Wei and Zunger [15], using the full relativisticlinear augmented plane-wave (FLAPW) method, presented thefirst picture of the electronic structure of ferromagnetic CdMnTe2.

S. Sharma et al. / Physica B 406 (2011) 4547–45534548

Recently, Merad et al. [16] and Touat et al. [11] have studiedthis compound by employing the local spin density approxima-tion (LSDA) with 25% and 50% concentrations of Mn, respectively.Also, Verma et al. [12] have studied this compound by employingthe generalized gradient approximation (GGA) with 75% and 100%concentrations of Mn. In the present work, we aim to give acomplete and comprehensive view of the structural, electronic,magnetic and optical properties of the compound Cd1–xMnxTe fordifferent values of ‘x’.

This paper is organized as follows. A description of the methodof calculations is given in Section 2. The results obtained for thestructural properties of Cd1–xMnxTe are described in Section 3.The results concerning the electronic properties, including bandstructures and density of states (DOS), are presented and dis-cussed in Section 4. In Section 5, we have given the results relatedto the exchange constants and in Section 6 we paid attention tothe magnetic properties of the DMS Cd1–xMnxTe. The opticalproperties of Cd1–xMnxTe are discussed and presented in Section7. Finally, in Section 8 we have summarized the work presented inthis paper.

Table 2

Calculated equilibrium lattice constant a0 (A), bulk modulus B0 (GPa) and its

pressure derivative B00 of Cd1–xMnxTe (x¼0.0, 0.125, 0.25 and 0.50) along with the

available theoretical and experimental data. PW stands for the present work.

Compound a0 (A) B0 (GPa) B00

PW Others PW Others PW Others

Cd1.0Mn0.0Te 6.604 6.46 [15] 37.02 – 3.58 –

Cd.875Mn.125Te 6.577 6.481 [22] 34.92 44.50 [22] 4.54 6.40 [22]

– – –

Cd.75Mn.25Te 6.544 6.354 [16] 35.61 47.10 [16] 4.64 4.58 [16]

Cd.50Mn.50Te 6.485 6.32 [11] 37.78 49.94 [11] 4.99 7.46 [11]

6.39 [22] – –

2. Computational details

The calculations of the structural, electronic, magnetic andoptical properties of the compound Cd1–xMnxTe were performedin the framework of spin-polarized density functional theory(SP-DFT) [17]. For the calculations of these properties weemployed the full potential linearized augmented plane waveplus local orbitals (FP-LAPWþ lo) method as implemented in theWien2k code [18]. The generalized gradient approximation (GGA)parameterized by Perdew, Burke and Ernzerhof (PBE) [19] wasemployed to deal with the exchange and correlation effects. Inorder to obtain the equilibrium structural parameters, we carriedout optimization of the total energy with respect to the differentvalues of the unit cell volume using Murnaghan’s equation ofstate [20]. The calculations were performed with RMTkmax¼7,which determines matrix size in order to achieve energy eigen-value convergence, where RMT is the smallest radius of themuffin-tin (MT) spheres and kmax is the maximum value of thewave vector. The respective values of muffin-tin radii (RMT) for Cd,Mn and Te were taken to be 2.1, 2.0 and 2.5 a.u. (atomic units),respectively, for all the calculations. The maximum value of theangular momentum lmax is set equal to 10 for the wave functionexpansion inside the atomic spheres. The k-points used in thecalculations were based on the 7�7�7 Monkhorst–Pack scheme[21]. The iteration process was repeated until the calculated total

Table 1Atomic positions of Mn atoms in the 2�2�2 supercell of Cd1–xMnxTe (x¼0.125,

0.25, 0.50 and 0.75).

Value of ‘x’ Mn atom Positions of Mn atom

x y z

0.125 1 0.500 0.250 0.250

0.25 1 0.500 0.000 0.000

2 0.750 0.250 0.000

0.50 1 0.500 0.000 0.000

2 0.750 0.250 0.000

3 0.750 0.000 0.250

4 0.500 0.250 0.250

0.75 1 0.250 0.000 0.250

2 0.750 0.000 0.250

3 0.000 0.250 0.250

4 0.500 0.250 0.250

5 0.750 0.250 0.000

6 0.250 0.250 0.000

energy and charge of the crystal converged to less than 0.0001 Ryand 0.001e� , respectively.

In order to simulate the ordered zinc blende structure of Cd1–x

MnxTe, we considered a 2�2�2 supercell model with fcc symmetrythat is composed of 16 atoms (8 Te atoms and eight atoms shared outbetween Cd and Mn). The bulk CdTe exhibits zinc blende structure(space group F43m). The Cd and Te atoms are located at the latticecoordinates (0, 0, 0) and (0.25, 0.25, 0.25), respectively. The lattices ofthe DMSs Cd0.875Mn0.125Te, Cd0.75Mn0.25Te and Cd0.50Mn0.50Te areobtained by substituting one, two and four Mn atoms, respectively,for an equal number of Cd atoms in the supercell. The correspondingatomic positions of Mn atoms in the 2�2�2 supercell of Cd1–x

MnxTe are given in Table 1 for x¼0.125, 0.25, 0.50 and 0.75.

3. Structural properties

The ground-state structural properties of the DMSsCd0.875Mn0.125Te, Cd0.75Mn0.25Te and Cd0.50Mn0.50Te in the zinc-blende (ZB) phase are determined by the minimization of thetotal energy for different values of the supercell volume andfitting the results to the Murnaghan’s equation of state [20]:

ETðVÞ ¼B0V

B00

ðV0=VÞB0

0

B00�1þ1

" #þE0�

V0B0

B00�1ð1Þ

In Table 2, we show our GGA results regarding the equilibriumlattice constant a0, bulk modulus B0 and its pressure derivative B0

0

for the ZB structure of the binary CdTe and ternary Cd1–xMnxTe(x¼0.125, 0.25 and 0.50) alloys at zero pressure; we havementioned the available theoretical and experimental results[11,15,16,22] as well.

6.35

6.4

6.45

6.5

6.55

6.6

6.65

0

Lat

tica

Con

stan

t (Å

)

Mn Concentration 'x'

Vegard's LawCalculated

0.25 0.5 0.75 1

Fig. 1. Variation in the lattice constant of Cd1–xMnxTe with the Mn concentration ‘x’.

S. Sharma et al. / Physica B 406 (2011) 4547–4553 4549

Usually, in the treatment of alloys, it is assumed that the atomsare located at the ideal lattice sites and the lattice constant varieslinearly with the increase in composition ‘x’ according to the so-called Vegard’s law [23]:

aðA1�xBxCÞ ¼ xaBCþð1�xÞaAC ð2Þ

where aAC and aBC are the lattice constants of the binarycompounds AC and BC, respectively, and aðA1�xBxCÞ is the latticeconstant of the ternary alloy (in our case its Cd1–xMnxTe).However, violation of Vegard’s law has been reported in thesemiconductor alloys both experimentally [24] and theoretically[25,26]. Hence, the lattice constant of the alloy can be written as

aðA1�xBxCÞ ¼ xaBCþð1�xÞaAC�xð1�xÞb, ð3Þ

where the quadratic term ‘b’ stands for the bowing parameter.Fig. 1 shows the variation of the calculated equilibrium latticeconstants of the Cd1–xMnxTe alloys against the Mn concentration‘x’. It is observed that the lattice constants of Cd1–xMnxTe

Fig. 2. Electronic band structures of Cd.875Mn.125Te

Fig. 3. Electronic band structures of Cd.75Mn.25Te fo

calculated for different ‘x’ values exhibit a tendency towardsVegard’s law with a marginal downward bowing parameter thatequals 0.04.

4. Electronic properties

The equilibrium lattice constants are used to calculate theelectronic band structures and the density of states for the zincblende Cd1–xMnxTe. The calculated electronic band structures ofthe ferromagnetic Cd0.875Mn0.125Te, Cd0.75Mn0.25Te and Cd0.50

Mn0.50Te in the ZB phase for the spin-up and spin-down align-ments are shown in Figs. 2, 3 and 4, respectively. We have takenthe zero of the energy scale (Fermi energy level) at the top of thevalence band (VB) for the spin-up case. The energy band struc-tures are calculated along the way that contains the highsymmetry points of the first Brillouin zone, namely W-L-!-X-W-K. From these band structures we observe that the top of

for the (a) spin-up and (b) spin-down channels.

r the (a) spin-up and (b) spin-down channels.

Fig. 4. Electronic band structures of Cd.50Mn.50Te for the (a) spin-up and (b) spin-down channels.

Fig. 5. Local density of states (LDOS) plots of the zinc blende Cd.875Mn.125Te

for Cd, Mn and Te sites.

Fig. 6. Local density of states (LDOS) plots of the zinc blende Cd.75Mn.25Te for Cd,

Mn and Te sites.

S. Sharma et al. / Physica B 406 (2011) 4547–45534550

Fig. 7. Local density of states (LDOS) plots of the zinc blende Cd.50Mn.50Te for Cd,

Mn and Te sites.

Table 3Calculated conduction and valence band edge spin splittings and the exchange

constants in eV for Cd1–xMnxTe (x¼0.125, 0.25 and 0.50). PW stands for the

present work.

DEc DEv N0a N0b

Cd.875Mn.125Te PW 0.08 �0.36 0.32 �1.42

Cd.75Mn.25Te PW 0.14 �0.58 0.28 �1.13

LSDA [16] 0.24 �0.80 0.39 �1.28

Cd.50Mn.50Te PW 0.11 �1.10 0.11 �1.08

LSDA [11] 0.46 �1.57 0.19 �0.63

N0a [expt.]¼0.22, N0b[expt.]

¼�0.88; for expt. results see Ref. [28].

S. Sharma et al. / Physica B 406 (2011) 4547–4553 4551

the VB and bottom of the conduction band (CB) are located at the! point of the Brillouin zone; this is in agreement with the bandstructures of the parent compound CdTe.

The local density of states (LDOS) plots for Cd0.875Mn0.125Te,Cd0.75Mn0.25Te and Cd0.50Mn0.50Te are presented in Figs. 5, 6 and7, respectively. These plots provide a qualitative explanation ofthe atomic and orbital origins of the different band states. Fromthe LDOS plots of these DMSs we observe that near the Fermilevel, the upper part of the valence band possesses Mn-3d and

Te-5p characteristics, which differ widely for the spin-up andspin-down channels. For the spin-up case, the Mn-3d bands areoccupied and mixed with Te-5p bands, whereas for the spin-down case the Mn-3d bands are unoccupied. Furthermore, fromthe band structures and LDOS plots of these DMSs we observethat the Mn-d–eg states were slightly broadened by hybridizationwith the Te-5p states, while d–t2g states were strongly hybridizedwith the Te-5p states. The band structures plots for the spin-down case show that with the increase of Mn concentration inCd1–xMnxTe the Fermi level shifts toward higher energy.

The LDOS plots of Cd1–xMnxTe for x¼0.125, 0.25 and 0.50,respectively, reveal that for the spin-up channel the Mn-3d bandsare occupied and centered at �2.87, �3.06 and �3.34 eV, whereasfor the spin-down channel the Mn-3d bands are empty and centeredat 1.41, 1.62 and 1.90 eV. The separation between correspondingspin-up and spin-down peaks, due to the effective Mn-3d states, isknown as the spin-exchange splitting energy and is denoted as Dx(d).For x¼0.125, 0.25 and 0.50, respectively, the obtained values of Dx(d)are þ4.32 eV, þ4.43 eV and þ4.48 eV. In order to illustrate thenature of attraction in these DMSs, we calculated the p–d exchangesplitting Dv

xðpdÞ ¼ Ekv�Em

v and DcxðpdÞ ¼ Ek

c�Emc . The values of Dv

xðpdÞ�0:36,�0:58,�1:10 eV, and that of Dc

xðpdÞ 0.08, 0.14, 0.11 eV are forx¼0.125, 0.25, 0.50, respectively. The negative value of Dv

xðpdÞimplies that the effective potential for the minority spin is moreattractive than that of e majority spin, which is usually the case in thespin-polarized systems [15,27].

5. Exchange constants

The significant parameters determining the magnetic properties ofDMSs are the s–d exchange constant N0a and the p–d exchangeconstant N0b, where N0 is the concentration of cations. In Cd1–xMnxTe,N0a describes the exchange interactions between the conductionelectrons (Cd-s state) and the Mn-d states here, as N0b explains theexchange interaction between the holes (Te-p states) and the Mn-dstates. These parameters describe how the valence and conductionbands contribute in the process of exchange and splitting.

The exchange constants have been calculated by using thefollowing [28]:

N0a¼DEc

x/SS; N0b¼

DEv

x/SSð4Þ

Here DEc and DEv are the respective band edge spin splitting ofthe conduction band maxima (CBM) and valence band maxima(VBM) at the ! point, x is the concentration of Mn and /SS is one-half of the magnetization per Mn atom. The computed values ofDEc, DEv, N0a and N0b are given in Table 3 along with theavailable theoretical [11,16] and experimental data [28].

6. Magnetic properties

The total magnetic moments for the DMSs Cd0.875Mn0.125Te,Cd0.75Mn0.25Te and Cd0.50Mn0.50Te in the ZB phase along with totalmagnetic moments on the atomic and the interstitial sites are listedin Table 4. This table shows that the partially occupied Mn-3d levelsproduce permanent local magnetic moments in these DMSs. In factdue to p–d hybridization, the free space charge value 5mB of Mnreduces to 4.074mB in Cd0.875Mn0.125Te, 4.078 in Cd0.75Mn0.25Te, 4.089in Cd0.50Mn0.50Te and the difference in charge results into small localmagnetic moments on the Cd and Te sites, which are otherwise non-magnetic. It is found that the magnetic moments of all the atoms areparallel in these DMSs. The value of the total magnetic moment inthese DMSs is found to increase in proportion with the number of Mnatoms doped in the crystal lattice of CdTe.

Table 4Calculated magnetic moments (in mB) of several sites and the total magnetic moment of the ferromagnetic Cd1–xMnxTe (x¼0.125, 0.25 and 0.50). PW¼present work.

Site x¼0.125 x¼0.25 x¼0.50

No. of atoms Magnetic moment No. of atoms Magnetic moment No. of atoms Magnetic moment

PW PW Other [16] PW Other [11]

Mn 1 4.074 2 4.078 4.210 4 4.089 4.326

Cd 7 0.005 6 0.009 0.120 4 0.016 0.048

Te 8 0.018 8 0.035 0.068 8 0.043 0.064

Interstitial 0.817 1.633 0.567 3.251

Total magnetic moment 4.999 10.003 20.005

Total magnetic moment Per Mn atom 4.999 5.001 5.001

-4-202468

10121416

ε 1 (ω

)

Photon Energy (eV)

x = 0.0x = 0.125x = 0.25x = 0.50x = 0.75x = 1.0

x = 0.0x = 0.125x = 0.25x = 0.50x = 0.75x = 1.0

x = 0.0x = 0.125x = 0.25x = 0.50x = 0.75x = 1.0

x = 0.0x = 0.125x = 0.25x = 0.50x = 0.75x = 1.0

x = 0.0x = 0.125x = 0.25x = 0.50x = 0.75x = 1.0

0

2

4

6

8

10

12

14

ε 2 (ω

)

Photon Energy (eV)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

L (ω

)

Photon Energy (eV)

00.5

11.5

22.5

33.5

4

n (ω

)

Photon Energy (eV)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0

R (ω

)

Photon Energy (eV)3 6 9 12 15

0 3 6 9 12 15 0 3 6 9 12 15

0 3 6 9 12 150 3 6 9 12 15

Fig. 8. Plots of the optical properties of the zinc blende Cd1–xMnxTe (a) e1(o)—real part of the dielectric function, (b) e2(o)—imaginary part of the dielectric function,

(c) L(o)—the electron energy-loss function, (d) n(o)—the refractive index and (e) R(o)—the reflectivity spectrum versus the photon energy.

S. Sharma et al. / Physica B 406 (2011) 4547–45534552

7. Optical properties

The optical properties of a material can be depicted by thefrequency dependent complex dielectric function e(o)¼e1(o)þie2(o), where e1(o) is the real and e2(o) is the imaginary part. Theimaginary part e2(o) was obtained by calculating the electronicstructure, using the joint density of states and the optical matrix

elements. The real part e1(o) of the complex dielectric functione(o) can be derived from the imaginary part e2(o) using theKramers–Kronig relation

e1ðoÞ ¼ 1þ2

p P

Z 10

o0e2ðo0Þo02�o2

do0 ð5Þ

S. Sharma et al. / Physica B 406 (2011) 4547–4553 4553

where P implies the principal value of the integral and o0represents the complex angular frequency. The variations ofe1(o) and e2(o) with the photon energy (eV) are shown inFig. 8(a) and (b), respectively. The e2(o) plots show that theabsorption threshold shifts slightly toward higher energy with theincrease in the value of ‘x’ in Cd1–xMnxTe, except for x¼1.0,because of the half metallic character of Cd0.0Mn1.0Te (i.e. MnTe).The most important contribution to the first prominent peak ofe2(o) can be attributed to the transitions from the occupiedstates, with Te-5p character, to the unoccupied Mn-3d states.The e2(o) plots contain some structures around 3.55 eV thatcorrespond to the transitions between the spin–orbit split valencebands and the conduction bands. It is clear from Fig. 8(a) thatthese additional structures are more prominent for x¼0.75. Theseobservations are in accordance with the calculated magnitude ofspin-exchange splitting energy Dx(d) of Cd1–xMnxTe. From thespectra of e2(o) it can be readily seen that there existssomeabsorption bands in Cd1–xMnxTe before the fundamental absorp-tion edge. These absorptions were attributed to intra-ion transi-tions of Mn2þ in the 3d5 configuration. For the real part of thedielectric function the most important quantity is e1(0), whichcorresponds to the zero frequency limit. The phonon contribu-tions to the dielectric screening have not been considered ande1(0) corresponds to the static electronic dielectric constant. Itsvalue is observed to decrease with increasing x in Cd1–xMnxTe.

The calculated results on the electron energy-loss functionL(o), the refractive index n(o) and the reflectivity R(o), areshown in Fig. 8(c), (d) and (e), respectively. The spectrum of theelectron energy-loss function L(o) describes the energy-loss of afast electron traversing in the material [29]. Its main peak isgenerally defined as the bulk plasma frequency op, which occurswhere e2(o)o1 and e1(o) reaches the zero value [30]. FromFig. 8(c), we observe that the main peaks of electron energy-lossfunction of Cd1–xMnxTe for different values of x (¼0.0, 0.125, 0.25,0.50, 0.75 and 1.0) are located at 13.10, 12.18, 12.39, 12.55, 12.50and 13.13 eV, respectively. In addition, the peaks of L(o) corre-spond to the trailing edges in the reflection spectra R(o) or vice-versa, for instance, the peak of R(o) is at 13.54 eV, whichcorresponds to the abrupt reduction of L(o). In the range from0 to 1.20 eV the reflectivity R(o) of Cd1–xMnxTe is estimated to belower than 30% for almost all values of x, which implies that thenature of the material is transmitting for the frequencieso1.20 eV. The values obtained for the static refractive index ofCd1–xMnxTe for x (¼0.0, 0.125, 0.25, 0.50, 0.75 and 1.0) are 2.93,2.92, 2.89, 2.85, 2.80 and 2.76, respectively.

8. Conclusions

This paper reports a systematic study of the structural,electronic, magnetic and optical properties of the ZB ternary alloyCd1–xMnxTe for different Mn concentrations using the spin-polarized density functional theory. The calculated lattice con-stants of Cd1–xMnxTe alloys at different Mn concentrations exhibita tendency towards Vegard’s law with downward bowing para-meter equal to 0.04. For the spin-up channel, the Mn-3d bands areoccupied and mixed with Te-5p bands, whereas for the spin-down channel the Mn-3d bands are unoccupied. The DOS plotsreveal a strong hybridization between the Mn-d and Te-5p statesand the valence band maxima are observed to be dominated bythe Mn-d states. Our calculations show that the effective potential

for the minority spin is more attractive than that for the majorityspin as is typical in the spin-polarized systems. The exchangeconstant N0a decreases while N0b increases with the increase inthe value of ‘x’ in Cd1–xMnxTe. The results of magnetic momentindicate that Mn impurity adds no hole carrier to the perfect CdTecrystal. Finally, the linear optical properties such as dielectricfunction, electron energy-loss, refractive index and reflectivity areobtained. In the plots of the imaginary part of the complexdielectric function the absorption threshold shifts toward thehigher energy with the increasing ‘x’ in Cd1–xMnxTe, except forx¼1.0. The static refractive index of Cd1–xMnxTe decreases withthe increasing value of ‘x’.

Acknowledgments

One of the authors (UPV) acknowledges the financial assis-tance provided by MPCST, Bhopal, Sanction no. 1928/CST/R&D/08and UGC, New Delhi, F. No. 36-124/2008(SR).

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