First-principles investigation on the electronic and magnetic properties of cubic Be0.75Mn0.25X (X = S, Se, Te)

Journal of Alloys and Compounds 575 (2013) 190–197

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First-principles investigation on the electronic and magnetic properties of cubic Be0.75Mn0.25X (X = S, Se, Te) Jian Li a,c,⇑, Xueli Xu a, Yong Zhou a, Ming Zhang b, Xian Luo c a

School of Materials Science and Engineering, Xi’an Shiyou University, Xi’an 710065, China School of Petroleum Engineering, Xi’an Shiyou University, Xi’an 710065, China c School of Materials, Northwestern Polytechnical University, Xi’an 710072, China b

a r t i c l e

i n f o

Article history: Received 12 February 2013 Accepted 13 April 2013 Available online 22 April 2013 Keywords: Beryllium chalcogenides Mn doped semiconductor Dilute magnetic semiconductor First-principles

a b s t r a c t The structural, electronic and magnetic parameters of Be0.75Mn0.25X (X = S, Se, Te) are investigated using first-principles calculations. The thermodynamic stability of these Mn-doped semiconductors can be confirmed by the negative energetic quantities of formation energy and cohesive energy, and the stability decrease from Be0.75Mn0.25S to Be0.75Mn0.25Te with the magnitude of energetic quantities decrease as the same order. Calculated from the band structures, Be0.75Mn0.25X have smaller band gaps (1.49 eV, 1.36 eV, 0.78 eV for X = S, Se, Te, respectively) than BeX. The density of states and valence electron distribution plots indicate that the atomic bonding of Be0.75Mn0.25X is mainly contributed from the interactions between Mn-d and X-p. And the electronic interaction weakens from Be0.75Mn0.25S to Be0.75Mn0.25Te. The local magnetic moment of Mn, the exchange splitting energies, and exchange constants can be obtained from the spin-polarized electronic structures and density of states plots, the splitting energy Dx(d) is positive while Dx(pd) is negative, the exchange constants N0a and N0b are negative. And all of them increase along with X atom radius increasing, which implies the effective potential for down-spin is more attractive than that for up-spin, and it decreases along with the X atom changing from S to Te. N0a and N0b suggest that the interactions of Be(2s)–Mn(3d) states and X(p)–Mn(3d) states are all attractive, and the interactions of s–d and p–d weakens with the same sequence. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Beryllium chalcogenides (BeS, BeSe and BeTe) and Be-containing II–VI mixed crystals have attracted considerable attention for their promising applications in microelectronic, optoelectronic and spintronic devices. For example, the Be-containing binary, ternary, and quaternary II–VI alloys which grown on the substrates of InP or GaAs could be used in the light emitting diodes (LEDs) and laser diodes (LDs) [1–7]. Except for beryllium monoxide (BeO), Be-VI compounds BeS, BeSe and BeTe are zinc-blende structure (B3) at ambient temperature and pressure, and they are partially ionic semiconductors with large band gaps (2–5 eV) [8–14]. Because of the toxicity, especially beryllium sulfide (BeS), the experimental studies on the BeX (X = S, Se, Te) are seldom reported. Moreover, these experiments mainly focus on the electronic and optoelectronic properties of these materials. For example, Akimoto, Waag and Maksimov et al. [13–23] prepared the ZnSe/BeTe based heterostructures, and deeply discussed the physics of quantum well. As for beryllium ⇑ Corresponding author at: School of Materials Science and Engineering, Xi’an Shiyou University, Xi’an 710065, China. Tel.: +86 29 88382598. E-mail address: [email protected] (J. Li). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.04.096

selenide (BeSe), Pagès et al. [24–26] investigated the longitudinaloptical phonons cooperative phenomenon of ZnSe–BeSe mixed crystals. Waag et al. [14,27] synthesized BeMgZnSe and BeCdSe alloys on GaAs, and the quantum well of them was also stressed. The BeSe and Zn(Mg)BeSe layers grown on the Si(0 0 1) and GaAs(0 0 1) were synthesized by Tournie et al. [28,29], and their band gaps and optoelectronic properties were investigated. Vigué et al. [30] presented the growth and characterization of p-i-n photodiodes based on ZnBeSe and ZnMgBeSe compounds. However, for the beryllium sulfide (BeS), the experimental studies are very few and limited on its basic features, such as electrical conductivity [31], and its bulk modulus and phase transformation under high pressure [32]. Although the experimental studies are difficult, however, the theoretical studies of bulk beryllium chalcogenides are enormous, especially the calculations using first-principles methods. The quantities such as structural properties [10,33–39], electronic properties [8–10,12,33–36,39,40], optical properties [9,11,33], elastic constants and mechanical stability [8,10,11,35–37,39,41– 44], and phase transition under high pressure [10,35–37,40– 42,45,46] are calculated and discussed. Further, there are also many first-principles investigations about the ternary or quaternary Be-VI based alloys. For example, Berghout and Hacini et al. [47,48] studied the structural, electronic and optical properties

J. Li et al. / Journal of Alloys and Compounds 575 (2013) 190–197

and the energy-gap composition dependence of ternary Zn1xBexSe and quaternary Zn1xBexSySe1y alloys. Khan and Bouamama et al. [49,50] calculated the electronic, optical, structural and elastic properties of BeSxSe1x, BeSxTe1x and BeSexTe1x under ambient and high pressure. Gurevich and Shen et al. [20,21] investigated the interface carrier states and spatially separated indirect photoemission of ZnSe/BeTe heterostructures. Sandu and Kirk [51] studied the electronic and optical properties of beryllium chalcogenide/ silicon heterostructures. Alay-e-Abbas et al. [52] studied the structural, electronic and magnetic properties of ferromagnetism in Crdoped BeSe and BeTe. Moreover, in the studies of dilute magnetic semiconductors (DMSs) to explore new spintronic materials with high Curie temperature, the researchers have found that II–VI and III–V semiconductors alloyed with 3d transition metals (such as Mn [53–60], Cr [58,60–63], Co [59]) exhibit good ferromagnetism, and II–VI semiconductors can be doped with larger concentration of transition metals up to 25% [57,60,64,65]. According to the above literatures, Be-VI compounds alloyed with manganese are worthy investigated for their promising usage as new DMS materials. For a deeper insight into the intrinsic nature and a theoretical evaluation of their electronic and magnetic properties, ordered bulk Be0.75Mn0.25X (X = S, Se, Te) are modeled and calculated by using first-principles method in this paper.

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according to the equations between bulk modulus and elastic constants. For a cubic crystal, there are only three independent elastic constants, namely C11, C12 and C44, and the bulk modulus is related to C11 and C12, B = 1/3(C11 + 2C12) [77]. The band gaps of these beryllium chalcogenides are also calculated, our results and other theoretical and experimental data are presented in Table 2. From the data of previous studies [8,10,35,74,79] in Table 1, one can see that the equilibrium lattice constants with GGA method are rather larger than the ones with LDA methods, which is usually called ‘‘LDA underestimating effect’’. Considering this difference between GGA and LDA, our calculations were performed with GGA-PBE potential. And the comparison between our results and experimental data [32,71] shows that the agreements of lattice constants are very good, the divergences are only 0.14%, 0.05%, 0.85% for BeS, BeSe, BeTe, respectively. However, the deviations of Bulk moduli are slightly larger as 13.85%, 13.04%, 9.37% for BeS, BeSe, BeTe, respectively. We further note that the same tendency exists in other previous theoretical results calculated with GGA method, and our Bulk moduli are in good accordance with these GGA calculation results [8,10,35,74,79]. In Table 2, the calculated band gaps of three beryllium chalcogenides are accordance with the previous calculations [9,33,34,81], and our results of BeSe and BeTe are close to the available experimental values [13,14,83–85]. All of these comparisons demonstrate and confirm the validity and correctness of our calculation method.

2. Computation methodology and details First-principles calculations were performed by using Cambridge serial total energy package (CASTEP) [66,67], which employs plane-wave ultrasoft pseudopotential method [68] based on DFT theory. By solving Kohn–Sham equation [69] with the self consistent field (SCF) procedure to implement the electronic minimization, the ground state can be found. The SCF convergence threshold was set 5.0  107 eV/atom. Meanwhile, the atoms were relaxed to achieve the minimum total energy of the system to fulfill the geometry optimization by using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm [70]. The convergence tolerance were set as energy for 5.0  106 eV/atom, maximum force for 0.01 eV/Å. For the different atoms, the valence electrons considered in their pseudopotentials are Be 2s2, S 3s23p4, Se 4s24p4, Te 5s25p4, Mn 3d54s2, respectively. Since the different exchange–correlation functional, k-point sampling grids, and cutoff energy, atom layers also have the influence on the calculation accuracy. All the calculations were performed with the parameters after the convergence tests. The calculations of bulk beryllium chalcogenides have been performed as the first step. By comparing these results with experimental or other computational data, the appropriate exchange–correlation functional and parameters were adopted to assure the calculation validity. The stable BeX (X = S, Se, Te) at ambient temperature and pressure are zincblende structure, space group: F-43m (No. 216). The structures of Be0.75Mn0.25X (X = S, Se, Te) are modeled by replacing one Be atom at the corner position of BeX unit cell with Mn atom. Thus their space group is P-43M (No. 215) with cubic structures (Fig. 1b).

3. Results and discussions 3.1. Bulk beryllium chalcogenides and parameters validation The unit cell of bulk BeS, BeSe and BeTe were molded according to the literatures [32,71–73]. Based on the previous calculations [8–10,33,35,40,43,74,75], the exchange correlation functional of GGA-PBE [76] is suitable to the calculation of beryllium chalcogenides. The convergence tests were conducted by examining the dependence of Monkhorst–Pack k-point sampling grids and cutoff energy to the total energy. For the cutoff energy of 450 eV, and kpoints meshes of 10  10  10 for BeX unit cells, their total energy converged less than 5  103 eV/atom. In the following calculations of Be0.75Mn0.25X structures, the k-points were set as 10  10  10 to ensure the calculation accuracy. The lattice constants (a), volume per atom (V0), elastic constants (Cij) and bulk modulus (B) were calculated and the results are presented in Table 1, and the previous theoretical and experimental values are listed as comparison. Some bulk moduli in Table 1 were calculated

3.2. Formation energy and cohesive energy of ternary compounds The formation energies are calculated to assess the stability of Mn alloyed ternary compounds. Based on the previous calculating methods for the formation energy of other systems [52,86], the formation energy per atom (Ef) of Be0.75Mn0.25X can be estimated as:

Ef ðBe0:75 Mn0:25 XÞ ¼ ½EðBeX : MnÞ  4Ebulk ðXÞ  Ebulk ðMnÞ  3Ebulk ðBeÞ=8

ð1Þ

where E(BeX:Mn) is the total energy of alloyed structures by replacing one Be atom with Mn in BeX unit cell, the Ebulk(Mn) and Ebulk(Be) are total energies per atom of fully relaxed bulk hexagonal Be (space group: P63/MMC, 194), cubic Mn (space group: I-43M, 217), respectively. And Ebulk(X) denotes the total energy per atom for orthorhombic alpha-sulfur (space group: FDDD, 70), monoclinic alpha-selenium (space group: P21/N, 14), and trigonal tellurium (space group: P3121, 152) respectively. Cohesive energy (Ec) is the difference between the energy per atom of the bulk material at equilibrium and the energy of free atoms in its ground state, which can be used to evaluate the stability and other thermodynamic properties. And base on the calculation method for other systems [87,88], the cohesive energies of these three structures can be calculated as the following equation:

Ec ðBe0:75 Mn0:25 XÞ ¼ ½EðBeX : MnÞ  4Eatom ðXÞ  Eatom ðMnÞ  3Eatom ðBeÞ=8

ð2Þ

where Eatom is the energy of a free atom in its ground state, and calculated from each isolated atom in a cubic cell with 10 Å lattice constant, so as to avoid the interactions between neighbor atoms. From Table 3, one can find that the lattice constant increases as the sequence from Be0.75Mn0.25S to Be0.75Mn0.25Te with the increase of atomic radius and the electro-negativity of the anions. Their formation energies and cohesive energies are all negative, and the both energetic quantities increase as the same order too. These results show that Be0.75Mn0.25S is more thermodynamic stable than the others, and Be0.75Mn0.25Te is the least stable one among the three structures.

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Fig. 1. The schematic structures of (a) BeX and (b) Be0.75Mn0.25X (X = S, Se, Te).

Table 1 Calculated and experimental values of lattice constants (a), volume per atom (V0), elastic constants (Cij) and bulk modulus (B). XC potential

BeS

Present work Other calc.

Exp.g BeSe

Present work Other calc.

Exp. BeTe

Present work Other calc.

Exp. a b c d e f g h i

Ref. [8]. Ref. [10]. Ref. [35]. Ref. [74]. Ref. [78]. Ref. [79]. Ref. [32]. Ref.[80]. Ref. [71].

i

i

a (Å)

V0 (Å3/atom)

Cij (GPa)

B (GPa)

C11

C12

C44

GGA-PBE LDAa LDAb LDAc LDAd LDAe LDAf GGAPBEa GGAb GGAc GGAd GGAe GGA-WCf 

4.8766 4.800 4.803 4.80 4.798 4.82 4.836 4.878 4.880 4.88 4.879 4.88 4.866 4.87

14.50 13.82 13.85 13.82 13.81 14.00 14.14 14.51 14.53 14.53 14.52 14.53 14.40 14.44

154.85 169 143.1 187  162.4 150.97 146 153.7   158.2 153.15 

58.26 68 84.0 59  64.6 61.59 67 60.6   61.1 60.34 

80.69 106 91.1 93  97.6 78.72 103 110.7   92.7 81.34 

90.46 102 103.7 98 102 97.2 91.38 93 91.60 90 92.1 93.4 91.28 105

GGA-PBE LDA a LDA b LDA c LDA d LDA e GGA-PBE GGA b GGA c GGA d GGA e GGA h 

5.1396 5.085 5.084 5.09 5.081 5.11 5.179 5.178 5.19 5.13 5.15 5.228 5.137

16.97 16.44 16.43 16.48 16.40 16.68 17.36 17.35 17.47 16.88 17.07 17.86 16.94

136.86 137 151.7 145  82.6 117 149.9   126.4  

51.57 58 53.3 51  132.3 57 44.5   50.8  

73.73 90 53.7 61  57.8 90 60.3   79.6  

80.00 84 86.08 85 83.6 83.1 76 79.66 74 75 76 83.87 92

5.6648 5.557 5.556 5.56 5.553 5.57 5.662 5.646 5.67 5.663 5.66 5.617

22.72 21.45 21.44 21.48 21.40 21.60 22.69 22.50 22.79 22.70 22.67 22.15

106.57 98 104.2 102  100.4 104 111.7   96.4 

55.82 46 44.0 39  43.4 35 35.5   39.3 

37.79 68 53.4 63  66.9 59 63.7   60.7 

60.72 63 64.90 68 63.2 62.4 58 60.87 55 56.2 58.4 67

GGA-PBE LDA a LDA b LDA c LDA d LDA e GGA-PBE GGA b GGA c GGA d GGA e 

a

a

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Table 2 Calculated energy band gap (eV) for beryllium chalcogenides (BeS, BeSe and BeTe) in zinc-blende structure and their comparison with other available theoretical and experimental data.

BeS BeSe BeTe a b c d e f g h i j k l

Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref.

Energy band gap (eV)

Present

Other calculations

Indirect (C ? X) Direct (C ? C) Indirect (C ? X) Direct (C ? C) Indirect (C ? X) Direct (C ? C)

3.16 5.51 2.74 4.51 1.99 3.58

3.11a, 5.51a, 2.63a, 4.47a, 1.91a, 3.53a,

3.13b, 5.65b, 2.63b, 4.37b, 1.98b, 3.62b,

2.83c, 5.39c, 2.43c, 4.50c, 1.80c, 3.57c,

Experimental values 2.75d, 5.51d, 2.39d, 4.72d, 1.80d, 3.68d,

3.19e 5.61e 2.79e, 2.63f 4.41e, 4.30f 1.99e 3.58e

4.0g 5.55h 2.8i,j, 2.7k 4.10j, 4.53l

[9]. [33]. [34]. [81]. [78]. [80]. [82]. [83]. [84]. [14]. [85]. [13].

Table 3 Calculated lattice constants (a), formation energies (Ef) and cohesive energies (Ec) of three Be0.75Mn0.25X (X = S, Se, Te) structures. Structures

a (Å)

Ef (eV/atom)

Ec (eV/atom)

Be0.75Mn0.25S Be0.75Mn0.25Se Be0.75Mn0.25Te

5.076 5.323 5.851

0.86353 0.68705 0.25589

4.425 4.050 3.436

3.3. Electronic structure and bonding nature The electronic structures, including band structures, density of states (DOS) and valence electron density plots, are calculated to investigate the bonding nature of Be0.75Mn0.25X. The spin-polarized band structures of three structures are presented in Fig. 2, the DOS and partial density of states (PDOS) plots are depicted in Fig. 3, and valence electron density plots are shown in Fig. 4. The band structures in Fig. 2 obviously show that these three structures are still insulating, as there are band gaps between valence and conduction bands, and the Fermi line does not go through either valence band or conduction band. The minimum of conduction band and maximum of valence band locate at C point, and the band gaps are 1.49 eV, 1.36 eV, 0.78 eV for Be0.75Mn0.25S, Be0.75Mn0.25Se and Be0.75Mn0.25Te respectively. Because the literatures about Mn-alloyed beryllium chalcogenides are hardly found, our above results is reasonable comparing with the

band gap (Eg = 1.31 eV) of Mg0.75Mn0.25Te calculated by Noor et al. [89]. Comparing with BeX (X = S, Se, Te), all the band gaps of three Mn-doped alloys decrease about 53%, 50%, 61%, respectively. The band gap decreases along with the increasing of X atom radius, which is in line with the previous calculations about Zn0.75Cr0.25X (X = S, Se, Te) [90], and Cr-doped BeSe and BeTe [52]. The DOS and PDOS of Be0.75Mn0.25X (X = S, Se, Te) provide a qualitative explanation for the electronic and atomic interactions, and is helpful to understand the bonding nature of these structures. From Fig. 3a–c, one can see that the lower part range around 1114 eV are dominated by the s electrons of S, Se and Te atoms respectively. The middle part range from 6 eV to Fermi level is mainly occupied by the p electrons of S, Se and Te atoms respectively. The parts range around 1–2 eV are mainly contributed by the d electrons of Mn atoms, and the higher parts range around 3–7 eV are dominated by the p electrons of Be atoms. We further note that this is very similar to the PDOS plots of Mg0.75Mn0.25Te [89]. From Fig. 3a–c, the resonant peaks of PDOS curves of Mn, Be and X (X = S, Se, Te) imply that the bonding mainly comes from the electronic interaction between the electrons of Mn-d, Bep and X-p. For a deeper investigation and confirmation of this viewpoint, the C point band composition ranges from 6 eV to Fermi level are calculated and listed in Table 4, the data in this table confessed the same conclusion. In the table, the band number 1–4 which range from 6 eV to 4.5 eV mainly come from the hybridization of Be(s, p) and p electrons of X (X = S, Se, Te) atoms. The band number 5–12 which range from 4 eV to Fermi level are mainly

Fig. 2. Band structures of (a) Be0.75Mn0.25S, (b) Be0.75Mn0.25Se, and (c) Be0.75Mn0.25Te.

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Fig. 3. DOS and PDOS plots of (a) Be0.75Mn0.25S, (b) Be0.75Mn0.25Se, and (c) Be0.75Mn0.25Te.

contributed by the interaction of Mn-d, Be-p and X-p (X = S, Se, Te) electrons. It reveals that the electrons of Mn-d have a positive effect to strengthen the bonding, especially for the higher part occupied energy levels below Fermi level. Besides that, for the band number 13 which range around 0.8–1.5 eV, the electrons are mainly contributed by Mn-d, and the electronic conduction of Be0.75Mn0.25X (X = S, Se, Te) will be affected by the behavior of d electrons of Mn atoms. The charge density distribution directly reflects the electronic structures and interactions. Fig. 4 gives the valence charge density

plots along (1 1 0) plane of Be0.75Mn0.25X (X = S, Se, Te). Moreover, these plots show that the electronic interactions between Mn and X (S, Se, Te) atoms are stronger than other atom pairs, which indicates that the replacement of 25% Be with Mn will strengthen the bonding strength, and makes Be0.75Mn0.25X more stable than BeX. Besides that, by comparing three plots of Fig. 4a–c, one can find that, along with the order from Be0.75Mn0.25S to Be0.75Mn0.25Te, the charge distribution will be more localized around the sites of Mn and X atoms, and the electronic interaction between Mn–X atom pairs will be less intensified as the same order. That phenomenon

Fig. 4. Valence electron density (electrons/Å3) plots along (1 1 0) plane of (a) Be0.75Mn0.25S, (b) Be0.75Mn0.25Se, and (c) Be0.75Mn0.25Te.

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J. Li et al. / Journal of Alloys and Compounds 575 (2013) 190–197 Table 4 Band composition at C point from 6 eV to Fermi level for the structures of Be0.75Mn0.25X (X = S, Se, Te). Band number

Energy (eV)

Mn

Be0.75Mn0.25S 1 2 3 4 5 6 7 8 9 10 11 12 13

5.86 5.68 5.23 4.82 3.72 3.44 3.37 3.20 2.66 2.08 1.56 0.01 1.49

s s s s s s s s s s s s s

Band number

Energy (eV)

Mn

Be0.75Mn0.25Se 1 2 3 4 5 6 7 8 9 10 11 12 13

5.70 5.54 5.09 4.68 3.57 3.19 3.25 3.02 2.56 2.28 1.33 0.00 1.36

s s s s s s s s s s s s s

Band number

Energy (eV)

Mn

Be0.75Mn0.25Te 1 2 3 4 5 6 7 8 9 10 11 12 13

5.37 5.24 4.89 4.46 3.45 2.90 2.84 2.74 2.70 2.44 1.05 0.00 0.78

s s s s s s s s s s s s s

0.85%; 0.88%; 1.74%; 2.35%; 1.82%; 1.55%; 1.52%; 1.49%; 1.95%; 0.90%; 0.19%; 0.13%; 0.11%;

1.08%; 1.08%; 2.03%; 3.16%; 2.21%; 1.51%; 1.59%; 1.40%; 1.38%; 1.24%; 0.46%; 0.07%; 0.18%;

1.37%; 1.41%; 2.31%; 4.97%; 2.08%; 1.35%; 1.31%; 1.25%; 1.23%; 1.16%; 0.61%; 0.14%; 0.12%;

p p p p p p p p p p p p p

p p p p p p p p p p p p p

p p p p p p p p p p p p p

0.02%; d 0.06%; d 0.31%; d 0.87%; d 0.85%; d 1.01%; d 1.08%; d 1.27%; d 1.38%; d 2.03%; d 1.18%; d 9.46%; d 2.52%; d

0.34%; 0.36%; 0.53%; 0.99%; 1.08%; 1.48%; 1.41%; 1.62%; 1.62%; 1.61%; 2.76%; 9.54%; 1.45%;

d d d d d d d d d d d d d

0.87%; d 0.79%; d 0.64%; d 0.82%; d 1.01%; d 1.82%; d 1.85%; d 1.88%; d 1.88%; d 1.93%; d 8.00%; d 9.86%; d 1.57%; d

Table 5 Calculated total magnetic moment hMi of Be0.75Mn0.25X (X = S, Se, Te) and local magnetic moment of Mn, Be and X. Structures

hMi (lB)

Mn (lB)

Be (lB)

X (lB)

Be0.75Mn0.25S Be0.75Mn0.25Se Be0.75Mn0.25Te

5.00 5.00 5.00

4.74 4.84 4.90

0.02 0.04 0.06

0.04 0.02 0.02

can be interpreted as that the atomic bonding will be less strong along with the order from Be0.75Mn0.25S to Be0.75Mn0.25Te, and the thermodynamic stability of these three alloys will decrease as the same order, which is accordance with the aforementioned conclusion in the part of 3.2 according to the formation energy and cohesive energy. Moreover, the previous investigation of Zn1xMnxY (Y = S, Se, Te) [91] also support the similar result: there is a decreasing d charge transfer goes from S to Te. Summarily, the large amount (25%) Mn doping in BeX (X = S, Se, Te) is positive to decrease the band gap, and has a direct influence to the electronic conduction ability. And the atomic bonding of Be0.75Mn0.25X are mainly contributed by the electronic

2.69% 3.35% 4.12% 8.25% 15.65% 19.40% 19.87% 19.41% 13.55% 25.92% 44.92% 34.51% 84.08%

2.25% 2.65% 3.27% 7.30% 19.73% 23.94% 24.00% 21.65% 15.65% 20.33% 35.90% 25.70% 78.60%

1.93% 2.17% 2.77% 7.06% 34.38% 26.37% 24.67% 22.30% 21.83% 20.23% 18.99% 13.50% 79.99%

Be

S

s s s s s s s s s s s s s

s s s s s s s s s s s s s

14.36%; p 10.73% 15.37%; p 9.30% 14.56%; p 7.80% 8.05%; p 8.57% 2.66%; p 15.01% 1.89%; p 14.18% 1.78%; p 13.95% 1.53%; p 13.79% 1.02%; p 13.75% 1.20%; p 7.58% 1.07%; p 7.81% 0.51%; p 1.89% 2.85%; p 7.74%

0.48%; 0.61%; 0.95%; 1.16%; 0.53%; 0.52%; 0.52%; 0.52%; 0.39%; 0.35%; 0.36%; 0.10%; 0.36%;

Be

Se

s s s s s s s s s s s s s

s s s s s s s s s s s s s

15.96%; p 10.36% 17.27%; p 9.11% 17.20%; p 7.83% 10.01%; p 9.40% 2.42%; p 14.87% 1.65%; p 14.11% 1.71%; p 14.11% 1.54%; p 14.65% 1.10%; p 15.53% 1.28%; p 13.40% 0.58%; p 7.88% 0.39%; p 2.04% 3.18%; p 6.05%

70.86% 70.42% 70.52% 70.74% 63.48% 61.46% 61.28% 61.99% 67.97% 62.03% 44.48% 53.39% 2.34%

1.06%; p 68.95% 1.24%; p 68.29% 1.94%; p 67.20% 2.35%; p 66.79% 1.60%; p 58.10% 1.63%; p 55.68% 1.58%; p 55.60% 1.75%; p 57.38% 1.60%; p 63.11% 1.7 4%; p 60.40% 2.63%; p 49.80% 1.95%; p 60.31% 8.69%; p 1.84%

Be

Te

s s s s s s s s s s s s s

s s s s s s s s s s s s s

21.37%; p 8.68% 22.76%; p 7.81% 23.31%; p 6.68% 14.67%; p 7.68% 2.76%; p 11.94% 2.34%; p 16.62% 2.38%; p 17.27% 2.37%; p 18.22% 2.33%; p 18.43% 1.95%; p 18.85% 0.96%; p 8.24% 0.40%; p 4.36% 6.01%; p 5.41%

p p p p p p p p p p p p p

1.48%; 1.70%; 2.33%; 3.09%; 2.47%; 1.96%; 1.89%; 1.72%; 1.66%; 1.43%; 2.63%; 1.59%; 5.34%;

p p p p p p p p p p p p p

64.31% 63.37% 61.96% 61.71% 45.37% 49.55% 50.63% 52.25% 52.64% 54.45% 60.57% 70.14% 1.56%

interactions and hybridizations between Mn-d and X-p, especially for the higher occupied levels range from 4 eV to Fermi level. Mn dopant is helpful to strengthen the atomic bonding, and makes the ternary compounds of Be0.75Mn0.25X more stable than BeX. 3.4. Magnetic properties For the investigation of the magnetic properties, the total magnetic moments of Be0.75Mn0.25X and local magnetic moments of Mn, Be and X are calculated and listed in Table 5. Although the accuracy of magnetic moment calculated by using first-principles method is still disputable, especially there is significant deviation between the magnetic moments calculated with different exchange correlation functionals. However, from Table 5, one can qualitatively find that the total magnetic moments of three structures are identical, and the main part of them is mainly contributed from Mn. Meanwhile, the local magnetic moments of Mn and Be increase as the order of Be0.75Mn0.25S, Be0.75Mn0.25Se and Be0.75Mn0.25Te, while the local magnetic moment of X decrease as the same sequence. Considering Table 5 and PDOS plots in Fig 3, it is obvious that the Mn 3d states overlap significantly with those of p states of S, Se and Te near Fermi level, especially in the range from  1 eV

196

J. Li et al. / Journal of Alloys and Compounds 575 (2013) 190–197

Fig. 5. Spin density (electrons/Å3) plots along (1 1 0) plane of (a) Be0.75Mn0.25S, (b) Be0.75Mn0.25Se, and (c) Be0.75Mn0.25Te.

Table 6 Calculated spin-exchange splitting energies (Dx(d)) for Mn-3d state, exchange splitting energies (Dx(pd)) (eV) and exchange constants (N0a and N0b) for three Be0.75Mn0.25X (X = S, Se, Te).

a

Structures

Dx(d) (eV)

Dx(pd) (eV)

N0a

N0b

Be0.75Mn0.25S Be0.75Mn0.25Se Be0.75Mn0.25Te

3.55 3.59 4.46

1.54 1.32 1.05

2.02 1.73 1.68

2.46 2.11 1.68 1.31a

Ref. [101].

to 2.5 eV. And this indicates there is a strong interaction between Mn-d and X-p, which will result in the splitting of the energy levels near Fermi level. For the structures of Be0.75Mn0.25X, Mn atom locates in a tetrahedral interstice surrounded by four X atoms. According to the crystal field theory (CFT) [92,93], the Mn-3d orbi2 2 tals will split into t2g (dxy, dxz and dyz) and eg (dx  y2 and dz ) sets of states. For the valence band, although the up-spin and down-spin are all filled (refer to Fig. 3), but the energy levels of up-spin states are much higher than down-spin states. And for the conduction band, there are only unoccupied down-spin states around 1 eV to 2.5 eV. That is very helpful to understand the reason of the local magnetic-moment formation. The corresponding spin-density distributions alone (1 1 0) plane are shown in Fig. 5. Most of the spin densities in the three Mn-alloyed structures are localized around Mn sites. It is obvious that their magnetic moment is mainly contributed from the splitting 3 d orbitals of Mn. Spin exchange splitting energy of Mn-3d (Dx(d)) is usually defined as the difference between the energy levels corresponding to the up-spin and down-spin peaks. Another important exchange splitting energy is Dx(pd) defined as the difference between the tops of valence bands for up-spin and down-spin respectively, namely Dx ðpdÞ ¼ E#v  E"v . And the two quantities are commonly used to evaluate the magnetic properties of DMSs [94–97]. The calculated Dx(d) for Mn-d states and Dx(pd) of three Mn-alloyed compounds are listed in Table 6. The Dx(d) and Dx(pd) increase along with the increasing of X atomic radius from S to Te. The negative values of Dx(pd) indicate that the effective potential for the down-spin is more attractive than that of up-spin, which is consistent with the previous studies of other Mn-doped systems [97–100]. The exchange constants N0a and N0b are calculated from the band structures of ferromagnetic Be0.25Mn0.75X according to the following equations [102,103]:

N0 a ¼

DE c ; xhSi

ð3Þ

N0 b ¼

DEv ; xhSi

ð4Þ

where DEc and DEv are the band edge splitting of the conduction band minima and valence band maxima at the C point (namely, DEc ¼ E#c  E"c , DEc ¼ E#v  E"v ), x is the concentration of Mn, and hSi ¼ hMi=2, in which hMi is the total magnetic moment of the unit cell. In this paper, the values of Dx(pd) and DEv are equal. Calculated N0a and N0b are given in Table 6. N0b = 1.68 for Be0.75Mn0.25Te in our results is very close to the data (1.31) in the available literature [101]. From Table 6, one can find that the magnitude (absolute value) of both constants decreases along with the atom radius increasing from S to Te, which implies the interaction of valence electrons between Mn-3d, X-p and Be-2s will be more and more weak as the X changing from S to Te. And both negative N0a and N0b for Be0.75Mn0.25X indicate that the interactions of Be(2s)Mn(3d) states and X(p)-Mn(3d) states are all attractive. For the Be0.75Mn0.25S and Be0.75Mn0.25Se, the magnetic contribution from p–d interaction is slightly stronger than the s–d interaction, while for Be0.75Mn0.25Te, the interactions of p–d and s–d are basically equal. 4. Conclusions The ordered Be0.75Mn0.25X (X = S, Se, Te) are fully optimized by using first-principles method, and the equilibrium lattice parameter, energy quantities, electronic structures and magnetic parameters are calculated for a insight of their electronic and magnetic properties. The calculations of electronic structures, including band structure, DOS and PDOS, valence electron distribution and band composition at C point, reveal that: (1) comparing with BeX, there are smaller band gaps of 1.49 eV, 1.36 eV, 0.78 eV for Be0.75Mn0.25S, Be0.75Mn0.25Se, Be0.75Mn0.25Te, respectively. (2) The atomic bonding of Be0.75Mn0.25X is mainly contributed by the interactions between Mn-d and X-p. (3) The electronic interaction decreases from Be0.75Mn0.25S to Be0.75Mn0.25Te, and subsequently, the bonding strength should have a downward tendency as the same order. The local magnetic moment of Mn, the exchange splitting energies of Dx(pd) for Mn-3d increase along with the increasing of X atom radius. And the effective potential for down-spin is more attractive than that for up-spin, and it decreases along with the increasing of X atom radius. Negative N0a and N0b indicate that the interactions of Be(2s)-Mn(3d) states and X(p)-Mn(3d) states are all attractive. And the interactions of s–d and p–d decrease along with the atom X changing from S to Te. Acknowledgements The authors acknowledge the financial support for the research from the material processing key subject of Xi’an Shiyou University

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