Spin-polarized structural, elastic, electronic and magnetic properties of half-metallic ferromagnetism in V-doped ZnSe

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Spin-polarized structural, elastic, electronic and magnetic properties of half-metallic ferromagnetism in V-doped ZnSe M. El Amine. Monir, H. Baltache, G. Murtaza, R. Khenata, Waleed K. Ahmed, A. Bouhemadou, S. Bin Omran, T. Seddik

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Received date: 4 March 2014 Revised date: 25 July 2014 Cite this article as: M. El Amine. Monir, H. Baltache, G. Murtaza, R. Khenata, Waleed K. Ahmed, A. Bouhemadou, S. Bin Omran, T. Seddik, Spin-polarized structural, elastic, electronic and magnetic properties of half-metallic ferromagnetism in V-doped ZnSe, Journal of Magnetism and Magnetic Materials, http://dx.doi.org/10.1016/j.jmmm.2014.08.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Spin-polarized structural, elastic, electronic and magnetic properties of half-metallic ferromagnetism in V-doped ZnSe M. El Amine. Monir a, H. Baltache a, G. Murtazab, R. Khenata a , Waleed K. Ahmed c, A. Bouhemadou d, S. Bin Omran e, T. Seddika a Laboratoire de Physique Quantique de la Matière et de la Modélisation Mathématique (LPQ3M), Faculté des Sciences, Université de Mascara, Mascara 29000, Algeria. b Materials Modeling Lab, Department of Physics, Islamia College University, Peshawar c ERU, Faculty of Engineering, United Arab Emirates University, Al Ain, UAE. d Laboratory for Developing New Materials and their Characterization, Department of Physics, Faculty of Science, University of Setif, 19000 Setif, Algeria e Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia Abstract Based on first principles spin-polarized density functional theory, the structural, elastic electronic and magnetic properties of Zn1-xVxSe (for x = 0.25, 0.50, 0.75) in zinc blende structure have been studied. The investigation was done using the full-potential augmented plane wave method as implemented in WIEN2k code. The exchange-correlation potential was treated with the generalized gradient approximation PBE-GGA for the structural and elastic properties. Moreover, the PBE-GGA+U approximation (where U is the Hubbard correlation terms) is employed to treat the “d” electrons properly. A comparative study between the band structures, electronic structures, total and partial densities of states and local moments calculated within both GGA and GGA+U schemes is presented. The analysis of spinpolarized band structure and density of states shows the half-metallic ferromagnetic character and are also used to determine s(p)-d exchange constants N0α (conduction band ) and N0β (valence band) due to Se(4p)-V(3d) hybridization. It has been clearly evidence that the magnetic moment of V is reduced from its free space change value of 3µB and the minor atomic magnetic moment on Zn and Se are generated.

Keywords: half-metallic; magnetic moment; band structure; FP-LAPW; GGA. ---------------------------------------------------------------------------------------------------------*Corresponding author. LPQ3M-Laboratory, Faculty of Science and Technology, Mascara University - 29000 Mascara, Algeria.

Fax: (213) 45802923; E-mail [email protected] (G. Murtaza).

address:

[email protected]

(R.

Khenata);

1. Introduction The half-metallic (HM) ferromagnetic and the diluted magnetic semiconductors (DMS) materials based on II-VI compounds and their alloys have seen a vast technological application in spintronics [1], in photovoltaic devices [2] as electron-optic crystals, electron acoustic, high density optical memories, photo-detectors, solar cells and short wavelength lasers, which are due to their magnetic and magneto-optical properties. The DMS are the compounds in which a part of their atom is substituted by transition metal atoms such as V, Cr, Mn, Fe, Co and Ni [3]. It was reported that the II-VI zinc blende semiconductors doped with transition materials are half-metals with ferromagnetic (FM) or antiferromagnetic (AFM) ordering [4-5]. Half metallic ferromagnets have an exceptional electronic structure, two spin channels: spin up has a metallic character while spin down has a gap at the Fermi level. The half metallic ferromagnet becomes DMSs when the fraction of the transition metal cation substitute is very small. Since the first prediction of Groot et al., on the half-Heuster alloys NiMnSb and PtMnSb [6], many theoretical studies have been discovered that predict stable HM ferromagnetism that include metal oxides such as Fe3O4 [7] and CrO2 [8], full-Heusler compounds Co2MnSi [9] and Co2FeSi [10], perovskite alloys La0.7Sr0.3MnO3 [11], Sr2FeMoO6 [12] and transition metals doped II-VI semiconductors in zinc blende structure, such as Cr-doped BeSe and BeTe [13-14], Mn-doped GaN and AlSb [15-16] yet the established experimentally applications have only realized by doping Mn and Cr in ZnTe [1718]. It is well known that the calculations based on the DFT within the local-density approximation (LDA) and the generalized gradient approximation (GGA) are qualitatively

accurate and mostly helpful for the interpretation of experimental data [19]. However, the major drawback of DFT formalism with LDA and GGA is the improper interpretation of the excited state properties, such as the underestimation of the band gap value [20,21] or the overestimation of the electron delocalization, particularly for systems with localized d and f electrons [22-24]. At present other approximations beyond the LDA and GGA, such as the “Scissor operator” [25],

HSE-hybrid functional [24,26] ,

LSDA+U [27,28 ] and the

quasiparticle Green’s- function based- methods [29], like the GW approximation [30] are developed in order to describe accurately the electronic structure of semiconductors In the present work, we have performed first principle DFT calculations on the structural, elastic, magnetic and electronic structure of V doped zinc blende ZnSe using the generalized gradient approximation (PBE-GGA) plus optimized effective Hubbard parameter U (PBE-GGA +U) within the framework of density functional theory (DFT). It is found that for the doping concentrations (x = 0.25, 0.50, 0.75), the investigated alloy has a half-metallic character. The rest of the paper is as follows, Sec. 2 deals with the brief description of the computational detail of this study. In Sec. 3, details of the obtained results and discussion related to the structural, elastic, electronic and magnetic properties of V-doped zinc blende ZnSe compound are given. Main conclusions of our present work are summarized in Sec. 4. 2. Calculation method The first principle calculations on the structural, elastic, electronic structure as well as the magnetic properties of Zn1-xVxSe for x = 0.25, 0.50 and 0.75 compounds was accomplished through the full-potential linear augmented plane-wave (FP-LAPW) method [31]. The approach is based on the density functional theory [32], as implemented in the WIEN2k package [33]. The generalized gradient approximation proposed by Perdew-BurkeErnzerhof (PBE-GGA) [34] is adopted for the calculations of the structural and elastic properties. Since the GGA is known do not describe exactly the electronic ground state of systems with delocalized “d” electrons. Hence, we have calculated the electronic and

magnetic properties of the herein studied compounds by using the generalized gradient approximation plus the optimized Hubbard term U (PBE-GGA +U) [27, 28,35]. The value of Hubbard term U is generally estimated through the comparison between the calculated physical properties and the experimental ones if its experimental value is not available (See Ref.[36]). In this present work, the value of Coulomb repulsion term U of vanadium was taken as 2.73 from Ref. [37] while its value for the zinc was optimized and shown in Fig. 3. The muffin-tin radii RMT are taken to be 2.34, 2.08 and 2.34 atomic units (a.u.) for Zn, Se and V, respectively. The convergence parameter RMTKmax, which controls the size of the basis sets in these calculations, was set to 8. The Brillouin zone integration was performed using 35 kpoints where are based on the mesh of 9×9×9. The self-consistent calculations process is repeated the total energy convergence is less than 10-4 Ry per formula unit. The semiconductor ZnSe crystallizes in zinc blende structure with a space group C

F 4 3m (No.216) and experimental lattice constant of 5.667 Å [38]. The Zn atom occupies the origin, and the Se atom is localized at (1/4, 1/4, 1/4). The substitution of V in ZnSe gives the Zn1-xVxSe alloys. For x = 0.25 and 0.75, V atoms occupy the apex and the face-center sites in C

the unit cells, respectively, with space group P 4 3m (No.215). In the case of x =0.50, V atoms are localized at the four face-center sites in the crystal and the structure crystalline belong to C

space group P 4 m2 (No.115). 3. Results and discussion 3.1. Structural properties

In order to determine the structural properties of the herein studied binary compounds and their ternary alloys such as lattice parameter a0 , the bulk modulus B and its first derivative B’, the calculated total energy versus volume curve is fitted by the BirchMurnaghan’s equation of state (EOS) [39] given by the following expression:

ETot (V ) = E0 (V ) +

B' ⎤ B0V ⎡ ⎛ V0 ⎞ ⎛ V0 ⎞ ⎢ B ⎜ 1 − ⎟ + ⎜ ⎟ − 1⎥ B '( B '− 1) ⎣⎢ ⎝ V ⎠ ⎝ V ⎠ ⎦⎥

(1)

where V0 is the volume of static equilibrium of the mesh, E0 is the total energy per primitive cell in the ground state, B is the bulk modulus and B' is the pressure derivative of the bulk modulus. Fig.1 shows the ferromagnetic total energy optimization plots of Zn1-xVxSe for x = 0.25, 0.50, 0.75 and 1 with PBE-GGA in zincblende structure as a function of volume. The summarized results on the structural parameters are compiled in Table 1. It is clear that the calculated equilibrium lattice constants of ZnSe and VSe are in good agreement with the others experimental and theoretical data. Moreover, it is shown that the maximum discard between the present work of the lattice parameters and the other theoretical calculations and experimental data is 0.95% and 3.08% for ZnSe and VSe, respectively. For the ternary Zn1xVxSe

alloys, no experimental data in the literature have been reported to compare with the

present work. It is observed from Fig.2 that the increase of the lattice parameter and the decrease of the bulk modulii with the increase of the V-doped concentration, which confirms the augmentation of the V-doped percentage force the robustness of the crystal. The overestimation of the lattice parameters and the underestimation of the bulk modulus in comparison with the experimental data of ZnSe and VSe compounds are due to using of the PBE-GGA approximation.

3.1. Elastic properties

The using of the numerical first-principles calculation method developed by Thomas Charpin [21] which was integrated in the WIEN2k package is to predict the elastic constants for cubic crystal of Zn1-xVxSe alloys. The aforementioned method is employed for small strains of the strain tensor δ. The cubic structure has just three independent elastic constants C11, C12 and C44 that we need three independent equations to determine their values. To calculate C11 and C12, the first equation involves calculating the bulk modulus is applied: (2)

B = (C11 + 2C12)/3 And the second equation involves the volume conserving tetragonal strain tensor, ⎡ ⎢δ ⎢ ⎢0 ⎢ ⎢0 ⎢⎣

0

δ 0

⎤ ⎥ 0 ⎥ 0 ⎥ ⎥ 1 ⎥ − 1 (1 + δ ) 2 ⎥⎦

(3)

Where the total energy has the following expression:

E (δ) = E (0) + 3(C11 - C12) V0 δ2 + O (δ3)

(4)

Where V0 is the volume of the unit cell. Finally, to calculate C44 the third equation involves the volume conserving rhombohedral strain tensor which is presented as follows: ⎡1 1 1⎤

δ⎢ ⎥ ⎢1 1 1⎥ 3

(5)

⎢⎣1 1 1⎥⎦

The total energy then expressed as a function of deformation

1 E (δ ) = E (0) + (C11 + 2C12 + 4C44 ) V0δ 2 + O(δ 3 ) 6 (6) The mechanical stability of the cubic crystal can be satisfied only by Born stability criteria [40].

                    C44 > 0 (7a) C11 − | C12 |> 0 (7b) C11 + 2C12 > 0 (7c) 

                                                                          In view on Table 2, it is seen that the difference between the present results and the experimental data is not more than 69.46 %. For the binary ZnSe and VSe compounds, it was found that present results for C11 and C12 are in reasonable agreement with the other experimental and theoretical values, whereas C44 has a large relative error than those available

in the literature. Due to the lack of any theoretical and experimental data for the ternary Zn1xVxSe

alloys which gives the opportunity to considerate the elastic constants obtained in the

present work as a good reference for further work. Based on the Born stability criteria, the Zn1-xVxSe alloys are considered as mechanically stable. Another important parameter is the internal strain parameter ξ introduced by Kleinman [41] and describes the relative positions of the cation and anion sublattices under volume, defined by the relation [42, 43]:

ζ =

C11 + 8C12 7C11 + 2C12

(8)

The obtained values of ξ parameter show the conserving strain distortion positions are not fixed by symmetry.

3.3. Electronic properties 3.3.1. Electronic structure The spin-polarized band structures of zinc blende Zn1-xVxSe alloys (x = 0.25, 0.50 and 0.75) are calculated at their equilibrium lattice constants within the PBE-GGA and PBEGGA+U schemes. Figs. 4-6 depict the spin-up (majority spin) and spin down (minority spin) electronic band structures of the alloys at 0.25, 0.50 and 0.75, respectively, along the high symmetry direction of the first Brillouin zone. Following these figures, the bottom of the conduction bands and the top of the valence bands are situated at the Γ point in the Brillouin zone, resulting in direct band gap. It is clear for the majority spin states of the alloys, the energy bands cross the Fermi level while in the minority spin states are localized underneath the Fermi level, confirming the half-metallic characteristic of these alloys. For the minorityspin states of Zn0.25V0.75Se and Zn0.75V0.25Se, one energy band cuts the Fermi level, so these compounds are nearly half-metallic. In the majority-spin states case, the Zn d states appear the bands around -8 eV for PBE-GGA and between -14.5 eV and -13 eV for PBE-GGA+U,

the bands between (-7 eV and -2 eV) and (-7 eV and -2.5 eV) for PBE-GGA and PBEGGA+U, respectively, came globally from Se p states, for the bands that are situated around the Fermi level originate from d states of V atom. The half-metallic gap (EHM) is defined as the minimum between the lowest energy of majority-spin and minority-spin conduction bands with respect to the Fermi level, and the absolute values of the highest energy of majority-spin and minority-spin valence bands [44, 45]. The estimated values of spin-down energy gap (Eg) and the half-metallic gap (EHM) values were obtained using the PBE-GGA and PBE-GGA+U approximations for these alloys are reported in Table 3, which show increases with the increase of the V concentrations. The values of the calculated band gaps with PBE-GGA+U scheme are significantly improved over the results based on PBE-GGA compared to the experimental and theoretical values which is due to fact that the U-Hubbard correlation is fully influenced the V-3d states. The HM gaps obtained by using the PBE-GGA+U of Vdoped ZnSe lead to high Curie temperature are comparable with experiments [46].

3.3.2. Density of states To study the nature of the electronic structure of the investigated alloys for different concentrations, the total and the partial density of states (TDOS and PDOS) of the ferromagnetic zinc blende phase for spin-up and spin-down channels are also calculated by employing both the PBE-GGA and PBE-GGA+U parameterizations. These are displayed in Figs.7 and 8. Fig.8 shows a large exchange splitting between the majority and the minority spins states around the Fermi level. The spin-up electrons have a metallic character while the apparition of the band gap at the Fermi level in the spin-down electrons which explain the semiconducting nature of the alloys. Therefore, the half-metallic characteristic of Zn0.50V0.50Se in zinc blende phase is confirmed. From the PDOS plots, we remark that the part around -9 eV is mainly originate from Zn d states, in the both spin cases, the bands between 7.058 eV and -3.439 eV for PBE-GGA and between -6.993 eV and -2.451 eV for PBE-

GGA+U are the states of Se atom with small contributions of V-3d, Zn-3s and 3p states, whereas the bands that approach the Fermi level, are the source of strong hybridization between Se-4p and V-3d states. These states occupy mainly the upper part of the valence band and the bottom part of the conduction band.

3.2. Magnetic properties 3.2.1. Exchange coupling

From the ferromagnetic spin-polarized band structure, we have defined the exchange constants N0α and N0β as s-d exchange constant (conduction band) and p-d exchange constant (valence band), respectively, where N0 is the concentration of the cation. Assuming the usual Kondo interactions N0α and N0β are given as [47]. N 0α =

ΔEc ΔEv ; N0 β = x〈 S 〉 x〈 S 〉

(9)

Where ΔEc and ΔEv are the conduction and valence band edge splitting at the Γ point of the Brillouin zone, respectively, x is the concentration of V atom and 〈S〉 is one-half of magnetization per V atom. The nature of attraction is deducted from the p-d exchange constants Δxc(pd) = Ec(↓)-Ec(↑) and Δxv(pd) = Ev(↓)-Ev(↑). Employing PBE-GGA and PBEGGA+U schemes, the calculated data of Δxc(pd), Δxv(pd) , N0α and N0β are presented in Table 4. The results show that the exchange constants of the alloys decrease with the increasing concentration of vanadium, which confirm the magnetic character of these alloys. Also we note that the p-d exchange constants N0β have negative values that demonstrate the important attraction of the effective potential which came from the minority spin states.

3.2.2. Magnetic moment With the help of PBE-GGA and PBE-GGA+U schemes, the total magnetic moments (MTot) of Zn1-xVxSe alloys (x = 0.25, 0.50, 0.75 and 1) and atomic magnetic moments of Zn, V and Se are calculated and presented in Table 5. Values obtained illustrate that the total

magnetic moment is mainly originated from transition metal of V atom with small contribution of Zn and Se atoms. It is can be seen from Fig.9 that the MTot increases with the increasing of V concentration, which confirms the ferromagnetic nature of the compounds. It is clear that the change of the total magnetic moment follow Hund’s rule. We can also remark that the free space charge value of V-3d is reduced from 3µB due to the p-d hybridization between V-3d and Se-4p states; also it causes the birth of small atomic moments on the nonmagnetic Zn and Se sites. The atomic magnetic moments of V and Se are in opposition signs that explain the valence band spins having mostly Se p character interact antiferromagnetically with V-3d spins, such as the earlier work reported in Zn1-xCrxSe [48].

4. Conclusions In summary, the present work contributes to the structural, elastic, electronic and magnetic properties of zinc blende Zn1-xVxSe alloys for x = 0.25, 0.50 and 0.75, using the FPLAPW approach within the spin-polarized density functional theory (SP-DFT). The generalized gradient approximation of (PBE-GGA) is applied in calculations of structural and elastic properties whereas the electronic and magnetic properties are approached by the both (PBE-GGA) and (PBE-GGA+U) schemes where the GGA+U is generally improved which is due to the influenced of the U-Hubbard correlation on the V-3d states. The electronic properties calculations at the equilibrium lattice parameters disclose that the Zn0.25V0.75Se and Zn0.75V0.25Se alloys have nearly half-metallic nature whereas the Zn0.50V0.50Se alloy has a complete half-metallic character. The parameters p-d exchange splitting Δxv(pd) and Δxc(pd) are evaluated from the both TDOS and PDOS while the negative sign of Δxv(pd) is explained by the more attractive of the effective potential for spin-down potential than for spin-up case. The elastic constants for the binary compounds ZnSe and VSe are in good agreement with other calculations and experimental data apart from C44. For the elastic constants of the ternary alloys, we have not found any other reference in the literature to compare our

estimated values. The exchange constants N0α and N0β values are in opposition signs which confirm that the valence and the conduction states interact with opposite manner during the exchange splitting operation. The total magnetic moment progress as concentration of V increases from 0.25 to 1 which is mostly contributed by V atom. For all alloys, the hybridization between V-3d and Se-4p reduces the atomic magnetic moment of V atom from its free space charge and contribute small local magnetic moments on the nonmagnetic Zn and Se sites.

Acknowledgements Author (K. R., A. B. and S. B. O.) acknowledge the financial support provided by the Deanship of Scientific Research at King Saud University for funding the work through the research group project N0 RPG-VPP-088.

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Figure captions Fig.1 Calculated total energy optimization variation versus volumes for ZB Zn1-xVxSe alloys at (a) x = 0.25, (b) x = 0.50, (c) x = 0.75 and (d) x = 1. Fig.2 Comparison between the lattice parameters of lattice constant and bulk modulus for ZB Zn1-xVxSe alloys with Vegard’s law as a function of concentration x. Fig.3 Optimized band gap energy (Eg) versus U-Hubbard correlation of zincblende ZnSe compound. Fig.4 Spin polarized electronic band structure of ZB Zn0.75V0.25Se alloy at the equilibrium lattice parameter using PBE-GGA and PBE-GGA+U.

Fig.5 Spin polarized electronic band structure of ZB Zn0.50V0.50Se alloy at the equilibrium lattice parameter using GGA and GGA+U. Fig.6 Spin polarized electronic band structure of ZB Zn0.25V0.75Se alloy at the equilibrium lattice parameter using PBE-GGA and PBE-GGA+U.. Fig.7 Spin-dependent total density of states (TDOS) of the equilibrium ZB Zn1-xVxSe alloys at (a) x = 0.25, (b) x = 0.50 and (c) x = 0.75 using PBE-GGA and PBE-GGA+U. Fig.8 Spin-dependent partial density of states (PDOS) of the equilibrium ZB Zn1-xVxSe alloys at (a) x = 0.25, (b) x = 0.50 and (c) x = 0.75 using PBE-GGA and PBE-GGA+U. Fig.9 Total magnetic moment of ZB Zn1-xVxSe alloys per unit cell as a function of x concentration using PBEGGA and PBE-GGA+U.

Fig.1 Calculated total energy optimization variation versus volumes for ZB Zn1-xVxSe alloys at (a) x = 0.25, (b) x = 0.50, (c) x = 0.75 and (d) x = 1.

Fig.2 Comparison between the lattice parameters of lattice constant and bulk modulus for ZB Zn1-xVxSe alloys with Vegard’s law as a function of x.

Fig.3 Optimized band gap energy (Eg) versus U-Hubbard correlation of zincblende ZnSe compound.

4

4

Zn0.75V0.25Se with GGA

Spin Up

Spin Dn

2

2

EF

-2

-4

-2

-4

-6

-6

-8

-8

W

L

Λ

Γ

Δ

EF

0

Energy (eV)

Energy (eV)

0

X Z W K

W

L

Λ

Γ

Δ

X Z W

K

4

4

Spin Up

Spin Dn

Zn0.75V0.25Se with GGA+U

Zn0.75V0.25Se with GGA+U

2

2

EF

-2

-4

-2

-4

-6

-6

-8

-8

W

L

Λ

Γ

Δ

X Z W

K

EF

0

Energy (eV)

0

Energy (eV)

Zn0.75V0.25Se with GGA

W

L

Λ

Γ

Δ

X Z W K

Fig.4 Spin polarized electronic band structure of ZB Zn0.75V0.25Se alloy at the equilibrium lattice parameter using PBE-GGA and PBE-GGA+U.

4

4

Spin Up

Spin Dn

Zn0.50V0.50Se with GGA

2

2

EF

-2

-4

-4

-6

-8

-8

L

Λ

Γ

Δ

X

Z W

K

W

L

Λ

Γ

Δ

X

Z W

K

4

Spin Up

Zn0.50V0.50Se with GGA+U

Zn0.50V0.50Se with GGA+U

Spin Dn

2

2

EF

-2

-4

-2

-4

-6

-6

-8

-8

W

L

Λ

Γ

Δ

X Z

W

K

EF

0

Energy (eV)

0

Energy (eV)

-2

-6

W

EF

0

Energy (eV)

Energy (eV)

0

4

Zn0.50V0.50Se with GGA

W

L

Λ

Γ

Δ

X

Z

W K

Fig.5 Spin polarized electronic band structure of ZB Zn0.50V0.50Se alloy at the equilibrium lattice parameter using PBE-GGA and PBE-GGA+U.

4

4

Spin Up

Spin Dn

Zn0.25V0.75Se with GGA

2

2

EF

-2

-4

-2

-4

-6

-6

-8

-8

W

L

Λ

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Δ

EF

0

Energy (eV)

Energy (eV)

0

W

X Z W K

L

Λ

Γ

Δ

X Z W K

4

4

Spin Up

Zn0.25V0.75Se with GGA+U

Spin Dn

2

Zn0.25V0.75Se with GGA+U

2

EF

-2

-4

-2

-4

-6

-6

-8

-8

W

L

Λ

Γ

Δ

X Z W

K

EF

0

Energy (eV)

0

Energy (eV)

Zn0.25V0.75Se with GGA

W

L

Λ

Γ

Δ

X Z W K

Fig.6 Spin polarized electronic band structure of ZB Zn0.25V0.75Se alloy at the equilibrium lattice parameter using PBE-GGA and PBE-GGA+U..

0 -10 -20 -30 -40

-14 -12 -10

-8

-6

-4 -2 0 Energy (eV)

2

4

EF

30

6

8

10

b)

Spin Up Spin Dn

20 10 0 -10 -20 -30 -40

-14 -12 -10

-8

-6

40

-4 -2 0 Energy (eV)

2

4

EF

30

6

8

c)

Spin Up Spin Dn

10 0 -10 -20 -30 -14 -12 -10

-8

-6

-4

-2

0

2

4

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8

10

30

Spin Up Spin Dn

20 10 0 -10 -20 -30 -40

-14 -12 -10

-8

-6

40

10

20

-40

Total Density Of States (States/eV)

10

Total Density Of States (States/eV)

Total Density Of States (States/eV)

20

with GGA +U EF

40

-4 -2 0 Energy (eV)

2

4

EF

30

6

8

10

Spin Up Spin Dn

20 10 0 -10 -20 -30 -40

-14 -12 -10

-8

-6

40 Total Density Of States (States/eV)

c)

30

a)

Spin Up Spin Dn

EF

40 Total Density Of States (States/eV)

b)

with GGA

40

Total Density Of States (States/eV)

a)

-4 -2 0 Energy (eV)

2

4

EF

30

6

8

10

Spin Up Spin Dn

20 10 0 -10 -20 -30 -40

-14 -12 -10

-8

Energy (eV)

-6

-4 -2 0 Energy (eV)

2

4

6

8

10

Fig.7: Spin-dependent total density of states (TDOS) of ZB -Zn1-xVxSe alloys at (a) x = 0.25, (b) x = 0.50 and (c) x = 0.75 using PBE-GGA and PBE-GGA+U..

V(3d) Zn(3d) Se(4s) Se(4p) V(3d) Zn(3d) Se(4s) Se(4p)

0

-5

-10 Spin Dn -14 -12 -10

-8

-6

-4 -2 0 Energy (eV)

Spin Up

2

4

6

EF

8

10

b)

Zn(3d) V(3d) Se(4s) Se(4p) Zn(3d) V(3d) Se(4s) Se(4p)

5

0

-5

-10 10

Spin Dn -14 -12 -10

-8

-6

-4 -2 0 Energy (eV)

Spin Up

2

4

6

EF

8

c)

5

0

-5

-10

Spin Dn -14 -12 -10

-8

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-4 -2 0 Energy (eV)

2

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8

10

V(3d) Zn(3d) Se(4s) Se(4p) V(3d) Zn(3d) Se(4s) Se(4p)

5

0

-5

-10

-14 -12 -10

-8

-6

10

10

Zn(3d) V(3d) Se(4s) Se(4p) Zn(3d) V(3d) Se(4s) Se(4p)

with GGA+U EF

10 Partial Density Of States (States/eV)

a)

Partial Density Of States (States/eV)

Partial Density Of States (States/eV)

EF

-4 -2 0 Energy (eV)

2

4

6

EF

8

10

Zn(3d) V(3d) Se(4s) Se(4p) Zn(3d) V(3d) Se(4s) Se(4p)

5

0

-5

-10

-14 -12 -10

-8

-6

10 Partial Density Of States (States/eV)

c)

with GGA Spin Up

5

10 Partial Density Of States (States/eV)

b)

10

Partial Density Of States (States/eV)

a)

-4 -2 0 Energy (eV)

2

4

6

EF

8

10

Zn(3d) V(3d) Se(4s) Se(4p) Zn(3d) V(3d) Se(4s) Se(4p)

5

0

-5

-10

-14 -12 -10

-8

-6

-4 -2 0 Energy (eV)

2

4

6

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10

Fig.8 Spin-dependent partial density of states (PDOS) of the equilibrium ZB Zn1-xVxSe alloys at (a) x = 0.25, (b) x = 0.50 and (c) x = 0.75 using PBE-GGA and PBE-GGA+U..

Fig.9 Total magnetic moment of ZB Zn1-xVxSe alloys per unit cell as a function of x concentration using PBEGGA and PBE-GGA+U.

Tables Table 1 Equilibrium lattice constant a0, bulk modulus B and its pressure derivatives B’ for Zn1-xVxSe. Experimental data are also quoted for comparison Bulk modulus B (GPa) B’ Composition Lattice parameter a0 (Å) x TW Cal. Exp. TW Cal. Exp. TW Cal. Exp. 0.00 5.667a 64.7a 4.77a 62.43 4.67 5.721 71.84c 4.599c 5.578c 5.618d 67.6d 4.67d 5.667b 69.3b -e e 5.77 -4.6e 54.79 -0.25 -63.20 4.64 5.718 5.77e 56.62e 4.68e --0.50 -71.13 4.73 5.655 5.78e 59.52e 3.65e --0.75 -84.19 3.68 5.603 e e e 5.74 48.64 3.5 --1.00 -90.55 3.52 5.563 a Ref. [38] b Ref. [49] c Ref. [50] d Ref. [51] e Ref. [52]

Table 2 Elastic constant (in GPa) for Zn1-xVxSe Composition C11 x TW Cal. Exp. 0.00 85.9a 99.12 95.9b 94.66c -0.25 85.92 --0.50 87.08 --0.75 72.21 --1.00 71.04 -a Ref. [38] b Ref. [51] c Ref. [53]

C12 TW 44.89 52.90 64.46 82.47 100.95

Cal. 53.6b 44.46c -----

Exp. 50.6a

C44 TW 69.80

-----

62.31 54.81 47.32 39.82

Cal. 48.9b 36.8c -----

Exp. 40.6a

ξ TW 0.58

-----

0.72 0.82 0.94 1.26

Cal. 0.74b 0.59c -----

Exp. ------

Table 3 The calculated results of the half-metallic EHM (eV) band gaps and spin-minority band gaps Eg (eV) of each site in Zn1-xVxSe alloys obtained using the PBE-GGA and PBE-GGA+U schemes. EHM Alloy Composition Eg x TW Cal Exp TW Cal Exp -2.82a -0.00 -1.36 (1.50) 2.76b ZnSe 2.82c ----2.23 (2.45) 2.23d Zn0.75V0.25Se 0.25 --0.04 (0.43) 0.31d 2.53 (2.91) 2.70d Zn0.50V0.50Se 0.50 d ----2.64 (2.91) 2.75 Zn0.25V0.75Se 0.75 ----1.00 3.12 (2.80) 3.11d VSe a Ref. [54] b Ref. [55] c Ref. [56] d Ref. [52]

Table 4 The calculated results of the total magnetic moment (Mtot in µB) per V atom and local magnetic moment of each concentration for Zn1-xVxSe using the PBE-GGA and PBE-GGA+U schemes. Zn0.50V0.50Se Zn0.25V0.75Se VSe Alloy Zn0.75V0.25Se 3.003 (3.006) 3.019 (2.999) 2.808 (2.962) 2.353 (2.353) MTot 2.353 (2.434) 2.368 (2.492) 2.291 (2.418) 2.018 (2.018) MV 0.039 (0.034) 0.081 (0.051) 0.075 (0.076) -MZn -0.021 (-0.025) -0.042 (-0.044) -0.039 (-0.047) -0051 (-0.053) MSe

Table 5 The calculated conduction and valance band-edge spin-splitting Δxc(pd), Δxv(pd) and exchange constants of Zn1xVxSe for (a) x = 0.25, (b) x = 0.50 and (c) x = 0.75 using the PBE-GGA and PBE-GGA+U parameterization schemes. Δxv(pd) N0α N0β Alloy x Δxc(pd) 0.25 -0.070 (-0.002) -2.302 (-2.450) -0.141 (-0.004) -4.603 (-4.902) Zn1-xVxSe 0.50 0.037 (0.434) -2.521 (-2.477) 0.037 (0.434) -2.521 (-2.477) 0.75 -0.364 (-0.190) -3.004 (-3.102) -0.243 (-0.127) -2.002 (-2.068)

•

Half metallicity origins by doping V in ZnSe.

•

PBE-GGA+U approximation is employed to treat the “d” electrons properly.

•

s(p)-d exchange constants N0α (conduction band ) and N0β (valence band) are due to

Se(4p)-V(3d) hybridization.