The electronic structure calculations of the DMS are performed based on the local density approximation with the parameterization by Perdew-Wang [10]. For the (FP-LMTO) calculations, we have used the available computer code Lmtart [11].

We employ the muffin-tin approximation to describe the crystal potential, and the wave functions in each Muffin-tin sphere are expanded with real spherical harmonics up to lmax = 6. The k integration over Brillouin zone is performed using the tetrahedron method [12].

ZnS, ZnSe, and ZnTe have the zinc blende crystal structure, and their lattice constants are a = 5.4093 A°, a = 5.6676 A ° and a = 6.089 A°, respectively. Muffin-tin radii are chosen so that they touch with each other

We first calculated the structural properties of the binary compounds ZnSe, ZnTe, ZnS and MnTe, MnSe, MnS in the zincblende structure. As for the semiconductor ternary alloy in the type B_1-xA_xC, we have started our FP-LMTO calculation of the structural properties with the zinc-blende structure and let the calculation forces to move the atoms to their equilibrium positions. For divers concentrations x = 0.25, 0.5, 0.75. We perform the structural optimization by calculating the total energies for different volumes around the equilibrium cell volume V₀ of the binary and their alloy. The calculated total energies are fitted to the Murnaghan’s equation of state [13] to determine the ground state properties such as the equilibrium lattice constant a₀, the bulk modulus B and its pressure derivative B’. The calculated equilibrium parameters (a₀, B and B’) are given in Table 1 Our results are compared with the experiment and with the FP-LAPW (method) results.

Table 1

The Calculated Lattice Parameter a, the Bulk Modulus B and its Pressure Derivative B’ for Zn1-xMnxY(Y = S, Se, Te) and its Binary Compounds

Usually, in the treatment of alloys, it is assumed that the atoms are located at the ideal lattice sites and the lattice constant varies linearly with the composition x according to the so-called Vegard’s law [14]:

a _(AxB1-xC) = xa_AC + (1 – x) a_BC, (1)

where a_AC and a_BC are the equilibrium lattice constants of the binary compounds AC and BC, respectively, and a (A_xB_1-xC) is the alloy lattice constant. The obtained equilibrium lattice constant, of the ferromagnetic Zn_1-xMn_xY (Y = S, Se, Te) semi-magnetic semiconductors are given in Table 1.

The equilibrium lattice parameter of the zinc-blende Zn_1-xMn_xTe and Zn_1-xMn_xS. We found a good agreement with the experiment on the other. We have determined the equilibrium lattice parameter of the zinc-blende MnY (Y = S, Se, Te), which is found to be underestimated compared to the experimental.

The equilibrium lattice constants a shows a linear variation versus Mn concentration of Zn_1-xMn_xS and Zn_1-xMn_xTe, but a small deviation from Vegard’s law is clearly visible for the Zn_1-xMn_xSe.

There are no results to compare with our values. Thus finds new values for various concentrations, our result to take as reference. Fig. (1), show the variation of the calculated equilibrium lattice constant versus concentration x for Zn_1-xMn_xY(Y = S, Se, Te). The Mn mole fraction (x) was determined by using the linear relation: a(x) = -0.4044X + 5.3374 (A°).

Fig. (1) Variation of the calculated equilibrium lattice constant versus concentration x for Zn1-xMnx Y (Y = S, Se, Te).

Obtained for lattice parameter of Zn_1-xMn_xS and lattice parameter for Zn_1-xMn_xSe vary according to the linear relation: a(x) = - 0.3416X + 5.6022 (A°).

Fig. (2) shows the variation of the bulk modulus versus concentration. The bulk modulus grew linearly with the composition Mn for the Zn_1-xMn_xSe.

Fig. (2) Variation of the calculated bulk modulus versus concentration x for Zn1-xMnxY(Y = S, Se, Te).

We observe in Fig. (2) that bulk modulus grew with concentration (x) and with the nuclear charge of the element of the VIa column.

The calculated band structure energies of binary compounds as well as their alloy using FP-LMTO method within LDA approximation exhibit a direct band gap at Г point for Zn_1-xMn_xY(Y = Zn, Se, S)with x vary between 0.25 and 0.75, the valence band maximum (VBM) and the conduction band minimum (CBM) occur at the Г and X, respectively. The important features of the band structure (main band gaps) are given in Table 2.

Table 2

Direct (Г – Г) and Indirect (Г– X) Band Gaps of BeSe and ZnSe and Their Alloy at Equilibrium Volume

As well as the theoretical and experimental ones. It is clearly seen that the band gap are underestimated in comparison with experiment results. This underestimation of the band gaps is mainly due to the fact that the simple form of LDA does not take into account the quasiparticle self-energy correctly [25].

The carrier induced ferromagnetism by hole doping was observed in (Zn, Mn) Te [32], and II–VI based-DMSs have been of much interest also from the scientific point of view. Taking these aspects into account, it is important to investigate the carrier induced effects in ZnS, ZnSe and ZnTe based DMSs.

In order to elucidate underlying mechanism of the ferromagnetism in II–VI compound-based DMSs, the density of states (DOS) is calculated. Figs. (3-5) shows the DOS of 25% TM-doped ZnTe based DMSs in the ferromagnetic state. It is found that the impurity states appear in the band gap.

Fig. (3) DOS for the ferromagnetic Zn1-xMnxS for spin up and spin down.

Fig. (4) DOS for the ferromagnetic Zn1-xMnxTe for spin up and spin down.

Fig. (5) DOS for the ferromagnetic Zn1-xMnxTe for spin up and spin down.

The spin-polarized band structures of ferromagnetic ZnMnTe, ZnMnS and ZnMnSe compounds at the calculated lattice constants are depicted in Figs. (3-5).

The figures show for each compound, the band structures corresponding to spin up and down alignments. We have referenced the zero energy at the top of the valence band for spin up. The bottom of the conduction bands and the top of the valence bands are at the Г point in the Brillouin zone, it is well known that the calculations of the local densities of states (DOS) serve as a qualitative description of the atomic and orbital origins of the various band states. We illustrate our calculations of DOS in Figs. (3-5) for ZnMnS and ZnMnSe, ZnMnTe, respectively. The spin-dependent density of states (DOS) for the ferromagnetic phase is presented in Fig. (2, upper panel). The lower panel presents the contributions to the DOS from the Mn-3d orbitals. We can see that the upper valence band complex has Mn d and Te p characteristics, which differ widely for spin up and spin down. On the other hand, there strong contribution of the Mn spin down states to the valence band. We observe also that the spin up Mn d band is occupied (Figs. 3c, 4c, 5c), and cantered at EV↑=−3.42eV for ZnMnTe and at Ev↑=−4.15eVfor ZnMnSe, and at EV↑=−4.06eVfor ZnMnS whereas the spin down d band is empty (Figs. 3c, 4c) and 5(c)), and centred at Ev↓=+1.37eV for ZnMnTe Ev↓=+1.5eVand for ZnMnSe, and at Ev↓=+1.57eVfor ZnMnS where E^↑ and E^↓ denote the valence band maxima (VBM) for spin up and spin down, respectively. The negative values obtained, for ZnMnTe and for ZnMnSe, and for ZnMnS indicate that the effective potential for the minority spin is more attractive than that for the majority spin, as is usually the case in spin-polarized systems [26]. It has been shown that ferromagnetic band structure calculations can be used to estimate the exchange constants N₀α and N₀β. Assuming the usual K onto interactions, N₀α and N₀β are defined as [27]. Where ΔEc and ΔEv are the band edge spin splitting of the valence bands and conduction bands, respectively, and <3> is the average Mn spin. We have calculated the exchange constant by evaluating the spin splitting of the conduction and valence bands, which mimics a typical magneto-optical experiment [28].

We summarize in Table 2 our results of ΔEc, ΔEv, N₀α and N₀β for both ZnMnY (Y = S, Se, Te).

Our calculated total and local magnetic moments as well as that of the interstitial site are given in Table 3. It is expected in Mn doped DMSs [29] that: (i) the number of valence minority spin electrons is not changed by the Mn impurity and (ii) each Mn impurity adds five additional majority spin states to the valence band. In Table 3 we show that this description is also valid for ZnMnTe and ZnMnSe and ZnMnS.

Table 3

Calculated Magnetic Moments (in Bohr Magneton μB of Several Sites and the Total Magnetic Moment for Each Mn for the Ferromagnetic ZnMnY (Y = S, Se, Te) with 25%

The total magnetic moment of materials ZnMnY(Y = S, Se, Te) equal ≈5μ_B (μ_B is the Bohr magneton).

From Table 3 we can see that the p–d hybridization is found to reduce the local magnetic moment of Mn.

We observed the small local magnetic moments on the nonmagnetic S, Se, Te and Zn sites.