J Supercond Nov Magn DOI 10.1007/s10948-014-2593-1
ORIGINAL PAPER
Theoretical Investigation of Structural, Electronic, and Magnetic Properties of V-Doped MgSe and MgTe Semiconductors M. Sajjad · H. X. Zhang · N. A. Noor · S. M. Alay-e-Abbas · M. Younas · M. Abid · A. Shaukat
Received: 19 April 2014 / Accepted: 18 May 2014 © Springer Science+Business Media New York 2014
Abstract In this study, we have explored the structural, electronic, and magnetic properties of V-doped zincblende MgSe and MgTe compounds using density functional calculations. The Wu-Cohen generalized gradient approximation is used for optimizing the structural properties, while the modified Becke and Johnson local (spin) density approximation functional has been employed to compute the electronic and magnetic properties. The spin dependent band structures, electronic density of state, and magnetic moments calculated for V-doped MgSe and MgTe semiconductors exhibit occurrence of 100 % spin polarization at the Fermi level which confirms stable half-metallic ferromagnetism in these materials. The spin-down gaps and the M. Sajjad () · H. X. Zhang School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China e-mail:
[email protected] N. A. Noor · M. Younas Department of Physics, University of the Punjab Quaid-e-Azam Campus, 54590 Lahore, Pakistan S. M. Alay-e-Abbas · A. Shaukat Department of Physics, University of Sargodha, Sargodha 40100, Pakistan S. M. Alay-e-Abbas Department of Physics, GC University Faisalabad, Allama Iqbal Road, Faisalabad 38000, Pakistan M. Abid Department of Physics, Beijing Institute of Technology, Beijing 10008, China H. X. Zhang Beijing Key Laboratory of Work Safety Intelligent Monitoring, Beijing University of Posts and Telecommunications, Beijing 100876, China
half-metallic gaps are analyzed in terms of V-3d and Se-4p (Te-5p) hybridization, where it is observed that the V-3d states play a key role in generating spin polarization and the magnetic moment in these compounds. The exchange constants N0 αand N0 β have been calculated to demonstrate the effects resulting from exchange splitting process. Furthermore, spin-polarized charge density calculation is presented for elucidating the bonding nature, while pressure dependence of total magnetic moment for three concentrations of V-doped MgSe and MgTe are also discussed. Keywords Ab initio calculations · Ferromagnetic materials · Electronic properties · Doped semiconductors
1 Introduction The ever growing research interest for discovering smarter and more efficient materials originates from the rapidly increasing demands of electronic industry. In this regard, the quest for ferromagnetic (FM) semiconducting materials for their utilization in spintronic devices [1–3] is still an area of ongoing research work. In the past decades, significant attention has been paid on diluted magnetic semiconductors (DMSs) [4] for engineering composite materials having both ferromagnetic and semiconducting properties. The success in achieving higher Curie temperatures TC (∼150 K) in Mn-doped III–V [5] and III–IV [6] semiconductors has triggered an immense amount of research work exploring potential FM semiconductors with higher TC [7–14]. These consistent efforts have lead to TM doped nitrides [8, 9] and oxides [11–14] with TC > 300 K. Moreover, since the prediction of half-metallic ferromagnet (HMF) NiMnSb by de Groot et al. [15], compounds such as Fe- and Co-doped ZnO [16], Fe3 O4 [17], V-doped MgSiN2 [18], V-doped BeX
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(X = S, Se, and Te) [19], CrX (X = S, Se, and Te) [20, 21], and Mn-doped BN2 [22] have also been explored for their applications in spintronics. The wide energy band gap magnesium selenide (MgSe) and telluride (MgTe) semiconductors have diverse technological importance due to their use in optoelectronic devices [23]. Many comprehensive studies have been conducted for MgSe and MgTe in the rock salt, wurtzite, and zincblende (ZB) phases which predict the energy band gap variations between ground state and high pressure structural phases [24–28]. At ambient conditions, MgTe [29] and MgSe [24] crystallize stably in wurtzite and ZB phases, respectively; however the ZB phase for MgTe has also been achieved [25, 26]. Contrary to the selenide and telluride of Zn and Cd, little attention has been paid to magnetic ion-doped MgSe and MgTe semiconductors for their utilization as HMF. Importantly, the systems Mg1−x Vx Se and Mg1−x Vx Te have not been explored with recently proposed exchange-correlation functionals of density functional theory (DFT) which provide great improvement in the so-called band gap problem faced in the market standard local density approximation (LDA) and generalized gradient approximation functionals [12]. Moreover, important values like HM gaps, impurity atoms’ 3d orbitals exchange splitting, p − d exchange splitting and exchange constants, which play crucially role in evaluating practical device applications of HMF materials, have not been reported yet. Therefore, in this work, we consider V-doped MgSe and MgTe in the cubic ZB phase and computed the structural, electronic, and magnetic properties of these alloys for a doping range x = 0.25, 0.50, and 0.75 by using the all electron full-potential linearized augmented plane wave plus local-orbital (FP-LAPW + lo) method.
2 Method of Calculations For the purpose of computing ground state properties of Mg1−x Vx Y (Y = Se and Te) compounds at doping concentrations 0 ≤ x ≤ 1, we used FP-LAPW + lo method as implemented in WIEN2k code [30], which has been successfully utilized for predicting the ground state properties of bulk materials as well as nanostructures [7, 10, 12, 31, 32]. For treating the exchange correlation effects, the generalized gradient approximation functionals of Wu and Cohen (WC-GGA) [33] have been utilized for computing the structural properties and enthalpy of formation (we must omit this), while the functional proposed by Tran and Blaha (mBJLDA) [34] has been used for exploring the electronic and magnetic properties of the V-doped MgSe and MgTe. The reason for choosing WC-GGA functional for structural properties calculations is based on its better performance for structural optimization [12] which arises from the
fourth-order gradient expansion of exchange-correlation functional [33]. On the other hand, the advantage of mBJLDA is its significantly improved performance for evaluating semiconductors and importantly, HMFs electronic band structure. Since the construction of this mBJLDA parametrization scheme from semilocal Becke and Jhonson exchange potentials and LDA correlation leaves this functional unable to provide any useful information about structural properties, we have adopted the standard procedure for computing the electronic and magnetic properties with mBJLDA by performing the electronic structure calculations at structural parameters obtained using WC-GGA [34]. In the FP-LAPW + lo calculations, we treated the core and valence electrons with full and scalar relativistic approximations, respectively. The radii of the muffin-tin spheres (RMT) for Mg, V, Se, and Te have been set as large as possible such that no overlapping occurs. In order to ensure symmetric total energy calculation for binary and ternary compounds, the values for the important cut-off parameters for the plane waves (that is angular momentum, plane-wave factor, and Fourier expansion vector) have been set to Imax = 10, Kmax /RMT = 8.0, and Gmax = 16 (Ry)1/2. The self-consistent total energy calculations have been carried out until the convergence of total energy to a value less than 10−3 Ry, and the charge is converged to 0.001 e. A dense mesh of 1,000 k-points is used for the pure and V-doped compounds. 3 Results and Discussion 3.1 Structural Properties Through the supercell approach [31, 32], an eight-atom cubic cell was constructed for modeling vanadium-doped MgSe and MgTe. At x = 0.25 and 0.75, V atom takes the position at apex and face-center sites by replacing Mg atoms in MgY (Y = Se and Te) unit cells that belong to space group (No. 215). For x = 0.50, the modeled structure has a tetragonal symmetry (No. 115). The structural optimization for ZB Mg1−x Vx Y (Y = Se and Te) compounds at 0.25 ≤ x ≤ 1 has been carried out using the WC-GGA by computing the minimum total energy for various unit cell volumes and then fitting the computed data to the equation of state for obtaining optimized lattice parameters (a0 ) and bulk modulii (B0 ). The total energy versus volume curves are displayed in Fig. 1, whereas the optimized structural parameters are listed in Table 1. In the doped semiconductors where dopant cation is assumed to reside at the ideal lattice sites, a linear variation of lattice parameters against concentration (x) is expected as dictated by the Vegard’s law [35]. However, for the HMF alloys, this linearity has been reported to be violated in earlier investigations
J Supercond Nov Magn Fig. 1 Structural optimizations plots obtained using WC-GGA for the zinc blende Mg1−x Vx Y (Y = Se, Te) at doping concentrations x = 0.25, 0.50, 0.75, and 1
[7, 10, 12, 36, 37]. From Table 1, it is evident that lattice parameters for both V-doped MgSe and MgTe decreases on going from x = 0 to x = 1, whereas bulk modulus shows a converse behavior and the increasing values revealing that the both doped MgY systems considered in this work become harder as the vanadium concentration increases. 3.2 Electronic and Magnetic Properties Since even the fourth-order gradient expansion of exchange energy available in WC-GGA is not sufficient to accurately predict the electronic structure of wide band gap semiconductors and HFM materials [10, 12, 38], we have computed the electronic and magnetic properties of Mg1−x Vx Y (Y = Se and Te) compounds with the mBJLDA at the optimized lattice parameters presented in Table 1. It is important
Table 1 The optimized lattice parameter, a0 , and bulk modulus, B0 , for Mg1−x Vx Y (Y = Se and Te) at doping concentrations x = 0, 0.25, 0.50, 0.75, and 1 x
˚ a0 (A)
B0 (GPa)
Mg1−x Vx Se
0 0.25 0.50 0.75 1.00
5.930 5.892 5.827 5.755 5.637
48.132 50.404 57.309 62.801 67.429
Mg1−x Vx Te
0 0.25 0.50 0.75 1.00
6.430 6.389 6.309 6.231 6.164
36.720 38.857 43.558 49.044 55.134
Results are obtained with WC-GGA
to point out here that the electronic structure of the all-end binary compounds (MgY and VY (Y = Se and Te)) have been explored in numerous earlier studies [24–27]; however, since the aim of this work is to explore HMF in the V-doped MgY, in our discussion, we restrict ourselves to the case where 0 < x < 1. The calculated spin-polarized electronic band structures for the composition x = 0.25, 0.50, and 0.75 in both spins (up and down) in the first Brillouin zones are depicted in Fig. 2. In the spin-down case, some of the valence band (VB) states are relocated in conduction band (CB) resulting in a wide energy band gap (Eg ) around the Fermi level (EF ). For both spin-up and spin-down cases, the semiconducting nature of MgSe and MgTe are conserved. Importantly, these alloys are HMFs with 100 % magnetic spin polarization that can result in ferromagnetic behavior at room temperature making these materials potential candidates for spintronic applications. It is worth pointing out here that the 100 % spin polarization governs the half-metallic nature of these materials [12, 39] and plays a vital role in HMFs which can be achieved by deactivating the spin-up states [40]. The calculated values of Eg and EHM are presented in Table 2, where a nonlinear decrease in both of these gaps is apparent with increasing V concentration which is due to the local electric field and local strain introduced by the magnetic impurity atoms. Interestingly, the indirect band gaps of MgSe and MgTe are transmuted into optically active direct band gaps in Mg1−x Vx Se and Mg1−x Vx Te due to V doping. Our predicted results provide experimentalists an interesting class of materials for exploring their electronic structure using modern experimental techniques [41, 42]. In order to estimate different atomic contributions to the electronic structure of ternary alloys Mg1−x Vx Y (Y = Se and Te), the total spin-polarized density of states (TDOS) computed using the mBJLDA are shown in Fig. 3. The results reveal formation of a spin-polarized impurity band
J Supercond Nov Magn Fig. 2 The electronic band structures of ternaries Mg1−x Vx Se (right column) and Mg1−x Vx Te (left column) calculated using mBJLDA at x = 0.25, 0.50, and 0.75 for spin-up and spin-down cases
which is due to vanadium doping. For a further elaboration of the TDOS plots, the partial density of states (PDOS) plots are shown in Figs. 4 and 5. It is clear that in the spin-up channel, lower region of VB is primarily comprises
of the Se-4p (Te-5p) and V-3d-t2g states with relatively small influence of Mg-3s and V-3d-eg states. Near the Fermi level, the Se-4p (Te-5p) and V-3d-t2g states are dominant and show a strong hybridization which goes across the EF .
Table 2 The calculated Eg (spin-down band gap), EHM (half-metallic gap), N0 α and N0 β (exchange constants) for Mg1−x Vx Y (Y = Se and Te) using mBJLDA Compound
x
Eg (eV)
EHM (eV)
Ev (eV)
Ec (eV)
N0 α (eV)
N0 β (eV)
Mg1−x Vx Se
0.25 0.50 0.75 0.25 0.50 0.75 1.00
3.37 3.20 2.89 3.45 3.30 3.16 3.38
0.91 0.73 0.40
−2.46 −2.47 −2.49 −2.40 −2.48 −2.55 −3.08
0.91 0.73 0.40 1.00 0.82 0.61 0.30
2.854 1.147 0.422 3.040 1.241 0.619 0.226
−7.715 −3.880 −2.628 −7.447 −3.755 −2.589 −2.324
Mg1−x Vx Te
0.82 0.61 0.30
J Supercond Nov Magn Fig. 3 TDOS of the ternaries Mg1−x Vx Se (right column) and Mg1−x Vx T e (left column) at x = 0.25, 0.50, and 0.75 calculated using mBJLDA for spin-up and spin-down cases
Similar behavior is evident for the spin-down channel; however, the states crossing EF in the case of spin-up channel are pulled by the CB in the spin-down channel leading to a wide energy band gap. The difference between the two spin channels is due to the fact that V-3d-t2g and Se-3d-eg states reside at the bottom of CB in spin-down case. The V-3d states play an extremely important role in deciding the ferromagnetic character and the HM gaps. In present study, the calculated HM gaps show a decreasing trend with
increasing impurity doping concentrations, since V-3d states have a tendency of being localized. Consequently, the admixture of V-3d-t2g states with Se-4p (Te-5p) states allows the smallest separation between bonding (t2g ) and anti-bonding (eg ) states at the highest V doping in spindown channel. The tetrahedral environment of Se (Te) atom is responsible for splitting fivefold degenerate (V-3d) states into twofold degenerate (eg ) and three-fold degenerate (t2g ) states,
J Supercond Nov Magn Fig. 4 PDOS of the ternaries Mg1−x Vx Se at x = 0.25, 0.50, and 0.75 calculated using mBJLDA for spin-up and spin-down cases
such that the former states have comparatively lower energy ordering than that of latter states because of decreased Coulomb interaction [43]. In spin-up case the t2g states reside at the top of VB as well as at the bottom of CB, while the eg states are localized in VB. On the other hand, both the bonding an anti-bonding states are localized in the CB for spin-down case. As a matter of fact, for both spin cases, these states have little contributions (especially eg states) with Se4p (Te5p ) in making the bottom of VB. The p − dhybridization not only separates these symmetry states (eg and t2g ) from each other but also cause the double exchange interaction (DEI) which is the main cause
of introducing ferromagnetism in the compounds under investigation. 3.3 Magnetic Properties and Charge Densities For elucidating the role of CB and VB in the exchange splitting observed in the electronic band structure of HMFs Mg1−x Vx Y (Y = Se and Te), the exchange constants, N0 α and N0 β, have been estimated using [44] N0 α = Ec / x < S >
(1)
N0 β = Ev / x < S >
(2)
J Supercond Nov Magn Fig. 5 PDOS of the ternaries Mg1−x Vx T e at x = 0.25, 0.50, and 0.75 calculated using mBJLDA for spin-up and spin-down cases
where N0 is the cation concentration, x is the V concentration, is half of the magnetization per V ion, Ec = Ec (↓) − Ec (↑) is the CB edge splitting, Ev = Ev (↓) − Ev (↑) is the VB edge splitting, αand β are the exchange integrals, respectively. The negative values for N0 βpresented in Table 2 indicate that VB edge splitting, Ev , mainly define the nature of effective potential to be dominantly attractive in compliance with the p − d repulsion model [45]. This feature of effective potential is also evident in Fig. 2, where an additional downward shift in VB maxima is distinctly visible in spin-down channel as compared to its upward shift in spin-up case. Furthermore, decreasing values of N0 α
make the V-3d states more dominant over the Se-4p (Te5p) states with increasing V doping. The p − dexchange constant N0 β increases with the increase in V concentration and the exchange coupling between V impurity and the CB of Mg1−x Vx Y (Y = Se and Te) at x = 0.25, 0.50, and 0.75 is ferromagnetic, and consequently, the materials under study possess the important HMF character. In Table 3, the total and local magnetic moments of the materials Mg1−x Vx Y (Y = Se and Te) for 0.25 ≤ x ≤ 1 calculated using the mBJLDA are presented. The magnetic character of these materials comes from the unfilled V-3d states. Replacing the Mg atom with V provides two of the
J Supercond Nov Magn Table 3 Total magnetic moment Mtot and local magnetic moments MMg/V/Se/Te for Mg1−x Vx Y (Y = Se and Te) at doping concentrations x = 0.25, 0.50, 0.75, and 1 calculated using mBJLDA Composition x Magnetic moments
Mg1−x Vx Se 0.25 0.50 0.75 1 Mg1−x Vx Se 0.25 0.50 0.75 1
Mtot (μB )
MMg (μB ) MV (μB ) MSe/Te (μB )
– 3.000 3.000 3.000 2.570 – 3.000 3.000 3.000 3.000
– 0.014 0.026 0.037 – – 0.015 0.028 0.039 –
– 2.551 2.546 2.527 2.365 – 2.632 2.642 2.626 2.651
– −0.018 −0.037 −0.062 −0.037 – −0.026 −0.051 −0.081 −0.113
total five valence electrons of vanadium to make bonds with Se (Te) atoms while the rest of valence electrons stay in the impurity bands at EF . The HM behavior of these materials is in accordance with their integral magnetic moments [46, 47]. It is obvious from Table 3 that at all doping concentrations, the local magnetic moment of V (MV ) is less than the total magnetic moment 3 µB (μB is the Bohr magneton). The reason is the hybridization between Se-4p (Te-5p) states and V-3d states which induces small magnetic moments on the nonmagnetic (Mg, Se, Te) sites. Therefore, MV extensively contributes to Mtot at all doping concentrations. The induced magnetic moment for MMg (MSe/Te ) has positive (negative) sign which is due to the parallel (anti-parallel) alignment with MV . Hence, ferromagnetic/anti-ferromagnetic interaction exists between V and Mg/Se (Te) atoms. Finally, the MV values have minor variation with increasing V doping but a significant increase is found in the induced magnetic moments (MMg/Se/Te ) since more V-3d states are available for p − dhybridization at higher doping concentration.
Fig. 6 Total magnetic moment of V-doped MgSe and MgTe for x = 0.25, 0.50, and 0.75 as a function of lattice parameter
For applications in spictronic devices, the variation of half-metallicity under the application of pressure is essentially important. For DFT calculations the effect of pressure on magnetic moments can be analyzed by varying the lattice parameters to values above and below the ground state lattice parameter. In Fig. 6, we presented the variation of total magnetic moment as a function of lattice parameter where it can be seen that the total magnetic moment computed with decreasing the lattice parameters for V dopant concentration x = 0.25, 0.50, and 0.75 remains constant up to a certain reduced value of lattice parameter. It is therefore clear that HMF nature of the compounds under study is preserved under compression up to a certain value of pressure for the three dopant concentrations considered in this work. It is also interesting to note that the higher compression is needed for lower concentration of V dopant which is consistent with the larger spin polarization values listed in Table 2 for vanadium concentration x = 0.25 as compared to x = 0.50 and x = 0.75. In order to understand the anti-ferromagnetic alignment of Se (Te) atom with the dopant atom the charge spindensity contour plots in the ferromagnetic configuration for V doping concentrations at x = 0.25 have been calculated by considering the nature of the corresponding Mg–Se (Te) and V–Se (Te) bonds (Fig. 7). It can be seen that the bonding nature has partial ionic and covalent nature for both spin-up and spin-down cases. Moreover, the V–Se (Te) bond is covalent and there is a small negative magnetization around Se (Te) although the total magnetic moment in the cell is contributed mainly by V. Away from the core of the anion, there are some differences in the electron density which is due to the electrons in the valence p states of Se (Te) atoms which are confined to the core. A p-like spin polarization with Se (Te) atoms for spinup and spin-down cases is also evident. The spin density is mainly produced due to enhanced participation of V-3d states in bonding by preserving its localization on V atom. One can also observe the anti-ferromagnetic alignment of anion with dopant from the charge density plots shown in
J Supercond Nov Magn Fig. 7 Calculated spin-polarized charge density contour plots for V-doped a MgSe and b MgTe at x = 0.25
Fig. 7, which is in confirmatory with the negative values of N0 β in Table 2.These results are consistent with experimentally observed anti-ferromagnetic alignment in V-doped II–VI compounds [48].
4 Conclusion DFT calculations for the structural, electronic, and magnetic properties of Mg1−x Vx Y (Y = Se and Te) compounds at x = 0.25, 0.50, 0.75, and 1 have been performed for investigating the HMF. Half-metallic nature is observed at all doping concentrations with 100 % spin polarization at the Fermi level; however the HM gap EHM decreases with increasing V concentration. The hybridization between V3d and Se-4p(Te-5p) states gives rise to a wide band gap at EF by pushing the bonding V-3d-t2g states away from EF in spin-down channel. The V-3d states are responsible for introducing magnetization in the studied compounds whose HM nature is consistent with the integral value of total magnetic moment (Mtot = 3 µB ). The small local magnetic moments are induced on the nonmagnetic (Mg, Se, Te) sites due to impurity atom, such that major contribution to Mtot alwayscomes from MV . Calculated N0 α and N0 β (exchange constants) elucidate the role of CB and VB in exchange splitting process which is found to be consistent with typical magneto-optical experiments. Spin-polarized
charge density calculation reveals a p-like spin polarization of anion for spin-up and spin-down cases that aligns antiferromagnetically with the vanadium dopant and stabilizes ferromagnetism in these compounds. The pressure dependence of total magnetic moment for the V-doped MgSe and MgTe reveals that the robustness increases with decreasing dopant concentration. The results presented in this work are expected to lead to experimental study of these compounds which may yield potential wide HM gap materials for spintronic applications. Acknowledgments This work is supported by National Natural Science Foundation of China (Grant No. 61202399) and the Natural Science Foundation of Beijing, China (Grand No. 4112039).
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