Electronic structure and magnetization of Zn1-xCoxO ternary alloys with zinc-blende, rocksalt and wurtzite phases

First-principles all electrons density-functional calculations for the band structure and magnetization of Zn1−xCoxO ternary magnetic alloys, in three phases namely zinc-blende, rocksalt and wurtzite have been reported. The computations are spin-polarized. An inspection of our electronic properties showed that the alloy system of interest exhibits a semiconducting character where the nature of the gap depends on the considered phase. An analysis of electronic charge density suggests that the bonding has a partially covalent character for ZnO which becomes weaker as far as the Co concentration increases. CoO is found to reach a total magnetization of 3 μB per cell for zinc-blende and rocksalt phases and 6 μB per cell for wurtzite phase.


Introduction
Zinc-oxide (ZnO) is a II-VI semiconductor which is a promising material for device applications. This is because of its direct and wide band-gap energy and its high free-exciton binding energy (Janotti and Walle 2009;Ogale 2005;Jagadish and Pearton 2006;Saib and Bouarissa 2007). On the other hand, cobalt oxide (CoO) is an inorganic compound which appears as olive-green to red crystals and has been used extensively in the ceramics and chemical industries and regarded as a novel, highly active heterogeneous catalyst for key processes in future energy and environmental technology (Kannan and Seehra 1987;Silinsky and Seehra 1981). Alloys made for ZnO and CoO give Zn 1-x Co x O ternary alloys that are emerged as promising materials for different energy applications. As a matter of fact, the alloys under study offer a special interest in advanced spintronic devices. This is due to the fact that they may serve magnetism (spin) and semiconducting (charge) combined in one 'spintronic' device which makes it possible to exploit both charge and spin (Amita 2004;Tortosa et al. 2008;Dietl et al. 2001;Dinia et al. 2004;Kim and Park 2002;Lotin et al. 2014;Deng and Tüysüz 2014).
To take advantage of Zn 1-x Co x O ternary alloys one needs a thorough knowledge of their fundamental properties. These properties are essential for evaluating their expectable applications domain (Saib et al. 2008(Saib et al. , 2010Adachi 2005Adachi , 2009Daoud et al. 2015;Vurgaftman et al. 2001;Bouarissa 1998a;Hannachi and Bouarissa 2009). In fact, an accurate knowledge of the electronic properties of materials permits a precious information that may help in its synthesis and devices fabrication (Cohen and Chelikowsky 1989;Saib and Bouarissa 2006;Martin 2004;Bouarissa 2006). On the other hand, the knowledge of magnetic properties of materials plays an essential role in determining their suitability for a particular magnetic application (Ohno 1999;Moulai et al. 2019;Bouarissa et al. 2020;Harrache and Bouarissa 2019). Despite the importance of the fundamental properties of materials and the important technological applications of Zn 1−x Co x O, the amount of available information on this material system is still limited, to the best of our knowledge. This has motivated us to do such an investigation of the electronic and magnetic properties of Zn 1-x Co x O (0 ≤ x ≤ 1) with hypothetical zinc-blende, rocksalt and wurtzite structures. The computations are carried out using the density-functional theory (DFT) calculations within the generalized gradient approximation (GGA). All calculations are spin-polarized. More details about computations are given in Sect. 2 of this paper.

Computational details
The DFT has proven to be one of the most accurate theory for the calculation of the electronic structure of solids. The calculations are essentially based on the DFT (Hohenberg and Kohn 1964;Kohn and Sham 1965) using the full-potential linearized augmented plane wave (FP-LAPW) method as implemented within the WIEN2K package (Blaha et al. 2008). All calculations are spin-polarized. The exchange-correlation terms are described using the GGA of Tran-Blaha modified Becke-Johnson (TB-mBJ-GGA) (Tran and Blaha 2009).
An elementary crystal structure containing atoms is established. During the relaxation, the atomic positions are allowed to relax within the cubic symmetry of space group.
In order to compute the material properties, we have used the DFT-based self-consistent cycle of the FP-LAPW method into WIEN2k code. This is surprisingly appropriate for the importance of band gap energies of solids when compared to the conventional GGA and gives accurate values of the band gap electronics which are close to the experimental ones.
We divided the region as interior non-overlapping space between muffin-tin spheres and the remaining as at an interstitial region between these spheres.
For all structures zinc-blende, rocksalt and wurtzite, the R MT is adopted to be 1.8 Bohr for Zn and Co atoms and 1.6 Bohr for O atoms. For all structures being considered here and for all concentrations of Zn 1−x Co x O, we choose a grid of 12 × 12 × 12 meshes for sampling the Brillouin zone using the Monkhorst and pack scheme (Monkhorst and Pack 1976;Pack and Monkhorst 1977). A plane wave cutoff of R MT k max = 7 is used for all structures of interest and for all concentrations of Zn 1−x Co x O, where k max is the magnitude of the largest k vector in the plane wave expansions. The alloy concentrations x of Zn 1−x Co x O have been considered from 0 to 1 with a step of 0.25. The alloyed structures have been completely optimized and the iteration process is repeated till the convergence of the total energy of the crystal of interest is ensured to less than 10 -5 Ry.

Results and discussion
The electronic band structures of Zn 1-x Co x O in hypothetical zinc-blende, rocksalt and wurtzite structures with various Co compositions x (0 ≤ x ≤ 1) have been computed in this work using the TB-mBJ-GGA approach. For magnetic alloys and CoO compound the spin direction is taken into consideration. Since the picture of band structures for various concentrations x is similar, we display only the electronic structure of the equimolar alloy Zn 0.50 Co 0.50 O in the three structures being considered here and for both spin channels. Our results are shown in Fig. 1. We observe that qualitatively all bands for different structures of interest look like similar and resembles to those reported previously for other semiconducting materials (Zerroug et al. 2009;Benmakhlouf et al. 2003;Kassali and Bouarissa 2000;Bouarissa 2002). Quantitatively, the main difference lies in the magnitudes of the band gap energies. A close inspection of these band structures indicates that for a spin up channel, Zn 0.50 Co 0.50 O in its zinc-blende structure is a semiconductor material with a direct band gap (Г → Г) of magnitude 2.04 eV, and in its rocksalt structure is a semiconductor material with an indirect band gap (R → Г) of magnitude of 1.12 eV, whereas in its wurtzite structure is a semiconductor material with a direct band gap (Г → Г) of magnitude of 2.094 eV.
The fundamental band gap energy (E g ) has been determined from the electronic band structures of Zn 1-x Co x O in the interval 0-1 for all structures being considered in this work. The evolution of E g as a function of Co content for zinc-blende, rocksalt and wurtzite hypothetical structures of Zn 1-x Co x O is illustrated in Table 1 and Fig. 2. Note that for zincblende Zn 1-x Co x O as x increases, E g decreases monotonously in a non-linear way. It shows a red shift from that of pure ZnO (x = 0) reaching about 1.07 eV for x = 1 (CoO). The same behavior of E g versus x can be seen for rocksalt Zn 1−x Co x O, where E g decreases from 3.12 eV for ZnO to 1.06 eV for CoO, bearing in mind that the gap in this case is indirect. As far as wurtzite Zn 1-x Co x O is concerned, E g varies non-monotonously and in a non-linear way. It is 2.86 eV for ZnO and 1.98 eV for CoO. The same trend of E g versus x has been reported experimentally by Kim and Park (2002) for Zn 1−x Co x O alloys using spectroscopic ellipsometry at room temperature.
Hence, for ZnO (x = 0), the type of the band-gap structure is a direct (Г → Г), whereas for other types (starting from x = 0.25 to x = 1) of band-gap structure, it is an indirect bandgap structure (R → Г). On the other hand, the energy band-gap in ternary semiconductor alloys for Zn 1-x Co x O as a function of alloy composition x is decreased when going from 0 to 1, whereas the ternary alloy of interest becomes a R → Г indirect band-gap structure once its x value becomes 0.25 and so over. We cite some references here Jardow et al. 2019;Othman 2013Othman , 2020 to compare with. Our calculations have been done generally at a room temperature and ambient pressure. Remark that almost the same trend of Eg versus x was reported experimentally (Kim and Park 2002) for Zn 1-x Co x O alloys at a room temperature. The calculated value of E g (2.856 eV) for wurtzite ZnO is slightly underestimated with respect to that of experiment (3.23 eV) measured by Neogi et al. (Neogi et al. 2013). Nevertheless, this value looks closer to experiment than that of 2.77 eV reported very recently by Algarni et al. (Algarni et al. 2019) using the same approach as that used here but differs in details (a grid of 12 × 12 × 12 meshes is used here for sampling the Brillouin zone, whereas that used in Ref. (Algarni et al. 2019) is 10 × 10 × 8 meshes). The other E g s are also expected to be underestimated with respect to experiment. This is generally a common trend known for DFT in the GGA computation of E g s in semiconductors (Zerroug et al. 2007). Hence, one may say that the types of the band gap structures are direct when their types of interest belongs to a direct (Г → Г) transition (which corresponds to zinc-blende and wurtzite structures of Zn 1-x Co x O at ZnO (x = 0)) and are indirect (R → Г) when the types of band gap structures are indirect transition (which is the case for rocksalt Zn 1-x Co x O from x = 0.25 to x = 1).
The density of states (DOS) of Zn 1−x Co x O (0 ≤ x ≤ 1) has also been computed for zincblende, rocksalt and wurtzite structures so as to investigate the electrons distribution on various orbitals. Our results regarding DOS for ZnO, Zn 0.50 Co 0.50 O and CoO are plotted in Fig. 3. A close examination of DOS for zinc-blende structure (Fig. 3a) indicates that the predominant contribution for the energy bands near the Fermi level of the crystal ZnO is that coming from the Zn-d electrons. The situation appears to be similar for rocksalt (Fig. 3b) and wurtzite (Fig. 3c) ZnO structures. Thus, the Zn-d electrons are important in the conductibility of ZnO for the three phases of interest. At these regions the DOS consists mainly of Zn-d and O-p states. The first region of DOS for wurtzite ZnO is the most tightly bound energy band. For Co-alloyed ZnO with x = 0.50, one can note that the dominant contributions are due to the d electrons of the Zn and Co atoms and the p electrons of the O atoms. This is true for all structures being considered in this work. As far as CoO is concerned, the dominant contributions come from the d electrons of the Co atoms and p electrons of the O atoms for zinc-blende, rocksalt and wurtzite structures. The 2p electrons of oxygen atoms contribute to the minimum of the conduction band. When going from ZnO to CoO, one can observe that the intensity of O-p orbitals in the conduction bands is reduced.
The study of the electronic charge densities in semiconducting materials is of fundamental interest. This is because it gives important information on the chemical bonding properties, interstitial impurities and response to perturbations in the materials under study (Walter and Cohen 1971;Bouarissa 1998bBouarissa , 2000Richardson et al. 1986; Bouarissa  Fig. 4 the charge distributions in all structures of interest for Co compositions x = 0 (ZnO), x = 0.50 and x = 1 (CoO). As can be observed from the contour plots of Fig. 4, in ZnO (x = 0) most of the charges are located in the inter-atomic region and shifted towards the O anion. This is due to the fact that ZnO involves a charge transfer from the atoms II to the atoms VI indicating the ionic character of ZnO crystal. The bottom bands can be seen as s-like atomic orbitals. The middle gap of bands form the covalent bond. Practically, there is a total absence of charges in the interstitial regions. By alloying ZnO and CoO, for example Zn 0.50 Co 0.50 O (Fig. 4b), the shift towards the anion becomes more important than in ZnO, suggesting that the bonding has a more ionic character than that of ZnO. When reaching CoO (x = 1) (Fig. 4c), the Co-O interaction seems to be purely ionic which is consistent with the experimental results of Jauch and Reehuis (2002). The general features of the electronic charge distribution in zinc-blende structures seem to resemble to those in rocksalt structures but quite different in details from those of wurtzite structures. The total magnetic moment of Zn 1-x Co x O has also been computed in the alloy composition interval 0-1 and for all structures being considered in this work. The evolution of the total magnetic moment as a function of Co content is shown in Fig. 5. This has been done for zinc-blende (Fig. 5a), rocksalt (Fig. 5b) and wurtzite (Fig. 5c) structures. Note that as the Co concentration is augmented from 0 to 1, the total magnetic moment of Zn 1−x Co x O increases for all structures of interest. The behavior of the total magnetic moment is monotonous and in a linear way. Interestingly, at the extreme case of CoO (Zn 1−x Co x O, x = 1) the total magnetic moment is 3.0, 3.0 and 6.0 μ B per cell for zinc-blende, rocksalt and wurtzite structures, respectively, whereas for the equimolar alloy Zn 0.50 Co 0.50 O the total magnetic moment is calculated to be 1.50, 1.50 and 3.0 μ B per cell for zinc-blende, rocksalt and wurtzite structures, respectively. The magnetic moment of Co 2+ is associated to localized d electrons and the magnetic properties of CoO originate from the atomic magnetic moments of Co 2+ ions.

Conclusions
The electronic band structure and magnetic properties of ZnO alloyed with CoO were studied. The computations were performed in the DFT framework using the FP-LAPW method. The exchange-correlation potential was described using the TB-mBJ-GGA approach. The hypothetical zinc-blende, rocksalt and wurtzite structures were considered for Zn 1-x Co x O. The examination of the band structure and DOS showed that the alloy system under study exhibits a semiconducting character and that the nature of its gap depends on the considered phase. The bonding character of Zn 1-x Co x O was inspected and discussed via the electronic charge distributions. Our results showed that while a partially covalent character appears for ZnO, this covalent character becomes weaker as far as the Co content is increased increasing thus the ionicity character. The total magnetic moment was found to augment in a linear way with enhancing the alloy composition x from 0 to 1, reaching a value of 3.0 μ B per cell for CoO in the zinc-blende and rocksalt structures and that of 6.0 μ B per cell for CoO in the wurtzite structure. The present results may be useful for the spintronics applications.