Physica B 5 (21) 17 151 Contents lists available at ScienceDirect Physica B journal homepage: www.elsevier.com/locate/physb First principles calculations of Co-doped zinc-blende ZnO magnetic semiconductor J. Zhang a,, K.L. Yao a,b, Z.L. Liu a, G.Y. Gao a a School of Physics, Huazhong University of Science and Technology, Wuhan 37, China b International Center of Materials Physics, Chinese Academy of Science, Shenyang1115, China article info Article history: Received 22 November 28 Received in revised form 25 September 29 Accepted 1 November 29 Keywords: Electronic structure First-principles Diluted magnetic semiconductor abstract We have investigated the electronic structure of Co-doped zinc-blende ZnO using first principles full potential linearized augmented plane-wave (FP-LAPW) method. The relative stability of the ground state, the density of states and the electronic band structure are examined. The results reveal that the antiferromagnetism (AFM) state is the ground state and the ferromagnetism (FM) state is the metastable one. The obtained electronic structure reveal that the Co-doped zinc-blende ZnO exhibits metallic with while a semiconductor within the scheme in the AFM ground state. The magnetic moments mainly arise from the Co atom with a little contribution from the nearestneighboring O atoms due to the hybridization between the Co 3d states and the nearest-neighboring O 2p states. & 29 Elsevier B.V. All rights reserved. 1. Introduction Recently, diluted magnetic semiconductors (DMS) have been studied extensively in both theory and experiment, because of their potential usage of both charge and spin of freedom of carriers in the electronic devise, namely, the spintronics [1,2]. A chief goal of current research is to find DMS with Curie temperature as high as possible for the spintronic applications. There have been trials based on two types of DMS families: II VI, such as Mn-doped ZnSe and CdTe [3], and III V, such as Mn-doped GaAs []. However, they have Tc about 11 K or less. The higher Curie temperature T C reported in (Ga, Mn) As grown by molecular beam epitaxy (MBE), however, is about 17 K, which sets T C higher than room temperature as the major challenge for GaAsbased DMS. In the past few years, room temperature ferromagnetism have been observed in Mn-doped ZnSnAs 2 [5], Ni-doped wurtzite ZnO [6], Cu-doped wurtzite ZnO [7] and Co-doped anatase TiO 2 [8]. As wide band gap semiconductors, ZnO and GaN have attracted much attention in searching for high Tc ferromagnetic DMS materials since Dietl et al. [9] predicted that ZnO- and GaN-based DMSs could exhibit ferromagnetism above room temperature when doped sufficient carriers and magnetic atoms. This work motivated intensive studies on the structural and physical properties of ZnO and GaN. Studies on electronic structure and magnetism of wurtzite ZnO-doped by transition metals (TM) such as Mn, Fe, Ni, Co, V and Cr have also been widely performed [1 15]. We know that ZnO have three Corresponding author. Tel.: +86 27 87556265; fax: +86 27 875525. E-mail address: zhangjing_35@126.com (J. Zhang). different crystal structures: the normal low-pressure phase hexagonal wurtzite (B) structure, the rocksalt (NaCl or B1) structure and the cubic zinc-blende (B3) structure [16 18]. Generally speaking, many studies of TM-doped ZnO have been concentrated on the wurtzite structure, and room ferromagnetic semiconductor or half-metal ferromagnetism have been predicted or synthesized, however, the electronic structure of the TM-doped zinc-blende ZnO are not widely studied both in theory and experiment. In this paper, the purpose of our work is to study the electronic structure and magnetism of Co-doped zinc-blende ZnO by means of first principles full potential linearized augmented plane-wave (FP-LAPW) method based on density functional theory (DFT). This paper is organized as follows. In Section 2, we describe the theoretical background and computational method. In Section 3, we show the computational results and discussion. The summary of our calculations is presented in Section. 2. Method of calculation First principles calculation based on the density functional theory (DFT) is one of the most powerful tools to study the ground-state property of materials. In this paper, we use the WIEN2 K [19] package, it is based on the FP-LAPW+local orbital (lo) method, one among the most accurate schemes for band structure calculations, which allows inclusion of local orbits in basis, improving upon linearization and making possible a consistent treatment of semi-core and valence in one energy window. The electronic structure and magnetic studies on Co-doped zinc-blende ZnO are based on the Zn 1 x Co x O (x=.125). 921526/$ - see front matter & 29 Elsevier B.V. All rights reserved. doi:1.116/j.physb.29.11.1
18 J. Zhang et al. / Physica B 5 (21) 17 151 According to the Ref. [16], the zinc-blende ZnO has a cubic crystal system (space group F3M, a=b=c=.6 Å, and a=b=g=91). The doping of x=.125 (Zn 1 x Co x O) is based on the 1 2 2 supercell containing sixteen ZnO (Fig. 1), where the two nearest-neighboring or next nearest-neighboring Zn atoms are replaced by two Co atoms. We investigate the electronic structure and magnetic coupling via the density of states (DOS) and the electronic band structure. These results will help us to further understand the origin of magnetism in the Zn 1 x Co x O. In our calculations, the radii of atom spheres are 2., 1.97, 1.77 a.u. for Zn, Co and O atoms, respectively. The cutoff parameter R MT K MAX is taken as 7., where R MT is the smallest radius of atoms and K MAX is the maximum value of the reciprocal lattice vectors used in the plane wave expansion. In our calculation, the as well as [2,21] method are used to treat exchange and correlation, we choose the 3d 3d Coulomb interaction U on Co sites with an effective value of Hubbard parameter U eff =U J [11]. For the Brillouin zone integration, we used 2 k-points in the first Brillouin. The self-consistent calculations are considered to be converge only when the integrate charge difference per formula R unit, jrn r n 1 jdr, between input charge density ½r n 1 Š and output ½r n Š is less than.1. 3. Results and discussion To examine the energetic between the FM, AFM and NM (nonmagnetism) electronic spin configurations of the Co ions, we have performed the energy calculation for zinc-blende Zn 1 x Co x O (x=.125). In this case, there are two Co ions in the Zn 1 Co 2 O 16, which is based 1 2 2 supercell of zinc-blende ZnO for two possible different configurations: the nearest-neighboring Zn (1) and Zn (2) atoms (represented by C-1 configuration) and the next nearest-neighboring Zn (1) and Zn (3) atoms (represented by C-2 configuration) are replaced by two Co atoms. Based on above two different configurations, we carry out both geometric optimization and atomic relaxation to find the equilibrium configuration. For the C-1 and C-2 configurations, the optimized length of the nearest Zn O bond is 2.3 and 2.61 Å, respectively. The calculated lattice constants of the two different configurations are listed in Table 1. In FM, AFM and NM phase with, we considered parallel, antiparallel and none spin for the two Co atoms. The energy calculations (Table 2) show that the AFM state both in C-1 and C-2 configurations are energetically more favorable than its FM state, so the AFM state should be the ground state, the FM state is the metastable state for Zn 1 Co 2 O 16. Moreover, in the AFM ground state we find that the total energy of C-1 configuration is lower than that of C-2 configuration. Therefore, we mainly give the results of the electronic structure calculations in C-1 configuration. In the calculations, we choose the different U eff (from 3 to 6 ev) to find the appropriate value. By comparing the total energies and magnetic moments with different U eff, it is found that above 3 ev these values have no difference, so in our calculation we use U eff =3 ev as the computational value in this paper. Then, we perform the electronic structure calculations for zinc-blende Zn 1 x Co x O (x=.125) in the FM and AFM configurations. First, we present the total DOS of Zn 1 x Co x O(x=.125) in the FM metastable state in Fig. 2 by using and schemes, respectively. The highest-occupied energy band in the valence bond (VB), i.e., E f, is marked by the dotted line. From Fig. 2(a), the total DOS of spin-up electrons shows an insulator characteristic, while spin-down electrons shows semiconducting behavior with about 1 ev energy gap. In the vicinity of the Fermi level, and the total DOS distribution of the spin-up and spin-down electrons is obviously split, hence the spin arrangement is dominated by the exchange interaction. Moreover, the total magnetic moments of Zn 1 Co 2 O 16 are 6.366m B, so the FM phase has semiconducting electronic structure. Then, we take account of the Coulomb correlation interaction of Co 3d electrons within the method to calculate the band structure in the FM state, with parameter U=3. ev and J=. With scheme, the total DOS also shows a semiconducting characteristic in the FM state. Comparing the DOS with and in Fig. 2(a) and (b), we can see clearly that the energy levels and peaks of DOS have a tendency shifting: the conduction band energy levels and peaks of DOS shift to higher positions and the valence band energy levels and peaks of DOS shift to lower positions, so the calculated energy gap arises from about 1. ev to nearly 2. ev due to the influence of the Coulomb repulsion interaction. Table 1 The calculated lattice constants of the Zn 1 Co 2 O 16 supercell in C-1 and C-2 configurations. Lattice constants (Å) a b C C-1.692 9.819 9.787 C-2.7731 9.786 9.685 In C-1 and C-2 configurations, the two nearest-neighboring and near nearestneighboring Zn atoms are replaced by Co atoms, respectively. Table 2 The total energy for two different configurations of Zn 1 Co 2 O 16 supercell. Configurations E NM (Ry) E FM (Ry) E AFM (Ry) C-1 58273.692 5827.992 5827.119 C-2 58273.335 5827.638 5827.165 Fig. 1. The 1 2 2 supercell of zinc-blende ZnO. The large and small balls represent Zn and O atoms, respectively. E NM, E FM and E AFM represent the total energy in the NM, FM and AFM states, respectively.
J. Zhang et al. / Physica B 5 (21) 17 151 19 6 2-2 5 25-25 -5-2 2 Fig. 2. The spin-dependent total DOS of Zn 1 Co 2 O 16 in FM state within and, respectively. The Fermi levels are located at ev. 6 Co t 2g 3-3 1 5 Co e g -5-1 -15-2 2 2 Co t 2g -2 2 Co e g -2-2 2 Fig. 3. The spin-dependent partial DOS of Co 3d electrons in FM state: (a) and (b). The Fermi levels are located at ev.
15 J. Zhang et al. / Physica B 5 (21) 17 151 The following discussion mainly focuses on the partial DOS of Co 2+ (3d 7 ) electrons in the FM state, which is presented in Fig. 3. Both in the and schemes, the splitting of the exchange and crystal field leads to the asymmetry of the DOS of spin-up and spin-down electrons. There exists some similar character that Co 2+ 3d orbital are split into double e g (d z2 and d x2 y2 ) states with lower energy and triple t 2g (d xy, d xz and d yz ) states with higher energy by the crystal field in tetrahedral symmetry. This is similar to what was found for Co-doped wurtzite ZnO [11]. These results reveal that exchange splitting is larger than the crystal field, resulting in the nearly full-filled e g states and the half-filled t 2g spin-down states. In the Fig. 3(a) with, the top of the valence band (VB) is near the Fermi level; however in Fig. 3(b) with, the top of the VB and the peak of e g spin-down states are depressed by.7 ev. The Fermi level locates at the conduction band minimum between e g spin-down and t 2g spin-down minority states, it reveals the semiconducting character and no half-metal [22 26] nature. The total and per Co ion spin magnetic moments of Zn 1 Co 2 O 16 in FM state are 6.366 and 2.77m B, 6. and 2.569m B within and schemes, respectively. It is obviously that total magnetic moment mainly comes from the Co atom, i.e., the spin-polarization occurs at the Co site, and the results reveal that the nearest-neighboring O can be polarized to.76 and.518m B within and, respectively, due to the hybridization between the Co 3d states and the nearest-neighboring O 2p states. In the AFM ground state, there are two different configurations of C1 and C2. According to the above results of energy calculations, it is found that the total energy of C-1 configuration is lower than that in C-2 configuration. In order to consider the influence of the doping position of Co in zinc-blende ZnO, we have carried out the calculations of electronic structure of the two different configurations in the AFM state. However, there is no obviously difference between the two AFM configurations. Hence, we only give the results of AFM state in C-1 configuration. The total and Co 3d DOS in the AFM states in is shown in Fig. (a), 6 total 2-2 12 6 Co 3d -12-2 2 9 6 total 3-3 -9 12 8 Co 3d -12-2 2 Fig.. The spin-dependent total DOS and partial DOS of Co 3d electrons in AFM state: (a) and (b). The Fermi levels are located at ev.
J. Zhang et al. / Physica B 5 (21) 17 151 151 from which we can find finite DOS values in the vicinity of the Fermi level. As spin-up and spin-down DOS are all cut the Fermi level, the AFM configuration exhibits metallic character in the band calculation. In the vicinity of the Fermi level, it is found that the total DOS mainly arises from the Co 3d electrons and the partial O 2p electrons due to the hybridization between the Co 3d and nearest-neighboring O 2p states. To the best of our knowledge, the success of shows that this treatment is actually sufficient for many materials, both for calculating ground state energies and band structures, implying that electronic correlations are rather weak in these materials. But, there are other important materials where fails, such as transition metal oxides or heavy Fermions systems, so application of the band in these strongly correlated materials usually leads to a serve underestimation of the band gap and in some case predicts metallic behavior for systems that are known to be insulators or semiconductors [27,28]. In order to further investigate the influence of effective on-site Coulomb interaction between the Co 3d electrons in the AFM state, we also perform the electronic structure calculations based on scheme. The total and partial DOS are presented in Fig. (b). In the AFM state, comparing the DOSs of with that of, we find that there is obviously difference. The total DOS in shows a semiconducting characteristic with the energy gap of near 1.2 ev due to the Co 3d Coulomb exchange interaction. Considering the shortcoming of the approximation which leads to underestimate the band gap of the transition metal oxides, the band structure of scheme is in good agreement with the experimental results. In the AFM ground state with and schemes, the Zn 1 x Co x O (x=.125) system shows a transition from a metal state to semiconductor. The similar phenomenon of metal/ insulator transition also was found on Fe x Mn 1 x Si [29] and (V 1 x Cr x ) 2 O 3 [3]. By investigating to the partial DOS Co and O atoms, the distribution of their electron clouds occur an obviously overlap. The strong hybridization between Co 3d and O 2p orbitals play an important role on the magnetic order. In Zn 1 x Co x O (x=.125) system, the Zn 2+ has a completely filled 3d shell, however the substitutional impurities Co 2+ provide no charge carries. In order to determine the exchange coupling of the two localized magnetic Co 2+ ions with a local spin S i, we adopt the Heisenberg Hamiltonian for a localized pair of spins given by H= 2JS i S j. The Co 2+ (3d 7 ) has a pin S=3/2. The energy difference between the FM and AFM arrangements can be used to calculate the exchange coupling parameters J. From Table 2, it is found that the total energies In AFM state are lower than that in FM state, hence the exchange coupling coefficient is negative in the ground state. In addition, the absolute values of total magnetic moments of Zn 1 Co 2 O 16 are 5.89 and 5.91 with and schemes in its AFM state, respectively.. Conclusions In conclusion, we have investigated the electronic structure and the magnetic properties of Co-doped zinc-blende ZnO using the first principles FP-LAPW method within and schemes. The energy calculations show that the AFM state is more energetically favorable than its FM state. In the FM state within, the energy gap becomes larger than which within, we find there exists large exchange splitting and crystal field splitting in the Co 3d orbital. In the AFM ground state, the obtained electronic structure reveals that the Zn.875 Co.125 O system exhibits metallic character with. However, the result of shows that this system is a semiconductor. As the results of do not correctly take into account the localized character of the transitional metal Co atoms, the predictions should be in good agreement with the experimental results. In the AFM ground state with and schemes, the interesting metal/semiconductor phase transition mainly attributes to Co 3d strong Coulomb repulsion interaction. Acknowledgments The authors would like to acknowledge the support from the National 973 Project (no. 26CB92165) and Major Project of the National Natural Science Foundation of China (no. 2921). 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