First-principles study on electronic and magnetic propertiesof (Mn,Fe)-codoped ZnO

Huawei Cao a, Pengfei Lu a,n, Ningning Cai a, Xianlong Zhang a, Zhongyuan Yu a,Tao Gao b, Shumin Wang c,d

a Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), Ministry of Education,Beijing 100876, Chinab Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, Chinac State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences,Shanghai 200050, Chinad Photonics Laboratory, Department of Microtechnology and Nanoscience, Chalmers University of Technology, 41296 Gothenburg, Sweden

a r t i c l e i n f o

Article history:Received 1 July 2013Received in revised form29 September 2013Available online 15 October 2013

Keywords:ZnOBulkElectronic structureMagnetic propertySpintronic

a b s t r a c t

First-principle calculations have been performed to investigate the electronic and magnetic properties of(Mn,Fe)-codoped ZnO within the generalized gradient approximation (GGA) and GGAþU schemes.The formation energy of five different configurations is investigated and the ground state is demon-strated to be ferromagnetic ordering. By applying the U correction, the band gap energy of pure ZnO isclose to the experimental values, while the ferromagnetic ordering of the ground state remainsunchanged. The ferromagnetic stabilization is mediated by double exchange mechanism. In addition,defects corresponding to Zn-vacancy and O-vacancy cannot enhance the ferromagnetism obviously. Theseresults indicate that (Mn,Fe)-codoped ZnO are promising magneto-electronic and spintronic materials.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Dilute magnetic semiconductors (DMS) are considered promisingmaterials to build novel magneto-electronic and spintronic devices[1]. This opens the door to combine the advantage of having logic,memory and communication on a single chip by the use of spin andcharge properties of electrons [2,3]. In the extensive study on DMS,the focus is mainly concentrated in two aspects.

It is known that the Curie temperature (Tc) of most DMSmaterials is below room temperature and it has been the majorchallenge for the commercial applications. The first task is tosearch for DMS with room temperature ferromagnetism. Varioustheoretical and experimental attempts have shown that chemicaldoping, especially the 3d transition metal doping is a key processto raise Tc to the values above room temperature. Ohno H [1,4]et al. fabricated GaMnAs magnetic films with Tc as high as 110 K bymolecular beam epitaxy (MBE). Matsumoto [5] et al. reported onthe observation of 400 K ferromagnetism in Co doped anatase thinfilms. As the ferromagnetic (FM) mechanisms of DMS are still

controversial, the second task is to explore the origin and exchangemanner of ferromagnetism.

ZnO based DMS are predicted to be promising host materials toobtain room temperature FM properties [6]. In the past few years,there have been systemic studies of 3d TMs (Fe, Mn, Cr, Co, Ni andCu) doped ZnO bulk or film and a large number of ideal high Tcresults have been reported [7–10]. By plasma assisted molecularbeam epitaxy (p-MBE) techniques, Fe doped ZnO with different Feconcentrations have been successfully prepared that display FMordering at room temperature [11]. However, with different Mnconcentration and sample preparation conditions at room tem-perature, both FM and nonmagnetic orderings were observed byBondino [12] et al., which was confirmed by the recent researches[13–15]. Taking into account the controversial results of Mn dopedZnO DMS, an effective route to obtain room temperature ferro-magnetism is codoping with two different 3d TM impurities.Hailing Yang [16] et al. performed (Mn,Fe)-codoped ZnO thin filmsby pulsed laser deposition (PLD) and observed room temperatureferromagnetism through the magnetic hysteresis loops. Further-more, similar results have been confirmed by hydrothermalmethod [17]. These relevant experiments stimulate us to give atheoretical investigation of (Mn,Fe)-codoped bulk ZnO.

In this article, we systematically investigate the electronicstructure and magnetic properties of (Mn,Fe)-codoped ZnO.

Contents lists available at ScienceDirect

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Journal of Magnetism and Magnetic Materials

0304-8853/$ - see front matter & 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jmmm.2013.10.008

n Correspondence to: P.O.Box 72, Xitucheng Road No.10, Beijing, 100876, China.Tel.:þ86 10 61198062.

E-mail address: photon.bupt@gmail.com (P. Lu).

Journal of Magnetism and Magnetic Materials 352 (2014) 66–71

The theoretical simulations are based on density functional theory(DFT) via first-principle calculations. The purpose of this article isto provide a theoretical foundation for the fabrication of high Tc ofZnO materials. This article is presented as follows. The theoreticalmethod and computational details are described in Section 2. Ourresults and discussions are given in Section 3. Finally, a briefsummary is made in Section 4.

2. Theoretical method and computational details

Our calculations are performed with the Vienna ab initiosimulation package (VASP) [18] code, which is based on thespin-polarized density functional theory (DFT) [19] and theplane-wave pseudo potential method. The electrons exchange-correlation function is treated using generalized gradient approx-imation (GGA) [20] with Perdew-Wang 91 (PW91) [21] approach.To give a proper description of the strong correlation effects,GGAþU methods [22,23] are considered. The on-site Coulombparameter U for 3d states of Mn, Fe, Zn and 2p states of O are 5, 3.5,10.5 and 7 eV. The exchange parameter is set to the typical value ofJ¼1 eV [23,24]. In order to ensure a good convergence of thegeometry optimization, the cutoff energy is chosen as 460 eV aftera series of test. The valence electron configurations for Zn, O, Mn,Fe atoms are selected as: 4s23d10, 2s22p4, 4s23d5 and 4s23d6,respectively. For the self-consistent Brillouin zone integration,the Monkhorst-Pack k-points mesh for pure ZnO and (Mn,Fe)-codoped ZnO are 7�7�4 and 4�4�2 respectively, in order toprovide sufficient accuracy. The process of geometry optimizationis considered to be finished when the following parameters aresatisfied (maximum force on each atom is 0.01 eV/Å, maximum

energy change between two ionic steps is 10�5 eV and maximumstress is 0.1 GPa).

Moreover, a periodic 2�2�2 wurtzite (WZ) bulk ZnO super-cell is employed in our simulation and the size has been verified tosatisfy the calculations [25]. The supercell contains 32 atoms with16 O and 16 Zn atoms as shown in Fig. 1(a). In order to simulate(Mn,Fe)-codoped ZnO, two Zn atoms are substituted with one Mnand Fe atoms corresponding to the dopant concentration about6.25% Mn and 6.25% Fe. As we all know, the ionic states of Mn andFe atoms are divalent and their substitutions are readily fordivalent Zn cations. Furthermore, the ionic radius of Mn2þ

(0.80 Å) and Fe2þ (0.76 Å) are close to that of ion Zn2þ (0.74 Å).Five possible magnetic coupling configurations are introduced. Forconfiguration I and II, Mn and Fe atoms are paired via intermediateO atom. While in configuration III, VI and V, Mn and Fe atoms areseparated by O–Zn–O or O–Zn–O–Zn–O. The 5 dopant configura-tions are plotted in Fig. 1. The simulation is arranged as follows:first, all these five configurations are subjected to the spinpolarized calculations corresponding to the FM and antiferromagnetic(AFM) orderings. Second, both the Zn-vacancy and O-vacancy areinvestigated to verify whether defects can induce FM coupling. Finally,the origin of FM coupling is discussed from the above-mentionedcalculations.

3. Results and discussion

3.1. Structural optimization

The lattice constants of unrelaxed ZnO with stable hexagonalWZ structure in P63mc space group are: a¼b¼3.249 Å and

Fig. 1. Pure bulk Zn16O16 supercell and five configurations of (Mn,Fe)-codoped ZnO (the red, gray, blue, yellow spheres represent O, Zn, Mn and Fe atoms, respectively. For thesake of highlighting Mn and Fe atoms, their dimensions are enlarged). (a) Pure bulk Zn16O16, (b) Configuration I, (c) Configuration II, (d) Configuration III, (e) Configuration IVand (f) Configuration V. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

H. Cao et al. / Journal of Magnetism and Magnetic Materials 352 (2014) 66–71 67

c¼5.202 Å [26]. The structural optimization is performed for thepristine ZnO supercell. From Table 1, after relaxation, the latticeconstants elongate by 0.9% in a and b and 1.77% in c compared tothe original constants. However, the hexagonal structure remainsunchanged. The lattice constants of codoped Zn14MnFeO16 (takingconfiguration I as an example) are also listed in Table 1 toinvestigate the impact of Mn–Fe incorporation. In contrast withthe original constants, the lattice constants increased by 1.07% in aand b and 2.17% in c after structural optimization. These changesare mainly due to that the ionic radius of Mn2þ (0.80 Å) and Fe2þ

(0.76 Å) are little larger than that of ion Zn2þ (0.74 Å). Theoptimized hexagonal structure still keeps unchanged. Based onthe above discussions, it is obvious that the relaxation of the atomsin a and b directions is much less than that in the c crystal-lographic direction which is in accordance to the previous theore-tical reports [14].

3.2. Electronic properties

The band structure of pure ZnO is presented in Fig. 2(a). It isobviously shown to be a direct band gap semiconductor. The bandgap width between valence band maximum (VBM) and conductionband minimum (CBM) is 0.813 eV at the highly symmetric G point.Our theoretical simulations are close to the previous theoreticalreports [14,27] which are lower than the experimental results(3.27 eV). The underestimation of the band gap is mainly ascribedthat the GGA or the local density approximation (LDA) calculationhas the limitation in reproducing well the unoccupied electronicstates. To figure out the effect of the Coulomb interactions, we applyGGAþU to improve the band gap energy. In Fig. 2(b), the band gap ofpure ZnO is increased to 3.172 eV which is close to the experimentalvalues. With Mn/Fe incorporation, the system behaves as a half metalcharacteristic with the down spin being semiconductor and the upspin being metallic displayed in Fig. 2(c) and (d). Furthermore, theconduction and valence band is shifted to the lower energy. It meansthat atoms' interaction is increased in Mn/Fe codoped ZnO.

3.3. Magnetic properties

In this section, the magnetic properties of five configurations of(Mn,Fe)-codoped ZnO are calculated by means of the GGAþUmethods. As listed in Table 2, it contains the variations in energy,magnetic moments and bond lengths of parallel and antiparallel

Table 1Lattice constants of relaxed structures of pristine Zn16O16 and Zn14MnFeO16.

Latticeconstant

Experimental [26]results

RelaxedZn16O16

Relaxed Zn14MnFeO16

(Con I)

a 3.249 3.278 3.284b 3.249 3.278 3.285c 5.202 5.294 5.315

Fig. 2. The band structure of pure ZnO (a) based on GGA (b) based on GGAþU. Spin-polarized band structure of Mn/Fe codoped ZnO for (c) the down spin and (d) theup spin.

H. Cao et al. / Journal of Magnetism and Magnetic Materials 352 (2014) 66–7168

spin alignments for codoped ZnO. The formation energy Ef is firstlycomputed to investigate the structural stability of these fiveconfigurations. According to the following formula:

Ef ¼ Eðcodoped_ZnOÞ�EðZnOÞþ∑nkμðkÞ ð1Þ

where E(codoped_ZnO) and E(ZnO) are the total energies of thebulk ZnO with and without the impurities. nk is the number ofatoms (Mn, Fe or Zn) changed from a pristine ZnO supercell (nk ispositive for removing one atom and vice versa). μk is the chemicalpotential of Mn, Fe or Zn atoms, respectively. It is depends on thereservoir with which the system is assumed to be in thermo-dynamic equilibrium conditions. Here, we consider two chemicalextremes. The μZn (Zn-rich conditions) and μO (O-rich conditions)of the upper limits are calculated as hexagonal closed pack Zn andmolecular O2. According to the thermodynamic equilibrium:μZnþμO¼μZnO (μZnO is defined as the total energy of bulk ZnOper Zn–O pair), the lower limits for μZn under O-rich condition is:

μZnðO�richÞ ¼ μZnO�ð1=2ÞμO2ð2Þ

The reservoirs of μMn and μFe are chosen as the energy per Fe orMn atom of cubic crystal structure. The calculated formationenergy under both Zn-rich and O-rich conditions are summarizedin Table 2. It is noted that the trend of the formation energy underboth Zn-rich and O-rich conditions are nearly the same. Further-more, the codoping is preferred to realize under O-rich conditions(The formation energy is lower than that under Zn-rich conditions).For the sake of convenience, the following discussion of formationenergy is all based on the O-rich condition. Based on the resultsof Ef which is the most important parameter to determine thestructural stability, configuration II is more likely to form with the

lowest formation energy of 0.587 eV. As a result, the configurationII is the ground state.

The total energy of the FM and AFM orderings for the (Mn,Fe)-codoped ZnO are also displayed in Table 2. Their relative energyΔE (ΔE¼EAFM�EFM) is a good indicator to determine the magneticstability. When ΔE is positive, the FM coupling plays a dominantrole, and vice versa. As can be seen in Table 2, the relative energyΔE corresponding to the ground state of configuration II based onGGAþU (94 meV) is lower than that (137 meV) based on GGAcalculations. It is still higher than the heat energy KBT (30 meV) [9].Therefore, the stable FM coupling is likely to be a real effectindicating that room temperature ferromagnetic could be obtainedfrom the (Mn,Fe)-codoped ZnO. These results give verificationto the previous experimental reports [16,17]. It is also noted thatthe relative energy ΔE decreases rapidly in the Mn–Fe distanceranging from 3.109 Å to 4.377 Å; while in the range of 4.377–5.874 Å, ΔE is nearly degenerate in energy. The reason is likely tobe that there is no intermediate O atom which enhances theinteraction between Mn 3d and Fe 3d states. We conclude that themagnetic coupling of (Mn,Fe)-codoped ZnO is short-ranged.

The local magnetic moments of Mn, Fe and the nearestneighboring O atoms are also summarized in Table 2. To figureout the relations between the magnetic coupling and localmagnetic moments, the case of configuration II where Mn andFe atoms are paired via One O atom in FM ordering is discussed.The local magnetic moments on Mn, Fe and the intermediate Oatoms are 4.588 μB, 3.657 μB, 0.077 μB. In order to more intuitivelyreflect the influence of the local magnetic moments, the spindistribution for configuration II is displayed in Fig. 3. When thespin-polarized directions of Mn and Fe atoms are upward in Fig. 3(a),

Table 2The formation energy Ef (in eV) under both Zn-rich (EZn-rich) and O-rich (EO-rich) conditions, total energy (in eV) after geometry optimization corresponding to FM and AFMorderings, the relative energy ΔE (in meV) of FM and AFM states, optimized Mn–Fe distances (in Å) and magnetic moment (in μB) among Mn, Fe, and the nearest neighboringO atoms. The relative energy ΔE based on GGA is also collected.

Configurations EZN–rich EO–rich EFM EAFM ΔE Coupling dMn–Fe μMn μFe μO (ΔE)GGA

I 2.803 0.666 �75.905 �76.030 �125 AFM 3.109 4.564 �3.620 �0.051 �103II 2.724 0.587 �76.109 �75.999 94 FM 3.125 4.588 3.657 0.077 137III 3.533 1.396 �75.289 �75.300 �11 AFM 4.377 4.590 �3.655 �0.061 �12IV 2.929 0.792 �75.904 �75.892 12 FM 5.012 4.588 3.653 0.058 17V 3.511 1.374 �75.319 �75.322 �3 AFM 5.874 4.592 �3.661 �0.057 �2IV(VO) 4.341 2.155 �71.470 �71.450 20 FM 4.838 4.592 4.101 0.160 47IV(VZn) 5.312 3.075 �71.525 �71.533 �8 AFM 4.973 4.554 �3.631 �0.043 �18

Fig. 3. The 3D iso-surface of the spin density for configuration II in (a) FM ordering and in (b) AFM ordering (The blue and yellow spheres indicate spin-up and spin-downdirections, respectively). The average charge density is 0.0263 e/Å3. (For interpretation of the references to color in this figure legend, the reader is referred to the webversion of this article).

H. Cao et al. / Journal of Magnetism and Magnetic Materials 352 (2014) 66–71 69

the neighboring O atoms are all induced to the same direction.However, when the spin-polarized directions of Mn and Fe atomsare different in Fig. 3(b), each TM atom only magnetizes theirneighboring O atoms leading to the opposite directions. To furtherinvestigate the influence of the local magnetic moments, themagnetic moments and total magnetic moments of Mn, Fe andthe intermediate O atoms of configuration II are displayed inTable 3. As can be seen in Table 3, the magnetic moments aremainly derived from 3d orbitals of Mn and Fe atoms. Therefore, the3d states of Mn and Fe are responsible for the spin polarization.

In the following, we explore the origin of FM coupling. Previousreports [14,27] have summarized that bound magnetic polarons, localmagnetic moments and itinerant carrier are the internal causes offerromagnetism in ZnO DMS system. The density of states (DOS)of (Mn,Fe)-codoped ZnO is investigated to gain further insight ofthe complex magnetic properties. In configuration II, as shown inFig. 4(a) and (b), there exists obvious overlap between Mn and Fe 3dbut little with O 2p states from �1.5 to 2.0 eV. For (Mn,Fe)-codopedZnO, both Mn and Fe are in crystalline field of tetrahedron.

The surrounding O ligands splits the Mn and Fe 3d states into doublydegenerate e states (dz2 and dx

2�y

2) and triply degenerate t2 states (dxy,dxz and dyz) displayed in Fig. 4(b). The exchange splitting is larger thanthe crystal field splitting between the e and t2 states. It means thatconfiguration II is a high spin configuration with Mn/Fe incorporation.In addition, the total DOS around Fermi level is attributed to the spin-up channel and there are no contributions to the DOS from the spin-down channel. So the system behaves as a half metallic nature.

In Fig. 4(c) and (d), the total and partial DOS based on GGAþUcalculations are presented. It is noted the impurity bands arebroadened resulting in the e states of Fe 3d shifting down inenergy while the t2 states of Mn 3d shifting up in energy. The FMordering is stabilized by the wide impurity bands [28,29]. In thespin-up channel around the Fermi level, there exist obviousoverlap between Mn 3d and Fe 3d and the contribution from O2p are nearly zero which can be seen in Fig. 4(d). Thus the electronin the d orbit of Mn/Fe can reduce its kinetic energy by hopping inthe FM state. As a results, the FM coupling can be explained bydouble exchange mechanism proposed by Sato [30,31] et al. Basedon the above analysis, (Mn,Fe)-codoped bulk ZnO is a goodcandidate to obtain room temperature ferromagnetism.

3.4. (Mn,Fe)-codoped ZnO with defects

In the presence of intrinsic defects, there is a possibility ofintroducing room temperature ferromagnetism [25,32]. To under-stand the microscopic mechanisms of defects, Zn-vacancy (VZn) andO-vacancy (VO) at neutral charge states are both investigated in thissection. We have computed the influence of defects in the pristineZnO and the results suggest that the material is still nonmagnetic.

Table 3The magnetic moments and total magnetic moments of Mn, Fe and the inter-mediate O atoms of configuration II.

Configuration II s p d total

μMn(FM) 0.026 0.050 4.512 4.588μMn(AFM) 0.027 0.050 4.507 4.584μFe(FM) 0.020 0.050 3.588 3.657μFe(AFM) �0.020 �0.051 �3.569 �3.640μO(FM) 0.005 0.072 0.000 0.077μO(AFM) �0.003 �0.047 0.000 �0.050

Fig. 4. Total (a) and partial (b) DOS of configuration II in FM ordering from GGA. Spin DOS calculated from GGAþU of total (c) and partial and (d) for configuration II in FMordering.

H. Cao et al. / Journal of Magnetism and Magnetic Materials 352 (2014) 66–7170

As can be seen in Table 2, the magnetic state of configuration IV is FMordering, but it does not meet the standard of room temperatureferromagnetism (the relative energy ΔE is less than 30 meV [9]).To verifying whether defects can enhance the magnetic properties,configuration IV corresponding to VZn and VO are both calculated inthe following.

The positions of VZn and VO are labeled in Fig. 5(a). As displayed inTable 2, the relative energy ΔE corresponding to VZn and VO are �8and 20 meV, respectively. We can see that VO slightly improves theFM coupling of configuration IV. However, the relative energy of VO islower than the heat energy KBT (30 meV) indicating that roomtemperature ferromagnetism still cannot obtain. To determine thestability of Mn/Fe codoped ZnO with VZn and VO, the formationenergy are also calculated. It is noted that the formation energy withdefects is very high. Therefore, the doping in the bulk ZnO withdefects becomes more difficult. As a result, VZn and VO may not be theeffective method to get room temperature ferromagnetism.

4. Conclusion

In summary, we have investigated the electronic and magneticproperties of (Mn,Fe)-codoped ZnO in terms of first-principle calcu-lations. In order to simulate codoping, five different configurationsare subjected to the spin polarized calculations. The calculated resultsof formation energy indicate configuration II is the ground state andtends to exhibit stable FM ordering. To study the strong correlationeffects, GGAþU calculations are performed. The corrected band gapenergy is close to the experimental values and the magnetic couplingof configuration II is still stable FM states. The FM coupling ismediated by double exchange interaction. Finally, defects are verifiednot to be effective methods to get room temperature ferromagnet-ism. Our present results are conductive to design room temperatureZnO based dilute magnetic semiconductors.

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (No. 61102024), and by the FundamentalResearch Funds for the Central Universities (No. 2012RC0401).

References

[1] H. Ohno, Making nonmagnetic semiconductors ferromagnetic, Science 281(1998) 951–956.

[2] N.S. Rogado, J. Li, A.W. Sleight, M.A. Subramanian, Magnetocapacitance andmagnetoresistance near room temperature in a ferromagnetic semiconductor:La2NiMnO6, Adv. Mater. 17 (2005) 2225–2227.

[3] D.D. Awschalom, M.E. Flatte, Challenges for semiconductor spintronics, Nat.Phys. 3 (2007) 153–159.

[4] H. Ohno, A. Shen, F. Matsukura, A. Oiwa, A. Endo, S. Katsumoto, Y. Iye, (Ga, Mn)As: a new diluted magnetic semiconductor based on GaAs, Appl. Phys. Lett. 69(1996) 363–365.

[5] Y. Matsumoto, M. Murakami, T. Shono, T. Hasegawa, T. Fukumura, M. Kawasaki,P. Ahmet, T. Chikyow, S.-y. Koshihara, H. Koinuma, Room-temperature ferro-magnetism in transparent transition metal-doped titanium dioxide, Science291 (2001) 854–856.

[6] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Zener model description offerromagnetism in zinc-blende magnetic semiconductors, Science 287 (2000)1019–1022.

[7] M. Sluiter, Y. Kawazoe, P. Sharma, A. Inoue, A. Raju, C. Rout, U. Waghmare, Firstprinciples based design and experimental evidence for a ZNO-based ferro-magnet at room temperature, Phys. Rev. Lett. 94 (2005).

[8] T. Zhu, W.S. Zhan, W.G. Wang, J.Q. Xiao, Room temperature ferromagnetism intwo-step-prepared Co-doped ZnO bulks, Appl. Phys. Lett. 89 (2006) 022508.

[9] P. Gopal, N.A. Spaldin, Magnetic interactions in transition-metal-doped ZnO:An ab initio study, Phys. Rev. B 74 (2006) 094418.

[10] Q. Wang, Q. Sun, P. Jena, Y. Kawazoe, Magnetic properties of transition-metal-doped Zn_{1�x}T_{x}O (T¼Cr, Mn, Fe, Co, and Ni) thin films with and withoutintrinsic defects: a density functional study, Phys. Rev. B 79 (2009) 115407.

[11] T. Chen, L. Cao, W. Zhang, W. Zhang, Y. Han, Z. Zheng, F. Xu, I. Kurash, H. Qian, J.o. Wang, Correlation between electronic structure and magnetic properties ofFe-doped ZnO films, J. Appl. Phys. 111 (2012) 123715–123718.

[12] F. Bondino, K. Garg, E. Magnano, E. Carleschi, M. Heinonen, R. Singhal, S. Gaur,F. Parmigiani, Electronic structure of Mn-doped ZnO by x-ray emission andabsorption spectroscopy, J. Phys.: Condens. Matter 20 (2008) 275205.

[13] Y. Zhu, J. Cao, Z. Yang, R. Wu, Origin of the codopant-induced enhancement offerromagnetism in (Zn,Mn)O: density functional calculations, Phys. Rev. B 79(2009).

[14] L. Zhao, P.F. Lu, Z.Y. Yu, X.T. Guo, Y. Shen, H. Ye, G.F. Yuan, L. Zhang, Theelectronic and magnetic properties of (Mn,N)-codoped ZnO from first princi-ples, J. Appl. Phys. 108 (2010) 113924.

[15] J. Luo, J.K. Liang, Q.L. Liu, F.S. Liu, Y. Zhang, B.J. Sun, G.H. Rao, Structure andmagnetic properties of Mn-doped ZnO nanoparticles, J. Appl. Phys. 97 (2005)086103–086106.

[16] H. Yang, X. Xu, G. Zhang, J. Miao, X. Zhang, S. Wu, Y. Jiang, Effect of defectcomplex on magnetic properties of (Fe, Mn)-doped ZnO thin films, Rare Metals31 (2012) 154–157.

[17] H.-W. Zhang, Z.-R. Wei, Z.-Q. Li, G.-Y. Dong, Room-temperature ferromagnet-ism in Fe-doped, Fe-and Cu-codoped ZnO diluted magnetic semiconductor,Mater. Lett. 61 (2007) 3605–3607.

[18] Q. Wang, Q. Sun, P. Jena, Y. Kawazoe, Magnetic coupling between Cr atomsdoped at bulk and surface sites of ZnO, Appl. Phys. Lett. 87 (2005)162503–162509.

[19] W. Kohn, L.J. Sham, Self-consistent equations including exchange and correla-tion effects, APS (1965).

[20] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation madesimple, Phys. rev. lett. 77 (1996) 3865–3868.

[21] J.P. Perdew, J. Chevary, S. Vosko, K.A. Jackson, M.R. Pederson, D. Singh,C. Fiolhais, Atoms, molecules, solids, and surfaces: applications of the general-ized gradient approximation for exchange and correlation, Phys. Rev. B 46(1992) 6671.

[22] G.-Y. Huang, C.-Y. Wang, J.-T. Wang, Detailed check of the LDAþU and GGAþUcorrected method for defect calculations in wurtzite ZnO, Comput. Phys.Commun. 183 (2012) 1749–1752.

[23] Q.-B. Wang, C. Zhou, J. Wu, T. Lü, A GGA, þU study of the optical properties ofvanadium doped ZnO with and without single intrinsic vacancy, Opt. Com-mun. 297 (2013) 79–84.

[24] H. Wang, Y. Yan, Y.S. Mohammed, X. Du, K. Li, H. Jin, The role of Co impuritiesand oxygen vacancies in the ferromagnetism of Co-doped SnO2: GGA andGGAþU studies, J. Magn. Magn. Mater. 321 (2009) 3114–3119.

[25] H. Chen, First-principle study on magnetic properties of Mn/Fe codoped ZnS, J.Magn. Magn. Mater. 324 (2012) 2086–2090.

[26] F.-C. ZHANG, W.-H. ZHANG, J.-T. DONG, Z.-Y. ZHANG, Electronic structure andmagnetism of Ni-doped ZnO nanowires, Acta Phys. Chim. Sin. 27 (2011)2326–2332.

[27] T. Souza, I. da Cunha Lima, M. Boselli, Carrier induced ferromagnetism in Mn-doped ZnO: Monte Carlo simulations, Appl. Phys. Lett. (2008)152511–152513.

[28] K. Sato, H. Katayama-Yoshida, First principles materials design for semicon-ductor spintronics, Semicond. Sci. Technol. 17 (2002) 367.

[29] N. Mamouni, A. El Kenz, H. Ez-Zahraouy, M. Loulidi, A. Benyoussef,M. Bououdina, Stabilization of ferromagnetism in (Cr, V) co-doped ZnO dilutedmagnetic semiconductors, J. Magn. Magn. Mater. 340 (2013) 86–90.

[30] G. Yao, G. Fan, H. Xing, S. Zheng, J. Ma, Y. Zhang, L. He, Electronic structure andmagnetism of V-doped AlN, J. Magn. Magn. Mater. 331 (2013) 117–121.

[31] K. Sato, P.H. Dederics, H. Katayama-Yoshida, Curie temperatures of III–Vdiluted magnetic semiconductors calculated from first principles, EPL (Euro-phys. Lett.) 61 (2003) 403.

[32] A. Debernardi, M. Fanciulli, The magnetic interaction of Fe doped ZnO withintrinsic defects: a first principles study, Physica B: Condens. Matter 401–402(2007) 451–453.

Fig. 5. Vacancy positions of configuration IV.

H. Cao et al. / Journal of Magnetism and Magnetic Materials 352 (2014) 66–71 71