Possible Origin of Ferromagnetism in an Undoped ZnO d0

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Possible Origin of Ferromagnetism in an Undoped ZnO d0 Semiconductor Chengxiao Peng, Yong Liang, Kefan Wang, Yang Zhang, Gaofeng Zhao, and Yuanxu Wang* Institute for Computational Materials Science, School of Physics and Electronics, Henan University, Kaifeng, 475004, China ABSTRACT: First-principles calculations were employed to investigate the effect of native defects and a hydrogen-related defect complex on ferromagnetism in an undoped ZnO semiconductor. The results show that the zinc vacancy (VZn) could lead to a moment of 1.73 μB in the undoped ZnO supercell, while the oxygen vacancy could not, but the formation energy of the zinc vacancy is much higher than that of the oxygen vacancy. When the hydrogen atom is doped in imperfect ZnO, the formation energy of VZn+HI sharply decreases, compared with that of VZn. Meanwhile, the VZn+HI defect complex can induce a 0.99(0.65) μB moment in the Zn15HIO16 supercell. Furthermore, the total energy of the ZnO supercell with two defect complexes for the ferromagnetic phase is lower than that for the antiferromagnetic phase, and the calculated results show that a strong magnetic coupling exists in the ferromagnetic phase. As an unintentionally doped element, H usually appears in ZnO prepared by many methods. So the ferromagnetism in the ZnO d0 semiconductor most probably arises from the defect complex of the zinc vacancy and H.

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INTRODUCTION Dilute magnetic semiconductors (DMSs) are attracting great interest due to their potential applications in spintronics, which could combine their electronic and magnetic properties.1 DMSs are usually achieved in the host material-doped magnetic ions which are partially filled with d or f electrons. Among various host materials, ZnO has been extensively studied due to the predication of ferromagnetism above room temperature for it.2 Numerous experiments have indeed confirmed the room temperature ferromagnetism in ZnO-based DMSs.3−8 However, some groups observed an unexpected high temperature ferromagnetism in ZnO without magnetic ions.9−13 This type d0 ferromagnetism provides an opportunity to search for new high temperature ferromagnetism materials. Moreover, it challenges the understanding of the origin and mechanism of ferromagnetism for researchers. Several groups have proposed that the ferromagnetism in nominally undoped ZnO arises from the intrinsic defects. These defects include oxygen vacancy,11,14−17 oxygen vacancy cluster,18 zinc interstitial,11,16,17,19 zinc vacancy,9,10,12,13,20 and oxygen interstitial.20 Therefore, the origin of ferromagnetism in undoped ZnO is still an open question. Recently, the zinc vacancy as a main defect in ZnO has been observed by the positron annihilation technique.9,10,12,21 Meanwhile, firstprinciples calculations predicted that the room temperature ferromagnetism could stem from the zinc vacancy in the ZnO bulk and thin film.22−25 However, the calculated formation energy of the zinc vacancy in ZnO is so high that it could not preferably form in ZnO. Hence, it is desirable to explore the defects in the ZnO bulk. In ZnO samples, the hydrogen impurity should be paid particular attention. Hydrogen is the lightest element and © 2012 American Chemical Society

undetectable by most experimental techniques. Unintentional undoped ZnO is usually contaminated by hydrogen in many preparation processes. In ZnO, H usually is regraded as a shallow donor to account for the n-type conductivity. For various configurations of H interstitial in the ZnO bulk, the bond-center configuration preferably appears and is stable.26 The H impurity affects not only the electrical characteristic but also the magnetic one. Sanchez et al. reported that the hydrogen atom adsorbs on the ZnO (0001) polar surface atop the Zn atoms, forming strong H−Zn bonds and leading to a metallic, hole-doped surface with a net magnetic moment according to first-principles calculation27 whereas the subsequent experiments exhibited that the room temperature ferromagnetism in nonmagnetic ZnO films after hydrogen annealing at elevated temperatures is due to the formation of OH bonds on its surface.28 The hydrogen interstitial (HI) in ZnO can mediate a strong short-ranged ferromagnetic spin− spin interaction between neighboring Co dopants through formation of a bridge bond, which in sufficiently high concentration can lead to a long-range ferromagnetic ordering in ZnO:Co.29 Park et al. have studied the effect of the interstitial hydrogen on the magnetism in Mn-doped ZnO films. They found that the interstitial hydrogen leads to the changes in the magnetic hysteresis loop as well as the enhancement of carrier concentration.30 Xia et al. utilized the thermal decomposition of Zn5(OH)8Ac2·2H2O to prepare ZnO porous spheres and explored the origin of room temperature ferromagnetism in ZnO porous microspheres. The results Received: October 27, 2011 Revised: March 22, 2012 Published: April 10, 2012 9709

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showed that both zinc vacancies and shallow donors induced by hydrogen may play an important role in triggering magnetic order in ZnO samples through electron paramagnetic resonance (EPR) spectroscopy and other means.31 In this work, we mainly focus on the effect of hydrogen incorporation in the ZnO single crystal on the formation of native defects and we subsequently explore the possible origin of room temperature ferromagnetism. We find that the Zn vacancy could give rise to a net magnetic moment in the ZnO single crystal, while the oxygen vacancy could not. Under the oxygen-rich condition, the formation energy of the zinc vacancy and oxygen vacancy are 2.39 and 3.71 eV, respectively. Under the zinc-rich condition, the formation energy of the zinc vacancy and oxygen vacancy are 5.25 and 0.85 eV, respectively. When a hydrogen is introduced into an imperfect ZnO single crystal, the formation energy of the complex for the zinc vacancy and hydrogen is strongly decreased under the oxygenrich condition. This complex could lead to a 0.99(0.65) μB magnetic moment. The ferromagnetic phase is more stable than the antiferromagnetic phase in the Zn14H2O16 supercell.

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COMPUTATIONAL METHODS All calculations were performed using the plane-wave pseudopotential approach and the generalized gradient approximation (GGA) within Perdew−Burke−Ernzerhof scheme as implanted in CASTEP.32−34 Valence electronic configurations for Zn, O, and H are 3d104s2, 2s22p4, and 1s1, respectively. The cutoff energy was 450 eV and a 4 × 4 × 2 κpoint mesh was adopted for integration in the first Brillouin zone. The crystal structure and the atomic coordinates were fully relaxed without any restriction using the Broyden− Fletcher−Goldfarb−Shanno method.35 The density-mixing scheme was applied for electronic minimization. In all calculations, self-consistency was achieved with a tolerance in the total energy of at least 1.0 × 10−5 eV. Hellman−Feynman force components on each ion are converged to less than 0.02 eV/Å.12 All chosen parameters have been referenced to the previous calculation, and these parameters have been tested and accepted due to the balance between the calculation accuracy and the time spent. The defects in the ZnO bulk were constructed as follows: the zinc (oxygen) vacancy was constructed by removing one zinc (oxygen) atom in the supercell, labeled as VZn(VO). Unintentional HI, another common point defect in ZnO, has been reported to preferably sit on bond-center and less likely on antibond positions of a Zn−O bond in pure ZnO.26 The H interstitial was at the bondcentered (BC∥ and BC⊥) positions, respectively, where ∥ and denotes configuration with the O−H bond parallel to the c axis, and the other bond direction is denoted by the symbol ⊥. Figure 1, parts a and b, shows the defect configuration, where V denotes the vacancy and labels 1, 2, 3, and 4 denote the nearest neighbor atoms around the vacancy.

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Figure 1. The configurations of the VZn+HI complex. Red, gray, and pink balls represent O, Zn, and H atoms, respectively. Blue balls denote a Zn vacancy.

n = Nsites exp( −E f /kBT )

(1)

where Nsites is the number of sites on which the defect can be incorporated, kB is Boltzmann’s constant, and T is temperature.

RESULTS AND DISCUSSION

We first optimized pure ZnO bulk in the wurtzite structure. The obtained lattice parameters a = 3.283 Å, c = 5.290 Å are in good agreement with the experimental values of a = 3.250 Å, c = 5.207 Å.36 On the basis of the optimized unit cell, a 2 × 2 × 2 ZnO supercell containing 32 atoms was constructed. The Formation Energy of the Defect and Its Complex. In thermodynamic equilibrium, the defect concentration n and defect formation energy Ef meet the expression

Figure 2. The various defect formation energies under different conditions. 9710

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Figure 3. (a) DOS of ZnO without a vacancy defect. (b) DOS of ZnO with VZn. (c) DOS of ZnO with VZn+HI∥ defect complex. (d) DOS of ZnO with the VZn+HI⊥ defect complex, and the details near the Fermi energy level are shown in the inset.

Figure 5. (a) Partial DOS of the H atom in ZnO with the VZn+HI∥ defect complex. (b) Partial DOS of the O4 atom in ZnO with the VZn defect. (c) Partial DOS of the O4 atom in ZnO with the VZn+HI∥ defect complex.

Figure 4. (a) The total DOS for ZnO with the Zn vacancy defect, as well as partial DOS for O atoms and Zn atom. (b) The total DOS for ZnO with the Zn vacancy and H interstitial, as well as partial DOS for O atoms and the Zn atom. (c) Partial DOS for the O atom 2p orbital and the Zn 3d orbital in ZnO with the Zn vacancy defect.

Figure 6. The isosurface spin−density plot ρ = ρ↑ − ρ↓ = 8 × 1022 e/ cm3 in the Zn15HO16 supercell containing one VZn+HI defect complex.

This equation shows that a larger defect formation energy means a lower defect concentration. The formation energy of a point defect in ZnO depends on the relative abundance of Zn

and O atoms, i.e., the chemical potentials μZn and μO. The formation energy of defect α with a charge q is:

Table 1. Calculated Defect Formation Energy under O-Rich and Zn-Rich Conditions, and the Magnetic Moment of O Atoms Surrounding the VZn and VZn+HI defect formation energy (eV)

E f (q ,α) = Etot(q ,α) − Etot(ZnO) + naμa + q(E F + Ev ) (2)

where Etot(q,α) is the total energy of supercell containing the defect α in charge state q, Etot(ZnO) is the total energy of a ZnO perfect crystal in the same supercell, μα is the a element chemical potential. nα is the number of atoms removed during the defect formation from the host crystal, and its sign is positive and vice versa. EF is the Fermi energy and Ev is the valence-band maximum of the host crystal. Here defect α

magnetic moment (μB)

defect type

O-rich

Zn-rich

O1

O2

O3

O4

VZn VZn+HI∥ VZn+HI⊥

2.39 −0.067 −0.088

5.25 2.8 2.78

0.21 0.14 0.11

0.21 0.14 0.11

0.21 0.14 0.01

0.10 0.0 0.0 9711

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Table 2. Distance between Two VZns, the Total Magnetic Moment for FM Ordering per Supercell, ΔE, and J0 for Various Configurations with Defect Complexes configuration

distance (Å)

magnetic moment (μB)

ΔE (meV)

J0 (meV)

1 2 3

3.21 4.57 5.21

1.97 2.00 1.97

42 −2 122

42 −2 122

The chemical potentials depend on the experimental growth conditions. The boundaries on μZn in ZnO are determined by the stability limits of ZnO with respect to metallic Zn and molecular oxygen. To prevent pure Zn formation, μZn < μZn(bulk), where μZn(bulk) is the total energy per atom of bulk Zn in a hexagonal close-packed structure. The upper limit of the Zn chemical potential for the zinc-rich limit in ZnO meets μZn = μZn(bulk). To prevent oxygen loss, μO < μO(O2), where μO(O2) is half of the energy of an oxygen molecular, EO2. The upper limit of the oxygen chemical potential for the oxygen-rich limit in ZnO meets μO = μO(O2). For calculating the energy of an oxygen molecule, it was placed within a 10 Å cubic cell. Only the Γ point was used. Spin polarization is included in the calculation for the energy of the oxygen molecule. The calculated bond length for O2 is 1.24 Å, which agrees well with the experimental value of 1.21 Å.37 Limited by the thermodynamic stability condition for ZnO, μZn and μO are variables correlated as μZn + μO = ΔH(ZnO)

where ΔH(ZnO) is the enthalpy of formation of bulk ZnO. The calculated formation enthalpy of ZnO is −2.86 eV, which is close to −2.93 eV38 and is smaller than the experimental value −3.61 eV.39 Under the O-rich limit condition, μO = 1 /2EO2, μZn = ΔH(ZnO) − 1/2EO2; similarly, under the Zn-rich limit condition, μZn = EZn, μO = ΔH(ZnO) − EZn. Figure 2 shows the calculated formation energy of various defects. The formation energy of the oxygen vacancy is 0.85 eV (3.71 eV) under the Zn-rich (oxygen-rich) condition, while that of the zinc vacancy is 5.25 eV (2.39 eV) under the Zn-rich (oxygenrich) condition. These results are fairly consistent with the previous results.24 H is often present in the unintentional undoped ZnO. Among various configurations of the H interstitial in the ZnO bulk, the bond-center configuration favorably appears and is stable. Here we calculate the formation energies of the H interstitial at the bond-centered (BC∥ and BC⊥) positions. The calculated formation energies of HI are 0.96 and 1.12 eV at BC∥ and BC⊥ positions, respectively. The latter agrees well with the result reported by Van de Walle.26 Furthermore, the formation energy of the defect complex of VZn+HI∥ is −0.07 eV (2.80 eV) under the oxygen-rich (Zn-rich) condition, while that of VZn+HI⊥ is −0.09 eV (2.78 eV) under the same condition. The formation energy of VZn and the complex of VZn+HI is 2.39 eV and −0.07(or −0.09) eV under the oxygen-rich condition, and the formation energy sharply decreases due to H incorporation. So the defect complex of VZn+HI forms preferably to VZn under the oxygen-rich condition. In fact, this defect complex has indeed been observed by positron annihilation spectroscopy in the undoped ZnO single crystal.40 The Influence of Point Defects on Magnetism. The calculated magnetic moment is 0 μB, 1.73 μB, 0.99 μB, and

Figure 7. The three configurations with double VZn + HI∥s in the Zn14H2O16 supercell. The distance between two VZns is shown in parts a, b, and c.

charge state is neutral, i.e., q = 0. For the zinc vacancy, its formation energy could be written as: E f (VZn) = Etot(VZn) − Etot(ZnO) + μZn

(4)

(3)

Expressions similar to eq 3 apply to VO, HI, and VZn+HI. 9712

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0.65 μB in the presence of VO, VZn, VZn+HI∥, and VZn+HI⊥ in the ZnO supercell, respectively. The zinc vacancy and its defect complex could result in a net magnetic moment, but the oxygen vacancy could not. The calculated magnetic moments of VO and VZn are well consistent with the previous results.24,41 As mentioned above, the defect formation energy of VZn+HI is lower, compared with its native defects in the ZnO bulk. Hence, the defect complex of VZn+HI is favorable to be presented. At the same time, this complex could give rise to a 0.99 (0.65 μB) magnetic moment. These results have been strongly supported by Xia’s results, which indicated that both the zinc vacancies and H atoms play a critical role to induce room temperature ferromagnetism in ZnO porous microspheres.31 Thus, in combination with the formation energy of VZn+HI, the ferromagnetism in the ZnO bulk possibly arises from the defect complex for VZn+HI. Figure 3 shows the total density of states (DOS) for a perfect ZnO single crystal and other defect systems. As seen in this figure, the spin-up and spin-down DOS near the Fermi level are totally symmetrical in perfect ZnO single crystal, indicating that perfect ZnO is nonmagnetic. However, it is asymmetrical between spin-up and spin-down DOS near the Fermi level in imperfect ZnO crystals containing the zinc vacancy and its complexes, suggesting the appearance of the magnetic moment in defect systems. Furthermore, the difference between spin-up and spin-down DOS near the Fermi level is increasingly less from part b to part d of Figure 3, which indicates that the net magnetic moment decreases with the incorporation of hydrogen around the zinc vacancy. Figure 4 displays the DOS for the defect systems and the partial DOS of the O 2p orbital and the Zn 3d orbital. In Figure 4, parts a and b, the difference between the total spin-up and spin-down DOS near the Fermi level from −1 to 1 eV for defect systems mainly comes from that for O atoms and Zn atoms. O atoms and Zn atoms give about 76% and 24% contributions to the difference. Therefore, O atoms play more important roles in the net magnetic moment for defect systems. It is asymmetrical between spin-up and spin-down DOS near the Fermi level for the O 2p orbital in Figure 4c. Thus, the magnetic moment mainly comes from the O 2p orbital in ZnO containing the zinc vacancy, as well as in ZnO with the defect complex VZn+HI . In addition, a small difference between spinup and spin-down DOS for the Zn 3d orbital also appears in Figure 4c. The overlap near the Fermi level between the oxygen 2p orbital and the zinc 3d orbital, i.e., the p−d coupling, is strongly associated with the magnetic coupling in d0 semiconductors.42 Table 1 lists the magnetic moment of O atoms surrounding the VZn and VZn+HI. The magnetic moment for defect systems is mainly contributed by the oxygen atoms surrounding the zinc vacancy or its complex. However, the nearest neighbor oxygen atoms around the zinc vacancy play different roles in the magnetic moment in defect system. The oxygen atoms in ab plane have more contributions to the magnetic moment than that of the oxygen atom along the c axis. Moreover, when a hydrogen is incorporated as an interstitial at the bond-centered (BC∥) position and the complex of VZn+HI∥ is formed, the magnetic moments of the nearest oxygen atoms O1, O2, and O3 surrounding the zinc vacancy decrease by 30%, and that of the O4 atom disappears. In VZn and VZn+HI∥ defect systems, the difference in the local magnetic moment for the O4 atom is due to the hydrogen incorporation. Compared with that in Figure 5b, a noticeable change occurs from −7 to −5 eV in

Figure 5c. This suggests that the electron of the hydrogen atom transfers to the O4 atom, which results in a change of spin-up and spin-down DOS for the O4 atom. As for the defect system with a VZn+HI⊥, the magnetic moments of the O1 and O2 atoms further decrease, and the O3 atom shows little magnetic moment. The magnetic moment of O3 decreases from 0.14 to 0.01 μB, as the configurations change from VZn+HI∥ to VZn+HI⊥. This decrease is mainly caused by the bonding between the O3 and H atoms, but the experimental results showed that the formation of the OH bond induced the room temperature ferromagnetism in ZnO films with no vacancies.28 Figure 6 shows the isosurface plot of the spin density (ρ = ρ↑ − ρ↓) in the 32 atom supercell containing one VZn+HI defect complex. It is evident that all spin moments are localized near the three oxygen atoms around the Zn vacancy. This conclusion is consistent with the calculated DOS for oxygen atoms. He et al. reported that the magnetic moments within ultrafine systems arise from the imbalance between the spatial spin density distributions. This mechanism is distinct from that of the two well-known paradigms for magnetism, i.e., localized ferromagnetism and itinerant ferromagnetism.43 We focus on the ZnO bulk, so this mechanism is unsuitable for our systems. The mechanism of magnetization in ZnO with the defect complex of VZn+HI could be understood according to Stoner’s criterion. Stoner’s criterion could be expressed as D(Ef)J > 1, where D(Ef) is the DOS at the Fermi energy Ef, and J is the energy of exchange interaction. As discussed above, the magnetic moments in defect systems come from the oxygen 2p orbital. Peng et al. reported that the exchange interaction is proportional to the splitting. The splitting energy for the O 2p orbital is even larger than that for the Mn 3d orbitals with the same moment.23 D(Ef) is proportional to m3/2(EVBM − Ef)1/2 when holes are introduced. The effective mass m is large in oxides. Thus, magnetization depends on the relative level between the valence band top and the Ef level. A neutral zinc vacancy is present with two holes and acts as an acceptor. When there are more holes, the Fermi energy level moves into the valence band, so D(Ef) increases and Stoner’s criterion is satisfied, but the calculation results show that the zinc vacancies are not favorable to form due to large formation energy. While the hydrogen impurity is introduced, the formation energy of the VZn+HI complex decreases significantly; hence, the complex preferably forms. It is well-known that hydrogen with one electron usually acts as a donor in ZnO. When the complex of VZn+HI forms, one of two holes introduced by the zinc vacancy is annihilated by the electron donated by hydrogen, but the defect complex remains one hole. Given sufficient defect complexes, there are so many holes that the Ef level still moves into the valence band. Thus, Stoner’s criterion is still met, and the net magnetic moment is present in ZnO with the defect complex. On the other hand, in comparison with Figure 3b, the reduction in D(Ef) is confirmed, as shown in Figure 3, parts c and d; thus, the magnetic moment is reduced by 60% due to one of two holes annihilated with one electron donated by a H atom. Ferromagnetism in ZnO with the Defect Complex. The local moments are induced by the VZn and the VZn+HI defect complex as mentioned above, but the existence of local moments does not necessarily result in a collective magnetism. Thus, two important questions are critical to be clarified. One is that the coupling among moments induced by the defect complex is ferromagnetic or antiferromagnetic. The other is 9713

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The Journal of Physical Chemistry C that this coupling is long- or short-ranged. A long-range magnetic coupling is critical to achieve the high-temperature ferromagnetism at low defect concentrations.44 To investigate the magnetic coupling of moments induced by the defect complex, three possible configurations of double VZn+HI defect complexes are considered in the ZnO supercell, which are shown in Figure 7, parts a, b, and c, respectively. The distances between two VZns in Figure 7, parts a, b, and c, are 3.21 Å, 4.57 Å, and 5.21 Å, respectively. The total energy of each configuration for ferromagnetic (FM) and antiferromagnetic (AFM) spin alignments was calculated. The energy difference between the two phases, ΔE = EAFM − EFM, was used to evaluate the magnetic interactions. In addition, if ΔE > 0, it suggests that FM spin alignment is more stable. According to the Heisenberg model, the nearest-neighbor magnetic coupling J0 can be evaluated using the expression: ΔE = 4J0(R)S2, where S is the net spin of the defect states.45 It is known that the main source of the magnetic moment for the VZn defect arises from the two holes in the 2p band at the O sites surrounding the Zn vacancy. Because hydrogen is known to be a donor, this annihilates one hole of the oxygen 2p bands around the Zn vacancy.26,46,47 For the neutral VZn+HI defect complex, S is 0.5. The ΔE and coupling parameter J0 for various configurations are listed in Table 2. As seen in Table 2, J0 > 0 for configurations 1 and 3, and ferromagnetic coupling is energetically favorable for each case whereas the AFM ordering is slightly more stable than the FM ordering for configuration 2. Such a large energy difference between the ferromagnetic and antiferromagnetic state for configurations 1 and 3 imply that the room temperature ferromagnetism for ZnO with the defect complex is expected. In addition, the total energy for configuration 1 with the FM phase is 233 meV lower than that for configuration 3; therefore, the VZn+HI defect complex may be present in configuration 1 with the FM phase. For configurations 1 and 3, the stabilization of the FM phase can be understood using the band-coupling model,23,48 and it is believed that the long-range FM coupling interaction is due to the O 2p states coupled with the same spin.

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CONCLUSION

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AUTHOR INFORMATION

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ACKNOWLEDGMENTS

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REFERENCES

Article

This research was sponsored by the National Natural Science Foundation of China (No. 21071045), the Program for New Century Excellent Talents in University (No. NCET-10-0132).

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We have studied the effect of native point defects and the defect complex on ferromagnetism in the ZnO bulk by firstprinciples calculations. VZn and VZn+HI could effectively give rise to the ferromagnetism in the ZnO bulk, but the formation energy of the defect complex VZn+HI is much lower than that of VZn, so the observed ferromagnetism in ZnO possibly stems from the defect complex VZn+HI. The most neighboring oxygen atoms surrounding the zinc vacancy give important contributions to the magnetic moment, but they play different roles in the magnetic moment according to their positions relative to VZn and HI .

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 9714

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dx.doi.org/10.1021/jp2103148 | J. Phys. Chem. C 2012, 116, 9709−9715