Article pubs.acs.org/JPCC
Temperature-Mediated Magnetism in Fe-Doped ZnO Semiconductors Jianping Xiao,†,‡ Thomas Frauenheim,‡ Thomas Heine,† and Agnieszka Kuc*,† †
School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany Bremen Center for Computational Materials Science, Universität Bremen, Am Fallturm 1, 28359 Bremen, Germany
‡
ABSTRACT: We have employed first-principles calculations with PBE0 hybrid functional to study the magnetic origin of Fe-doped ZnO semiconductors. Density functional theory predicts antiferromagnetic ordering for Fe2+-substituted ZnO materials. Origins of magnetic ordering are attributed directly to the local ordering of Fe in the ZnO matrix. Fe3+ induced magnetism is studied for models exhibiting a zinc vacancy or an interstitial oxygen atom. In both cases Fe 3+ couples antiferromagnetically. Taking into account the temperature-dependent relative Gibbs energy, the magnetic ordering of Fe2+ and Fe3+ with interstitial oxygen atoms is changed from anti- to ferromagnetic with increasing T. This indicates that the Fedoped ZnO magnetism is highly dependent on temperature.
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stable as Fe2+-doped ZnO phase if no additional carrier dopants are introduced. These results were obtained employing the Korringa−Kohn−Rostoker (KKR) method based on the local density approximation (LDA). Gopal et al.,1 however, have studied the nature of magnetic interactions in TM-doped ZnO materials using the LSDA+U (spin polarized LDA with Hubbard U parameter) method, and the results indicate that AFM ordering is favorable. In agreement, Karmakar et al.2 have found that AFM prefers to stabilize the Fe2+-doped ZnO without any native defects. These results have been obtained by means of the tight-binding linear muffin-tin orbital method in the atomic sphere approximation within the LSDA method. Employing the same quantum method, Spaldin15 has found that robust FM ordering is not possible when Zn sites are substituted with Co or Mn, unless additional hole carriers are incorporated. These additional hole carriers might be FM clusters or precipitated secondary phases. Thus, the magnetism of ZnO-doped materials is still unknown and requires more detailed and extensive survey. Among others, the information about the thermal influence on the magnetic ordering in Fedoped semiconductors is missing in the available literature. In this article, we have studied the magnetic origin and electronic structure of Fe-doped ZnO materials. (Hereafter, we will use Fe−ZnO to refer to Fe-doped ZnO semiconductors, unless otherwise stated). The results show that ZnO doped with Fe2+ and Fe3+ is most likely to be in the AFM configuration at 0 K and that the magnetism is sensitive to thermal contributions. The calculations indicate that AFM transforms into FM at liquid nitrogen temperature (77 K) for
INTRODUCTION Dilute magnetic semiconductors (DMS) can be potentially applied for spintronic devices due to their coupling of electronic and magnetic properties. Recently, experimental and theoretical investigations of DMS have drawn much attention.1,2 ZnO is a transparent semiconductor with a direct band gap of 3.4 eV.3 It is a cheap material with a rich variety of properties. It has been widely investigated in the past decades because of its applications in optoelectronic,4 piezoelectric,5,6 optical, and other7,8 fields. When doped with other transition metals, ZnO can be transformed into an interesting DMS. Various experimental techniques can be used to fabricate ZnObased DMS. Depending on the synthesis conditions, different nanoscale ZnO materials, exhibiting different magnetic properties, can be obtained. Chen et al.9 have fabricated Fe-doped ZnO thin films by radio frequency magnetron sputtering. They concluded that Fe mainly exists in the form of Fe2+ on the basis of X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) characterization studies. Ahn et al.10 have successfully prepared a single-phase Fe-doped ZnO semiconductor using the sol−gel method with hydrogen treatment. In this material Fe2+ prefers ferromagnetic (FM) ordering. Wei et al. have obtained FM ordering for a single phase Fe-doped ZnO with low Fe content, where Fe2+ is incorporated into the wurtzite lattice of ZnO.11 However, other studies have shown that Fe-doped bulk ZnO is antiferromagnetic (AFM), rather than FM, although there is no secondary phase present in XRD patterns.12,13 In addition to the experiments, there have been many theoretical investigations on the magnetic properties of doped ZnO systems. The results are, however, controversial. Sato et al.14 have investigated the magnetism of transition-metal (TM)doped ZnO. The authors argue that the FM ordering is more © 2013 American Chemical Society
Received: January 14, 2013 Revised: February 20, 2013 Published: February 22, 2013 5338
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Fe2+−ZnO and at 600 K for Fe3+−ZnOi (Hereafter, ZnOi denotes an interstitial oxygen and ZnvO denotes a Zn vacancy).
placed two Fe atoms, what results in 12.5 at % concentration. Two of the models account for the closest possible configuration of the Fe atoms with respect to each other: the first one (model FeZn(a)−2Fe@(1 + 2)), where the Fe atoms are located in the adjacent hexagonal planes and are separated by only one O atom, and the second one (model FeZn(b)− 2Fe@(1 + 4)), where the Fe atoms are located within the same hexagonal plane and are also separated by one O atom (see Figure 1). The remaining two models describe the largest possible separation of the two Fe atoms in the considered supercell: both models have Fe atoms separated by a −O−Zn− O− bridge, and they differ in the arrangement of the second Fe atom with respect to the reference Fe position (N = 1). In the FeZn(c)−2Fe@(1 + 3) model, the two Fe atoms lie along the z axis, while in the FeZn(d)−2Fe@(1 + 5) model, they are arranged along a diagonal line. These four models were used to study the Fe2+ and Fe3+ oxidation states; however, in the latter case we have considered additional defects in the lattice in order to compensate for charge neutrality. Two types of defects have been introduced, namely, a Zn vacancy and an O interstitial, for each FeZn model to obtain the Fe3+ oxidation state. In addition, for each Fe3+ model, two different positions of defects (placed at the high symmetry points with respect to the Fe atoms) were considered. For example, in the FeZn(a) model, the corresponding Fe3+ models are labeled as a1 and a2 (cf. Table 1) for both Fe3+−ZnvO and Fe3+−ZnOi cases. In total, we have considered eight configurations for each Fe3+ model. In the following, we will use the notation Fe@N (where N = 1−5), in order to specify the location of the Fe atoms at the given substitutional site, N. We will discuss only the most stable magnetic configurations. Thermodynamic calculations were performed to elucidate temperature (T) dependence of magnetism at 77, 300, and 600 K (corresponding to the low, ambient, and high temperatures). The harmonic approximation was employed to calculate the free enthalpy, GT, at nonzero temperatures according to the equation:
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METHODS AND MODELS The fully optimized models of Fe2+- and Fe3+-doped ZnO were taken from our previous work.16 For computational details and optimized structures of Fe−ZnO, the reader is referred to ref 16. In short: all the calculations on geometry, energetic stability, and electronic properties have been carried out using density functional theory (DFT) employing the PBE0 (Perdew− Burke−Ernzerhof) hybrid functional17 as implemented in the CRYSTAL09 code.18 We have further used the PBE+U method using the DFT implementation in VASP19−21 in order to confirm the results with an alternative treatment of the common band gap problem in DFT. The projector augmented wave (PAW) formalism22 was employed with electronic configurations of 3d104s2 for Zn, 2s22p4 for O, and 3d74s1 for Fe atoms. Here, we have used typical values of U = 4.5 eV and J = 0.5 eV1 for Zn and Fe. We have chosen 550 eV kinetic energy cutoff for the plane wave expansion converging the total energy of the system. The 4 × 4 × 3 k-point grid was selected resulting in 26 k-points. The same geometries for all the Fe−ZnO models were used in the CRYSTAL09 and VASP calculations. We have considered four possible Fe arrangements in the Fe−ZnO (see Figure 1). In the reference supercell, we have
GT = Epot + EZPE + E T + pV − TS
(1)
where Epot is the potential energy, EZPE is the zero-point energy of various Fe2+ and Fe3+ configurations, and ET is the thermal contribution to the lattice vibrations; p, V, T, and S denote pressure, volume, temperature, and entropy, respectively. In this work, we have used a constant pressure of 1 bar. We have neglected the configuration contributions to the Gibbs free energy as it was shown in the literature that the experimental findings are well reproduced using only thermal contribu-
Figure 1. Atomic representation of the ZnO supercell used for Fe doping. Numbers indicate the Zn sites substituted with Fe atom (N = 1−5), with N = 1 being the reference position. The models with two Fe atoms in the supercell considered in this work are FeZn(a) (2Fe@(1 + 2)), FeZn(b) (2Fe@(1 + 4)), FeZn(c) (2Fe@(1 + 3)), and FeZn(d) (2Fe@(1 + 5)): blue, Zn; red, O.
Table 1. Formation Energy (in eV) Calculated at the PBE0 Level for FM and AFM Ordering in Our Models with Respect to the Isolated Pure ZnO and FeO (Fe2O3) Phasesa Fe2+ AFM FM Fe3+−ZnvO
a1
AFM FM Fe3+−ZnOi
−1.31 −1.15 a1
AFM FM
−0.17 5.68
a
b
c
d
−2.30 −2.28
3.49 −2.20
−2.32(4) −2.32(1)
−2.31 −2.32
a2 −1.34 −1.30 a2 −0.96(9) −0.96(7)
b1
b2
c1
c2
d1
d2
−1.79 −1.59
5.53 5.42
−0.97 3.44
−0.96(6) −0.96(9) c2
−0.66 −0.61 d1
−1.21 −1.30 d2
b1
b2
c1
−0.46 −0.28
4.87 −0.14
0.90 1.15
−0.44 −0.26
0.87 1.30
0.70 0.88
a
For each Fe3+ model, two different positions of defects are labeled as 1 and 2 together with the model type. More negative energies correspond to more stable configurations. 5339
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tions.23−25 Moreover, these configuration contributions are expected to be similar for both FM and AFM cases and therefore safely neglected. We have specified an equilibrium constant Ka→b for isomerizations from an AFM (a) configuration to an FM (b) isomer.26 This equilibrium constant is interrelated to the change of the standard free enthalpy as follows: ΔGT0 , a → b = −RT ln Ka → b
(2)
where R is the gas constant. It is convenient to evaluate the relative concentration of, e.g., the isomer a in the mixture:
xa =
Kb → a m ∑a = b Kb → a
(3)
The relative concentration (x) of the isomer mixture (m) can be further expressed as the isomeric partition function (Q): xa =
Q exp[−ΔGa /(RT)]
a m ∑b = a Q b
exp[−ΔGb /(RT)]
(4)
Equation 4 corresponds to the enthalpies at the absolute zero temperature. We also presume that the isomeric mixture of noninteracting particles has achieved thermodynamic equilibrium, and therefore, we can estimate a molar fraction xa of all isomers (m).
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RESULTS AND DISCUSSION A. Magnetic Properties. The most common oxidation states of Fe atoms are Fe2+ and Fe3+, which correspond to the d6 and d5 electronic configurations, respectively. In the crystal field theory, the d-orbitals of Fe in the tetrahedral coordination split into 3-fold t2g (dxy, dxz, and dyz) and 2-fold eg (dx2−y2, dz2) degenerate levels, where the latter is of lower energy. In addition, oxygen is a weak field ligand that results in the highspin systems. Therefore, five α-spin d-electrons are accommodated in the eg and t2g levels, while the remaining sixth electron fills the eg level with β spin (see Figure 2, A1−A3). Figure 3. PDOS of Fe d-states in the (A) FeZn(c), (B) FeZn(b)−ZnvO, and (C) FeZn(a)−ZnOi models at the DFT level. The Fe@N denotes Fe atoms at the doping sites N. α and β correspond to the majority and minority spin states. Fermi level is indicated by the vertical red line.
The most stable arrangement for the Fe2+ oxidation state (see Figure 2, A1−A3) is when the two Fe atoms are in the same line (model FeZn(c) with Fe−O−Zn−O−Fe). This system shows AFM ordering, in agreement with the results of Yoon et al. and Kolesnik et al.12,13 In the FeZn(c) model, an AFM superexchange occurs, which results in the intensive coupling between two next-to-nearest neighbor Fe2+ cations via a nonmagnetic oxygen anion. FM ordering is only slightly disfavored, namely, by 3 meV per Fe, in excellent agreement with 2 meV energy difference obtained using PBE+U method. Experimentally, the AFM ordering has been observed also at low temperatures.12,13 Our analyses of isomeric fractions at specific temperatures (77, 300, and 600 K) will be addressed in the next section. In the case of Fe3+ oxidation state, the most stable Fe configuration is in the case of the FeZn(b)−ZnvO model, where Fe atoms have the same oxygen coordination and d-orbital
Figure 2. Schematic representation of the most stable structures and magnetic ordering (A1, B1, and C1), local environment of Fe atoms in Fe−ZnO (A2, B2, and C2), and the crystal field splitting together with the electronic configuration (A3, B3, and C3): (left) FeZn(c), (middle) FeZn(b)−ZnvO, and (right) FeZn(a)−ZnOi. Solid arrows, α spin electron; dash arrows, β spin electron; blue, Zn; red, O; green, Fe. 5340
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Table 2. Calculated Standard Free Enthalpy Change (kJ mol−1) and Mole Fraction (%) of AFM and FM Mixture in the Fe2+, Fe3+ (ZnvO), and Fe3+ (ZnOi) Models at 77, 300, and 600 K Fe2+ 77 K AFM FM 300 K AFM FM 600 K AFM FM
Fe3+ (ZnvO)
Fe3+ (ZnOi)
ΔG
xi
ΔG
xi
−1.44 −1.85
33.4% 66.6%
−1.71 17.3
100% 0%
−1.7 −0.5
86.1% 13.9%
−79.3 −79.9
40.5% 59.5%
−75.7 −56.9
99.9% 0.1%
−79.2 −78.5
57.4% 42.6%
−331.7 −332.9
39.5% 60.5%
−316.7 −298.1
97.4% 2.6%
−335.5 −335.5
44.7% 55.3%
ΔG
xi
shown in the work of Karmakar et al.2 This confirms that the superexchange results in the AFM ordering for the linear Fe− O−Fe arrangement, while its spin states reverse under thermal vibration and form 59.5% FM and 40.5% AFM ordering at room temperature (300 K) for the Fe2+−ZnO system (in the FeZn(c) model). When the Zn vacancy was incorporated in Fe−ZnO (in the FeZn(b)−ZnvO model), the overall trend of Fe3+ d-orbital splitting is similar to the case of Fe2+ substitution. Thus, the five electrons are rearranged in d-orbitals of Fe3+ with the configuration of eg (2↑), t2g (3↑) (see Figure 3B). The AFM ordering dominates in Fe−ZnO with less than 3% FM ordering at the entire range of studied temperatures. In the FeZn(a)− ZnOi case, the local structure of Fe atoms is similar to trigonal bipyramidal coordination, and hence, the Fe d-orbitals are split into three levels, involving double 2-fold levels (dxz and dyz; dxy and dx2−y2) and another level of higher energy (dz2) (see Figure 3C). The probability of the AFM and FM orderings is reversed going from T = 300 K to T = 600 K. This provides tunable magnetism based on Fe−ZnO systems with the presence of interstitial oxygen.
splitting as in the case of Fe2+ in the FeZn(c) model (see Figure 2, B1−B3). Generally, the TM−O−TM type of clusters prefers to bend under 90° bond angle in the FM coupling via a superexchange.1 However, we have found that the two Fe atoms arrange themselves in the Fe−O−Fe cluster with a larger bond angle of 116° (FeZn(b)−ZnvO). Thus, we conclude that the FM and AFM orderings strongly compete and eventually are compromised into an AFM ordering (PBE0, 207 meV; PBE +U, 164 meV). These results indicate that the observed FM ordering was not caused by zinc vacancy in the Fe3+−ZnvO model. We have also obtained an AFM arrangement in the case of Fe3+ in the FeZn(a)−ZnOi model. Again, the energy difference between the AFM and FM phases is only 2 meV (PBE0, 2 meV; PBE+U, 20 meV), resulting in strong temperature dependence. In contrast, the local environment of the Fe3+ atoms and the d-orbital splitting are essentially much different than in the case of the FeZn(b)−ZnvO model (see Figure 2 C1−C3). Such a system is typical, for example, at grain boundaries of partially precipitated secondary phases.2,27 B. Thermodynamic Analysis. We have calculated the relative concentration and the change of the standard free enthalpy of the FM and AFM species in the Fe−ZnO at 77, 300, and 600 K. The results are given in Table 2 for all the Fe2+ and Fe3+ models studied in this work. The results show that the AFM ordering is the main component in the Fe3+ (FeZn(b)−ZnvO) model with a fraction of about 97% at all studied temperatures. However, in the case of Fe2+ in the FeZn(c) model, we have found that the FM ordering is the most favorable and that it dominates in the entire temperature range with approximately 60% probability. Furthermore, the probability of FM ordering in the FeZn(a)− ZnOi model overtakes its AFM ordering at 600 K. These results indicate that the magnetism of Fe-doped ZnO is sensitive to temperature. C. Electronic Properties. The electronic structure is the basis to interpret the magnetic behavior in Fe−ZnO systems. We have analyzed the projected density of state (PDOS) of the most stable Fe−ZnO models in order to interpret their magnetic origins. Figure 3A shows the PDOS of Fe d-orbitals with different spin states of the FeZn(c) model. The results show that the exchange splitting is much larger in comparison to the crystal field splitting. Therefore, Fe@1 favors high-spin configuration with eg (2↑, 1↓), t2g (3↑), while the Fe@3 exhibits opposite paramagnetic character (Here, the numbers in parentheses denote the number of electrons in the given spin channel.). Furthermore, Fe-derived states in the Fe−ZnO are hybridized with O p-states in the valence band, which was also
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CONCLUSIONS In summary, we have employed density functional theory using two types of exchange-correlation functionals, PBE0 and PBE +U, in order to study the origin of magnetism in Fe−ZnO. Four Fe2+ models and eight Fe3+ models with local defects were taken into account. Temperature affects the magnetic ordering in two ways: In Fe2+-substituted ZnO phases, the AFM ordering will stabilize ZnO matrix, while vibrational contributions to the free enthalpy reverse its stability. The magnetism of Fe−ZnO, in the presence of interstitial oxygens, can be tuned by temperature, while the relative stability and magnetic preference of zinc vacancy induced Fe3+ in ZnO is not intensively temperature-dependent. Because of the small energy difference, the effect of the site entropy is significant.
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
The authors thank the Computational Laboratory for Analysis, Modeling, and Visualization (CLAMV) for computational support. J. Xiao would like to acknowledge the financial support by the China Scholarship Council (CSC). 5341
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