Temperature-Mediated Magnetism in Fe-Doped ZnOSemiconductorsJianping 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, Universitat Bremen, Am Fallturm 1, 28359 Bremen, Germany

ABSTRACT: We have employed first-principles calculations with PBE0 hybridfunctional to study the magnetic origin of Fe-doped ZnO semiconductors. Densityfunctional theory predicts antiferromagnetic ordering for Fe2+-substituted ZnOmaterials. Origins of magnetic ordering are attributed directly to the local orderingof Fe in the ZnO matrix. Fe3+ induced magnetism is studied for models exhibiting azinc vacancy or an interstitial oxygen atom. In both cases Fe3+ couplesantiferromagnetically. Taking into account the temperature-dependent relative Gibbsenergy, the magnetic ordering of Fe2+ and Fe3+ with interstitial oxygen atoms ischanged from anti- to ferromagnetic with increasing T. This indicates that the Fe-doped ZnO magnetism is highly dependent on temperature.

■ INTRODUCTION

Dilute magnetic semiconductors (DMS) can be potentiallyapplied for spintronic devices due to their coupling ofelectronic and magnetic properties. Recently, experimentaland theoretical investigations of DMS have drawn muchattention.1,2

ZnO is a transparent semiconductor with a direct band gapof 3.4 eV.3 It is a cheap material with a rich variety ofproperties. It has been widely investigated in the past decadesbecause of its applications in optoelectronic,4 piezoelectric,5,6

optical, and other7,8 fields. When doped with other transitionmetals, ZnO can be transformed into an interesting DMS.Various experimental techniques can be used to fabricate ZnO-based DMS. Depending on the synthesis conditions, differentnanoscale ZnO materials, exhibiting different magnetic proper-ties, can be obtained. Chen et al.9 have fabricated Fe-dopedZnO thin films by radio frequency magnetron sputtering. Theyconcluded that Fe mainly exists in the form of Fe2+ on the basisof X-ray diffraction (XRD) and X-ray photoelectron spectros-copy (XPS) characterization studies. Ahn et al.10 havesuccessfully prepared a single-phase Fe-doped ZnO semi-conductor using the sol−gel method with hydrogen treatment.In this material Fe2+ prefers ferromagnetic (FM) ordering. Weiet al. have obtained FM ordering for a single phase Fe-dopedZnO with low Fe content, where Fe2+ is incorporated into thewurtzite lattice of ZnO.11 However, other studies have shownthat Fe-doped bulk ZnO is antiferromagnetic (AFM), ratherthan FM, although there is no secondary phase present in XRDpatterns.12,13

In addition to the experiments, there have been manytheoretical investigations on the magnetic properties of dopedZnO systems. The results are, however, controversial. Sato etal.14 have investigated the magnetism of transition-metal (TM)-doped ZnO. The authors argue that the FM ordering is more

stable as Fe2+-doped ZnO phase if no additional carrier dopantsare introduced. These results were obtained employing theKorringa−Kohn−Rostoker (KKR) method based on the localdensity approximation (LDA). Gopal et al.,1 however, havestudied the nature of magnetic interactions in TM-doped ZnOmaterials using the LSDA+U (spin polarized LDA withHubbard U parameter) method, and the results indicate thatAFM ordering is favorable. In agreement, Karmakar et al.2 havefound that AFM prefers to stabilize the Fe2+-doped ZnOwithout any native defects. These results have been obtained bymeans of the tight-binding linear muffin-tin orbital method inthe atomic sphere approximation within the LSDA method.Employing the same quantum method, Spaldin15 has foundthat robust FM ordering is not possible when Zn sites aresubstituted with Co or Mn, unless additional hole carriers areincorporated. These additional hole carriers might be FMclusters or precipitated secondary phases. Thus, the magnetismof ZnO-doped materials is still unknown and requires moredetailed and extensive survey. Among others, the informationabout the thermal influence on the magnetic ordering in Fe-doped 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, wewill use Fe−ZnO to refer to Fe-doped ZnO semiconductors,unless otherwise stated). The results show that ZnO dopedwith Fe2+ and Fe3+ is most likely to be in the AFMconfiguration at 0 K and that the magnetism is sensitive tothermal contributions. The calculations indicate that AFMtransforms into FM at liquid nitrogen temperature (77 K) for

Received: January 14, 2013Revised: February 20, 2013Published: February 22, 2013

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Fe2+−ZnO and at 600 K for Fe3+−ZnOi (Hereafter, ZnOidenotes an interstitial oxygen and ZnvO denotes a Zn vacancy).

■ METHODS AND MODELSThe fully optimized models of Fe2+- and Fe3+-doped ZnO weretaken from our previous work.16 For computational details andoptimized structures of Fe−ZnO, the reader is referred to ref16. In short: all the calculations on geometry, energetic stability,and electronic properties have been carried out using densityfunctional theory (DFT) employing the PBE0 (Perdew−Burke−Ernzerhof) hybrid functional17 as implemented in theCRYSTAL09 code.18

We have further used the PBE+U method using the DFTimplementation in VASP19−21 in order to confirm the resultswith an alternative treatment of the common band gap problemin 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 usedtypical values of U = 4.5 eV and J = 0.5 eV1 for Zn and Fe. Wehave chosen 550 eV kinetic energy cutoff for the plane waveexpansion converging the total energy of the system. The 4 × 4× 3 k-point grid was selected resulting in 26 k-points. The samegeometries for all the Fe−ZnO models were used in theCRYSTAL09 and VASP calculations.We have considered four possible Fe arrangements in the

Fe−ZnO (see Figure 1). In the reference supercell, we have

placed two Fe atoms, what results in 12.5 at % concentration.Two of the models account for the closest possibleconfiguration of the Fe atoms with respect to each other: thefirst one (model FeZn(a)−2Fe@(1 + 2)), where the Fe atomsare located in the adjacent hexagonal planes and are separatedby only one O atom, and the second one (model FeZn(b)−2Fe@(1 + 4)), where the Fe atoms are located within the samehexagonal plane and are also separated by one O atom (seeFigure 1). The remaining two models describe the largestpossible separation of the two Fe atoms in the consideredsupercell: both models have Fe atoms separated by a −O−Zn−O− bridge, and they differ in the arrangement of the second Featom with respect to the reference Fe position (N = 1). In theFeZn(c)−2Fe@(1 + 3) model, the two Fe atoms lie along the zaxis, while in the FeZn(d)−2Fe@(1 + 5) model, they arearranged along a diagonal line. These four models were used tostudy the Fe2+ and Fe3+ oxidation states; however, in the lattercase we have considered additional defects in the lattice inorder to compensate for charge neutrality. Two types of defectshave been introduced, namely, a Zn vacancy and an Ointerstitial, for each FeZn model to obtain the Fe3+ oxidationstate. In addition, for each Fe3+ model, two different positionsof defects (placed at the high symmetry points with respect tothe 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. Intotal, we have considered eight configurations for each Fe3+

model. In the following, we will use the notation Fe@N (whereN = 1−5), in order to specify the location of the Fe atoms atthe given substitutional site, N. We will discuss only the moststable magnetic configurations.Thermodynamic calculations were performed to elucidate

temperature (T) dependence of magnetism at 77, 300, and 600K (corresponding to the low, ambient, and high temperatures).The harmonic approximation was employed to calculate thefree enthalpy, GT, at nonzero temperatures according to theequation:

= + + + −G E E E pV TST pot ZPE T (1)

where Epot is the potential energy, EZPE is the zero-point energyof various Fe2+ and Fe3+ configurations, and ET is the thermalcontribution to the lattice vibrations; p, V, T, and S denotepressure, volume, temperature, and entropy, respectively. Inthis work, we have used a constant pressure of 1 bar. We haveneglected the configuration contributions to the Gibbs freeenergy as it was shown in the literature that the experimentalfindings are well reproduced using only thermal contribu-

Figure 1. Atomic representation of the ZnO supercell used for Fedoping. Numbers indicate the Zn sites substituted with Fe atom (N =1−5), with N = 1 being the reference position. The models with twoFe 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 theIsolated Pure ZnO and FeO (Fe2O3) Phases

a

Fe2+ a b c d

AFM −2.30 3.49 −2.32(4) −2.31FM −2.28 −2.20 −2.32(1) −2.32

Fe3+−ZnvO a1 a2 b1 b2 c1 c2 d1 d2

AFM −1.31 −1.34 −1.79 5.53 −0.97 −0.96(6) −0.66 −1.21FM −1.15 −1.30 −1.59 5.42 3.44 −0.96(9) −0.61 −1.30

Fe3+−ZnOi a1 a2 b1 b2 c1 c2 d1 d2

AFM −0.17 −0.96(9) −0.46 4.87 0.90 −0.44 0.87 0.70FM 5.68 −0.96(7) −0.28 −0.14 1.15 −0.26 1.30 0.88

aFor each Fe3+ model, two different positions of defects are labeled as 1 and 2 together with the model type. More negative energies correspond tomore stable configurations.

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tions.23−25 Moreover, these configuration contributions areexpected to be similar for both FM and AFM cases andtherefore 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 thechange of the standard free enthalpy as follows:

Δ = −→ →RT KG lnT a b a b,0

(2)

where R is the gas constant. It is convenient to evaluate therelative concentration of, e.g., the isomer a in the mixture:

=∑

→

= →x

KKa

b a

a bm

b a (3)

The relative concentration (x) of the isomer mixture (m) canbe further expressed as the isomeric partition function (Q):

=−Δ

∑ −Δ=x

Q exp[ G /(RT)]

Q exp[ G /(RT)]aa a

b am

b b (4)

Equation 4 corresponds to the enthalpies at the absolute zerotemperature. We also presume that the isomeric mixture ofnoninteracting particles has achieved thermodynamic equili-brium, and therefore, we can estimate a molar fraction xa of allisomers (m).

■ RESULTS AND DISCUSSIONA. Magnetic Properties. The most common oxidation

states of Fe atoms are Fe2+ and Fe3+, which correspond to thed6 and d5 electronic configurations, respectively. In the crystalfield theory, the d-orbitals of Fe in the tetrahedral coordinationsplit into 3-fold t2g (dxy, dxz, and dyz) and 2-fold eg (dx2−y2, dz2)degenerate levels, where the latter is of lower energy. Inaddition, oxygen is a weak field ligand that results in the high-spin systems. Therefore, five α-spin d-electrons are accom-modated in the eg and t2g levels, while the remaining sixthelectron fills the eg level with β spin (see Figure 2, A1−A3).

The most stable arrangement for the Fe2+ oxidation state(see Figure 2, A1−A3) is when the two Fe atoms are in thesame line (model FeZn(c) with Fe−O−Zn−O−Fe). Thissystem shows AFM ordering, in agreement with the results ofYoon et al. and Kolesnik et al.12,13 In the FeZn(c) model, anAFM superexchange occurs, which results in the intensivecoupling between two next-to-nearest neighbor Fe2+ cations viaa nonmagnetic oxygen anion. FM ordering is only slightlydisfavored, namely, by 3 meV per Fe, in excellent agreementwith 2 meV energy difference obtained using PBE+U method.Experimentally, the AFM ordering has been observed also atlow temperatures.12,13 Our analyses of isomeric fractions atspecific temperatures (77, 300, and 600 K) will be addressed inthe next section.In the case of Fe3+ oxidation state, the most stable Fe

configuration is in the case of the FeZn(b)−ZnvO model, whereFe atoms have the same oxygen coordination and d-orbital

Figure 2. Schematic representation of the most stable structures andmagnetic ordering (A1, B1, and C1), local environment of Fe atoms inFe−ZnO (A2, B2, and C2), and the crystal field splitting together withthe electronic configuration (A3, B3, and C3): (left) FeZn(c), (middle)FeZn(b)−ZnvO, and (right) FeZn(a)−ZnOi. Solid arrows, α spinelectron; dash arrows, β spin electron; blue, Zn; red, O; green, Fe.

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 denotesFe atoms at the doping sites N. α and β correspond to the majorityand minority spin states. Fermi level is indicated by the vertical redline.

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splitting as in the case of Fe2+ in the FeZn(c) model (see Figure2, B1−B3). Generally, the TM−O−TM type of clusters prefersto bend under 90° bond angle in the FM coupling via asuperexchange.1 However, we have found that the two Featoms arrange themselves in the Fe−O−Fe cluster with a largerbond angle of 116° (FeZn(b)−ZnvO). Thus, we conclude thatthe FM and AFM orderings strongly compete and eventuallyare compromised into an AFM ordering (PBE0, 207 meV; PBE+U, 164 meV). These results indicate that the observed FMordering was not caused by zinc vacancy in the Fe3+−ZnvOmodel.We have also obtained an AFM arrangement in the case of

Fe3+ in the FeZn(a)−ZnOi model. Again, the energy differencebetween the AFM and FM phases is only 2 meV (PBE0, 2meV; PBE+U, 20 meV), resulting in strong temperaturedependence. In contrast, the local environment of the Fe3+

atoms and the d-orbital splitting are essentially much differentthan in the case of the FeZn(b)−ZnvO model (see Figure 2C1−C3). Such a system is typical, for example, at grainboundaries of partially precipitated secondary phases.2,27

B. Thermodynamic Analysis. We have calculated therelative concentration and the change of the standard freeenthalpy 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 fractionof about 97% at all studied temperatures. However, in the caseof Fe2+ in the FeZn(c) model, we have found that the FMordering is the most favorable and that it dominates in theentire 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 resultsindicate that the magnetism of Fe-doped ZnO is sensitive totemperature.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 themost stable Fe−ZnO models in order to interpret theirmagnetic origins. Figure 3A shows the PDOS of Fe d-orbitalswith different spin states of the FeZn(c) model. The resultsshow that the exchange splitting is much larger in comparisonto the crystal field splitting. Therefore, Fe@1 favors high-spinconfiguration with eg (2↑, 1↓), t2g (3↑), while the Fe@3exhibits opposite paramagnetic character (Here, the numbers inparentheses denote the number of electrons in the given spinchannel.). Furthermore, Fe-derived states in the Fe−ZnO arehybridized with O p-states in the valence band, which was also

shown in the work of Karmakar et al.2 This confirms that thesuperexchange results in the AFM ordering for the linear Fe−O−Fe arrangement, while its spin states reverse under thermalvibration and form 59.5% FM and 40.5% AFM ordering atroom temperature (300 K) for the Fe2+−ZnO system (in theFeZn(c) model).When the Zn vacancy was incorporated in Fe−ZnO (in the

FeZn(b)−ZnvO model), the overall trend of Fe3+ d-orbitalsplitting is similar to the case of Fe2+ substitution. Thus, the fiveelectrons are rearranged in d-orbitals of Fe3+ with theconfiguration of eg (2↑), t2g (3↑) (see Figure 3B). The AFMordering dominates in Fe−ZnO with less than 3% FM orderingat the entire range of studied temperatures. In the FeZn(a)−ZnOi case, the local structure of Fe atoms is similar to trigonalbipyramidal coordination, and hence, the Fe d-orbitals are splitinto three levels, involving double 2-fold levels (dxz and dyz; dxyand dx2−y2) and another level of higher energy (dz2) (see Figure3C). The probability of the AFM and FM orderings is reversedgoing from T = 300 K to T = 600 K. This provides tunablemagnetism based on Fe−ZnO systems with the presence ofinterstitial oxygen.

■ CONCLUSIONS

In summary, we have employed density functional theory usingtwo 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 weretaken into account. Temperature affects the magnetic orderingin two ways: In Fe2+-substituted ZnO phases, the AFMordering will stabilize ZnO matrix, while vibrational contribu-tions to the free enthalpy reverse its stability. The magnetism ofFe−ZnO, in the presence of interstitial oxygens, can be tunedby temperature, while the relative stability and magneticpreference of zinc vacancy induced Fe3+ in ZnO is notintensively temperature-dependent. Because of the small energydifference, the effect of the site entropy is significant.

■ AUTHOR INFORMATION

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

The authors thank the Computational Laboratory for Analysis,Modeling, and Visualization (CLAMV) for computationalsupport. J. Xiao would like to acknowledge the financialsupport by the China Scholarship Council (CSC).

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+ Fe3+ (ZnvO) Fe3+ (ZnOi)

ΔG xi ΔG xi ΔG xi

77 KAFM −1.44 33.4% −1.71 100% −1.7 86.1%FM −1.85 66.6% 17.3 0% −0.5 13.9%300 KAFM −79.3 40.5% −75.7 99.9% −79.2 57.4%FM −79.9 59.5% −56.9 0.1% −78.5 42.6%600 KAFM −331.7 39.5% −316.7 97.4% −335.5 44.7%FM −332.9 60.5% −298.1 2.6% −335.5 55.3%

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