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Electronic structure origins ofpolarity-dependent high-TC

ferromagnetism in oxide-diluted magneticsemiconductorsKEVIN R. KITTILSTVED, WILLIAM K. LIU AND DANIEL R. GAMELIN*Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, USA*e-mail: Gamelin@chem.washington.edu

Published online: 26 March 2006; doi:10.1038/nmat1616

Future spintronics technologies based on diluted

magnetic semiconductors (DMSs) will rely heavily on

a sound understanding of the microscopic origins

of ferromagnetism in such materials. Discoveries of

room-temperature ferromagnetism in wide-bandgap

DMSs hold great promise, but this ferromagnetism remains

poorly understood. Here we demonstrate a close link

between the electronic structures and polarity-dependent

high-TC ferromagnetism of TM2+:ZnO DMSs, where TM2+

denotes 3d transition metal ions. Trends in ferromagnetism

across the 3d series of TM2+:ZnO DMSs predicted from

the energies of donor- and acceptor-type excited states

reproduce experimental trends well. These results provide

a unified basis for understanding both n- and p-type

ferromagnetic oxide DMSs.

Diluted magnetic semiconductors (DMSs) are attractingintense interest for potential new device applicationsin spin-based information-processing technologies. For

practical spintronics applications, ferromagnetic DMSs with Curietemperatures (TC) greatly exceeding room temperature will berequired. Theoretical predictions1,2 of high-TC ferromagnetismin DMSs of GaN and ZnO stimulated efforts to develop theseand related wide-bandgap materials3. In many regards, ZnO isthe archetypical wide-bandgap semiconductor. Compared withother oxides that have been investigated as DMSs (for example,TiO2 and SnO2), ZnO is relatively well behaved from anexperimental point of view, affording the possibility for extensivesystematic experimentation and data analysis. Well-defined dopingand defect chemistries, suitability for transparent high-powerhigh-temperature applications, and the ability to lase or emitspontaneously at ultraviolet wavelengths combine to make ZnOattractive for many potential device applications4. For spintronicsapplications, the relatively long room-temperature spin-coherencetime of n-type ZnO is advantageous5. Additionally, the potentialto generate both p- and n-type ZnO of low resistivity makesbipolar spintronics based on ZnO a realistic possibility, andreports of both hole-6–9 and electron-mediated10–12 ferromagnetismin ZnO DMSs are encouraging in this regard. However, themicroscopic origins of this high-TC ferromagnetism remain poorlyunderstood. A detailed understanding of high-TC ferromagnetismin wide-bandgap DMSs is required to harness functionality fordevice applications. The development of such an understandinghas emerged as one of the most important challenges inmodern magnetism13,14.

In this article, we demonstrate that ferromagnetism in ZnODMSs is intimately related to the electronic structures of themagnetic impurity ions. Electronic absorption, magnetic circulardichroism (MCD), and photocurrent action spectroscopies areused to identify and assign dopant-derived donor- and acceptor-type ionization excited states, and to analyse the properties of thesestates related to carrier-mediated ferromagnetism. The opposite

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–3 0 3 –3 0 3Field (kOe) Field (kOe)

M (×10

–2 μ

B /Co2+)

M (μ

B /Mn

2+)Mn2+

:ZnO

Chemical polarityCo

2+:Z

nO

p-type n-type

–4

0

4

–1

0

1a b

dc

Figure 1 300 K magnetization data for 0.2%Mn2+:ZnO and 3.5% Co2+:ZnOfilms prepared by direct chemical synthesis with or without addition ofnitrogen. a, 0.2% Mn2+:ZnO with added nitrogen, b, 0.2% Mn2+:ZnO without addednitrogen, c, 3.5% Co2+:ZnO with added nitrogen, and d, 3.5% Co2+:ZnO withoutadded nitrogen.

polarities predicted2 and observed6 for ferromagnetic Co2+:ZnO(n-type) and Mn2+:ZnO (p-type) are of particular interest. Fromexperimentally calibrated excited-state energies and configuration-interaction considerations, trends in ferromagnetism across the3d series of n- and p-type TM2+:ZnO DMSs are predicted andcompared to experimental results. The predicted trends reproduceexperimental trends remarkably well, confirming the role of donorand acceptor excited-state configurations in the ferromagnetismof TM2+:ZnO DMSs and, by extension, wide-bandgap DMSs asa class.

EXPERIMENTAL TRENDS IN TM2+:ZnO DMS FERROMAGNETISM

Several groups have reported ferromagnetism in TM2+:ZnO DMSs(ref. 3). To minimize potential sources of experimental error,some groups have compared different TM2+:ZnO DMSs preparedunder identical conditions. Ueda et al. examined a series of n-typeTM2+:ZnO (TM2+ = Co2+,Mn2+,Cr2+, and Ni2+) films preparedby pulsed-laser deposition15. High-TC ferromagnetism was onlyobserved in Co2+-doped films and not in any of the others.Venkatesan and collaborators12,14 prepared a broader series ofn-type ZnO DMSs by pulsed-laser deposition and observed twomaxima in the 300 K ferromagnetic saturation moments, one atCo2+:ZnO (d7) and the other at V2+:ZnO (d3). Mn2+:ZnO (d5)showed little or no ferromagnetism under the sample-preparationconditions of either laboratory. Kittilstved et al. observed thesame trend in natively n-type Co2+:ZnO and Mn2+:ZnO preparedusing an oxidative direct chemical route that unambiguouslyprecluded formation of metal precipitates6. The chemical approachalso allowed investigation of the influence of nitrogen, ap-type dopant in ZnO. When nitrogen was introduced duringmaterials preparation, Mn2+:ZnO showed strong ferromagnetism,whereas Co2+:ZnO showed none6,9,16. When plotted in table formatas in Fig. 1, the opposite carrier polarities of ferromagneticCo2+:ZnO and Mn2+:ZnO become strikingly apparent. Thispolarity-dependent ferromagnetism is shown below to derive from

specific electronic structural properties of the Co2+ and Mn2+ ionsin the ZnO host semiconductor.

The experimental trends described above and in Fig. 1 arein general agreement with most theoretical predictions, despitethe use of a variety of different theoretical models1,2,14,17,18. Akey property common to all of the models describing ZnO-DMS ferromagnetism is strong electronic coupling betweenthe magnetic ions and charge carriers at the Fermi level. Asisovalent TM2+ doping of ZnO does not itself introduce carriers,carriers in TM2+:ZnO DMSs are associated with additionalshallow donor or acceptor defects. The dopant–carrier exchangeenergy is parameterized variously as Jsd , Jpd , N0α, N0β, andso on1,14,19, depending on the specific interaction and modelunder consideration. Microscopically, these exchange-couplingparameters account for partial carrier delocalization onto themagnetic dopant. In a configuration-interaction picture, thisimplies mixing between the relevant localized and charge-separated electronic configurations of the magnetic impurity ion.The striking differences between Co2+:ZnO and Mn2+:ZnO inFig. 1 indicate that TM2+ electronic structures must regulatethe abilities of holes and electrons to delocalize onto thesedopants. Specifically, the data in Fig. 1 suggest that the resonancesdescribed by equations (1a) and (1b) are relevant, whereas those ofequations (1c) and (1d) are not.

Co2+ +e−donor ←→ Co+ (1a)

Mn2+ +h+acceptor ←→ Mn3+ (1b)

Co2+ +h+acceptor ←→× Co3+ (1c)

Mn2+ +e−donor ←→× Mn+ (1d)

The forward direction in equation (1a) describes the formaltransfer of a shallow donor’s electron (e−

donor) onto Co2+ toform Co+, whereas in equation (1b) it describes the transferof a shallow acceptor’s hole (h+

acceptor) onto Mn2+ to formMn3+. The reverse directions describe formal donor- andacceptor-type ionization processes of the one-electron reduced(Co+) or oxidized (Mn3+) magnetic dopants. As equilibria,equations (1a) and (1b) thus describe dopant–donor/acceptorhybridization. This hybridization is the pivotal feature determiningTC in theoretical models describing DMS ferromagnetism. In thespin-split donor impurity-band model for n-type ferromagneticDMSs (ref. 14), a phenomenological dopant effective radius scalingparameter (reff

c /ro)3 was introduced to account for hybridization

enhancement of the s–d exchange parameter (Jsd) required toincrease the predicted TC from 1 to ∼500 K. The actual extentof hybridization was small, and 1–2% electron transfer to thedopant was considered sufficient14, that is, the ground state liesfar to the left in equation (1a), a conclusion consistent withferromagnetic X-ray MCD data showing a multiplet structurecharacteristic of tetrahedral Co2+ in ZnO (ref. 20). Similarly,in the Zener model description of p-type ferromagnetic DMSs,the high TC predicted for p-type Mn2+:ZnO is derived from itslarge p–d exchange parameter1 (N0β), the magnitude of which isdetermined primarily by p–d hybridization19. Ab initio local spin-density approximation of the density-functional theory (LSDA-DFT) calculations2,17,18 have predicted ferromagnetism in p-typeMn2+:ZnO that results from partial delocalization of h+

acceptor ontoMn2+, which imparts manganese 3d character at the Fermi level,but e−

donor did not delocalize onto Mn2+ and consequently noferromagnetism was predicted for n-type Mn2+:ZnO (ref. 2). Tounderstand the resonances described by equation (1), and todevelop a comprehensive model that describes both n- and p-typehigh-TC ferromagnetic ZnO DMSs, it is imperative to understand

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εCo2+ = ε

100 M–1 cm–1

÷ 200 ÷ 200

εMn2+ = ε

1,000 M–1 cm–1

28 24 20 16 28 24 20 16Energy (×103 cm–1)

ML CB

CT

ML CB

CT

L VBM

CT

0.40.20βH/2kTβ

0.40.20βH/2kTβ

I MCD

I MCD

S = 3/2 S = 5/2

0.02°0.5°

Mn2+:ZnOCo2+:ZnOM

CDAb

sorb

ance

IQE

(arb

. uni

ts)

a

b

c

d

f

e

Figure 2 Electronic absorption, photocurrent IQE, and MCD spectroscopic datafor Co2+:ZnO and Mn2+:ZnO. a,d, 300 K electronic absorption spectra.b,e, Photocurrent IQEs of photovoltaic cells. c,f, Variable-field 5 K MCD spectra. Theinsets show MCD saturation magnetization data measured at the energies marked,superimposed on S= 3/2 and S= 5/2 Brillouin curves. Data in parts b, c and f arefrom refs 26, 33 and 9, respectively.

the dopant-derived donor- and acceptor-type ionization processesof these DMSs.

EXCITED STATES AND ELECTRONIC STRUCTURES

The sub-bandgap electronic excited states of Co2+:ZnO andMn2+:ZnO were investigated using optical spectroscopic andphotoelectrochemical probes. In addition to intra-ion ligand-fieldexcitations, light-induced donor- and acceptor-type ionizations ofthe transition metal dopants may also be observed in this energyregion. This class of electronic transitions in DMSs has been studiedextensively by both experimental21–26 and theoretical27–31 methods.In donor-type ionizations, an electron is formally promoted fromthe TM2+d shell donor orbitals to ZnO-based acceptor orbitalsof the conduction band (CB), that is, dn(CB)0 → dn−1(CB)1. Inacceptor-type ionizations, an electron is formally promoted to theTM2+d shell acceptor orbitals from ZnO-based donor orbitals ofthe valence band (VB), that is, (VB)q dn → (VB)q−1dn+1, where q isthe number of electrons in the valence band. Because considerablecharge is shifted between the dopant and the semiconductor ineach of these electronic transitions they are often referred tocollectively as charge-transfer (CT) processes21–29. Treating thesemiconductor lattice as a ligand to the dopant, the donor- andacceptor-type ionization transitions are thus formally metal-to-ligand conduction band CT (MLCBCT) and ligand valence band-to-metal CT (LVBMCT) transitions, as summarized in equation (2).

TM2+ → TM+ +h+VB (LVBMCT,TM2+ acts as acceptor) (2a)

TM2+ → TM3+ +e−CB (MLCBCT,TM2+ acts as donor) (2b)

Figure 2 shows electronic absorption spectra, photocurrentinternal quantum efficiencies26 (IQEs), and MCD spectra ofparamagnetic Co2+:ZnO and Mn2+:ZnO. The intense absorptionand MCD feature at ∼28,000 cm−1 in both DMSs arises fromthe first excitonic configuration of ZnO at the band edge. Thestructured intensity of Co2+:ZnO centred at 16,000 cm−1 is thespin–orbit split 4A2 → 4T1(P) ligand-field band of Co2+ dopedsubstitutionally into wurtzite ZnO (refs 32,33). Two additionalsub-bandgap features are observed in the MCD and photocurrentaction spectra of Co2+:ZnO that were not evident by absorption,one a strong negative MCD peak at ∼25,000 cm−1 and the othera very weak, broad band that extends down to 14,000 cm−1.Both features show S = 3/2 (axial, D = +2.75 cm−1) MCDsaturation magnetization, confirming that they come from isolatedparamagnetic Co2+ ions. The breadths of the two bands indicatethey are due to ionization transitions. Their origin from twodistinct excited states is evident from their approximately fourfolddifferent photocurrent IQEs (Fig. 2b)26. The higher energy bandis assigned as the LVBMCT transition (equation (2a)) on the basisof its relationship to a similar band in Ni2+:ZnO (ref. 33). Thelower energy band is the MLCBCT transition (equation (2b))26.These assignments are supported by calculations using Jørgensen’soptical electronegativity model34,35, in which LVBMCT and MLCBCTtransition energies are related to differences in donor (D) andacceptor (A) optical electronegativities (χopt(D) and χopt(A)) aftertaking into account differences in multi-electron spin-pairingenergies (SPEs) and dopant ligand-field effects between the groundand excited states (equation (3)).

ECT = 30,000 cm−1(χopt(D)−χopt(A))+�SPE±10 Dq (3)

The SPEs account for Coulomb and electron–electron exchangeinteractions at the 3d ions, and are evaluated using the Racahparameters B and C. From equation (3), χopt(Co2+) = 1.9,χopt(ZnOVB) = 2.4, χopt(ZnOCB) = 1.1, and the ligand-fieldparameters of Co2+ in ZnO (B = 775 cm−1, C/B = 4.5,Dq = 390 cm−1); refs 26,33, the energies of the LVBMCTand MLCBCT transitions are estimated to be ∼25,000 and11,300 cm−1, respectively, in reasonable agreement with theexperimental energies.

In the spectra of Mn2+:ZnO (Fig. 2d–f), only one sub-bandgap absorption band is observed, a photoactive state having anassociated pseudo-A-term MCD signal centred at ∼24,000 cm−1.From equation (3), the LVBMCT and MLCBCT transitions ofMn2+:ZnO (χopt(Mn2+) = 1.45,B = 596 cm−1,C/B = 6.5,Dq =420 cm−1) are predicted to occur at ∼49,000 and 24,000 cm−1,respectively, leading to assignment of this band as the MLCBCTtransition9. Its assignment to ligand-field transitions is ruled out byits high molar extinction coefficent (ε(Mn2+) ≈ 950 M−1 cm−1 at24,000 cm−1 and 300 K, compared with ε(Mn2+) ≈ 1–10 M−1 cm−1

at ∼24,850 cm−1 anticipated for the 4T1(G) ligand-field excitedstate9). The very high energy predicted for the LVBMCT transitionin Mn2+:ZnO agrees with that estimated from analysis ofMn2+:ZnO X-ray absorption data36 (∼62,000±12,000 cm−1).

Two key observations from Fig. 2 pertain to the magnetismof these ZnO DMSs: (1) both Co2+:ZnO and Mn2+:ZnO possessdonor- or acceptor-type ionization states immediately below theZnO band edge; (2) the identities of the ionization states at theband edge are different for Co2+:ZnO and Mn2+:ZnO, the formerbeing an LVBMCT state and the latter being an MLCBCT state.As described below, observation (1) relates to the existence ofhigh-TC ferromagnetism mediated by shallow donors or acceptors,whereas observation (2) relates to the polarity of the mediatingcharge carrier.

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ΔE1,3 {

ΔE2,3

ΔE2,3 {

Co+Co+ + h+VB

Co3+ + e–CB

Co3+

Co2+:ZnO Ground state

Mn2+:ZnO Ground state

Valence band

Valence band

Conduction band

Conduction band

Co2+ + e–CB + h+

VB

Mn2+ + e–CB + h+

VB

Eg

Eg

LVBM2+CT

M2+LCBCT

Mn3+ + e–CB

Mn3+

LVBM3+ CT

M+LCBCT } ΔE1,3

}

30

20

10

0

Ener

gy (×

103

cm–1

)

30

20

10

0

Ener

gy (×

103

cm–1

)a

b

Figure 3 Schematic summary of the spectroscopic analysis for Co2+- andMn2+-doped ZnO DMSs. This shows the relationship between excited-stateenergies and donor or acceptor energies derived from the Born cycle analysis.a, Co2+:ZnO. b, Mn2+:ZnO. From this analysis, Co+ should be a shallow donor andMn3+ a shallow acceptor in ZnO.

The spectroscopic data in Fig. 2 also provide informationabout excited-state wavefunctions. As discussed previously21–27,donor- and acceptor-type ionization excited states in DMSs maybe described as excitons bound to the isoelectronic impurity inwhich either the electron (LVBMCT) or the hole (MLCBCT) isstrongly localized at the TM2+ ion. The configuration-interactionwavefunctions describing these excited states in the perturbationlimit are given by equation (4d)26,27, where the mixing coefficientcn,3 = Hn3/�En,3, and Hn3 and �En,3 are the off-diagonal electroniccoupling matrix element and the energy difference between therelevant localized and delocalized configurations, respectively.

ψ1(LVBMCT): TM+ +h+VB (4a)

ψ2(MLCBCT): TM3+ +e−CB (4b)

ψ3(excitonic): TM2+ +e−CB +h+

VB (4c)

ψ′n = ψn + cn,3ψ3 (4d)

Excited states leading to detectable photocurrents in the TM2+:ZnOphotovoltaic cells must generate both electrons and holes atthe electrode surfaces. Although the absolute photocurrent IQEsdepend on cell-engineering parameters26, the ratio of photocurrentIQEs for the LVBMCT and MLCBCT transitions in Co2+:ZnO(IQE25,000/IQE20,000 ≈ 4 from Fig. 2b) is due to the intrinsicbranching ratios for charge separation in the respective excitedstates, and reflects differences in mixing between localized

(equations (4a) and (4b)) and delocalized (equation (4c)) excited-state configurations for the carrier transferred to the dopantupon excitation.

The relatively small energetic difference (�E1,3 ≈ 2,600 cm−1,Fig. 2) between the LVBMCT and excitonic states in Co2+:ZnOimparts substantial excitonic character to the LVBMCTwavefunction, and reflects a relatively small binding energy forthe photogenerated bound electron, favouring carrier escape.Conversely, the greater energetic difference (�E2,3 ≈ 13,400 cm−1,Fig. 2) between the MLCBCT and excitonic states does not allowextensive mixing of the two, so the photogenerated hole is stronglybound to the cobalt and charge recombination is favoured.The ratio of localization energies for the last bound chargecarriers in the LVBMCT and MLCBCT excited states in Co2+:ZnO(�E2,3/�E1,3 ≈ 5) is similar to the ratio of photocurrent IQEsmeasured for these two excited states (∼4, Fig. 2b), and bothIQEs are smaller than that for excitonic excitation in pure ZnO,consistent with the attribution of photocurrent to the admixtureof ψ3 into the LVBMCT and MLCBCT wavefunctions describedby equation (4d). Quantitative analysis of the transition oscillatorstrengths yields estimated mixing coefficients c1,3 =0.17±0.01 andc2,3 = 0.043±0.003 for Co2+:ZnO (ref. 26), and c2,3 = 0.19±0.03for Mn2+:ZnO.

The LVBMCT and MLCBCT energies of dopants in unstableoxidation states can be analysed using Born thermodynamic cycles.Following McClure et al.37, the energy of a MLCBCT transition forTM2+ in ZnO as defined by equation (2b) is given by equation (5),where I3(TM) is the third ionization potential of the dopant,�V (site) = V3 − V2 is the difference in total potential for TM3+

and TM2+ at the Zn2+ crystal site, and χ is the electron affinity ofthe semiconductor.

EM2+LCT = I3(TM)−�V (site)−χ (5)

Similarly, the LVBMCT energy involving the one-electron oxidizeddopant (TM3+) is given by equation (6), where Eg is the bandgapenergy of the host crystal.

ELM3+CT = Eg +�V (site)− I3(TM)+χ (6)

Concatenation of these two processes gives TM2+ → TM3+ +e−

CB → TM2+ + e−CB + h+

VB, which is identical to excitonic excitation(equation (4c)), and the sum of equations (5) and (6) yieldsEM2+LCT + ELM3+CT = Eg. Corresponding relationships hold for thereverse order of promotions, TM2+ → TM+ +h+

VB → TM2+ +h+VB +

e−CB, for which ELM2+CT + EM+LCT = Eg. ELM3+CT and EM+LCT are thus

identical to �E2,3 and �E1,3 from equations (4a)–(4c), respectively.This model assumes that e−

CB and h+VB are far from their sources in

the LVBMCT and MLCBCT excited states (equation (2)), a conditionthat is never actually fulfilled. Although additional correctionsshould be considered, these corrections are small compared withthe photon energies under consideration and empirically the modelaccounts well for experimental energies24,37. From these identitiesand the spectroscopic data in Fig. 2, EM+LCT and ELM3+CT can bededuced for cobalt and manganese in ZnO. From this analysis, thetransition Co+ → Co2+ + e−

CB occurs at very low energy (�E1,3 ≈2,600 cm−1) as does the transition Mn3+ → Mn2+ +h+

VB (�E2,3 ≈3,400 cm−1), whereas those involving Co3+ (�E2,3 ≈ 13,400 cm−1)and Mn+ (�E1,3 ≈ −21,600 cm−1) do not. This analysis issummarized schematically in Fig. 3 and numerically in Table 1.

ELECTRONIC STRUCTURE AND FERROMAGNETISM

In this section, we assume the basic framework of the spin-split donor impurity-band model described in ref. 14 and focus

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Table 1 Donor or acceptor properties for one-electron reduced or oxidized transition metal dopants in ZnO, estimated from equation (8) and the data in Fig. 2. Theproperties of commonly-invoked shallow donors and acceptors are included for comparison.

Donor or acceptor Carrier type Eb (cm−1) * Eb (eV) * rB (nm) Ref.

Mn3+:ZnO h+ 3,400 0.42 0.45 This workMn+:ZnO e− −21,600 −2.68 0.24 (but unstable) This workCo3+:ZnO h+ 13,400 1.66 0.23 This workCo+:ZnO e− 2,600 0.32 0.70 This workN2−

O :ZnO h+ 1,600 0.20 0.65 4Zn0

i :ZnO e− 240 0.03 2.31 38

* From �En,3 for TM dopants.

on the key microscopic property governing defect-mediatedferromagnetism in this model, namely hybridization between themagnetic dopant and the defect so that carriers at the Fermi levelare partially delocalized onto the magnetic dopant (equation (1),and accounted for in ref. 14 using the scaling parameter (reff

c /ro)3).

Although the model in ref. 14 was developed exclusively fordonor defects, the kernel of the model also applies to acceptordefects as shown below. From perturbation theory, dopant–defecthybridization is parameterized by the mixing coefficient, cDD

(equation (7)). For effective hybridization, the energy differencebetween dopant and defect levels (�EDD) must be small and theresonance integral (HDD) must be large.

cDD = HDD/�EDD (7)

To analyse �EDD, the thermodynamics of the four dopant–defect resonances described by equations (1a)–(1d) are plottedin Fig. 4 for commonly-invoked shallow donors and acceptorsin ZnO (shallow donor: interstitial zinc38 (Zni), shallow acceptor:substitutional nitrogen4 (N2−

O ), see Table 1). These plots exposecases where the dopant–defect resonance is approximatelythermoneutral (that is, where �EDD is small). The majorconclusion drawn from Fig. 4 is that dopant–defect hybridizationmaximizes when the one-electron-reduced (or oxidized) dopantapproaches a potential similar to that of the shallow donor (oracceptor). From Fig. 4 and Table 1, a near-thermoneutral dopant–defect resonance involving shallow donor or acceptor defectscan occur in p-type Mn2+:ZnO (|�EDD| ≈ 0.22 eV) and n-typeCo2+:ZnO (|�EDD| ≈ 0.27 eV), but not in n-type Mn2+:ZnO(|�EDD| ≈ 2.7 eV) or p-type Co2+:ZnO(|�EDD| ≈ 1.7 eV). Thesmall �EDD values for p-type Mn2+:ZnO and n-type Co2+:ZnOfavour effective hybridization (equation (7)) and hence high-TC ferromagnetism, whereas the large �EDD values for n-typeMn2+:ZnO and p-type Co2+:ZnO limit hybridization and arenot favourable for ferromagnetism. The polarity conditions forferromagnetism predicted by the spectroscopic analysis are thusin agreement with the experimental magnetic results summarizedin Fig. 1.

The resonance integral of equation (7) is proportional to thespatial overlap of dopant and defect wavefunctions39,40 which, forfixed concentrations of dopants and defects across the transitionmetal series, in turn relates to the effective Bohr radii of thelimiting charge carriers on each centre. Equation (8) allows effectiveBohr radii for the TMn+ and donor/acceptor species in Fig. 4 tobe estimated22,27,41.

rB = h√2m∗Eb

(8)

In equation (8), m∗ is the effective mass of the relevant carrier (inZnO, m∗

e ≈ 0.24me and m∗h ≈ 0.45me) and Eb is the binding energy

of the last bound carrier. Table 1 summarizes the relevant bindingenergies and Bohr radii. From the spectroscopic analysis (Fig. 3),

Co+ is a shallow donor and Mn3+ a shallow acceptor in ZnO, withcarrier binding energies Eb ≈ �En,3, whereas Co3+ and Mn+ areboth energetically misaligned with the band structure of ZnO. TheBohr radii for Mn+ and Co3+ are both substantially smaller thanthose of Co+, Zni, Mn3+ or N2−. Experimental confirmation of thiscomparison is obtained from the photocurrent IQEs of Fig. 2b,which show that e− hopping is considerably more favourable thanh+ hopping in photoexcited Co2+:ZnO. Dopant–donor/acceptorhybridization is thus favoured by energetic proximity of bothto the appropriate band edge of the host semiconductor. Ingeneral, although deeper donors or acceptors may be suitablefor thermoneutral resonance with deeper magnetic dopants, theirsmaller Bohr radii would require correspondingly increased dopantand defect concentrations to achieve sufficient overlap, at whichpoint short-range antiferromagnetic superexchange interactionsmay become problematic.

To test the broader applicability of this spectroscopic analysisfor understanding the magnetic properties of ZnO DMSs, trendsin cDD were investigated. For ZnO DMSs prepared under identicalconditions, the major changes in cDD across the series of 3dTM2+ ions occur in the energy denominator, �EDD. LVBMCTand MLCBCT energies for the 3d TM2+ series in ZnO werecalculated from Pauling electronegativities and literature ligand-field parameters using equation (3) (see the SupplementaryInformation). Equation (3) predicts substantial negative MLCBCTenergies for Sc2+ and Ti2+ in ZnO, consistent with the instability ofthese ions to spontaneous oxidation. Ti2+ and Sc2+ are therefore notconsidered in subsequent analyses.

Figure 5 compares the results of this analysis with availableexperimental and theoretical magnetic data across the same series.To retain generality, |1/�En,3| is plotted rather than |1/�EDD|, butboth yield identical trends for fixed shallow defects. The predictedtrends are in excellent overall agreement with the experimentaldata12,15, particularly considering the crudeness of the LVBMCTand MLCBCT energy calculations from equation (3) and thepotential experimental uncertainties. The predicted trends are alsoin excellent agreement with available LSDA-DFT results across theseries2. This agreement is a very strong confirmation that dopant–donor/acceptor hybridization (that is, exchange mediated byshallow bound carriers) is responsible for ferromagnetism in ZnODMSs. Of the three factors from equation (3) (electronegativities,spin-pairing energies, and ligand-field splittings), spin-pairingenergies are primarily responsible for the positions of the maximaand minima in Fig. 5. A comprehensive model of both hole- andelectron-mediated ferromagnetism in ZnO DMSs therefore mustaccount for Coulomb and electron–electron exchange interactionsof the 3d ions.

The scenario suggested by this spectroscopic analysis isessentially consistent with the spin-split donor impurity-bandmodel described in ref. 14. The spectroscopic results demonstratethat Co2+ ions can hybridize effectively with shallow-donorimpurity bands in ZnO because Co+ is also a relatively

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N3–:Mn2+:ZnO + h+VB

Zni(+):Mn+:ZnO

Zni:Mn2+:ZnO

Zni:Co2+:ZnO Zni(+):Co+:ZnO

Zni(+):Mn2+:ZnO + e–

CB

Zni(+):Co2+:ZnO + e–

CB

N3–:Co2+:ZnO + h–VB

N2–:Mn2+:ZnOMn2+

:ZnO

Co2+

:ZnO

N2–:Co2+:ZnO

+0.2 eV

+0.03 eV

–0.3 eV+0.03 eV

+2.7 eV

+0.2 eV

–0.4 eV

N3–:Mn3+:ZnO

–1.7 eV

N3–:Co3+:ZnO

Approx.

Thermoneutral

Approx.

Thermoneutral

Chemical polarity

p-type n-type

a b

dc

0.5 eV 0.5 eV

0.5 eV 0.5 eV

Figure 4 Schematic summary of dopant–donor/acceptor resonancethermodynamics determined from spectroscopic analysis and the bindingenergies of common shallow donors (Zni) or acceptors (N2−

O ) in ZnO. Theresulting values of |�EDD| are: a, 0.22, b, 2.7, c, 1.7, and d, 0.27 eV. Resonance isapproximately thermoneutral only for p-type Mn2+:ZnO and n-type Co2+:ZnO. Asmall |�EDD| favours dopant–donor/acceptor hybridization (equation (7)).

shallow donor in this lattice, making the Co2+-donor resonanceapproximately thermoneutral (Fig. 4d, equation (7)). Althoughthe donor impurity-band model considered exclusively n-typematerials, the mechanics of the model are sufficiently generalsuch that it is readily extended to accommodate ferromagnetisminvolving acceptor impurity bands as well. For this scenario,the spectroscopic results demonstrate that Mn2+ can hybridizeeffectively with shallow-acceptor impurity bands in ZnO becauseMn3+ is also a relatively shallow acceptor in this lattice(Fig. 4a, equation (7)). In both scenarios, strong dopant–defect hybridization favours high-TC ferromagnetism as describedin ref. 14. Finally, whereas the donor impurity-band modelassociated trends in the ferromagnetism of n-type ZnO DMSsacross the 3d TM2+ series (Fig. 5a) with a continuous trendin dopant electronegativity, the spectroscopic analysis revealsthat the magnetic trends are dominated by the contributionsof electron–electron repulsion, which must be included inaddition to electronegativities when estimating energies ofmulti-electron donor or acceptor configurations (equation (3),Fig. 5). Only with the inclusion of electron–electron repulsionterms may the origins of ferromagnetism in p-type Mn2+:ZnObe rationalized within this model. These modifications notwithstanding, the central hypothesis of the spin-split impurity-band model, namely that ferromagnetism depends strongly ondopant–donor/acceptor hybridization at the Fermi level, appearsto be supported by the spectroscopic data and analysis presentedhere. We note that although carriers are implicated, this analysisdoes not imply macroscopic conductivity. The magnetic phasediagrams for carrier-mediated ferromagnetism in ZnO DMSs maypossess a region in which the material is both insulating andferromagnetic. Such a region has been proposed previously forn-type oxide DMSs14 and has been observed experimentally inmanganese-doped GaAs (ref. 42), where the critical dependence offerromagnetism on carriers is generally accepted1.

Although this study has focused on ZnO DMSs,similar electronic structural properties also probably governferromagnetism in other wide-bandgap DMSs. From thespectroscopic analysis, the general conditions conducive to dopant–

(Sc) (Ti) V Cr Mn Fe Co Ni CuTM2+-doped ZnO

n-type

p-type3

2

1

0

4

2

0

a

b

1.0

0.5

0

1.0

0.5

0

Experimental

LSDA-DFT

1/|ΔE 2

,3| (

×10–4

cm

–1)

Ms /M

s (Mn

2+:ZnO)

1/|ΔE 1

,3| (

×10–4

cm

–1)

Ms /M

s (Co2+:ZnO)

CT analysis

Figure 5 Results of LVBMCT and MLCBCT analysis for the series ofTM2+:ZnO DMSs. Calculated trend (filled circles) for a, n-type polarity and b, p-typepolarity. LVBMCT and MLCBCT energies were calculated using equation (3) and areplotted as |1/�En,3| (left abscissa). Experimental magnetic data are from ref. 15(⊕), ref. 12 (+), and from Fig. 1 (�). Ab initio LSDA-DFT results are from ref. 2(filled diamond). For comparison purposes, each literature data set is plottednormalized to the values for Co2+:ZnO in a and Mn2+:ZnO in b that were reported forthe same data set (right abscissa). Sc and Ti are anticipated to be in the 3+oxidationstate and were therefore not included in the analysis.

donor/acceptor hybridization at the Fermi level, and hence to high-TC ferromagnetism, are (i) approximately thermoneutral dopant–defect resonances (small �EDD) and (ii) energetic proximity of thereduced or oxidized dopant to the semiconductor band structure(small �En,3).

Satisfaction of these conditions can be recognizedexperimentally by the appearance of dopant-derived donor- oracceptor-type ionization states in close proximity to the band edgeof the DMS. Moreover, assignment of these transitions (LVBMCTversus MLCBCT) can reveal the polarity of the carriers that mediatethe ferromagnetism (n-type versus p-type, respectively). LVBMCTor MLCBCT absorption and MCD intensities very near the bandedge are indeed observed in Co2+:TiO2 (ref. 43), Ni2+:SnO2

(ref. 44), and Cr3+:TiO2 (ref. 45), all three of which show high-TC

ferromagnetism under appropriate conditions. Careful analysis ofthe excited states in these and other wide-bandgap DMSs, coupledwith continued development of sophisticated theoretical models,can therefore be anticipated to provide valuable new insights intothe electronic structural origins of polarity dependent high-TC

ferromagnetism in this important class of materials.

METHODS

Nanocrystalline films of Mn2+:ZnO (up to 2% Mn2+) and Co2+:ZnO (up to3.5% Co2+) for magnetic6 and photovoltaic26 measurements were prepared as

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ARTICLES

described previously6,26. Dopant concentrations were determined byinductively coupled plasma-atomic emission spectrometry (Jarrel Ash model995). Electronic absorption spectra were collected using a Cary 5Espectrophotometer (Varian). MCD spectra were collected using anultraviolet/visible/near-infrared spectrophotometer constructed from an Aviv40DS with a sample compartment modified to house a high-fieldsuperconducting magneto-optical cryostat mounted in the Faradayconfiguration. MCD intensities were measured as the absorbance difference�A = AL −AR (where L and R refer to left- and right-circularly-polarizedphotons) and are reported as θ (deg) = 32.9�A/A. Magnetic susceptibilitymeasurements were carried out using a Quantum Design MPMS-5S SQUIDmagnetometer. The net diamagnetic background was subtracted from the rawmagnetization data (see the Supplementary Information). Photocurrent actionspectra were measured using a μAutolab Type II potentiostat (Eco ChemieB.V.) integrated with the Aviv 40DS spectropolarimeter and converted to IQEas described previously26. Details of the calculations of LVBMCT and MLCBCTtransition energies for Fig. 5 are provided as Supplementary Information.

Received 22 July 2005; accepted 24 January 2006; published 26 March 2006.

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AcknowledgementsFinancial support from the NSF (PECASE DMR-0239325 and ECS-0224138), the ResearchCorporation (Cottrell Scholar), the Dreyfus Foundation (Teacher/Scholar), and the NSF-IGERTprogram at U.W. (to W.K.L.) is gratefully acknowledged.Correspondence and requests for materials should be addressed to D.R.G.Supplementary Information accompanies this paper on www.nature.com/naturematerials.

Competing financial interestsThe authors declare that they have no competing financial interests.

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