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Jonah R. Adelman, Derek Fujimoto, Martin H. Dehn, Sarah R. Dunsiger, Victoria L. Karner, C. D. Philip Levy, Ruohong Li, Iain McKenzie, Ryan M. L. McFadden, Gerald D. Morris, Matthew R. Pearson, Monika Stachura, Edward Thoeng, John O. Ticknor, [Naoki Ohashi](https://orcid.org/0000-0002-4011-0031), Kenji M. Kojima, W. Andrew MacFarlane

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[Nuclear magnetic resonance of <math>  </math> ions implanted in ZnO](https://mdr.nims.go.jp/datasets/889a68a3-830d-48da-889e-3ca3077792fa)

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Nuclear magnetic resonance of ion implanted 8Li in ZnOJonah R. Adelman,1, ∗ Derek Fujimoto,2, 3 Martin H. Dehn,2, 3 Sarah R. Dunsiger,4, 5 VictoriaL. Karner,1, 2 C. D. Philip Levy,4 Ruohong Li,4 Iain McKenzie,4 Ryan M. L. McFadden,1, 2, †Gerald D. Morris,4 Matthew R. Pearson,4 Monika Stachura,4 Edward Thoeng,3, 4 JohnO. Ticknor,1, 2 Naoki Ohashi,6 Kenji M. Kojima,4 and W. Andrew MacFarlane1, 2, 4, ‡1Department of Chemistry, University of British Columbia, Vancouver, BC V6T 1Z1, Canada2Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada3Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada4TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada5Department of Physics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada6National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba 305-0044, Japan(Dated: September 20, 2021)We report on the stability and magnetic state of ion implanted 8Li in single crystals of thesemiconductor ZnO using β-detected nuclear magnetic resonance. At ultradilute concentrations,the spectra reveal distinct Li sites from 7.6 to 400 K. Ionized shallow donor interstitial Li is stableacross the entire temperature range, confirming its ability to self-compensate the acceptor characterof its (Zn) substitutional counterpart. Above 300 K, spin-lattice relaxation indicates the onset ofcorrelated local motion of interacting defects, and the spectra show a site change transition fromdisordered configurations to substitutional. Like the interstitial, the substitutional shows no resolvedhyperfine splitting, indicating it is also fully ionized above 210 K. The electric field gradient at theinterstitial 8Li exhibits substantial temperature dependence with a power law typical of non-cubicmetals.I. INTRODUCTIONFor many years the electronic properties of ZnO haveheld substantial practical appeal. It is a transparentwide bandgap (3.4 eV) semiconductor with a large ex-citon binding energy (60 meV) enabling potential roomtemperature optoelectronic applications.1,2 It can bedoped magnetically, either by replacing the nonmag-netic (3d10) Zn2+ with a magnetic transition metal (or,more subtly, by intrinsic magnetic defects3) to produce aroom temperature dilute magnetic semiconductor4 use-ful in spintronics.5 It also exhibits many interesting sur-face effects including photocatalysis, adsorbate sensi-tive photoconductivity,6 and a photogenerated metallicstate.7 Key to realizing the potential of this remarkablerange of properties is understanding and control of thepoint defects (both intrinsic and extrinsic) of its idealhexagonal wurtzite structure.8 Particularly, for p-typedoping this has proven difficult,9 but there are clear indi-cations of progress in the production of LEDs10 and evenextremely high mobility epitaxial structures exhibitingthe quantum Hall effect.11Consistent and stable hole doping of ZnO is an im-portant challenge that has remained the main barrier toimplementation in optoelectronic devices. Substitutionof divalent Zn for a monovalent alkali is an approachthat has been studied in some detail.1,8 While substi-tutional Li is an acceptor that compensates the naturaln-type doping to some extent, this has not led to a reli-able route to p-type ZnO. One reason for this is that Liis an amphoteric dopant: when interstitial it is a donor,so it can self-compensate. In addition to carrier doping,the magnetic aspect of Li defects is of interest for spinfiltering.3 In this context, detailed experimental charac-terization of the structure, stability, and magnetic stateof isolated Li defects would be very useful, particularlyas a test of theoretical calculations.To this end, we implanted a low energy (20-25 keV)beam of the shortlived radioisotope 8Li+ into high pu-rity single crystals of ZnO and studied the resulting iso-lated implant via its nuclear magnetic resonance as re-ported by its radioactive beta decay (β-NMR).12 Closelyrelated to muon spin rotation (µSR) which has yieldedan intricate understanding of isolated hydrogen impu-rities in ZnO,13,14 β-NMR enables complementary in-vestigations of other light isotope dopants in II-VIsemiconductors.15,16 Our purpose is threefold: 1) to elu-cidate the properties of the Li dopant, 2) as a controlfor future experiments focusing on thin films and sur-face effects in pure and intentionally doped ZnO, and 3)as a first step towards studying more complex relatedmaterials, such as indium gallium zinc oxide (IGZO)used in thin-film transistors.17 In the temperature (T )range of 7.6 to 400 K, we observe three distinct defectsand a broad resonance originating from a distribution ofmetastable complexes. Density functional theory calcula-tions of the electric field gradient (EFG) tensor, that de-termines the quadrupolar splitting of the NMR, supportthe assignment of (diamagnetic) defect configurations forthe interstitial (LiO+i ) and substitutional (Li−Zn). The in-terstitial is ionized and stable across the entire T rangeas a source of self-compensation, while the substitutionalbecomes prevalent only above 300 K as a shallow accep-tor. We attribute spin-lattice relaxation above 300K tothe onset of local defect dynamics. We observe a minorfraction of Li in a third characteristic site and discuss itspossible origins. Finally, we report the temperature de-pendence of the EFG for the interstitial, which exhibitsarXiv:2109.08637v1  [cond-mat.mtrl-sci]  17 Sep 20212a remarkable similarity to non-cubic metals.II. EXPERIMENTALA. Implanted Ion β-NMRIn this form of β-NMR, we measure the NMR of ashort-lived β-radioactive probe implanted into the crys-talline host as a low energy ion beam. Detection usesthe asymmetric β-decay (i.e. the direction of the emit-ted β electron is correlated to the nuclear spin directionat the instance of the decay), similar to µSR.12 The ex-periments were performed at TRIUMF’s ISAC facility inVancouver, Canada, where a 20-25 keV beam of spin-polarized 8Li+ with an intensity of ∼ 106 ions s−1 wasfocused into a beamspot ∼ 2 mm in diameter centredon the sample. In this energy range, SRIM Monte Carlosimulations18 predict a mean implantation depth ∼ 100nm (Appendix B). The 8Li nuclear spin I is polarizedin-flight using a collinear optical pumping scheme withcircularly polarized light.19 The beam is incident uponthe sample centred in a high homogeneity superconduct-ing solenoid producing a field B0 = 6.55 T parallel to thebeam and defining the z direction. The polarization pz,the expectation value Iz divided by I, of the implanted8Li is monitored through the experimental β-decay asym-metry,A(t) =NF (t)−NB(t)NF (t) +NB(t)= a0pz(t) (1)where NF and NB are the β-rates in two opposing scintil-lation detectors downstream (Forward, F ) and upstream(Backward, B) of the sample. a0 is a proportionality con-stant depending on properties of both the decay and thedetectors. The polarization direction is alternated, viathe sense of circular polarization of the pumping light,between parallel and antiparallel with the beam (± helic-ity), and data for each helicity is collected separately toenable accurate baseline determination, reduce system-atic error, and to sometimes identify helicity dependentfeatures. 8Li has a nuclear spin I = 2, gyromagnetic ra-tio γ/2π = 6.3016 MHz T−1, nuclear electric quadrupolemoment of Q = +32.6 mb,20 and mean radioactive life-time τ = 1.21 s. The short τ and a typical flux of ∼ 106ions s−1 ensures that the number of 8Li in the sample isnever higher than ∼ 107, so the probe is ultradilute, andthus Li-Li interactions are absent. Further details on themeasurements and samples are in section II C.B. 8Li NMRHere we summarize the NMR properties of 8Li thatwill be important in interpreting the results presentedbelow.Like its stable isotope counterparts, 8Li is a quadrupo-lar nucleus with I > 1/2, meaning its nuclear chargedistribution is not spherical, and its nuclear spin is thuscoupled to the tensor electric field gradient (EFG) Vijthat it finds at its site in the crystal. The quadrupo-lar interaction splits the NMR spectrum into a multipletof 2I = 4 quadrupolar satellites, each corresponding toa specific |∆m| = 1 transition among adjacent nuclearmagnetic sublevels indexed by m. Because I is an in-teger (rare among stable nuclei, but represented, for ex-ample, by the I = 1 6Li), there is no m = ±1/2 “mainline” transition at the centre of the quadrupolar multi-plet. The scale of the quadrupole splitting is given by theproduct of the EFG with the nuclear electric quadrupolemoment eQ. We quantify it by defining the quadrupolefrequency byhνq =3eQVzz4I(2I − 1)=eQVzz8, (2)where Vzz is the (largest) principal component of theEFG. Typical of light nuclei, Q is not very large, and νq istypically on the kHz scale in close-packed crystals. Onecan then treat the quadrupolar interaction accurately asa first order perturbation on the Zeeman Hamiltonian,whereupon the satellites are distributed symmetricallyabout the NMR frequency νr with positions given byνi = νr − niνq12( 3 cos2 θ − 1 + η sin2 θ cos 2φ) (3)where ni = ±1(±3).21 θ and φ are the polar and az-imuthal angles of the field B0 in the principal axis sys-tem of the EFG. The asymmetry parameter η ∈ [0, 1] is ameasure of the deviation of the EFG from axial symmetry(η = 0). If the site has threefold or higher symmetry, theEFG will be axial. If it is cubic, the EFG (and splitting)are zero.To measure a resonance spectrum we use a transverseRF field (B1) that induces magnetic dipolar transitions of|∆m| = 1. When the magnetic field of B1 is large enough,we can, in some cases, also observe nonlinear multiquan-tum transitions (MQ), e.g. with |∆m| = 2. These reso-nances interlace the single quantum satellites with posi-tions given by the same formula with ni = 0(±2). Asidefrom being very strongly dependent on B1, the multi-quantum satellites are unaffected by a distribution of νq(quadrupolar broadening) resulting from crystal imper-fections, so they are often noticably narrower than theirsingle quantum counterparts.22 We note that one majorsource of linewidth in solids, magnetic nuclear dipolarbroadening, is nearly absent in ZnO, since the nuclearmoments of Zn and O are small and/or low abundance.We thus expect the predominant broadening will be fromcrystalline disorder.We will use the quadrupolar splitting as a fingerprintof the specific crystallographic site for the implanted 8Li.Moreover, the EFG can be calculated accurately in den-sity functional theory,23–26 and we performed such cal-culations to aid in determining the sites, see section II Dbelow.3Aside from the quadrupolar splitting, the NMR fre-quency νr is shifted from the Larmor frequency ν0 =(γ/2π)B0 in the applied field by the magnetic responseof the host. We quantify this shift by comparison to astandard reference. With the superconducting magnet inpersistence mode, our conventional reference is a singlecrystal of cubic MgO, where the site is cubic, and the 8LiNMR consists of a single narrow line.27 We define therelative shift in parts per million (ppm) asδ =νr − νMgOνMgO· 106. (4)The resonance shift has contributions from the macro-scopic demagnetization field, local magnetic fields of un-paired spins in the vicinity, and the local screening re-sponse, i.e. the chemical (orbital) shift.12 The latter iswell-known from stable Li NMR to exhibit a very smallrange of a few ppm; while the demagnetization field de-pends on the shape of the sample, and it is near its largestin our geometry: a thin plate in a perpendicular field.In addition to the time average local fields that de-termine the spectral features, fluctuations of these fieldsat the NMR frequency determine the spin-lattice relax-ation (SLR). Like conventional NMR, 8Li relaxation isdescribed by a relaxation function (recovery curve) typ-ically parametrized by the rate 1/T1. The finite 8Lilifetime τ limits measurable T1 roughly to the range0.01τ < T1 < 100τ . Because the spin is polarized inflight, no RF is needed to measure the relaxation, butas a result, there is no spectral resolution to the relax-ation which is simply the average of all the 8Li in thesample. The type of fluctuations giving rise to the ob-served SLR can often be determined by the characteristictemperature dependence of 1/T1. In a nonmagnetic in-sulating host, fluctuations may arise from stochastic dif-fusive motion of interstitial 8Li or from lattice vibrations(phonons). In a semiconductor, mobile or localized carri-ers, if they are sufficiently abundant, may provide othersources for relaxation.28C. β-NMR MeasurementsWe used two transparent colorless commercial hy-drothermally grown ZnO single crystals (Tokyo DenpaCo. Ltd., Tokyo) in the form of thin plates 10 × 8 × 0.5mm3 perpendicular to (0001), the hexagonal crystallo-graphic c axis.29 One sample was used “as-grown” (AG)while the other(n+) was annealed at 1400 °C to removeimpurities. Typical AG carrier concentrations aroundroom temperature are 1012 - 1015 cm−3, while annealingraises it to 1016 - 1017 cm−3 by eliminating compensatingdefects (such as Li) residual from the growth process. An-nealing was done prior to polishing and the polished sur-faces had step-and-terrace structure with a typical stepheight ∼ 0.5 − 3 nm. The same crystals were used forµSR experiments which showed a shallow muonium sig-nal, typical of high quality ZnO. For the measurements,the crystals were clamped to the Al sample holder of anultra-high vacuum cold finger He flow cryostat.With B0 = 6.55 T parallel to the crystalline c-axis, weperformed three types of measurement as a function oftemperature. A) With a continuous beam, we measuredthe resonance spectrum by stepping the frequency of acontinuous wave transverse RF magnetic fieldB1 throughthe Larmor frequency. On-resonance, the RF causes the8Li spin to precess, decreasing the time integrated asym-metry.B) A second type of resonance measurement was usedin which the RF consisted of a four frequency comb withequal amplitude oscillations at frequencies determined bytwo parameters: ν̃0 and ν̃q. Specifically, at ν̃0 ± 3ν̃q andν̃0 ± ν̃q. The center ν̃0 was fixed at the resonance fre-quency from the normal spectrum described in A above,and the splitting parameter ν̃q was then stepped througha range of values. The quadrupole satellites in the sin-gle mode RF spectrum suffer from small amplitudes, as asingle transition is limited to at most 25% of the polariza-tion. As a result, only a few spectra were obtained, whichtake considerable time to accumulate. In contrast, withthe RF comb, when ν̃q matches the quadrupole splitting,all the single quantum transitions (∆m = 1) can be sat-urated at once, dramatically increasing the amplitude,even revealing otherwise undetectable signals. The RFcomb method has been previously applied to 12B and21Na β-NMR in II-VI semiconductors and a more de-tailed description can be found elsewhere.16,30,31Both types of resonance measurement differ in an im-portant way from familiar conventional pulsed NMR, be-cause the RF is applied continuously at each step of thescan for a relatively long integration time (1 s). In thismode, the resonance amplitudes are determined by sev-eral factors beyond the relative abundance of the corre-sponding 8Li site. These include the RF amplitude B1,the resonance linewidth, and, more subtly, slow dynamicsof the resonance frequency on the integration timescalewhich can cause 8Li spins to be double counted, since anindividual spin need only be on-resonance for a millisec-ond or so during the integration time to be fully depo-larized. As a result, it is difficult to make quantitativeconclusions about site fractions from the amplitudes.C) Measurements of the spin-lattice relaxation used apulsed 8Li+ beam and no RF field. The time evolution ofthe polarization was measured both during and after the4 second pulse. At its trailing edge, the polarization ap-proaches a dynamic steady state, while after the pulse, itdecays to its thermal equilibrium value near zero, givingrise to the characteristic bipartite NMR recovery curve.The helicity was alternated for each pulse every 20 sec-onds, and this process was repeated for about 30 minutesto accumulate statistics.4D. EFG CalculationsTo facilitate site assignment for the implanted 8Li, theEFG was calculated for various Li defect configurationsusing the supercell method. Here, Li is placed at a spe-cific site in a supercell composed of a small number ofZnO unit cells which is then subjected to periodic bound-ary conditions. The calculation thus represents a ficti-tious ordered phase LixZnO. While x in the calculationis vastly larger than in the experiment, by decreasing xto the extent possible, one can approach the dilute limit,particularly for quantities like the EFG that are predom-inantly sensitive to the immediate environment.25,32,33Structural calculations of the defects were performedwithin the density functional theory framework us-ing the plane wave pseudopotential method as imple-mented in Quantum Espresso.34 Troullier-Martins norm-conserving pseudopotentials35 were employed for treat-ment of core electrons and the generalized gradient ap-proximation PBE was used for the exchange and corre-lation functional.36 A supercell of 5a × 5b × 3c latticeunits was used with a kinetic energy cutoff of 1080 eVand 2× 2× 2 Monkhorst-Pack grid (MPG)37 centred atthe Γ point. The supercell had Li defects introducedat various sites with a compensating background jelliumcharge to maintain overall neutrality and avoid divergentCoulomb interactions. The atomic positions were allowedto fully relax under the constraint of fixed experimentallattice parameters.38 The total energy was numericallyconverged to less than 1 meV with respect to a cutoff of1210 eV and 6× 6× 6 MPG.For an isolated implanted Li+, the surrounding ZnOlattice will respond with a localized distortion about thedefect that leaves the more distant structure unchanged.The EFG has an r−3 dependence on distance and is thusvery sensitive to the local structure, so a realistic calcu-lation requires both the experimental lattice parametersand an accurate estimate of the local lattice relaxation.25EFG calculations were performed using the morecomputationally expensive all-electron augmented planewave plus local orbitals method (APW+lo) implementedin WIEN2k39 and the relaxed structure from the pseu-dopotential method. The angular momentum expansionof the lattice harmonics inside the atomic spheres wastruncated at L = 10 and the plane waves outside theatomic spheres expanded with a cutoff of RMTKMax = 8,the product of the smallest atomic sphere (RMT) with thelargest K-vector (KMax) of the plane wave expansion.III. RESULTS AND ANALYSISA. Resonance SpectraFig. 1 shows the single tone frequency spectrum inZnO at three temperatures. At all temperatures, the pri-mary feature is a quadrupolar multiplet pattern spread±45 kHz about its center. At 300 K, the predominant70 35 0 35 70MgO (kHz)Normalized Asymmetry (a.u.)MgOMM M-2 -12 11 0 1 07.6 K300 K400 KFIG. 1. The quadrupole split single tone RF spectra at severaltemperatures for 8Li in the as-grown ZnO single crystal with6.55 T‖ c. The frequency scale is relative to the MgO cali-bration frequency (dashed line). The vertical scale has beennormalized by the off-resonance asymmetry at each tempera-ture, and the spectra are vertically offset for clarity. At 300K, the single quantum satellites are labelled with their cor-responding m values, and multiquantum with M. The fittedA site spectrum is shaded grey and is the dominant feature.Above 300 K, a second unresolved line (site B) emerges.quadrupolar splitting is indexed by the correspondingmagnetic sub-level transition. In addition to the indexedsingle quantum satellites (SQ), there are interlaced multi-quantum lines labeled M that are substantially narrowerthan their SQ counterparts.The quadrupole splitting is expected, since no site inthe wurtzite lattice is cubic. However, its magnitude (e.g.defined by the difference between the outermost satel-lites) is quite modest, ∼ 10× smaller than in perovskiteoxides.40 The resolved multiplet indicates a well-definedcrystalline site, which we label “A”. The A multiplet isconspicuous at all temperatures, but its features evolve,with increased splitting and substantial broadening atlow T . At the lowest temperature, the multiplet is su-perimposed on a broad pedestal of intensity with a widthcomparable to the overall multiplet splitting. In additionto A, at 300 K and above, there is another unresolved lineclose to the Larmor frequency (see the 400 K spectrumin Fig. 1). The helicity-resolved spectra confirm it to be5quadrupolar but with a substantially smaller splitting,such that the individual satellites are not resolved (seeAppendix C). We conclude this corresponds to a second8Li+ site (B), with a much smaller EFG, whose popula-tion grows at high temperature.To quantify these observations, the data was fit us-ing using a custom python code based on the Minuit2library.41,42 At each temperature, the two helicities werefit simultaneously sharing the parameters that determinethe satellite positions. Note that for A, νq/νr ∼ 3×10−4,so Eq. (3) provides the satellite positions very accurately.The fit function thus consisted of 7 Lorentzians withsatellite positions determined by the single parameter νqvia Eq. (3), assuming the c-axis coincides with the prin-cipal EFG direction (θ = 0) and axial symmetry (η = 0).We discuss the validity of these assumptions below. Itwas further constrained by assuming all the SQ (MQ)satellites shared the same width ∆νS (∆νM ) at eachtemperature. Where necessary, signals corresponding tothe low T pedestal and the unresolved B site signal wereadded. A priori we expect the chemical shift at A and Bwill differ, but any such difference is too small to detect,and to reduce the number of parameters, the broad lineswere centred at the same νr as A. The resulting fits areshown as the lines in Fig. 1, and the shared parametersfor A are given in Table I.The resulting νq, determined by the splittings, arequite precise, and the differences in Table I are significantas confirmed below by the comb spectra. We include theraw relative shift defined by Eq. (4) in Table I. From thesample shape, we estimate the dimensionless demagneti-zation factor is N ≈ 0.92. A literature43 value for thevolume susceptibility of ZnO χv ≈ −2.2× 10−6 leads toan estimated demagnetization shift −4π (N − 1/3)χv ≈16 ppm, comparable to the value in the MgO referencecrystal (∼ 12 ppm27). From this, we conclude an accu-rate estimate of the corrected shift is impractical. How-ever, the chemical shifts in MgO and ZnO are evidentlysmall (a few ppm) and similar, consistent with expec-tations from conventional Li NMR. The reported shiftuncertainties in Table I are purely statistical. Unlike thesplitting, we do not regard the differences in the shiftas significant, because it is sensitive to small systematicchanges in the field at the sample, due to thermal con-traction, weak magnetization of the spectrometer, andreproducibility of the sample position.The annealed sample was measured briefly at 300 K(not shown). The SQ and MQ satellite linewidths at 300K in the two samples are similar, while any difference inthe quadrupole splitting is much smaller than the MQlinewidths and indistinguishable in a single tone spec-trum.In the AG sample, both the SQ and MQ satellitesbroaden significantly, and by a similar amount, at lowtemperature, indicating predominantly magnetic, ratherthan quadrupolar, broadening. Interestingly, the SQsatellites also broaden at high temperature above 300 K.The ni = ±2 MQ satellites were not observed at 400 K,so no comparison of their widths can be made.Aside from the A multiplet, the broad lines are con-siderably less well-determined. The low temperaturepedestal is very similar in the two helicities, meaning itshows little evidence of a resolved quadrupole splitting -or any such splitting is much less than the width which ison the order of 50 kHz FWHM. Without resolved satel-lites, it is not possible to reliably extract the quadrupolarsplitting of the B site. From the helicity resolved fits, weestimate a splitting of at most a few kHz with satellitelinewidths several times larger than this.B. Comb Spectra11 12 13 14 15 16q (kHz)0100200300400Temperature (K)Normalized Asymmetry (a.u.)FIG. 2. The RF comb spectra, for a narrow range aroundνq for site A, as a function of temperature. The spectra arevertically offset by an amount proportional to the tempera-ture. There is a clear reduction of νq with increasing T. Thesolid grey lines are bi-Lorentzian fits. Up to 300 K, the ampli-tude increases. Above this, there is a dramatic decrease andextensive broadening.We turn now to the RF comb spectra that reveal moredetail than the single frequency spectra above. Recallthe central frequency of the comb is set to coincide withthe centre of the multiplets in Fig. 1 and then the combsplitting is stepped over a range. When the comb’s split-ting parameter ν̃q matches νq, we find a single resonancemuch larger than any of the individual satellites. Thisis demonstrated for the A site multiplet as a functionof temperature in Fig. 2. The resonant ν̃q is entirely6TABLE I. The shared best fit parameters for the A multiplet, including values for the quadrupole frequency νq, frequency shiftδ, single quantum linewidths ∆νS , and multiquantum linewidths ∆νM for both AG and n+ samples. The errors in parenthesesare purely statistical.Sample Temperature (K) νq(kHz) δ(ppm) ∆νS(kHz) ∆νM (kHz)AG 7.6 14.23(2) 9.3(1) 6.0(4) 4(1)AG 300 13.22(1) 5.9(7) 3.9(3) 1.2(2)AG 400 12.56(2) 1.7(5) 5.2(2) 1.08(5)n+ 300 13.16(1) 1.0(6) 3.9(1) 1.38(6)consistent with the splitting in Fig. 1. With increas-ing temperature, the resonance position moves system-atically downward, confirming the trend in Table I andrevealing a thermal reduction in EFG which we discussbelow in section IV D. The spectra could not be fit witha single Lorentzian, but required a bi-Lorentzian (narrowplus broad) sharing the same νq. The fit parameters, asa function of temperature, are shown as the triangles inFig. 4. The resonance position provides a very accuratemeasurement of νq(T ). The amplitude increases with in-creasing T , reaching a maximum at ∼ 300 K, while it iswidest at 370 K, consistent with the high temperaturebroadening of the SQ satellites in Table I.For only a few high temperatures, we extended theν̃q scan range down to zero comb splitting. These spec-tra, shown in Fig. 3, reveal further structure. Distinctwell defined quadrupole splittings for ν̃q = νq resonancesare denoted by the vertical colored bands, with the greyband corresponding to the A resonance tracked with Tin Fig. 2. In scanning ν̃q over a wider range, it is im-portant to recognize that when the outer(inner) combfrequencies match the inner(outer) SQ satellites of theunderlying multiplet, we expect small aliased resonancesat ν̃q = νq/3 (and 3νq). These SQ resonances are denotedat 400 K by subscripts. There may also be aliased MQresonances at 2νq/3 and 2νq. Scans of ν̃q up to 82, 110kHz at 300 and 400 K (not shown) reveal no further res-onances with larger νq. The features at lower frequencyincludes a resolved resonance corresponding to the B site(shaded orange), with νq = 5.941(4) kHz at 400 K, andfit values as open squares in Fig. 4. This resonance isalso identifiable at 210 K (not shown), indicating a smallpopulation of site B far below where it becomes evidentin the single frequency spectra. The B resonance is alsobroader than A, and its position shifts higher from 370to 400 K opposite to the reduction shown by A.As discussed in section II C, the resonance amplitudesare determined by several factors, including the long in-tegration time (1 s) of the continuously applied RF fieldand off-resonance baseline asymmetry. In the presenceof slow spectral dynamics up to the integration time, theamplitude may be enhanced as 8Li can be double countedif they only transiently meet the resonance condition for atime as short as the RF precession period, on the order of1 ms. This results in spectra with resonance amplitudeswhose sum may exceed the full off-resonance asymmetry,010203040 (a)  400 KC3B1/3 A1/3B30 4 8 12 16q (kHz)0102030 (b)  370 KAsymmetry (%)C B AFIG. 3. The RF comb spectra for a broader range down toν̃q = 0 at 400 K (a) and 370 K (b). Primary resonances for dis-tinct sites are indicated with shaded regions, labelled A,B,C.The asymmetry has been normalized to its fitted off-resonancevalue. At 370 K, the lines are all broadened. Smaller featuresdenoted as subscripted labels are aliases of the primary reso-nances. There is also a substantial broad background.as is evidently the case in Fig. 3. This is strong confir-mation that 8Li is undergoing spectral dynamics in thistemperature range.The comb spectrum also reveals a third site (labelledC) with an even smaller νq = 3.63(5) kHz at 370 K, abouthalf the value for B, decreasing to 3.28(5) kHz at 400 K.It’s amplitude is small, so it corresponds to only a mi-nor population of implanted 8Li. The combination of thebreadth of B and the presence of C explains the absenceof resolved structure of the B line in Fig. 1, but note there7is substantial intensity in a broad background encom-passing B and C with a tail that reaches toward A. Thethree resolved quadrupole frequencies at 400 K are givenin Table II and the additional minor peaks are aliases ofthese resonances. The rich detail in these spectra demon-strates the power of the comb method to strongly amplifyquadrupolar split resonances within a narrow band of ν̃qand reveal structure that is otherwise hidden.TABLE II. Measured quadrupole frequency νq and principalcomponent of the EFG tensor Vzz for the three 8Li sites at400 K. Parenthetical values are statistical errors.Site νq(kHz) Vzz(1020V/m2)A 12.56(2) 1.275(2)B 5.941(4) 0.6029(4)C 3.28(5) 0.333(5)1.241.281.321.361.401.44Site A Vzz (1020 V/m2 ) (a)Site ASite B0.00.51.01.52.0FWHM (kHz)(b)0 100 200 300 400Temperature (K)0153045607590Amplitude (%)(c)0.530.550.570.590.61Site B Vzz (1020 V/m2 )1/Tmax1FIG. 4. Temperature dependence of the fit parameters forthe comb spectra in Figs. 2, 3. (a) From the resonance po-sitions, the principal component of the EFG for sites A andB calculated using Eq. 3. (b) the linewidth (FWHM) for thebi-Lorentzian. (c) the resonance amplitude. The lines areguides to the eye, except the solid line in (a) is a fit to Eq. 6for site A. The vertical band marks the position of the peakof the spin-lattice relaxation rate.C. Spin-Lattice Relaxation0 2 4 6 8 10 12Time (s)0.00.20.40.60.81.0Normalized AsymmetryBeam on Beam off4.2 K 300 K 360 K380 K 400 K FIG. 5. The time dependence of the asymmetry for 8Li+ inthe as-grown ZnO at 6.55 Tesla‖ c for several temperatures.The decay is due to spin-lattice relaxation of the isolated im-planted 8Li+. The black lines are global fits with a biexpo-nential relaxation function Eq. (5). Above 300 K, there is astrong temperature dependence with a maximum rate near370 K. The dashed line shows the calibrated value of A0 inMgO exceeds that in ZnO indicating a small missing fraction.Below 300 K, the spin-lattice relaxation in the AG sam-ple is very slow (T1 > 100 s), as seen in the recoverycurves in Fig. 5, where the time dependent asymmetryhas been normalized to its initial value A0. The corre-sponding rate is near the limit imposed by the 8Li life-time. This is typical for a nonmagnetic insulator when8Li+ is not diffusing. However, above 300 K it increasesrapidly, but not monotonically, with a maximum rate atabout 370 K (the lowest data in Fig. 6). Careful compar-ison between 300 K and low temperature shows there is asmall much faster relaxing component, corresponding toat most a few % of the signal. In addition, a calibration ofthe initial asymmetry A0 in MgO is about 10% larger at300 K, see the dashed horizontal line Fig. 5. Thus, thereappears to be a small “missing fraction” correspondingto a population of 8Li that are very rapidly depolarized.We briefly studied the n+ sample at 300 K and foundthe SLR rates to be similar. However, A0 was larger,only 3.3(1)% less than MgO (see Fig. 11 in AppendixD), i.e. the missing fraction is substantially reduced byannealing.8To fit the data consistently across the full temperaturerange, we adopt a biexponential relaxation function: for8Li arriving at time t′, the polarization at time t > t′followsR(t, t′) = [fse−λs(t−t′) + (1− fs)e−λf (t−t′)] (5)where fs is the slow fraction and λs = 1/T slow1 is its rate,while λf is the fast SLR rate. The data was fit to Eq.(5) convolved with the 4 second beam pulse using theMinuit241,42 library as implemented in ROOT44 with acustom C++ code. To reduce the number of free param-eters, below 300 K A0 = 0.07822(5) and fs = 0.962(1)were shared temperature independent global parameters,and the global reduced χ2 ∼ 0.85. The data above 300K was taken after the spectrometer had been modifiedto increase its maximum temperature. For this data, fswas allowed to vary with temperature and the sharedA0 = 0.0854(2) with χ2 = 0.87. This increase in A0is due to changes to the F β-detector. In both ranges,the χ2 values indicate the biexponential tends to over-parametrize the data (particularly at low temperature);however, it has the advantage that it isolates the fastcomponent, preventing it from biasing the slow rate. Therate and fraction of the large, slow-relaxing signal are pre-sented in Fig. 6 showing the rapid increase in λs above250 K toward a maximum at 370± 10 K. The fast signalis a very small fraction below 300 K, see Appendix A formore details.D. EFG calculationsAs the EFG is a ground state property of thecharge density which is accessible within all-electron self-consistent energy band calculations,23 we attempted todetermine the site of 8Li by comparison with the calcu-lated EFG tensor magnitude and symmetry. In semicon-ductors, defects generally exhibit distinct charge states,and the lowest energy charge state may change withtemperature (or doping) by exchanging electrons withband states at the Fermi level. Naturally, differentcharge states have different local lattice and electronicstructures.45 This modifies the EFG, allowing, in princi-ple, identification of charge states, particularly for deeplevel defects characterized by large lattice relaxation at acharge state transition.32,33 We indicate the charge stateof the calculation with a superscript q, where q = −1(+1)if an electron is added to (removed from) the supercell.There are only a few reasonable candidate Li sites inideal ZnO, with structure shown in Fig. 7. We calcu-late the defect structures for Li+ in the high symmetrytetrahedral LiT (Wykoff 2b) and octahedral LiOi (Wykoff2a) interstitial sites, where it would act as an electronicdonor. We also calculate the zinc substitutional site(LiZn), an established acceptor.46 Note that neutral LiZnhas a polaronic distortion around the localized hole, soit is not certain whether it is a shallow (and potentially0.00.51.0f s0 100 200 300 400Temperature (K)0.000.020.040.060.080.100.121/Tslow1 (s1 )FIG. 6. The spin-lattice relaxation rate, λs = 1/T slow1 andfraction fs for the large slow relaxing component from biex-ponential fits as shown in Fig. 5. Near 400 K, fs decreasesas more of the signal is accounted for by the fast component.There is a clear maximum at 370 K. The line is a fit to anactivated BPP temperature dependence as described in thetext. The grey region denotes the lower limit at which 1/T1is accurately measured.TABLE III. The electric field gradient Vzz in units of1020 V/m2 for selected relaxed Li defect configurations us-ing the 300 K ZnO lattice parameters.Site Vzz Principal Axes ηLiO+i 1.21 (0,0,1) 0Li?+T 0.47 (0.04,0.82,-0.57) 0.65Li−Zn 0.16 (0,0,1) 0useful) p-type dopant.47,48 The Li antisite defect (LiO) isnot considered, as it is reported to be unstable.48We find LiO+i is displaced from the symmetric 2a posi-tion along (0001) by 0.57 Å, creating a long and short setof Li-O coordinating bonds. The axially symmetric Li+Tis also found to relax spontaneously to Li?+T , a variantdisplaced from the 3-fold axis of symmetry. Consideringthe defects only in their diamagnetic ionized states, theEFG tensors, calculated using the 300 K lattice parame-ters are given in Table III. The Li−Zn center distorts thelocal environment, giving rise to an almost symmetrictetrahedral coordination with neighboring oxygens, re-sulting in a very small Vzz. LiO+i retains axial symmetry(along c), while Li?+T has a principal axis almost orthog-9onal to c, nearly parallel to b. The calculated structuresof the LiO+i and Li−Zn defects are shown in Fig. 7.(b) Lio+i (c) LiZnLi [0001]LiZnO(a) ZnOspace group: P63mc (#186) 5.207 ÅFIG. 7. Unit cell of ZnO (a) and the relaxed defects of LiO+i(b) and Li−Zn (c) in their diamagnetic states shown ‖c and ⊥ b.The off-center LiO+i is located at the 2a site with fractionalcoordinates (0,0,0.079) of the unit cell shown. The structureswere drawn using VESTA.49IV. DISCUSSIONA. Sites for Implanted Li+When an ion is implanted in a crystal, it loses energythrough collisions with host lattice atoms and graduallyslows down. In the process, it can knock a host atomout of its normal lattice position into a nearby vacantinterstitial site, forming a Frenkel (vacancy-interstitial)pair.50 The threshold for this process is typically 10s ofeV. So, after generating its final Frenkel pair, the im-planted ion continues for some distance before stoppingtypically at a high symmetry site. The host lattice willthen relax around the stopped implant, possibly loweringits site symmetry. Now if we consider the NMR spec-trum, such as we measure with β-NMR, to the extentthat the stopping site is isolated from other defects, itwill have a characteristic EFG tensor reflected by a well-resolved quadrupolar splitting. However, it is also pos-sible that the ion stops close enough to the last Frenkelpair that its EFG is modified. As there are many pos-sible configurations of the trio (ion+pair), this results ina distribution of EFGs and is reflected in a quadrupo-lar broadened resonance usually observed at low tem-perature. At higher T , the Frenkel defects tend to healrapidly, typically leading to the first stage of annealing.Depending on relative mobilities, the implanted ion maycompete for the vacancy with the intrinsic interstitial ofthe pair. With increasing T , the typical behaviour isthus a gradual loss of the broad “perturbed site” reso-nance together with an increase and sharpening of thewell-defined lines corresponding to the isolated site, andpotentially (if the implant reaches the vacancy) a changeof site to substitutional. As we shall see below, the im-planted 8Li+ in ZnO follows this phenomenology quiteclosely.The A site multiplet, with a well-resolved quadrupo-lar splitting, is evident at all temperatures, including thelowest, see Fig. 1, so it should correspond to 8Li+ atthe most stable interstitial. The octahedral site is sub-stantially more spacious than the tetrahedral, and theoryfinds it lower in energy by 0.62 eV.47 Moreover, there isonly a small barrier for the tetrahedral to migrate toan adjacent octahedral.47 The LiO+i assignment is un-ambiguously confirmed by the excellent agreement be-tween the calculated EFG of 1.21·1020 V/m2 in Table IIIwith the experimental value at room temperature of1.342(1) · 1020 V/m2. The unrelaxed 2a site is symmet-rically coordinated by six O2− ions. Axial lattice relax-ation brings the interstitial cation closer to three anions,lowering the energy. This off-centre site is also consistentwith emission channeling from other alkali radioisotopesin wurtzite crystals.51–53 We note the relaxed site is still3-fold symmetric about the c axis, so the EFG remainsaxial, consistent with Eq. (3) for the satellite splittings.As a corollary, we then attribute the broad low temper-ature resonance in Fig. 1 that disappears by 300 K toLiO+i in the vicinity of some implantation-related crys-talline disorder, also consistent with emission channelingin related materials.53Next we consider the B site resonance which is well-resolved only in the comb spectra. Though it can beidentified as low as 210 K, it only becomes substantialabove 300 K, increasing in amplitude towards the high-est T . This suggests B is the product of a site changetransition to a lower energy site, likely the substitutional.This is similar to 24Na implanted into ZnO where emis-sion channeling finds the interstitial twice as probable asthe substitutional at room temperature, while by 420 Kthe interstitial is largely converted to substitutional.51 Incontrast to the A site, the calculated EFG is substan-tially smaller than measured. However, Na β-NMR alsofinds two sites at room temperature, with the substitu-tional site having a factor of 2 smaller EFG than theinterstitial,30,51 very similar to 8Li. The evident under-prediction of the EFG by DFT (see Table III) is proba-bly due to its sensitivity to the detailed lattice relaxationaround the Li−Zn which may not be captured accuratelywith the GGA functional.The temperature dependence of the spectra reveals fur-ther aspects of the site change. The A site line (mostclearly revealed in the comb resonances in Fig. 2) in-creases in amplitude above 200 K, reaching a maximumnear room temperature. Some of this increase is due to10narrowing. The bi-Lorentzian lineshape also suggests twoA sites sharing the same average EFG, but distinguishedby the width of the EFG distribution. The broad com-ponent probably corresponds to the A site with somedisorder at distances of a few lattice constants, while thenarrow component probably represents an A site withideal local structure. The growth of the narrow com-ponent is consistent with annealing of some correlated(small) Frenkel pairs in the vicinity. This agrees with op-tically detected electron paramagnetic resonance in elec-tron irradiated ZnO that demonstrates low temperatureannealing of the zinc (65-170 K) and oxide (160-230 K)sublattices.54 As seen clearly in Fig. 3, above 300 K, theA line first broadens at 370 K, then narrows again by 400K, maintaining nearly the same integrated area, while Bincreases substantially. If the site change involved an iso-lated interstitial becoming substitutional, e.g. by a knockout mechanism,55 then we would expect a decrease in theA amplitude with the simultaneous growth of B, such asin the well-established site change in the FCC metals.56This is not the case, however. While it is possible thatdynamic effects on the amplitude are confounding here,a careful inspection of the spectra in Fig. 3 reveals thatthe increase in B appears to be at the expense of thevery broad background intensity that underlies the bet-ter resolved resonances. Production of Li−Zn in this Trange then appears to result from a perturbed (disor-dered) site as a starting point rather than the isolatedinterstitial directly. This is reasonable for a site changeinvolving a nearby vacancy (which is almost certainlyimplantation-related, since thermodynamic vacancies areextremely rare). Interstitials nearest to such vacancieswill be the first to become substitutional, and they willalso experience a significantly perturbed EFG in advanceof the site change. In the ideal crystal, the barrier for Znvacancy migration is quite high,57 so the site change isprobably driven by mobility of the interstitial Li. Weconsider further the mobility of LiO+i below in relationto the spin-lattice relaxation.Thus far, the 8Li in ZnO follows the scenario typicalfor light implanted isotopes as outlined above. However,we also find clear evidence for another site (denoted C)with a well-defined EFG in the comb spectrum in Fig.3(a). This site may correspond to a complex with an-other point defect, such as an oxygen vacancy, LiZn−VO,which is Coulombically bound. This would be consistentwith the high temperature appearance of the closely re-lated NaZn − VO complex seen by electron-nuclear dou-ble resonance,46 but the fact that the EFG for C is evensmaller than B seems inconsistent with a nearby chargedvacancy. Moreover, such a complex would have severalorientations relative to the applied field which shouldyield a more complex spectrum. However, if the complexis dynamic, e.g. with VO hopping rapidly (on the scaleof the quadrupolar splitting of several kHz) among thethree equivalent neighbours and axial position of Li−Zn,then a single reduced average EFG might result. Thissuggestion could be tested with more detailed calcula-tions.Finally, we consider the widths of the well-resolvedresonances. Without significant dipolar broadening,we might expect the resonances to be extremely nar-row. However, the widths in Table I are considerablylarger than similarly split satellites in crystals of Bi58 orSr2RuO4,59 probably due to local crystalline disorder.57The primary broadening mechanism is quadrupolar, asconfirmed by the substantially narrower MQ resonances.Another potential source of broadening is the inhomoge-neous magnetic fields due to a population of dilute para-magnetic centres, which could be intrinsic defects3 or im-purities such as Fe. In NMR, this results in a term in thelinewidth proportional to the impurity spin polarizationthat, in the dilute limit, is typically Curie-like (propor-tional to 1/T ). The absence of such a temperature de-pendent broadening is clear in Fig. 4(b), which shows thewidth to be quite independent of temperature below 150K. The slight narrowing above this is probably relatedto the healing of nearby Frenkel pairs. This is consis-tent with predominantly quadrupolar broadening downto the lowest temperature. However, the MQ satellites,which are not quadrupole broadened, do exhibit a low Tbroadening (see Table I), suggesting a Curie term maybe emerging at the lowest T . At the opposite end of theT range, the broadening at 370 K is probably dynamic,and we discuss it below with the spin-lattice relaxation.B. Magnetic State of Implanted 8LiIn the previous section, we found very little evidencefor broadening due to dilute paramagnetic defects. Herewe consider paramagnetism in the immediate vicinity ofthe 8Li. It is widely accepted that Li is an amphotericdopant in ZnO, where the Lii is a donor and LiZn anacceptor. The question then arises: what is the chargestate? In the ionized state, both would be diamagnetic,while un-ionized they would be paramagnetic with an un-paired electron/hole spin localized in the vicinity. Thisdistinction should be dramatic in the data, since the hy-perfine interaction provides a strong magnetic perturba-tion on the NMR. However, we see no evidence for ahyperfine splitting for either site. This appears inconsis-tent with the EPR of LiZn.60 However, the EPR signalrequires cross gap photoexcitation of carriers, meaningit is actually due to a metastable paramagnetic defect.From our data, we conclude that LiZn is fully ionized inthe temperature range where we observe it (above 200K), meaning it is quite a shallow acceptor. Similarly, Liiremains diamagnetic over the entire range down to thelowest T (7.6 K). Again this appears inconsistent withthe EPR (and ENDOR) of the interstitial,46 but this sig-nal is observed (without photoexcitation) at 1.6 K, soit may be simply that ionization occurs in the interven-ing factor of 5 in T . However, this signal is also fromnanoparticulate ZnO, and there is a strong size effect onthe hyperfine coupling, due to confinement of the impu-11rity wavefunction, which decreases strongly with increas-ing particle size. At 7.6 K, we place an upper bound ofa hyperfine splitting at 2 kHz (smaller than 3 Gauss atthe 8Li nucleus), corresponding to a fraction of the MQlinewidths in Table I, confirming that Lii is shallow as adonor in the bulk.While the carrier concentration in our samples is quitelow and far below the metallic limit, here we consider thepossibility that the Li defects are un-ionized but rapidlyexchanging with a population of free carriers. In thiscase, the hyperfine splitting is averaged out, but thereis a remnant time average shift of the NMR which typi-cally follows the Curie law.61,62 The observed shift valuesin Table I show no evidence for such a contribution, re-maining small (in the range of Li chemical shifts) at alltemperatures. This provides further confirmation thatthe observed Li is fully ionized.Fluctuations of the hyperfine field of an unpaired elec-tron in the vicinity may well cause the 8Li nuclear spinto relax so rapidly that it is not observed. This mightaccount for the small missing fraction in the AG crystal.If this is the case, its reduction in the annealed crystalsuggest that the probability of such a paramagnetic envi-ronment is reduced by annealing, i.e. it does not appearcharacteristic of pure ZnO.C. Spin-Lattice Relaxation and DynamicsSpin-lattice relaxation is driven by fluctuations of thelocal fields at the nucleus, specifically, the Fourier compo-nent at the NMR frequency (41.27 MHz). For quadrupo-lar nuclei, the most important contribution is usuallyEFG fluctuations, since this is the largest term in thenuclear spin Hamiltonian (after the Zeeman interactionwith B0). This hierarchy of interaction strengths is re-flected in the time average spectra above, where thequadrupolar splitting far exceeds the satellite linewidths.Below 300 K, the relaxation is so slow that it is dif-ficult to measure reliably, due to lifetime of the probe.In this temperature range, thermal phonons could causeSLR by a Raman process, producing a 1/T1 varying ap-proximately as T 2, e.g. in LaAlO3, see Ref. 63. Suchphonon relaxation is evidently too weak to measure.In contrast, with an onset around 300 K, there is anactivated increase in the 1/T slow1 above room tempera-ture. This could, in principle, be due to thermally excitedcarriers,28 but the peak in 1/T slow1 in Fig. 6 is not consis-tent with this. Such a peak is typical of some stochasticmotion, either of the probe ion itself or some other speciesin its vicinity, giving rise to a fluctuating field at the nu-cleus. In the simplest case of the isolated LiO+i hoppingdiffusively on the sublattice of octahedral sites, the EFGat each site is equivalent, both in magnitude and direc-tion, so fluctuations would occur only as the ion brieflytransits between sites. On the other hand, the fluctuat-ing EFG may be due to another nearby interstitial ion,probably the more mobile ZnI, which is likely part ofthe nearest Frenkel pair. If the corresponding vacancyremains nearby, then the dynamics of both interstitialcations would be modified by the Coulomb potential wellof the negatively charged vacancy. The 1/T slow1 max-imum may then correspond to a Bloembergen PurcellPound (BPP) peak,64 where a fluctuating field describedby a single exponential correlation time τc with an ac-tivated temperature dependence τ0exp(Ea/kbT ) sweepsthrough the NMR frequency, producing a peak when τcmatches ω−10 . Fitting the measured 1/T1 to the BPPmodel produces the curve shown in Fig. 6 with fittedvalues of Ea = 0.57(2) eV and τ0 = 3(1)· 10−16 s. Whilethe fit is not too bad, there are several important featuresthat are inconsistent with a simple BPP interpretation:1) The fitted “attempt frequency” 1/τ0 is several ordersof magnitude higher than expected. This value is relatedto the narrowness of the peak in temperature. 2) TheSLR peak coincides with a broadening in the resonances(see Fig. 4). In contrast, the spectrum should be motion-ally narrowed when τ−1c exceeds the linewidth (severalorders of magnitude smaller than ω0), i.e. at tempera-tures well below the SLR peak. 3) Taking the A site νqas the scale of fluctuations, the peak value of 1/T1 is alsotoo low. These inconsistencies suggest a more compli-cated situation than simple isolated interstitial diffusivemotion.For this reason, we seek an alternate explanation. Con-sider the line broadening at high temperature. It is notmagnetic as the MQ resonances are unaffected. Ratherit resembles the broadening expected for an NMR probefluctuating between different environments at a frequencycomparable to the spectral difference of the two. Thewidth is maximized simultaneously for both the A and Blines as well as the broad background in the comb spec-tra. From this we speculate that some activated localdynamics starts to relax the 8Li spin above 300 K, butbefore reaching the BPP peak, this relaxation channelis quenched. This might be LiO+i becoming mobile andthen finding a vacancy and becoming the immobile Li−Zn.On the other hand, it could also be ZnI beginning to hoplocally in the attractive potential of the vacancy, andthen detrapping and moving away. In either case, theactivated dynamics is interrupted and the relaxation di-minishes as this timescale becomes short enough to stopthe relaxation.D. Temperature Dependence of the EFGThe electric field gradient at the nucleus is sensitivelydetermined by the site symmetry and the local electronicstructure about the implanted ion. It is not surprisingthen to find that it is temperature dependent. For the Asite, it decreases by more than 10% from its low T valueto 400 K, see Fig. 2. The corresponding values of Vzz(T )shown in Fig. 4(c) were fit toVzz(T ) = Vzz(0)(1−BTα). (6)12TABLE IV. Fit Parameters from Eq. (6) for the temperaturedependence of the EFG at the Li+ A site in ZnO. Vzz(0) is inunits of 1020V/m2.Fit type Vzz(0) B(α) αFixed α 1.4507(2) 1.47(2)× 10−5 1.5Free α 1.4428(3) 4.4(2)× 10−6 1.697(6)The resulting parameters are reported in Table IV, wherea T 1.7 behavior is determined for an unconstrained fit,while fixing α = 1.5 produces a slightly worse fit withsmall deviations below 100 K.It is widely recognized that thermal expansion playsonly a minor role in determining Vzz(T ).65 Instead, popu-lation of phonon modes renders the EFG time dependent,and the time average value is reduced as the vibrationalamplitude increases,66,67 resulting in an average behav-ior captured by the simple phenomenological form of Eq.(6), in a similar vein to the temperature dependence ofthe energy gap in semiconductors.68 The exponent α isoften found to be 3/2 for implanted defects in non-cubicmetals and metallic compounds,69 but, while common, itis by no means universal.66 It’s occurrence here demon-strates that it is not particular to metals69,70 or narrowgap semiconductors,71 nor is it characteristic of heavy iso-tope perturbed angular correlation probes. It would bea strong confirmation of the ab initio models, if latticedynamic calculations66,67 could reproduce the observedVzz(T ).In contrast, site B exhibits an anomalously increasingEFG, which, while rare, is not unheard of.67 However,this should be interpreted with some caution, becausethe dynamic broadening at 370 K may also affect theapparent νq of the resonances. Confirmation of this be-havior must await more detailed future measurements.V. SUMMARYUsing ion-implanted 8Li β-NMR we characterized themicroscopic dynamics, stability, and magnetic states ofLi defects in high purity ZnO single crystals. RF combmeasurements, through a strong signal enhancement, en-abled identification of three distinct defects between 7.6and 400 K. Comparison to DFT calculations confirm thestability of ionized shallow donor LiO+i up to 400 K andcoexistence with Li−Zn confirming the amphoteric char-acter responsible for self-compensation of p-type doping.From the absence of a resonance shift or hyperfine split-ting, we find no evidence for localized holes near LiZndown to 210 K, indicating it is a shallow acceptor inisolated form. Above 370 K, a third unexpected defectis detected that we tentatively suggest to be a complexwith Li−Zn. From spin-lattice relaxation measurements,a T independent fraction of the initial polarization sug-gest some 8Li stop near magnetic defects with unpairedelectrons that are reduced in concentration by anneal-ing. The spin-lattice relaxation rate peaks at 370 K. Weascribe its temperature dependence to the coupled mo-tional dynamics of Li and other nearby defects.Our results using ultradilute 8Li reveal the defect prop-erties of Li in ZnO and indicate while p-type dopingis possible with Li, self-compensation by interstitial Liposes a barrier. Characterization of the local 8Li environ-ment is a first step toward studies on surface properties,intentionally doped crystals, and the structurally relatedbut more complex thin-film transistor material, IGZO.Finally, our measurements of Vzz(T ) for Lii demonstrat-ing a T 1.7 dependence resembling a non-cubic metal pro-vides a case to validate the ab initio lattice dynamicsmodels for a light interstitial in a semiconductor.66,67ACKNOWLEDGMENTSWe thank K. Foyevtsova and I. Elfimov for assistancewith the DFT calculations; S. Daviel and H. Hui of TRI-UMF for implementation of the RF comb; M. McLayand S. Chan for the high temperature detector upgrade;Y. Cai for help with measurements; Useful discussions:J. Stähler. This work was supported by NSERC Discov-ery. D.F., V.L.K., and J.O.T. acknowledge the additionalsupport from their SBQMI QuEST fellowship.Appendix A: The Fast Relaxing ComponentAs discussed above, we fit the spin-lattice relaxationdata to a biexponential relaxation function. Over muchof the temperature range, the fast component (ff = 1−fs) is small, accounting for only a few percent of thesignal. As a result, it is much less well-determined thanthe larger slow relaxing component. For this reason, wedid not discuss it in the main text. We include it herefor completeness. Fig. 8 shows its rate and fraction.For a spin-2 nucleus relaxing by slow quadrupolar fluc-tuations, one expects a biexponential with a fast compo-nent of about this amplitude.72 However, the observedsignal deviates from this model in several significantways: 1) λf is substantially faster relative to λs than pre-dicted; 2) λf (T ) should track λs(T ), while Fig. 8 showsthat the main peak is substantially lower in temperature,and there is a secondary peak around 100 K; 3) Whenthe fluctuations become fast, above the T1 minimum, thefast amplitude should go smoothly to zero. Instead, itgrows in this region. For these reasons, the fast compo-nent probably has a different origin. Below 350 K, whereits amplitude is small, it may correspond to 8Li in someexceptional environment with a significantly higher lo-cal relaxation rate, perhaps near the surface, but moremeasurements are required to make any firm conclusions.130.00.51.0f f0 100 200 300 400Temperature (K)0123451/Tfast1 (s1 )FIG. 8. The fast component’s spin-lattice relaxation rate,1/T fast1 from biexponential fits to the data as shown in Fig. 8at 6.55 T ‖ c. The peak occurs at about 300 K, significantlylower than the slow component.Appendix B: Stopping DistributionThe energy of the 8Li+ beam determines its implan-tation profile. We simulated this for 25 keV and 105ions normally incident on ZnO with the SRIM MonteCarlo code, calculating a mean depth of 112.7 nm and astraggle (standard deviation) of 50.8 nm. The stoppingdistribution is shown in Fig. 9, indicating that the vastmajority of 8Li+ are well beyond the surface region wherethe electronic properties are modified (∼ 2 nm).73 Thesimulation does not take into account implantation chan-neling which would result in a tail to the profile towardslarger depths due to the channeled fraction.Appendix C: Helicity-Resolved Resonance SpectraIn Figure 10, we present the single tone RF spectrumat 300 K, separately for the two helicities. The occur-rence of corresponding satellites on opposite sides of thecentre of the pattern in the two helicities is unambiguousconfirmation that the splittings are quadrupolar. Thecorresponding helicity combined spectrum is shown inFig. 1.0 50 100 150 200 250 300Depth (nm)Number of IonsMean depth:112.7 nmFIG. 9. SRIM18 stopping profile for 25 keV 8Li+ implantedin ZnO.Appendix D: Spin-Lattice Relaxation of theAnnealed CrystalIn Fig. 11 we present a comparison of the NMR recov-ery curves at 300 K in annealed ZnO, as-grown ZnO, and41225 41250 41275 41300 41325Frequency (kHz)128404812Asymmetry (%)300 Knegative  helicitypositive helicityFIG. 10. The single RF spectra for 8Li in the as-grown ZnOwith 6.55 T‖ c at 300 K showing the two helicities: initialspin state primarily m = 2 (open) and m = −2 (closed).The asymmetry is normalized to its off-resonance equilibriumvalue. The site A spectrum is shaded grey.14the MgO reference. Using Eq. (5)27 to fit the data, theinitial asymmetry A0 is extracted for n+ ZnO and MgO.For MgO A0 = 0.095(1), while n+ ZnO measured withthe standard forward β detector yielded A0 = 0.0864(8).0 2 4 6 8 10 12Time (s)0.00.20.40.60.81.0Normalized AsymmetryBeam on Beam offas-grown ZnOannealed ZnO MgO FIG. 11. The time dependence of the asymmetry for 8Li+ inthe as grown ZnO, annealed ZnO, and MgO reference at 300 Kand 6.55 Tesla‖ c. The decay is due to spin-lattice relaxationof the isolated implanted 8Li+. The asymmetry is normalizedto the initial asymmetry A0 in MgO extracted from fitting abiexponential relaxation function. The as grown ZnO has alarge reduction in the initial asymmetry, corresponding to amissing fraction.REFERENCES∗ Email: jradelman@berkeley.edu; Current address: Depart-ment of Chemistry, University of California, Berkeley, CA94720, USA† Current address: TRIUMF, 4004 Wesbrook Mall, Vancou-ver, BC V6T 2A3, Canada‡ Email: wam@chem.ubc.ca1 A. Janotti and C. G Van de Walle, Rep. Prog. 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