Journal of Magnetic Resonance 237 (2013) 110–114
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Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr
Identification of Fe3+–Li+ complexes in ZnO by means of high-frequency EPR/ENDOR spectroscopy Yu.S. Kutin ⇑, G.V. Mamin, S.B. Orlinskii Kazan Federal University, Institute of Physics, Kremlevskaya str. 18, 420008 Kazan, Russia
a r t i c l e
i n f o
Article history: Received 25 July 2013 Revised 23 September 2013 Available online 11 October 2013 Keywords: High-frequency EPR ENDOR W-band ZnO Iron Lithium Complex Charge-compensated centers Quadrupole interaction
a b s t r a c t Theoretical prediction of a high Curie temperature in ZnO doped with Mn, Fe, and other transition metals has stimulated the investigation of these materials by many research groups. Although charge-compensated Fe3+ centers in ZnO:Fe have been observed by means of EPR and have been known for decades, conclusions on the chemical nature of these defects are still contradictory. Originally, these centers were treated as Fe3+–Li+ complexes with both ions occupying adjacent cationic sites. Recently, however, the centers were interpreted as a substitutional Fe3+ ion with a vacancy at an adjacent zinc or oxygen site (Fe-VZn or Fe-VO). In order to determine the chemical nature of the impurity associated with Fe3+, electron-nuclear double resonance (ENDOR) spectroscopy was used. ENDOR measurements reveal NMR transitions corresponding to nuclei with g-factor gN = 2.171 and spin I = 3/2. This unambiguously shows presence of Li as a charge compensator and also resolves contradictions with the theoretical prediction of the Fe-VO formation energy. The electric field gradients at the 7Li nuclei (within the Fe3+– Li+ complexes) were estimated to be significantly lower than the gradient at undistorted Zn sites. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction ZnO is a II–VI semiconductor with a wide direct band gap of about 3.3 eV at room temperature. Due to its unique optical, electrical, and mechanical properties, it has recently regained a lot of attention as a material for UV light-emitting diodes, a transparent conducting oxide for photovoltaic applications, a radiation hard material, etc. [1,2]. Much effort is also made towards developing diluted magnetic semiconductors based on a theoretically predicted high Curie temperature in ZnO doped with high concentrations of transition metals (TM) [3,4]. Nominally undoped ZnO crystals often contain TM ions, which incorporate into the material at substitutional sites during the crystal growth process. Electron paramagnetic resonance (EPR) has been widely used to study various impurities in ZnO [5,6]. In ZnO crystals containing Fe, EPR experiments reveal the spectrum of the trigonal FeZn center [7,8], as well as multiple additional signals assigned to charge-compensated Fe3+ [7,9–11]. However, conclusions on the chemical nature of the charge-compensated Fe centers are contradictory. The older work [9] treats the centers as Fe–Li complexes, whereas authors of a more recent research [10] interpret the centers as an Fe3+ ion with a vacancy at an adjacent zinc or oxygen site (Fe-VZn, Fe-VO). As noted by the authors,
the latter model contradicts the theoretical prediction [12] that formation of the Fe-VO complex is not energetically favored. The hydrothermal growth method is commonly used for ZnO, since it allows for growing large single crystals. However, these crystals inevitably contain significant amounts of Li [13], in addition to TM ions. Therefore, establishing the real nature of the complex will contribute to a better understanding of incorporation of Fe and Li into the ZnO lattice and should resolve (or confirm) contradictions with the theoretical predictions concerning the FeVO formation energy. Since no hyperfine (HF) splitting is observed in the EPR spectra of the charge-compensated Fe centers, it is not possible to identify the chemical nature of the complex by means of conventional EPR. It should be supplemented with modern multiple resonance techniques. Electron-nuclear double resonance (ENDOR) has been successfully used to investigate numerous defects in ZnO single- and nanocrystals [14–17]. This method reveals interactions of the electrons with surrounding magnetic nuclei. Therefore, if Fe3+ ions form complexes with other elements (e.g., Li), this interaction should give rise to signals in ENDOR spectra that will correspond to the nuclear g-factor and spin of the charge compensating impurity.
2. Experimental details ⇑ Corresponding author. Fax: +7 843 2924448. E-mail address: [email protected] (Yu.S. Kutin). 1090-7807/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmr.2013.09.014
ZnO used in this investigation was a nominally undoped hydrothermally grown c-cut single crystal. For the EPR measurements, a
Yu.S. Kutin et al. / Journal of Magnetic Resonance 237 (2013) 110–114
111
part of the sample was cut along the ½1 1 20 direction. The external magnetic field was rotated in the ð1 1 2 0Þ plane. The magnetic resonance studies were done on a Bruker Elexsys 680 W-band spectrometer with the microwave frequency around 94 GHz in the temperature range of 6–50 K. EPR spectra were recorded by monitoring the electron spin echo signal. Electron-nuclear double resonance (ENDOR) measurements were performed using the standard Mims pulse sequence [18]. Radiofrequency pulses of 18 and/or 38 ls were used. The microwave p/2-pulses were 8 ns long with the time delay between the first and second pulses s = 280 ns.
A
3. Results and discussion The EPR spectrum of a hydrothermally grown ZnO crystal for the magnetic field parallel to the c axis is shown in Fig. 1. Spectra of the Mn2+ (d5, 55Mn, I = 5/2, abundance 100%) and Fe3+ (d5, 54,56,58 Fe, I = 0, abundance around 97.9%) ions at substitutional sites are easily recognized and correspond to known spin Hamiltonian parameters [7,19]. An EPR spectrum assigned to the Co2+ ion [6] was also observed at 6 K. The remaining fifteen EPR lines in Fig. 1 are grouped into three fine-structure quintets originating from three types of paramagnetic complexes, each with the electron spin S = 5/2. The paramagnetic centers are labeled C1, C2, and C3; with C1 showing the smallest fine-structure splitting and C3 showing the largest. The same spectra have previously been observed at Q-band, and the corresponding paramagnetic centers were interpreted as Fe3+–Li+ complexes [9], or as Fe3+-VO and Fe3+-VZn complexes [10]. Since it is impossible to conclusively determine the chemical nature of the charge compensators by means of conventional EPR, ENDOR spectra were recorded in the EPR signals of the three centers. The ENDOR data are shown in Figs. 2 and 3. Fig. 2 shows ENDOR spectra recorded in the MS = 5/2 M MS = 3/2, 3/2 M 1/2, and 1/2 M 3/2 fine-structure EPR transitions of the C1 and C2 centers. The spectra consist of two signals with a fixed spacing of about 0.88 MHz for C1 and 0.64 MHz for C2. Shifts in the positions of the lines with an increase in the magnetic field are consistent with the 7Li (I = 3/2, abundance 92.4%) gyromagnetic ratio. Fig. 3 shows ENDOR spectra recorded in the three transitions of the C3 center. Compared to the spectra in Fig. 2, each line is further split into a quadrupole triplet with a spacing of 58 kHz. The
Fig. 1. EPR spectrum of a hydrothermally grown ZnO single crystal for B||c. T = 20 K, frequency is around 93.9 GHz. The five high-intensity lines correspond to the trigonal Fe3+ impurity. The thirty-line spectrum around g = 2 originates from Mn2+. Three fine-structure quintets related to the charge-compensated Fe3+ centers labeled C1, C2, and C3 are indicated.
B
Fig. 2. ENDOR transitions of the 7Li nuclei recorded in three fine-structure EPR signals of the (A) C1 and (B) C2 centers for B||c. The corresponding EPR transitions with DMS = ± 1 are indicated in the plots. The magnetic field values are (left to right) (A) 3222, 3457, 3570 mT for C1 and (B) 2992, 3182 and 3506 mT for C2. The radiofrequency pulses in the Mims sequence were 18 ls, T = 20 K.
appearance of multiple lines can be explained by the fact that the magnetic field deviates slightly from the B||c direction. Therefore, EPR lines from magnetically inequivalent positions do not entirely coincide, and each EPR signal produces its own pair of quadrupole triplets. The resulting ENDOR signal is a superposition of several triplets. The HF splitting in the C3 ENDOR spectra is about 1.26 MHz.
Fig. 3. ENDOR transitions of the 7Li nuclei recorded in three fine-structure EPR signals of the C3 center for B||c at B = 2803, 3080 and 3606 mT. The corresponding EPR transitions with DMS = ± 1 are indicated in the plots. The radiofrequency pulses were 38 ls, T = 20 K and (for the bottom spectrum) 15 K.
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The EPR and ENDOR data for B||c were analyzed using a Hamiltonian of the form m 2 H ¼ RBm k Ok þ g lBSz g N lN BI z þ Azz Sz Iz þ F½I z 1=3IðI þ 1Þ:
ð1Þ
The first term represents the zero-field splitting and has been shown to have the Ci symmetry [10]. The second and third terms stand for the electron and nuclear Zeeman interactions; the nuclear Larmor frequency can be written as fL = gNlNB/h. The fourth term is the diagonal part of the hyperfine interaction (second-order corrections proportional to A2/glB are insignificant and not considered here). The quadrupole interaction is represented by the last term. To understand the quadrupole splitting in the ENDOR spectra we will simply consider F = 3eQVZZ/4I(2I 1)h, although, strictly speaking, this is only applicable when the principal Z-axis of the tensor Vij is along the hexagonal axis of the crystal. The quadrupole splitting of the ENDOR lines in Fig. 3 into triplets implies that the nuclear spin of the system is I = 3/2. Since the fine structure of the EPR spectra consists of five line, the electron spin is S = 5/2. The energy level diagram shown in Fig. 4 successively takes into account Hamiltonian terms of decreasing magnitude. Only the MS = 5/2 and MS = 3/2 manifolds are considered. The diagram is valid for the case when the nuclear Zeeman interaction is stronger than the hyperfine interaction (which is often the case for measurements at W-band), and A > 0. Solid and dashed arrows indicate allowed EPR (DmI = 0, DMS = ±1) and ENDOR (DmI = ±1, DMS = 0) transitions, respectively. No HF structure is resolved in the EPR spectra, which means that the HF interaction constant is small compared to the linewidth. The 8 ns microwave pulses used in the ENDOR measurements have a frequency spectrum that is broad enough to excite all electron spins within the EPR linewidth. Therefore, all four allowed
Fig. 4. Energy level diagram for the spin system with S = 5/2, I = 3/2 showing only the MS = 5/2 and MS = 3/2 manifolds. The allowed EPR (DmI = 0, DMS = ± 1) and ENDOR (DmI = ± 1, DMS = 0) transitions are shown with solid and dashed arrows, respectively. Positions of the corresponding ENDOR lines are indicated. The resulting ENDOR spectrum should consist of two quadrupole triplets with a spacing of A between them.
EPR transitions (shown in Fig. 4) are exited in the Mims ENDOR experiments simultaneously, and all six allowed nuclear transitions should occur in the ENDOR spectrum. Thus, the resulting ENDOR spectrum recorded in the MS = 5/2 M MS = 3/2 EPR transition should consist of two triplets at m = fL + 5/2A and m = fL + 3/2A, with the quadrupole splitting of 2F. The triplets are placed symmetrically around the fL + 2A frequency and the spacing between the triplets is equal to the HF interaction constant A. Frequencies of the ENDOR transitions recorded in the remaining four fine-structure EPR lines can be obtained in a similar way (more details are given in Appendix A). Therefore, it is possible to determine the HF interaction constant, nuclear gyromagnetic ratio (c = 2pfL/B) and quadrupole splitting from an ENDOR spectrum recorded in any of the five EPR transitions, provided that the initial and final states are known. Spin system parameters calculated from ENDOR data in Figs. 2 and 3 are collected in Table 1. The gyromagnetic ratio values calculated from the positions of the ENDOR lines correspond to the 7Li nuclei for all three centers: c(7Li) = 1.0396 108 rad/s T. The three centers differ in the hyperfine splitting for B||c: 0.88, 0.64, and 1.26 MHz for C1, C2, and C3, respectively. The observed hyperfine structure constants are much smaller than 1% of the free ion value of 364.9 MHz for 7Li [20]. Apart from the 7Li transitions shown in Figs. 2 and 3, no other signals were observed in the ENDOR spectra. Thus, all three EPR centers under investigation are Fe3+–Li+ complexes corresponding to three different relative placements of the substitutional Fe and Li impurities in the ZnO hexagonal lattice. For an arbitrary orientation of the magnetic field, each fine-structure EPR line of C1 is split into six. These six lines only coincide when the magnetic field is along the c axis (as shown in Fig. 1). Thus, there are six magnetically inequivalent orientations of the iron–lithium bond direction for the C1 complex. For the C2 and C3 complexes there are, respectively, twelve and six. Altogether the EPR spectrum of the charge compensated Fe centers consists of 120 lines. In a model proposed [9] for the twelve-fold configuration of the Fe–Li complex (C2), both impurity ions substitute Zn at the nearest sites in the same basal plane. The two six-fold configurations (C1 and C3) were interpreted as Fe in an axial cationic site with Li in one of the nearest basal plane sites, and vice versa. The obtained ENDOR data provide a direct confirmation that Li acts as a charge compensator in the low-symmetry Fe-related centers in ZnO. For B||c, the quadrupole splitting of ENDOR lines into triplets is resolved for the C3 center (see Fig. 3). The splitting is around 58 kHz. For C1 and C2, however, no quadrupole structure is resolved (see Fig. 2). The full width at half height of the ENDOR lines is about 30 kHz for C2 and 60 kHz for C1. The values were obtained using the same radiofrequency pulse length of 38 ls in the Mims sequence. Fig. 5A shows the low-field part of the EPR spectrum for 0 0. EPR lines from all three configurations (C1, C2, and C3) B||½1 1 of the Fe–Li complex are present in the chosen fragment. ENDOR signals of the 7Li nuclei recorded in the indicated EPR lines are shown in Fig. 5B and C. Two EPR lines of C2 in Fig. 5A correspond to the MS = 3/2 M MS = 5/2 transition of two magnetically inequivalent orientations of the complex. ENDOR spectra recorded in these two lines (Fig. 5C) differ in the hyperfine splitting: 1.10 and 0.91 MHz. This is due to the fact that the HF interaction tensor of C2 has a symmetry lower than axial. The quadrupole triplets are placed symmetrically around the frequency fL 2A. Therefore, the spectrum with the HF splitting of 1.10 MHz appears at lower frequencies than the spectrum with the HF splitting of 0.91 MHz. The quadrupole splitting of about 19 kHz is clearly resolved in one of the spectra. The ENDOR spectrum in Fig. 5B was recorded in the EPR transition of the C1 complex. The ENDOR signals show no quadru-
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Table 1 Nuclear gyromagnetic ratios and hyperfine interaction constants calculated from the ENDOR spectra (B||c) recorded in the five fine-structure transitions of the three complexes. For the C3 complex, the quadrupole splitting is also measured in four transitions. In the C1 and C2 ENDOR lines the quadrupole splitting is not resolved. The uncertainties in the gyromagnetic ratios are around 0.001 108 rad/s T and the uncertainties in the HF and quadrupole splitting are around 5 kHz. EPR transition (DMS = ± 1)
c (C1), 108 (rad/s T)
Azz (C1), (MHz)
c (C2), 108 (rad/s T)
Azz (C2), (MHz)
c (C3), 108 (rad/s T)
Azz (C3), (MHz)
2F (C3), (kHz)
5/2 M 3/2 3/2 M 1/2 1/2 M 1/2 1/2 M 3/2 3/2 M 5/2
1.040 1.040 1.041 1.040 1.041
0.88 0.88 0.85 0.89 0.91
1.039 1.039 1.040 1.039 1.040
0.63 0.64 0.65 0.65 0.65
1.040 1.039 – 1.039 1.040
1.27 1.27 – 1.23 1.25
57 55 – 58 60
We consider the largest observed quadrupole splitting of 58 kHz for the C3 center and assume for simplicity
A
2F ¼ 3eQV ZZ =2Ið2I 1Þh ¼ 58 kHz:
B
ð2Þ
Since I(7Li) = 3/2, the eQVZZ/h value is roughly 116 kHz. The nuclear quadrupole moment Q(7Li) = 4.06 1030 m2 [22]. From this we estimate the electric field gradient at the 7Li nuclei: VZZ 1.2 1020 V/m2. The value is around 5 times smaller, compared to the electric field gradient of 6.59 1020 V/m2 at the 67Zn sites [23]. For Li within the C1 and C2 configurations of the Fe–Li complex, the electric field gradients are even weaker, since the quadrupole splitting in the ENDOR spectra is smaller. This reduction can be explained by the fact that the Fe3+–Li+ complexes create a local electric field gradient, in addition to the internal gradient of ZnO. The resulting electric field gradient value should depend on the positions of the Fe3+ and Li+ ions in the lattice and can also be manipulated by the introduction of other elements (e.g., Na) instead of lithium into ZnO.
C
4. Conclusion
Fig. 5. (A) Fragment of the EPR spectrum of Fe–Li complexes in ZnO for B||½1 1 0 0, T = 20 K. (B) ENDOR transitions of 7Li recorded in the EPR signal of C1. (C) ENDOR transitions of 7Li recorded in the EPR signals of C2 corresponding to the 3/2 M 5/2 transition of two magnetically inequivalent orientations of the C2 complex. The triplets are placed symmetrically around the fL 2A frequency; the difference in the HF splitting is indicated. In the C3 EPR line no ENDOR transitions were observed.
0 0. The differences in the quadrupole pole splitting for B||½1 1 structures of C1, C2 and C3 for both B||c and B||½1 1 0 0 imply that the electric-field gradient at the 7Li nuclei is determined by the particular arrangement of the Fe–Li complex. The distortion of the ZnO crystal lattice caused by substitution of two adjacent zinc ions by Fe3+ and Li+ depends on a relative placement of the two impurity ions in the lattice. For B||c the quadrupole triplets of C2 are not resolved (Fig. 2), with a full width at half height of the lines around 30 kHz. For B||[½1 1 0 0, the splitting is resolved and is about 19 kHz. In the case of the axial symmetry of the electric field gradient tensor Vij with its principal Z-axis along the hexagonal c axis of the crystal, the quadrupole splitting for B||c is twice as large as for B\c. The obtained ENDOR data show that this is not the case for the Fe–Li complexes. Therefore, in order to calculate the precise values of the electric-field gradient on the 7Li nuclei, the full quadrupole Hamiltonian should be considered [21] and a full angular dependence of the ENDOR spectra is needed to determine the Hamiltonian parameters. This is beyond the scope of the present work. However, the electric-field gradients can still be roughly estimated.
Chemical nature of unknown impurities in semiconductor materials can be identified by means of ENDOR spectroscopy and other modern multiple-resonance techniques. A detailed study of the three charge-compensated Fe3+ centers in ZnO shows presence of the 7Li signals in all ENDOR spectra. Thus, formation of Fe3+–Li+ complexes is confirmed, and the chemical nature of the paramagnetic centers is unambiguously established. The previously unresolved hyperfine interactions are shown to be significantly anisotropic. The electric field gradients at the 7Li nuclei were estimated from the quadrupole splitting to be at least 5–6 times smaller than the gradient at the regular Zn sites. The measured hyperfine and quadrupole interaction values can be used in the development of detailed theoretical models of the three complexes. Acknowledgments The experiments were carried out at the Federal Center of Shared Facilities of Kazan Federal University. The authors would like to thank Prof. Pavel Baranov for providing samples and stimulating discussion. Appendix A In the main text we omitted some details of calculation of the spin system parameters collected in Table 1. Due to the Boltzmann distribution of populations, at T = 6 K a fine-structure EPR line of the lowest intensity corresponds to the MS = 3/2 M MS = 5/2 transition. In the EPR spectrum of the charge-compensated Fe centers this line is the leftmost for the C1 center and rightmost for C2 and C3. The rightmost line of the C1 spectrum corresponds, therefore, to the MS = 5/2 M MS = 3/2 transition. This agrees with the
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results of the previous study [10]. The assignment of the MS values to the EPR transitions allows us to determine the signs of the hyperfine interaction constants (positive for C1 and C3, negative for C2). As shown in Fig. 4 for MS = 5/2 M MS = 3/2, the allowed nuclear transitions in the MS = 3/2 manifold will appear at mENDOR1 = fL + 3/2A 2F, mENDOR2 = fL + 3/2A, and mENDOR3 = fL + 3/ 2A + 2F. In the MS = 5/2 manifold the frequencies are: mENDOR4 = fL + 5/2A 2F, mENDOR5 = fL + 5/2A, and mENDOR6 = fL + 5/2A + 2F. From the same calculations applied to the other MS manifolds we obtain the expressions for the ENDOR frequencies in all five fine-structure EPR transitions. For MS = 5/2 M MS = 3/2, 3/2 M 1/2, 1/2 M 1/2, 1/2 M 3/2, and 3/2 M 5/2 the centers of the ENDOR spectra will be at fL + 2A, fL + A, fL, fL A, and fL 2A, respectively. The hyperfine splitting between the two triplets is A in all five cases, and the quadrupole spitting within the triplets is 2F. References [1] C. Klingshirn, ZnO: from basics towards applications, Phys. Status Solidi B 244 (2007) 3027–3073. [2] Zinc oxide materials for electronic and optoelectronic device applications, in: P. Capper, S. Kasap, A. Willoughby (Eds.), Wiley Series in Materials for Electronic and Optoelectronic Applications, John Wiley and Sons Ltd., 2011. [3] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Zener model description of ferromagnetism in zinc-blended magnetic semiconductors, Science 287 (2000) 1019–1022. [4] D.P. Norton, M.E. Overberg, S.J. Pearton, K. Pruessner, J.D. Budai, L.A. Boatner, M.F. Chisholm, J.S. Lee, Z.G. Khim, Y.D. Park, R.G. Wilson, Ferromagnetism in cobalt-implanted ZnO, Appl. Phys. Lett. 83 (2003) 5488–5490. [5] B.K. Meyer, H. Alves, D.M. Hofmann, W. Kriegseis, D. Forster, F. Bertram, J. Christen, A. Hoffmann, M. Straßburg, M. Dworzak, U. Haboeck, A.V. Rodina, Bound exciton and donor–acceptor pair recombinations in ZnO, Phys. Status Solidi B 241 (2004) 231–260. [6] Y. Jiang, N.C. Giles, L.E. Halliburton, Persistent photoinduced changes in charge states of transition-metal donors in hydrothermally grown ZnO crystals, J. Appl. Phys. 101 (2007) 093706.
[7] W.M. Walsh Jr., L.W. Rupp Jr., Paramagnetic resonance of trivalent Fe57 in zinc oxide, Phys. Rev. 126 (1962) 952–955. [8] A. Hausmann, The cubic field parameter of 6S52 ions in zinc oxide crystals, Solid State Commun. 6 (1968) 457–459. [9] W.C. Holton, M. de Wit, T.L. Estle, B. Dischler, J. Schneider, Paramagnetic resonance of Fe–Cu, Fe–Ag, and Fe–Li associates in II–VI compounds, Phys. Rev. 169 (1968) 359–372. [10] D.V. Azamat, M. Fanciulli, The structure of charge-compensated Fe3+ ions in ZnO, Physica B 401–402 (2007) 382–385. [11] D.V. Azamat, J. Debus, D.R. Yakovlev, V.Y. Ivanov, M. Godlewski, M. Fanciulli, M. Bayer, Photo-EPR and magneto-optical spectroscopy of iron centres in ZnO, Phys. Status Solidi B 247 (2010) 1517–1520. [12] A. Debernardi, M. Fanciulli, Ab initio study of magnetic interaction of Fe doped ZnO with intrinsic vacancies, Appl. Phys. Lett. 90 (2007) 212510. [13] N. Sakagami, M. Yamashita, T. Sekiguchi, S. Miyashita, K. Obara, T. Shishido, Variation of electrical properties on growth sectors of ZnO single crystals, J. Cryst. Growth 229 (2001) 98–103. [14] D.M. Hofmann, A. Hofstaetter, F. Leiter, H. Zhou, F. Henecker, B.K. Meyer, S.B. Orlinskii, J. Schmidt, P.G. Baranov, Hydrogen: a relevant shallow donor in zinc oxide, Phys. Rev. Lett. 88 (2002) 045504. [15] S.B. Orlinskii, J. Schmidt, P.G. Baranov, D.M. Hofmann, C. de Mello Donegá, A. Meijerink, Probing the wave function of shallow Li and Na donors in ZnO nanoparticles, Phys. Rev. Lett. 92 (2004) 047603. [16] S.B. Orlinskii, J. Schmidt, P.G. Baranov, V. Lorrmann, I. Riedel, D. Rauh, V. Dyakonov, Identification of shallow Al donors in Al-doped ZnO nanocrystals: EPR and ENDOR spectroscopy, Phys. Rev. B 77 (2008) 115334. [17] F. Herklotz, E.V. Lavrov, J. Weber, G.V. Mamin, Y.S. Kutin, M.A. Volodin, S.B. Orlinskii, Identification of shallow Al donors in ZnO, Phys. Status Solidi B 248 (2011) 1532–1537. [18] W.B. Mims, Pulsed endor experiments, Proc. R. Soc. London, Ser. A 283 (1965) 452–457. [19] A. Hausmann, H. Huppertz, Paramagnetic resonance of ZnO:Mn++ single crystals, J. Phys. Chem. Solids 29 (1968) 1369–1375. [20] J.R. Morton, K.F. Preston, Atomic parameters for paramagnetic resonance data, J. Magn. Reson. 30 (1978) 577–582. [21] A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford, 1985. [22] N.J. Stone, Table of nuclear magnetic dipole and electric quadrupole moments, At. Data Nucl. Data Tables 90 (2005) 75–176. [23] D. Reiser, J. Blömker, G. Denninger, J. Schneider, A magnetic double-resonance investigation of the quadrupole interaction in ZnO single crystals, Solid State Commun. 102 (1997) 359–363.
Contents lists available at ScienceDirect
Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr
Identification of Fe3+–Li+ complexes in ZnO by means of high-frequency EPR/ENDOR spectroscopy Yu.S. Kutin ⇑, G.V. Mamin, S.B. Orlinskii Kazan Federal University, Institute of Physics, Kremlevskaya str. 18, 420008 Kazan, Russia
a r t i c l e
i n f o
Article history: Received 25 July 2013 Revised 23 September 2013 Available online 11 October 2013 Keywords: High-frequency EPR ENDOR W-band ZnO Iron Lithium Complex Charge-compensated centers Quadrupole interaction
a b s t r a c t Theoretical prediction of a high Curie temperature in ZnO doped with Mn, Fe, and other transition metals has stimulated the investigation of these materials by many research groups. Although charge-compensated Fe3+ centers in ZnO:Fe have been observed by means of EPR and have been known for decades, conclusions on the chemical nature of these defects are still contradictory. Originally, these centers were treated as Fe3+–Li+ complexes with both ions occupying adjacent cationic sites. Recently, however, the centers were interpreted as a substitutional Fe3+ ion with a vacancy at an adjacent zinc or oxygen site (Fe-VZn or Fe-VO). In order to determine the chemical nature of the impurity associated with Fe3+, electron-nuclear double resonance (ENDOR) spectroscopy was used. ENDOR measurements reveal NMR transitions corresponding to nuclei with g-factor gN = 2.171 and spin I = 3/2. This unambiguously shows presence of Li as a charge compensator and also resolves contradictions with the theoretical prediction of the Fe-VO formation energy. The electric field gradients at the 7Li nuclei (within the Fe3+– Li+ complexes) were estimated to be significantly lower than the gradient at undistorted Zn sites. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction ZnO is a II–VI semiconductor with a wide direct band gap of about 3.3 eV at room temperature. Due to its unique optical, electrical, and mechanical properties, it has recently regained a lot of attention as a material for UV light-emitting diodes, a transparent conducting oxide for photovoltaic applications, a radiation hard material, etc. [1,2]. Much effort is also made towards developing diluted magnetic semiconductors based on a theoretically predicted high Curie temperature in ZnO doped with high concentrations of transition metals (TM) [3,4]. Nominally undoped ZnO crystals often contain TM ions, which incorporate into the material at substitutional sites during the crystal growth process. Electron paramagnetic resonance (EPR) has been widely used to study various impurities in ZnO [5,6]. In ZnO crystals containing Fe, EPR experiments reveal the spectrum of the trigonal FeZn center [7,8], as well as multiple additional signals assigned to charge-compensated Fe3+ [7,9–11]. However, conclusions on the chemical nature of the charge-compensated Fe centers are contradictory. The older work [9] treats the centers as Fe–Li complexes, whereas authors of a more recent research [10] interpret the centers as an Fe3+ ion with a vacancy at an adjacent zinc or oxygen site (Fe-VZn, Fe-VO). As noted by the authors,
the latter model contradicts the theoretical prediction [12] that formation of the Fe-VO complex is not energetically favored. The hydrothermal growth method is commonly used for ZnO, since it allows for growing large single crystals. However, these crystals inevitably contain significant amounts of Li [13], in addition to TM ions. Therefore, establishing the real nature of the complex will contribute to a better understanding of incorporation of Fe and Li into the ZnO lattice and should resolve (or confirm) contradictions with the theoretical predictions concerning the FeVO formation energy. Since no hyperfine (HF) splitting is observed in the EPR spectra of the charge-compensated Fe centers, it is not possible to identify the chemical nature of the complex by means of conventional EPR. It should be supplemented with modern multiple resonance techniques. Electron-nuclear double resonance (ENDOR) has been successfully used to investigate numerous defects in ZnO single- and nanocrystals [14–17]. This method reveals interactions of the electrons with surrounding magnetic nuclei. Therefore, if Fe3+ ions form complexes with other elements (e.g., Li), this interaction should give rise to signals in ENDOR spectra that will correspond to the nuclear g-factor and spin of the charge compensating impurity.
2. Experimental details ⇑ Corresponding author. Fax: +7 843 2924448. E-mail address: [email protected] (Yu.S. Kutin). 1090-7807/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmr.2013.09.014
ZnO used in this investigation was a nominally undoped hydrothermally grown c-cut single crystal. For the EPR measurements, a
Yu.S. Kutin et al. / Journal of Magnetic Resonance 237 (2013) 110–114
111
part of the sample was cut along the ½1 1 20 direction. The external magnetic field was rotated in the ð1 1 2 0Þ plane. The magnetic resonance studies were done on a Bruker Elexsys 680 W-band spectrometer with the microwave frequency around 94 GHz in the temperature range of 6–50 K. EPR spectra were recorded by monitoring the electron spin echo signal. Electron-nuclear double resonance (ENDOR) measurements were performed using the standard Mims pulse sequence [18]. Radiofrequency pulses of 18 and/or 38 ls were used. The microwave p/2-pulses were 8 ns long with the time delay between the first and second pulses s = 280 ns.
A
3. Results and discussion The EPR spectrum of a hydrothermally grown ZnO crystal for the magnetic field parallel to the c axis is shown in Fig. 1. Spectra of the Mn2+ (d5, 55Mn, I = 5/2, abundance 100%) and Fe3+ (d5, 54,56,58 Fe, I = 0, abundance around 97.9%) ions at substitutional sites are easily recognized and correspond to known spin Hamiltonian parameters [7,19]. An EPR spectrum assigned to the Co2+ ion [6] was also observed at 6 K. The remaining fifteen EPR lines in Fig. 1 are grouped into three fine-structure quintets originating from three types of paramagnetic complexes, each with the electron spin S = 5/2. The paramagnetic centers are labeled C1, C2, and C3; with C1 showing the smallest fine-structure splitting and C3 showing the largest. The same spectra have previously been observed at Q-band, and the corresponding paramagnetic centers were interpreted as Fe3+–Li+ complexes [9], or as Fe3+-VO and Fe3+-VZn complexes [10]. Since it is impossible to conclusively determine the chemical nature of the charge compensators by means of conventional EPR, ENDOR spectra were recorded in the EPR signals of the three centers. The ENDOR data are shown in Figs. 2 and 3. Fig. 2 shows ENDOR spectra recorded in the MS = 5/2 M MS = 3/2, 3/2 M 1/2, and 1/2 M 3/2 fine-structure EPR transitions of the C1 and C2 centers. The spectra consist of two signals with a fixed spacing of about 0.88 MHz for C1 and 0.64 MHz for C2. Shifts in the positions of the lines with an increase in the magnetic field are consistent with the 7Li (I = 3/2, abundance 92.4%) gyromagnetic ratio. Fig. 3 shows ENDOR spectra recorded in the three transitions of the C3 center. Compared to the spectra in Fig. 2, each line is further split into a quadrupole triplet with a spacing of 58 kHz. The
Fig. 1. EPR spectrum of a hydrothermally grown ZnO single crystal for B||c. T = 20 K, frequency is around 93.9 GHz. The five high-intensity lines correspond to the trigonal Fe3+ impurity. The thirty-line spectrum around g = 2 originates from Mn2+. Three fine-structure quintets related to the charge-compensated Fe3+ centers labeled C1, C2, and C3 are indicated.
B
Fig. 2. ENDOR transitions of the 7Li nuclei recorded in three fine-structure EPR signals of the (A) C1 and (B) C2 centers for B||c. The corresponding EPR transitions with DMS = ± 1 are indicated in the plots. The magnetic field values are (left to right) (A) 3222, 3457, 3570 mT for C1 and (B) 2992, 3182 and 3506 mT for C2. The radiofrequency pulses in the Mims sequence were 18 ls, T = 20 K.
appearance of multiple lines can be explained by the fact that the magnetic field deviates slightly from the B||c direction. Therefore, EPR lines from magnetically inequivalent positions do not entirely coincide, and each EPR signal produces its own pair of quadrupole triplets. The resulting ENDOR signal is a superposition of several triplets. The HF splitting in the C3 ENDOR spectra is about 1.26 MHz.
Fig. 3. ENDOR transitions of the 7Li nuclei recorded in three fine-structure EPR signals of the C3 center for B||c at B = 2803, 3080 and 3606 mT. The corresponding EPR transitions with DMS = ± 1 are indicated in the plots. The radiofrequency pulses were 38 ls, T = 20 K and (for the bottom spectrum) 15 K.
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The EPR and ENDOR data for B||c were analyzed using a Hamiltonian of the form m 2 H ¼ RBm k Ok þ g lBSz g N lN BI z þ Azz Sz Iz þ F½I z 1=3IðI þ 1Þ:
ð1Þ
The first term represents the zero-field splitting and has been shown to have the Ci symmetry [10]. The second and third terms stand for the electron and nuclear Zeeman interactions; the nuclear Larmor frequency can be written as fL = gNlNB/h. The fourth term is the diagonal part of the hyperfine interaction (second-order corrections proportional to A2/glB are insignificant and not considered here). The quadrupole interaction is represented by the last term. To understand the quadrupole splitting in the ENDOR spectra we will simply consider F = 3eQVZZ/4I(2I 1)h, although, strictly speaking, this is only applicable when the principal Z-axis of the tensor Vij is along the hexagonal axis of the crystal. The quadrupole splitting of the ENDOR lines in Fig. 3 into triplets implies that the nuclear spin of the system is I = 3/2. Since the fine structure of the EPR spectra consists of five line, the electron spin is S = 5/2. The energy level diagram shown in Fig. 4 successively takes into account Hamiltonian terms of decreasing magnitude. Only the MS = 5/2 and MS = 3/2 manifolds are considered. The diagram is valid for the case when the nuclear Zeeman interaction is stronger than the hyperfine interaction (which is often the case for measurements at W-band), and A > 0. Solid and dashed arrows indicate allowed EPR (DmI = 0, DMS = ±1) and ENDOR (DmI = ±1, DMS = 0) transitions, respectively. No HF structure is resolved in the EPR spectra, which means that the HF interaction constant is small compared to the linewidth. The 8 ns microwave pulses used in the ENDOR measurements have a frequency spectrum that is broad enough to excite all electron spins within the EPR linewidth. Therefore, all four allowed
Fig. 4. Energy level diagram for the spin system with S = 5/2, I = 3/2 showing only the MS = 5/2 and MS = 3/2 manifolds. The allowed EPR (DmI = 0, DMS = ± 1) and ENDOR (DmI = ± 1, DMS = 0) transitions are shown with solid and dashed arrows, respectively. Positions of the corresponding ENDOR lines are indicated. The resulting ENDOR spectrum should consist of two quadrupole triplets with a spacing of A between them.
EPR transitions (shown in Fig. 4) are exited in the Mims ENDOR experiments simultaneously, and all six allowed nuclear transitions should occur in the ENDOR spectrum. Thus, the resulting ENDOR spectrum recorded in the MS = 5/2 M MS = 3/2 EPR transition should consist of two triplets at m = fL + 5/2A and m = fL + 3/2A, with the quadrupole splitting of 2F. The triplets are placed symmetrically around the fL + 2A frequency and the spacing between the triplets is equal to the HF interaction constant A. Frequencies of the ENDOR transitions recorded in the remaining four fine-structure EPR lines can be obtained in a similar way (more details are given in Appendix A). Therefore, it is possible to determine the HF interaction constant, nuclear gyromagnetic ratio (c = 2pfL/B) and quadrupole splitting from an ENDOR spectrum recorded in any of the five EPR transitions, provided that the initial and final states are known. Spin system parameters calculated from ENDOR data in Figs. 2 and 3 are collected in Table 1. The gyromagnetic ratio values calculated from the positions of the ENDOR lines correspond to the 7Li nuclei for all three centers: c(7Li) = 1.0396 108 rad/s T. The three centers differ in the hyperfine splitting for B||c: 0.88, 0.64, and 1.26 MHz for C1, C2, and C3, respectively. The observed hyperfine structure constants are much smaller than 1% of the free ion value of 364.9 MHz for 7Li [20]. Apart from the 7Li transitions shown in Figs. 2 and 3, no other signals were observed in the ENDOR spectra. Thus, all three EPR centers under investigation are Fe3+–Li+ complexes corresponding to three different relative placements of the substitutional Fe and Li impurities in the ZnO hexagonal lattice. For an arbitrary orientation of the magnetic field, each fine-structure EPR line of C1 is split into six. These six lines only coincide when the magnetic field is along the c axis (as shown in Fig. 1). Thus, there are six magnetically inequivalent orientations of the iron–lithium bond direction for the C1 complex. For the C2 and C3 complexes there are, respectively, twelve and six. Altogether the EPR spectrum of the charge compensated Fe centers consists of 120 lines. In a model proposed [9] for the twelve-fold configuration of the Fe–Li complex (C2), both impurity ions substitute Zn at the nearest sites in the same basal plane. The two six-fold configurations (C1 and C3) were interpreted as Fe in an axial cationic site with Li in one of the nearest basal plane sites, and vice versa. The obtained ENDOR data provide a direct confirmation that Li acts as a charge compensator in the low-symmetry Fe-related centers in ZnO. For B||c, the quadrupole splitting of ENDOR lines into triplets is resolved for the C3 center (see Fig. 3). The splitting is around 58 kHz. For C1 and C2, however, no quadrupole structure is resolved (see Fig. 2). The full width at half height of the ENDOR lines is about 30 kHz for C2 and 60 kHz for C1. The values were obtained using the same radiofrequency pulse length of 38 ls in the Mims sequence. Fig. 5A shows the low-field part of the EPR spectrum for 0 0. EPR lines from all three configurations (C1, C2, and C3) B||½1 1 of the Fe–Li complex are present in the chosen fragment. ENDOR signals of the 7Li nuclei recorded in the indicated EPR lines are shown in Fig. 5B and C. Two EPR lines of C2 in Fig. 5A correspond to the MS = 3/2 M MS = 5/2 transition of two magnetically inequivalent orientations of the complex. ENDOR spectra recorded in these two lines (Fig. 5C) differ in the hyperfine splitting: 1.10 and 0.91 MHz. This is due to the fact that the HF interaction tensor of C2 has a symmetry lower than axial. The quadrupole triplets are placed symmetrically around the frequency fL 2A. Therefore, the spectrum with the HF splitting of 1.10 MHz appears at lower frequencies than the spectrum with the HF splitting of 0.91 MHz. The quadrupole splitting of about 19 kHz is clearly resolved in one of the spectra. The ENDOR spectrum in Fig. 5B was recorded in the EPR transition of the C1 complex. The ENDOR signals show no quadru-
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Table 1 Nuclear gyromagnetic ratios and hyperfine interaction constants calculated from the ENDOR spectra (B||c) recorded in the five fine-structure transitions of the three complexes. For the C3 complex, the quadrupole splitting is also measured in four transitions. In the C1 and C2 ENDOR lines the quadrupole splitting is not resolved. The uncertainties in the gyromagnetic ratios are around 0.001 108 rad/s T and the uncertainties in the HF and quadrupole splitting are around 5 kHz. EPR transition (DMS = ± 1)
c (C1), 108 (rad/s T)
Azz (C1), (MHz)
c (C2), 108 (rad/s T)
Azz (C2), (MHz)
c (C3), 108 (rad/s T)
Azz (C3), (MHz)
2F (C3), (kHz)
5/2 M 3/2 3/2 M 1/2 1/2 M 1/2 1/2 M 3/2 3/2 M 5/2
1.040 1.040 1.041 1.040 1.041
0.88 0.88 0.85 0.89 0.91
1.039 1.039 1.040 1.039 1.040
0.63 0.64 0.65 0.65 0.65
1.040 1.039 – 1.039 1.040
1.27 1.27 – 1.23 1.25
57 55 – 58 60
We consider the largest observed quadrupole splitting of 58 kHz for the C3 center and assume for simplicity
A
2F ¼ 3eQV ZZ =2Ið2I 1Þh ¼ 58 kHz:
B
ð2Þ
Since I(7Li) = 3/2, the eQVZZ/h value is roughly 116 kHz. The nuclear quadrupole moment Q(7Li) = 4.06 1030 m2 [22]. From this we estimate the electric field gradient at the 7Li nuclei: VZZ 1.2 1020 V/m2. The value is around 5 times smaller, compared to the electric field gradient of 6.59 1020 V/m2 at the 67Zn sites [23]. For Li within the C1 and C2 configurations of the Fe–Li complex, the electric field gradients are even weaker, since the quadrupole splitting in the ENDOR spectra is smaller. This reduction can be explained by the fact that the Fe3+–Li+ complexes create a local electric field gradient, in addition to the internal gradient of ZnO. The resulting electric field gradient value should depend on the positions of the Fe3+ and Li+ ions in the lattice and can also be manipulated by the introduction of other elements (e.g., Na) instead of lithium into ZnO.
C
4. Conclusion
Fig. 5. (A) Fragment of the EPR spectrum of Fe–Li complexes in ZnO for B||½1 1 0 0, T = 20 K. (B) ENDOR transitions of 7Li recorded in the EPR signal of C1. (C) ENDOR transitions of 7Li recorded in the EPR signals of C2 corresponding to the 3/2 M 5/2 transition of two magnetically inequivalent orientations of the C2 complex. The triplets are placed symmetrically around the fL 2A frequency; the difference in the HF splitting is indicated. In the C3 EPR line no ENDOR transitions were observed.
0 0. The differences in the quadrupole pole splitting for B||½1 1 structures of C1, C2 and C3 for both B||c and B||½1 1 0 0 imply that the electric-field gradient at the 7Li nuclei is determined by the particular arrangement of the Fe–Li complex. The distortion of the ZnO crystal lattice caused by substitution of two adjacent zinc ions by Fe3+ and Li+ depends on a relative placement of the two impurity ions in the lattice. For B||c the quadrupole triplets of C2 are not resolved (Fig. 2), with a full width at half height of the lines around 30 kHz. For B||[½1 1 0 0, the splitting is resolved and is about 19 kHz. In the case of the axial symmetry of the electric field gradient tensor Vij with its principal Z-axis along the hexagonal c axis of the crystal, the quadrupole splitting for B||c is twice as large as for B\c. The obtained ENDOR data show that this is not the case for the Fe–Li complexes. Therefore, in order to calculate the precise values of the electric-field gradient on the 7Li nuclei, the full quadrupole Hamiltonian should be considered [21] and a full angular dependence of the ENDOR spectra is needed to determine the Hamiltonian parameters. This is beyond the scope of the present work. However, the electric-field gradients can still be roughly estimated.
Chemical nature of unknown impurities in semiconductor materials can be identified by means of ENDOR spectroscopy and other modern multiple-resonance techniques. A detailed study of the three charge-compensated Fe3+ centers in ZnO shows presence of the 7Li signals in all ENDOR spectra. Thus, formation of Fe3+–Li+ complexes is confirmed, and the chemical nature of the paramagnetic centers is unambiguously established. The previously unresolved hyperfine interactions are shown to be significantly anisotropic. The electric field gradients at the 7Li nuclei were estimated from the quadrupole splitting to be at least 5–6 times smaller than the gradient at the regular Zn sites. The measured hyperfine and quadrupole interaction values can be used in the development of detailed theoretical models of the three complexes. Acknowledgments The experiments were carried out at the Federal Center of Shared Facilities of Kazan Federal University. The authors would like to thank Prof. Pavel Baranov for providing samples and stimulating discussion. Appendix A In the main text we omitted some details of calculation of the spin system parameters collected in Table 1. Due to the Boltzmann distribution of populations, at T = 6 K a fine-structure EPR line of the lowest intensity corresponds to the MS = 3/2 M MS = 5/2 transition. In the EPR spectrum of the charge-compensated Fe centers this line is the leftmost for the C1 center and rightmost for C2 and C3. The rightmost line of the C1 spectrum corresponds, therefore, to the MS = 5/2 M MS = 3/2 transition. This agrees with the
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results of the previous study [10]. The assignment of the MS values to the EPR transitions allows us to determine the signs of the hyperfine interaction constants (positive for C1 and C3, negative for C2). As shown in Fig. 4 for MS = 5/2 M MS = 3/2, the allowed nuclear transitions in the MS = 3/2 manifold will appear at mENDOR1 = fL + 3/2A 2F, mENDOR2 = fL + 3/2A, and mENDOR3 = fL + 3/ 2A + 2F. In the MS = 5/2 manifold the frequencies are: mENDOR4 = fL + 5/2A 2F, mENDOR5 = fL + 5/2A, and mENDOR6 = fL + 5/2A + 2F. From the same calculations applied to the other MS manifolds we obtain the expressions for the ENDOR frequencies in all five fine-structure EPR transitions. For MS = 5/2 M MS = 3/2, 3/2 M 1/2, 1/2 M 1/2, 1/2 M 3/2, and 3/2 M 5/2 the centers of the ENDOR spectra will be at fL + 2A, fL + A, fL, fL A, and fL 2A, respectively. The hyperfine splitting between the two triplets is A in all five cases, and the quadrupole spitting within the triplets is 2F. References [1] C. Klingshirn, ZnO: from basics towards applications, Phys. Status Solidi B 244 (2007) 3027–3073. [2] Zinc oxide materials for electronic and optoelectronic device applications, in: P. Capper, S. Kasap, A. Willoughby (Eds.), Wiley Series in Materials for Electronic and Optoelectronic Applications, John Wiley and Sons Ltd., 2011. [3] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Zener model description of ferromagnetism in zinc-blended magnetic semiconductors, Science 287 (2000) 1019–1022. [4] D.P. Norton, M.E. Overberg, S.J. Pearton, K. Pruessner, J.D. Budai, L.A. Boatner, M.F. Chisholm, J.S. Lee, Z.G. Khim, Y.D. Park, R.G. Wilson, Ferromagnetism in cobalt-implanted ZnO, Appl. Phys. Lett. 83 (2003) 5488–5490. [5] B.K. Meyer, H. Alves, D.M. Hofmann, W. Kriegseis, D. Forster, F. Bertram, J. Christen, A. Hoffmann, M. Straßburg, M. Dworzak, U. Haboeck, A.V. Rodina, Bound exciton and donor–acceptor pair recombinations in ZnO, Phys. Status Solidi B 241 (2004) 231–260. [6] Y. Jiang, N.C. Giles, L.E. Halliburton, Persistent photoinduced changes in charge states of transition-metal donors in hydrothermally grown ZnO crystals, J. Appl. Phys. 101 (2007) 093706.
[7] W.M. Walsh Jr., L.W. Rupp Jr., Paramagnetic resonance of trivalent Fe57 in zinc oxide, Phys. Rev. 126 (1962) 952–955. [8] A. Hausmann, The cubic field parameter of 6S52 ions in zinc oxide crystals, Solid State Commun. 6 (1968) 457–459. [9] W.C. Holton, M. de Wit, T.L. Estle, B. Dischler, J. Schneider, Paramagnetic resonance of Fe–Cu, Fe–Ag, and Fe–Li associates in II–VI compounds, Phys. Rev. 169 (1968) 359–372. [10] D.V. Azamat, M. Fanciulli, The structure of charge-compensated Fe3+ ions in ZnO, Physica B 401–402 (2007) 382–385. [11] D.V. Azamat, J. Debus, D.R. Yakovlev, V.Y. Ivanov, M. Godlewski, M. Fanciulli, M. Bayer, Photo-EPR and magneto-optical spectroscopy of iron centres in ZnO, Phys. Status Solidi B 247 (2010) 1517–1520. [12] A. Debernardi, M. Fanciulli, Ab initio study of magnetic interaction of Fe doped ZnO with intrinsic vacancies, Appl. Phys. Lett. 90 (2007) 212510. [13] N. Sakagami, M. Yamashita, T. Sekiguchi, S. Miyashita, K. Obara, T. Shishido, Variation of electrical properties on growth sectors of ZnO single crystals, J. Cryst. Growth 229 (2001) 98–103. [14] D.M. Hofmann, A. Hofstaetter, F. Leiter, H. Zhou, F. Henecker, B.K. Meyer, S.B. Orlinskii, J. Schmidt, P.G. Baranov, Hydrogen: a relevant shallow donor in zinc oxide, Phys. Rev. Lett. 88 (2002) 045504. [15] S.B. Orlinskii, J. Schmidt, P.G. Baranov, D.M. Hofmann, C. de Mello Donegá, A. Meijerink, Probing the wave function of shallow Li and Na donors in ZnO nanoparticles, Phys. Rev. Lett. 92 (2004) 047603. [16] S.B. Orlinskii, J. Schmidt, P.G. Baranov, V. Lorrmann, I. Riedel, D. Rauh, V. Dyakonov, Identification of shallow Al donors in Al-doped ZnO nanocrystals: EPR and ENDOR spectroscopy, Phys. Rev. B 77 (2008) 115334. [17] F. Herklotz, E.V. Lavrov, J. Weber, G.V. Mamin, Y.S. Kutin, M.A. Volodin, S.B. Orlinskii, Identification of shallow Al donors in ZnO, Phys. Status Solidi B 248 (2011) 1532–1537. [18] W.B. Mims, Pulsed endor experiments, Proc. R. Soc. London, Ser. A 283 (1965) 452–457. [19] A. Hausmann, H. Huppertz, Paramagnetic resonance of ZnO:Mn++ single crystals, J. Phys. Chem. Solids 29 (1968) 1369–1375. [20] J.R. Morton, K.F. Preston, Atomic parameters for paramagnetic resonance data, J. Magn. Reson. 30 (1978) 577–582. [21] A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford, 1985. [22] N.J. Stone, Table of nuclear magnetic dipole and electric quadrupole moments, At. Data Nucl. Data Tables 90 (2005) 75–176. [23] D. Reiser, J. Blömker, G. Denninger, J. Schneider, A magnetic double-resonance investigation of the quadrupole interaction in ZnO single crystals, Solid State Commun. 102 (1997) 359–363.
