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Nuclear quadrupole resonance studies of transparent conducting oxides
ARTICLE IN PRESS
Solid State Nuclear Magnetic Resonance 26 (2004) 209–214
Nuclear quadrupole resonance studies of transparent conducting oxides W.W. Warren Jr.,a,* A. Rajabzadeh,a T. Olheiser,a,1 J. Liu,a,2 J. Tate, M.K. Jayaraj,a,3 and K.A. Vanajab,4 b
a Department of Physics, Oregon State University, Corvallis, OR 97331-6507, USA Department of Chemistry, Oregon State University, Corvallis, OR 97331-6507, USA
Received January 30, 2004; revised March 17, 2004
Abstract We report 63,65Cu spin–lattice relaxation rates measured by nuclear quadrupole resonance (NQR) in the delafossite compound CuYO2 and CuYO2:Ca over a temperature range from 200 to 450 K. CuYO2:Ca is a prototype transparent oxide exhibiting p-type electrical conductivity. Relaxation rates in CuYO2:Ca are enhanced by one to two orders of magnitude relative to undoped material, exhibit much stronger temperature dependence, and contain contributions from magnetic and quadrupolar relaxation mechanisms with roughly equal strengths. Relaxation in undoped CuYO2 is of purely quadrupolar origin and is attributed to interactions with lattice phonons. The main focus of this paper is the magnetic contribution to the relaxation rate in CuYO2:Ca which is attributed to the hyperfine fields of carriers. It is argued that the dynamics of the hyperfine field are dominated by the hopping rate for carrier transfers between neighboring atoms in the copper planes of the delafossite structure. Comparison of the magnetic relaxation rates with the DC conductivity permits an estimate of the carrier concentration and mobility. r 2004 Elsevier Inc. All rights reserved. Keywords: Nuclear quadrupole resonance (NQR); Transport conductors; Delafossites
I. Introduction Transparent materials exhibiting n-type electrical conductivity are well known and widely used as passive conductors in applications such as electronic displays and solar cells. The possibility of realizing transparent active devices has motivated the search for p-type materials of comparable conductivity and transparency. One class of promising materials is based on the delafossite-structure oxides of the form CuMO2 where *Corresponding author. Fax: +1-541-737-1683. E-mail address: [email protected] (W.W. Warren Jr.). 1 Present address: Department of Physics, University of Illinois, Urbana, IL 61801, USA. 2 Present address: Department of Physics, Stanford University, Stanford, CA 94305, USA. 3 Present address: Department of Physics, Cochin University of Science and Technology, Kochi 682022, India. 4 Present address: Department of Chemistry, Cochin University of Science and Technology, Kochi 682022, India. 0926-2040/$ - see front matter r 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.ssnmr.2004.03.008
M may be one of a number of trivalent elements including Al, Ga, Sc, Y or Cr [1–6]. Holes can be introduced into these materials by intrinsic defects, excess oxygen, or divalent dopants such as Ca or Mg. However, the p-type conductivities of these materials are still well below those typical of the n-type transparent materials in common use. It is therefore of considerable importance to achieve a fundamental microscopic understanding of the electronic transport processes. The series CuYO2:Ca, CuScO2:Mg, and CuCrO2:Mg are typical examples of p-type transparent conducting oxides. Polycrystalline films of CuYO2 :Ca exhibit room temperature electrical conductivities of about 1 S/cm with optical transparency averaging 40–50% over the visible range [4]. Near room temperature, the conductivity appears to be thermally activated with an activation energy of about 140 meV; below this temperature, the slope of an Arrhenius plot of the conductivity gradually decreases. The room temperature conductivities of CuScO2:Mg and CuCrO2:Mg are,
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respectively, about one and two orders of magnitude higher than that of CuYO2:Ca and the temperature dependence is progressively weaker in the order Y–Sc– Cr for the trivalent element. Measurements of the Seebeck coefficient have shown that the carriers are holes in these materials, but determination of the Hall coefficients has proven difficult, apparently because of very low carrier mobilities. As a result, measurements of electrical transport properties have been unable to establish whether the temperature dependent conductivity should be attributed to the carrier concentration, the mobility, say by thermally activated hopping, or by some combination of the two. The basic delafossite structure has hexagonal symmetry in which copper atoms form a planar triangular lattice. Each copper atom is bonded to two oxygen atoms located above and below the plane. In this structure, the local electric field gradient (EFG) has axial symmetry. This is confirmed by our observation of a characteristic axial-symmetry NMR powder pattern from our samples [7]. We have mainly been studying p-type delafossite materials using 63Cu and 65Cu nuclear quadrupole resonance (NQR) although we have also observed quadrupolar-perturbed NMR spectra in some samples. The goal is to obtain improved understanding of the concentrations and microscopic dynamics of carriers by measuring the spin–lattice relaxation rates. We have found that magnetic and electric quadrupolar hyperfine interactions between the nuclei and carriers dominate spin–lattice relaxation in the doped materials. Our detailed analysis of the relaxation rates in CuYO2:Ca indicates that the mobilities are sufficiently low that the hyperfine field dynamics are closely related to the microscopic transport mechanism. This low mobility limit contrasts with ordinary metals and highmobility semiconductors in which carrier mean free paths extend over many interatomic spacings and the local hyperfine dynamics are essentially decoupled from the transport properties. This paper focuses on some results of our studies of CuYO2:Ca although we note that we have also obtained preliminary results for a sample of CuScO2:Mg [8].
2. Experimental details 63
Cu and 65Cu quadrupolar spin echoes were observed in zero magnetic field using both a homemade coherent pulsed NMR spectrometer and a Chemagnetics/Varian CMX 340 NMR Spectrometer. Nuclear spin–lattice relaxation times were measured using the inversion-recovery technique whereby the spin-echo intensity was recorded as a function of the delay following an initial inverting ‘‘180 pulse’’. Sample temperatures over the range 175–450 K were obtained with a flowing gas (dried air) system. The air was either
heated electrically or cooled with a liquid nitrogen heat exchanger, depending on the temperature range. The samples used for these experiments were powders prepared by calcination from mixtures of CuO, Y2O3 and CaO. The mixtures were heated in air at 1050 C and allowed to react for a period of 48 h to form the Cu2Y2O5 phase. The material was subsequently reduced at 1150 C for 48 h in argon and cooled in an argon atmosphere at 10 C per minute. X-ray characterization showed that the final powdered samples were predominantly of the 2 H delafossite polytype. An alternative phase, the 3R, differs in the stacking order (like FCC and HCP).
3. Experimental results The 63Cu NQR frequencies nNQR for CuYO2 and CuYO2:Ca at 298 K were found to be 28,858 7 1 kHz and 28,840 7 5 kHz, respectively. The broader line observed in the doped material reveals local strains, most likely introduced by the presence of the dopant and, possibly, 2H–3R stacking faults. In both materials, the value of nNQR was observed to decrease linearly with increasing temperature. For this reason, it was necessary to retune the spectrometer frequency at each temperature for which spin–lattice relaxation times were measured. The recovery of the spin-echo amplitude after an inverting pulse was fit to a single-exponential recovery function of the form MðtÞ ¼ MN ½MN Mð0Þet=T1 ;
ð1Þ
where MN is the equilibrium (t=N) magnetization, M(0) is the magnetization following inversion, and T1 is the spin–lattice relaxation time. For undoped CuYO2 , the observed magnetization followed Eq. (1) with experimental error. The recovery curves for the doped material, however, consistently deviated from single exponential behavior. Since, as we discuss below, the overall relaxation process is strongly enhanced in the doped material, we attribute this non-exponential behavior to local variations in the dopant and carrier concentrations. For these materials, therefore, the values of T1 obtained from fits to Eq. (1) represent averages weighted somewhat to the more heavily doped, rapidly, relaxing portions of the samples. The relaxation rates 1/T1 for 63Cu and 65Cu in CuYO2 and CuYO2 Ca are presented as a function of temperature in the semi-logarithmic plot of Fig. 1. The effect of doping in enhancing the relaxation rates is clearly evident. Rates in the doped sample exceed those in the undoped material by one to two orders of magnitude, depending on the temperature. The 65Cu rates in the undoped sample are systematically lower than those obtained for 63Cu. The isotopic
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211
cesses, i.e. ð1=T1 Þi ¼ RiM þ RiQ ;
i ¼ 63; 65;
where RiM p g2i and RiQ p Q2i ; then experimental values of the isotopic ratio r can be used to decompose the total rate into magnetic and quadrupolar components: r rQ ¼ ð1=T Þ
R63 ð2aÞ 1 M 63 rM rQ and R63 Q
rM r ¼ ð1=T1 Þ63
: rM rQ
ð2bÞ
Fig. 1. 63Cu (solid points) and 65Cu (open points) NQR nuclear spin– lattice relaxation rates versus temperature for undoped CuYO2 and CuYO2:Ca.
To carry out the decomposition using Eqs. (2), the total relaxation rates for the two isotopes were first corrected for background (lattice vibration) relaxation by subtracting the respective rates observed in undoped material. The corrected rates were then used to obtain the isotope ratios r at each temperature. To reduce scatter in the decomposed rates introduced by the combined experimental errors in (1/T1)63 and (1/T1)65, the observed isotopic ratios were fit to a sigmoidal function of temperature. Values of the fitting function at each temperature were used for r in Eqs. (2). An alternative analysis, independent of the single-exponential fits to Eq. (1), yielded similar results for r.5 The decomposed magnetic rate for 63Cu, R63 M, is presented in a semi-logarithmic plot versus inverse temperature in Fig. 2.
ratio r; averaged over all temperatures,
4. Discussion
r ð1=T1 Þ65 =ð1=T1 Þ63 ¼ 0:85370:013
The magnetic relaxation rates shown in Fig. 2 are strongly temperature dependent and can be expressed in terms of thermal activation, i.e. R63 M p expðDEM =kTÞ; with activation energy DEM = 152 7 10 meV. In the following analysis, we attribute this relaxation to the magnetic hyperfine fields of mobile holes, essentially localized 3d9 (Cu2+) electronic configurations at the copper sites. The time dependence of the hyperfine field in this picture results from the diffusive transport of the Cu2+ configurations from site to site in the planes of mainly Cu+ (3d10) ions. This so-called Ioffe-Regel limit has been much studied in disordered semiconductors [10]. In this limit, the correlation time tc characterizing the hyperfine field fluctuations should be comparable
agrees within experimental error with the squared ratio of the nuclear quadrupole moments, i.e. rQ = (Q65/Q63)2 = 0.8564. This shows that the rates observed in undoped CuYO2 are of purely quadrupolar origin. We attribute this relaxation mainly to dynamic electric field gradients associated with lattice vibrations as described by the well-known theory of van Kranendonk [9]. We view this as a background process that should be present at roughly the same strength in the doped material. It is clear from the ratios r of the 65Cu and 63Cu rates in the doped material that the relaxation is not purely quadupolar. Throughout the temperature range investigated for the doped sample, the isotopic ratios were intermediate between the quadupolar value rQ and the analogous magnetic ratio rM (g65/g63)2=1.148 where g65 and g63 are, respectively, the gyromagnetic ratios of 65 Cu and 63Cu. Thus a magnetic process is also present and the quadrupolar contribution is considerably stronger than the background process observed in the undoped material. If one assumes that the observed rates are sums of contributions from magnetic and quadrupolar pro-
5 Two alternative approaches to decomposition were also used. In one method, the total relaxation rates were fit to smooth curves and the isotopic ratio r was computed from the smoothed curves. The second method recognized that the observed recovery curves were not single exponential. The recovery curve for 63Cu was fit to a stretched exponential function MðtÞ ¼ ½MN Mð0Þ exp½ðt=tÞm : The recovery curve for 65Cu was then fit to the same function, i.e. with the same value of the exponent m. The ratio r could be evaluated from the ratio t63/t65. The values of r obtained by these methods were generally within 5% of those obtained as described in the main text.
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The DC conductivity can be expressed by in terms of n and the carrier mobility, m, by the standard expression s ¼ nem:
ð4Þ
For diffusive transport, it is appropriate to introduce a hopping time th and a mobility m¼
ea2 ; kB Tth
ð5Þ
in which the hopping distance, a = 3.52 A˚, is the Cu–Cu separation in the delafossite structure. If it is the case that the correlation and hopping times tc and th are independent of temperature, Eqs. (3)–(5) imply RM 63 psTpn as the temperature is varied. This correlation is confirmed in Fig. 2 where the temperature dependence of RM 63 is compared with that of sT using conductivity data obtained by Jayaraj et al. on a thin film of YCuO2:Ca [4]. We conclude, therefore that at least above 200 K, the carrier concentration is thermally activated according to nðTÞ ¼ n0 expð152 meV=kB TÞ
Fig. 2. Magnetic contribution RM 63 to the Cu63 spin–lattice relaxation rate versus 1000/T (solid points). Solid line: DC electrical conductivity times temperature for CuYO2:Ca film [4] plotted with same vertical scale as RM 63. Dashed line: least-squares fit of RM 63 data to activated temperature dependence; slope corresponds to DE=152 meV.
with the ‘‘residence time’’ of a carrier on a given site. The relaxation rate measured by NQR can be written 2 R63 M ¼ ð3=2Þðn=NCu Þod tc ;
ð3Þ
where n is the carrier concentration, NCu is the concentration of Cu nuclei, and od = 1.19 109 s1 [11] is the d-electron hyperfine coupling.6 Comparison of the data in Fig. 2 with Eq. (3) leads immediately to the conclusion that the carrier concentration n increases strongly with temperature. If this were not the case, the correlation time would have to increase exponentially with increasing temperature, a result that we consider physically unreasonable. Moreover, as we show in the argument below, correlation of the magnetic relaxation rates with DC electrical conductivity, s; provides strong evidence that the temperature dependences of R63 M and s are both governed by the temperature dependence of the carrier concentration. The correlation time appears to be essentially independent of temperature over the range of temperatures investigated. 6
We assume that core-polarization and spin-dipolar interactions contribute to the effective hyperfine coupling according to o2d ¼ o2cp þ o2dip where ocp=8.86 108 s1 and odip=7.94 108 s1.
ð6Þ
while the hopping time, and hence the carrier mobility, are independent of temperature. It is likely that the carrier concentrations are not the same in our powdered samples and the thin films used for the conductivity measurements. However, our conclusion depends only on the assumption that the conductivities of the two samples have the same temperature dependence. It is possible to estimate the correlation time, the carrier concentration and the mobility by making the stronger assumptions (i) that the hyperfine correlation time tc and hole hopping time th are identical and (ii) that the magnitude of the conductivity in our powdered sample is approximately equal to that measured for the film. Taking the experimental values at 292 K, s=0.92 S/cm and RM 63=69 s1 in Eqs. (3)–(5), we obtain nE 0:8 1019 cm3 ; tc E th E7 1014 s; mE 0:7 cm2 =Vs: These estimates are, of course, sensitive to the above assumptions. To the extent that the conductivities of the bulk powder and thin film are unequal, the estimates of n and m would be in error by a factor (sfilm /sbulk )1/2 and that of th by a factor (sbulk /sfilm )1/2. It is not implausible that the film and bulk conductivities differ by a factor of two, in which case the above estimates would be in error by about 750%. The inferred hyperfine correlation time, tc E7 1014 s, is significantly longer than the effective correlation times characteristic of nearly free-electron metals. In typical metals, tfe D a/vF E 1016 s where vF is the Fermi velocity. The long correlation time in CuYO2:Ca can be understood in terms of the very flat bands associated
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with weakly interacting d-states at the top of the valence band [12]. The hopping rate for a hole to move from a Cu2+ to a neighboring Cu+ is governed by the overlap integral b between d-states located on neighboring atoms according to the approximate relation 1=th Dzb=h:
ð7Þ
In the triangular Cu lattice with coordination number z ¼ 6; a correlation time th D 7 1014 s corresponds to an overlap integral bD 10 meV. Tight-binding calculations7 yield a value b=9.45 meV for the interaction of 3dxz orbitals on neighboring Cu sites in the CuYO2 structure [13]. This excellent agreement with our estimate is probably fortuitous. However, it does indicate that our experiments and analysis are consistent with the assumed transport mechanism whereby holes diffuse in the copper planes by tunneling between neighboring ions. The low mobility of holes in CuYO2:Ca is a consequence of the weak interactions between d-states at the large Cu–Cu distance characteristic of this compound. There is, in fact, an inverse correlation of DC conductivity with Cu–Cu distance in various delafossite compounds [5], but it is not known whether this can be attributed to higher mobilities or to higher carrier concentrations in the more highly conducting compounds. The electric quadrupolar contributions to spin–lattice relaxation in CuYO2:Ca will be discussed in detail elsewhere [14]. In summary, however, it is clear from the isotopic ratios in Fig. 1 that strong quadrupolar relaxation is associated with dopants. Our initial analysis suggests that both mobile carriers and diffusing defects contribute to the quadrupolar relaxation. The contribution from carriers is very similar to the magnetic process except that the coupling is via the electric field gradient associated with the d-hole in the 3d9 configuration. We believe that defects are responsible for the subtle ‘‘bump’’ in the temperature dependence of the relaxation rate near room temperature. The identity of the diffusing defect or defects is unclear, but a likely candidate would be excess oxygen in the interstitial position of the triangular copper lattice.
5. Summary The p-type transparent conducting oxide CuYO2:Ca appears to be a material in which carrier mobility is so low that the dynamics of the local magnetic hyperfine field can be related to macroscopic transport properties. The temperature dependence of the magnetic contribu7 Tight-binding calculations of Matthiess show that the 3dxz – 3dxz interaction (b ¼ Eddp ¼ 9:45 meV) is the strongest Cu–Cu interaction. The next strongest is that of 3dz2 – 3dz2 (b ¼ 0:25Edds þ 0:75Eddd ¼ 6:14 meV).
213
tion to spin–lattice relaxation correlates well with the DC conductivity and an analysis of the correlation leads to the conclusion that the carrier concentration is thermally activated. The mobility is essentially independent of temperature above 200 K with a value of approximately 0.7 cm2/Vs inferred from the conductivity and relaxation rates. We have argued that this relatively low mobility results from weak overlap of d-states on neighboring Cu ions in the Cu plane of the delafossite structure. The strong temperature dependence of the inferred carrier concentration suggests that a significant fraction of the potential carriers are trapped in deep states. This is a major factor influencing the DC conductivity. Although there is an advantage to be expected from the use of compounds with reduced Cu–Cu distances, and hence higher mobilities, the present results suggest that the search for more highly conducting p-type delafossite transparent conductors may be aided by the identification of dopants with relatively shallow acceptor levels.
Acknowledgments This work was supported in part by National Science Foundation Grants DMR-0071898 and DMR-0071727. We are indebted to L.F. Matthiess who provided his unpublished tight-binding results for the Cu–Cu overlap integrals. We also wish to thank A.W. Sleight for use of sample preparation and characterization facilities, and for constructive criticism of this manuscript. The scientific life of one of us (WWW) has benefited from many years of collaboration and informal discussions with Prof. Ray Dupree. The author’s understanding of issues such as those described in this paper has been enriched and sharpened by these interactions and he wishes to express his appreciation on the occasion of Prof. Dupree’s retirement.
References [1] D.B. Rogers, R.D. Shannon, C.T. Prewitt, J.L. Gillson, Inorg. Chem. 10 (1971) 723. [2] H. Kawazoe, M. Yasukawa, H. Hyodo, M. Kurita, H. Yanagi, H. Hosono, Nature 389 (1997) 939. [3] H. Yanagi, S.-I. Inoue, K. Ueda, H. Kawazoe, H. Hosono, J. Appl. Phys. 88 (2000) 4159. [4] M.K. Jayaraj, A.D. Draeseke, J. Tate, A.W. Sleight, Thin Solid Films 397 (2001) 244. [5] R. Nagarajan, A.D. Draeseke, A.W. Sleight, J. Tate, J. Appl. Phys. 89 (2001) 8022. [6] J. Tate, M.K. Jayaraj, A.D. Draeseke, T. Ulbrich, A.W. Sleight, K.A. Vanaja, R. Nagarajan, J.F. Wager, R.L. Hoffman, Thin Solid Films 411 (2002) 119. [7] F. Monte, Thesis, Oregon State University, 2000. [8] V. Rossi, J. Tate, W. Warren, J. Li, A. Sleight, BAPS Northwest Section Meeting of the American Physical Society, H3.001 (2003).
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[9] J. van Kranendonk, Physica 20 (1954) 781. [10] A.F. Ioffe, A.R. Regel, Progr. Semicond. 4 (1960) 237. [11] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions, Clarendon, Oxford, 1970, pp. 456–459.
[12] L.F. Mattheiss, Phys. Rev. B 48 (1993) 18300. [13] L.F. Matthiess, private communication. [14] W.W. Warren Jr., et al., unpublished.
Solid State Nuclear Magnetic Resonance 26 (2004) 209–214
Nuclear quadrupole resonance studies of transparent conducting oxides W.W. Warren Jr.,a,* A. Rajabzadeh,a T. Olheiser,a,1 J. Liu,a,2 J. Tate, M.K. Jayaraj,a,3 and K.A. Vanajab,4 b
a Department of Physics, Oregon State University, Corvallis, OR 97331-6507, USA Department of Chemistry, Oregon State University, Corvallis, OR 97331-6507, USA
Received January 30, 2004; revised March 17, 2004
Abstract We report 63,65Cu spin–lattice relaxation rates measured by nuclear quadrupole resonance (NQR) in the delafossite compound CuYO2 and CuYO2:Ca over a temperature range from 200 to 450 K. CuYO2:Ca is a prototype transparent oxide exhibiting p-type electrical conductivity. Relaxation rates in CuYO2:Ca are enhanced by one to two orders of magnitude relative to undoped material, exhibit much stronger temperature dependence, and contain contributions from magnetic and quadrupolar relaxation mechanisms with roughly equal strengths. Relaxation in undoped CuYO2 is of purely quadrupolar origin and is attributed to interactions with lattice phonons. The main focus of this paper is the magnetic contribution to the relaxation rate in CuYO2:Ca which is attributed to the hyperfine fields of carriers. It is argued that the dynamics of the hyperfine field are dominated by the hopping rate for carrier transfers between neighboring atoms in the copper planes of the delafossite structure. Comparison of the magnetic relaxation rates with the DC conductivity permits an estimate of the carrier concentration and mobility. r 2004 Elsevier Inc. All rights reserved. Keywords: Nuclear quadrupole resonance (NQR); Transport conductors; Delafossites
I. Introduction Transparent materials exhibiting n-type electrical conductivity are well known and widely used as passive conductors in applications such as electronic displays and solar cells. The possibility of realizing transparent active devices has motivated the search for p-type materials of comparable conductivity and transparency. One class of promising materials is based on the delafossite-structure oxides of the form CuMO2 where *Corresponding author. Fax: +1-541-737-1683. E-mail address: [email protected] (W.W. Warren Jr.). 1 Present address: Department of Physics, University of Illinois, Urbana, IL 61801, USA. 2 Present address: Department of Physics, Stanford University, Stanford, CA 94305, USA. 3 Present address: Department of Physics, Cochin University of Science and Technology, Kochi 682022, India. 4 Present address: Department of Chemistry, Cochin University of Science and Technology, Kochi 682022, India. 0926-2040/$ - see front matter r 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.ssnmr.2004.03.008
M may be one of a number of trivalent elements including Al, Ga, Sc, Y or Cr [1–6]. Holes can be introduced into these materials by intrinsic defects, excess oxygen, or divalent dopants such as Ca or Mg. However, the p-type conductivities of these materials are still well below those typical of the n-type transparent materials in common use. It is therefore of considerable importance to achieve a fundamental microscopic understanding of the electronic transport processes. The series CuYO2:Ca, CuScO2:Mg, and CuCrO2:Mg are typical examples of p-type transparent conducting oxides. Polycrystalline films of CuYO2 :Ca exhibit room temperature electrical conductivities of about 1 S/cm with optical transparency averaging 40–50% over the visible range [4]. Near room temperature, the conductivity appears to be thermally activated with an activation energy of about 140 meV; below this temperature, the slope of an Arrhenius plot of the conductivity gradually decreases. The room temperature conductivities of CuScO2:Mg and CuCrO2:Mg are,
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respectively, about one and two orders of magnitude higher than that of CuYO2:Ca and the temperature dependence is progressively weaker in the order Y–Sc– Cr for the trivalent element. Measurements of the Seebeck coefficient have shown that the carriers are holes in these materials, but determination of the Hall coefficients has proven difficult, apparently because of very low carrier mobilities. As a result, measurements of electrical transport properties have been unable to establish whether the temperature dependent conductivity should be attributed to the carrier concentration, the mobility, say by thermally activated hopping, or by some combination of the two. The basic delafossite structure has hexagonal symmetry in which copper atoms form a planar triangular lattice. Each copper atom is bonded to two oxygen atoms located above and below the plane. In this structure, the local electric field gradient (EFG) has axial symmetry. This is confirmed by our observation of a characteristic axial-symmetry NMR powder pattern from our samples [7]. We have mainly been studying p-type delafossite materials using 63Cu and 65Cu nuclear quadrupole resonance (NQR) although we have also observed quadrupolar-perturbed NMR spectra in some samples. The goal is to obtain improved understanding of the concentrations and microscopic dynamics of carriers by measuring the spin–lattice relaxation rates. We have found that magnetic and electric quadrupolar hyperfine interactions between the nuclei and carriers dominate spin–lattice relaxation in the doped materials. Our detailed analysis of the relaxation rates in CuYO2:Ca indicates that the mobilities are sufficiently low that the hyperfine field dynamics are closely related to the microscopic transport mechanism. This low mobility limit contrasts with ordinary metals and highmobility semiconductors in which carrier mean free paths extend over many interatomic spacings and the local hyperfine dynamics are essentially decoupled from the transport properties. This paper focuses on some results of our studies of CuYO2:Ca although we note that we have also obtained preliminary results for a sample of CuScO2:Mg [8].
2. Experimental details 63
Cu and 65Cu quadrupolar spin echoes were observed in zero magnetic field using both a homemade coherent pulsed NMR spectrometer and a Chemagnetics/Varian CMX 340 NMR Spectrometer. Nuclear spin–lattice relaxation times were measured using the inversion-recovery technique whereby the spin-echo intensity was recorded as a function of the delay following an initial inverting ‘‘180 pulse’’. Sample temperatures over the range 175–450 K were obtained with a flowing gas (dried air) system. The air was either
heated electrically or cooled with a liquid nitrogen heat exchanger, depending on the temperature range. The samples used for these experiments were powders prepared by calcination from mixtures of CuO, Y2O3 and CaO. The mixtures were heated in air at 1050 C and allowed to react for a period of 48 h to form the Cu2Y2O5 phase. The material was subsequently reduced at 1150 C for 48 h in argon and cooled in an argon atmosphere at 10 C per minute. X-ray characterization showed that the final powdered samples were predominantly of the 2 H delafossite polytype. An alternative phase, the 3R, differs in the stacking order (like FCC and HCP).
3. Experimental results The 63Cu NQR frequencies nNQR for CuYO2 and CuYO2:Ca at 298 K were found to be 28,858 7 1 kHz and 28,840 7 5 kHz, respectively. The broader line observed in the doped material reveals local strains, most likely introduced by the presence of the dopant and, possibly, 2H–3R stacking faults. In both materials, the value of nNQR was observed to decrease linearly with increasing temperature. For this reason, it was necessary to retune the spectrometer frequency at each temperature for which spin–lattice relaxation times were measured. The recovery of the spin-echo amplitude after an inverting pulse was fit to a single-exponential recovery function of the form MðtÞ ¼ MN ½MN Mð0Þet=T1 ;
ð1Þ
where MN is the equilibrium (t=N) magnetization, M(0) is the magnetization following inversion, and T1 is the spin–lattice relaxation time. For undoped CuYO2 , the observed magnetization followed Eq. (1) with experimental error. The recovery curves for the doped material, however, consistently deviated from single exponential behavior. Since, as we discuss below, the overall relaxation process is strongly enhanced in the doped material, we attribute this non-exponential behavior to local variations in the dopant and carrier concentrations. For these materials, therefore, the values of T1 obtained from fits to Eq. (1) represent averages weighted somewhat to the more heavily doped, rapidly, relaxing portions of the samples. The relaxation rates 1/T1 for 63Cu and 65Cu in CuYO2 and CuYO2 Ca are presented as a function of temperature in the semi-logarithmic plot of Fig. 1. The effect of doping in enhancing the relaxation rates is clearly evident. Rates in the doped sample exceed those in the undoped material by one to two orders of magnitude, depending on the temperature. The 65Cu rates in the undoped sample are systematically lower than those obtained for 63Cu. The isotopic
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211
cesses, i.e. ð1=T1 Þi ¼ RiM þ RiQ ;
i ¼ 63; 65;
where RiM p g2i and RiQ p Q2i ; then experimental values of the isotopic ratio r can be used to decompose the total rate into magnetic and quadrupolar components: r rQ ¼ ð1=T Þ
R63 ð2aÞ 1 M 63 rM rQ and R63 Q
rM r ¼ ð1=T1 Þ63
: rM rQ
ð2bÞ
Fig. 1. 63Cu (solid points) and 65Cu (open points) NQR nuclear spin– lattice relaxation rates versus temperature for undoped CuYO2 and CuYO2:Ca.
To carry out the decomposition using Eqs. (2), the total relaxation rates for the two isotopes were first corrected for background (lattice vibration) relaxation by subtracting the respective rates observed in undoped material. The corrected rates were then used to obtain the isotope ratios r at each temperature. To reduce scatter in the decomposed rates introduced by the combined experimental errors in (1/T1)63 and (1/T1)65, the observed isotopic ratios were fit to a sigmoidal function of temperature. Values of the fitting function at each temperature were used for r in Eqs. (2). An alternative analysis, independent of the single-exponential fits to Eq. (1), yielded similar results for r.5 The decomposed magnetic rate for 63Cu, R63 M, is presented in a semi-logarithmic plot versus inverse temperature in Fig. 2.
ratio r; averaged over all temperatures,
4. Discussion
r ð1=T1 Þ65 =ð1=T1 Þ63 ¼ 0:85370:013
The magnetic relaxation rates shown in Fig. 2 are strongly temperature dependent and can be expressed in terms of thermal activation, i.e. R63 M p expðDEM =kTÞ; with activation energy DEM = 152 7 10 meV. In the following analysis, we attribute this relaxation to the magnetic hyperfine fields of mobile holes, essentially localized 3d9 (Cu2+) electronic configurations at the copper sites. The time dependence of the hyperfine field in this picture results from the diffusive transport of the Cu2+ configurations from site to site in the planes of mainly Cu+ (3d10) ions. This so-called Ioffe-Regel limit has been much studied in disordered semiconductors [10]. In this limit, the correlation time tc characterizing the hyperfine field fluctuations should be comparable
agrees within experimental error with the squared ratio of the nuclear quadrupole moments, i.e. rQ = (Q65/Q63)2 = 0.8564. This shows that the rates observed in undoped CuYO2 are of purely quadrupolar origin. We attribute this relaxation mainly to dynamic electric field gradients associated with lattice vibrations as described by the well-known theory of van Kranendonk [9]. We view this as a background process that should be present at roughly the same strength in the doped material. It is clear from the ratios r of the 65Cu and 63Cu rates in the doped material that the relaxation is not purely quadupolar. Throughout the temperature range investigated for the doped sample, the isotopic ratios were intermediate between the quadupolar value rQ and the analogous magnetic ratio rM (g65/g63)2=1.148 where g65 and g63 are, respectively, the gyromagnetic ratios of 65 Cu and 63Cu. Thus a magnetic process is also present and the quadrupolar contribution is considerably stronger than the background process observed in the undoped material. If one assumes that the observed rates are sums of contributions from magnetic and quadrupolar pro-
5 Two alternative approaches to decomposition were also used. In one method, the total relaxation rates were fit to smooth curves and the isotopic ratio r was computed from the smoothed curves. The second method recognized that the observed recovery curves were not single exponential. The recovery curve for 63Cu was fit to a stretched exponential function MðtÞ ¼ ½MN Mð0Þ exp½ðt=tÞm : The recovery curve for 65Cu was then fit to the same function, i.e. with the same value of the exponent m. The ratio r could be evaluated from the ratio t63/t65. The values of r obtained by these methods were generally within 5% of those obtained as described in the main text.
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The DC conductivity can be expressed by in terms of n and the carrier mobility, m, by the standard expression s ¼ nem:
ð4Þ
For diffusive transport, it is appropriate to introduce a hopping time th and a mobility m¼
ea2 ; kB Tth
ð5Þ
in which the hopping distance, a = 3.52 A˚, is the Cu–Cu separation in the delafossite structure. If it is the case that the correlation and hopping times tc and th are independent of temperature, Eqs. (3)–(5) imply RM 63 psTpn as the temperature is varied. This correlation is confirmed in Fig. 2 where the temperature dependence of RM 63 is compared with that of sT using conductivity data obtained by Jayaraj et al. on a thin film of YCuO2:Ca [4]. We conclude, therefore that at least above 200 K, the carrier concentration is thermally activated according to nðTÞ ¼ n0 expð152 meV=kB TÞ
Fig. 2. Magnetic contribution RM 63 to the Cu63 spin–lattice relaxation rate versus 1000/T (solid points). Solid line: DC electrical conductivity times temperature for CuYO2:Ca film [4] plotted with same vertical scale as RM 63. Dashed line: least-squares fit of RM 63 data to activated temperature dependence; slope corresponds to DE=152 meV.
with the ‘‘residence time’’ of a carrier on a given site. The relaxation rate measured by NQR can be written 2 R63 M ¼ ð3=2Þðn=NCu Þod tc ;
ð3Þ
where n is the carrier concentration, NCu is the concentration of Cu nuclei, and od = 1.19 109 s1 [11] is the d-electron hyperfine coupling.6 Comparison of the data in Fig. 2 with Eq. (3) leads immediately to the conclusion that the carrier concentration n increases strongly with temperature. If this were not the case, the correlation time would have to increase exponentially with increasing temperature, a result that we consider physically unreasonable. Moreover, as we show in the argument below, correlation of the magnetic relaxation rates with DC electrical conductivity, s; provides strong evidence that the temperature dependences of R63 M and s are both governed by the temperature dependence of the carrier concentration. The correlation time appears to be essentially independent of temperature over the range of temperatures investigated. 6
We assume that core-polarization and spin-dipolar interactions contribute to the effective hyperfine coupling according to o2d ¼ o2cp þ o2dip where ocp=8.86 108 s1 and odip=7.94 108 s1.
ð6Þ
while the hopping time, and hence the carrier mobility, are independent of temperature. It is likely that the carrier concentrations are not the same in our powdered samples and the thin films used for the conductivity measurements. However, our conclusion depends only on the assumption that the conductivities of the two samples have the same temperature dependence. It is possible to estimate the correlation time, the carrier concentration and the mobility by making the stronger assumptions (i) that the hyperfine correlation time tc and hole hopping time th are identical and (ii) that the magnitude of the conductivity in our powdered sample is approximately equal to that measured for the film. Taking the experimental values at 292 K, s=0.92 S/cm and RM 63=69 s1 in Eqs. (3)–(5), we obtain nE 0:8 1019 cm3 ; tc E th E7 1014 s; mE 0:7 cm2 =Vs: These estimates are, of course, sensitive to the above assumptions. To the extent that the conductivities of the bulk powder and thin film are unequal, the estimates of n and m would be in error by a factor (sfilm /sbulk )1/2 and that of th by a factor (sbulk /sfilm )1/2. It is not implausible that the film and bulk conductivities differ by a factor of two, in which case the above estimates would be in error by about 750%. The inferred hyperfine correlation time, tc E7 1014 s, is significantly longer than the effective correlation times characteristic of nearly free-electron metals. In typical metals, tfe D a/vF E 1016 s where vF is the Fermi velocity. The long correlation time in CuYO2:Ca can be understood in terms of the very flat bands associated
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with weakly interacting d-states at the top of the valence band [12]. The hopping rate for a hole to move from a Cu2+ to a neighboring Cu+ is governed by the overlap integral b between d-states located on neighboring atoms according to the approximate relation 1=th Dzb=h:
ð7Þ
In the triangular Cu lattice with coordination number z ¼ 6; a correlation time th D 7 1014 s corresponds to an overlap integral bD 10 meV. Tight-binding calculations7 yield a value b=9.45 meV for the interaction of 3dxz orbitals on neighboring Cu sites in the CuYO2 structure [13]. This excellent agreement with our estimate is probably fortuitous. However, it does indicate that our experiments and analysis are consistent with the assumed transport mechanism whereby holes diffuse in the copper planes by tunneling between neighboring ions. The low mobility of holes in CuYO2:Ca is a consequence of the weak interactions between d-states at the large Cu–Cu distance characteristic of this compound. There is, in fact, an inverse correlation of DC conductivity with Cu–Cu distance in various delafossite compounds [5], but it is not known whether this can be attributed to higher mobilities or to higher carrier concentrations in the more highly conducting compounds. The electric quadrupolar contributions to spin–lattice relaxation in CuYO2:Ca will be discussed in detail elsewhere [14]. In summary, however, it is clear from the isotopic ratios in Fig. 1 that strong quadrupolar relaxation is associated with dopants. Our initial analysis suggests that both mobile carriers and diffusing defects contribute to the quadrupolar relaxation. The contribution from carriers is very similar to the magnetic process except that the coupling is via the electric field gradient associated with the d-hole in the 3d9 configuration. We believe that defects are responsible for the subtle ‘‘bump’’ in the temperature dependence of the relaxation rate near room temperature. The identity of the diffusing defect or defects is unclear, but a likely candidate would be excess oxygen in the interstitial position of the triangular copper lattice.
5. Summary The p-type transparent conducting oxide CuYO2:Ca appears to be a material in which carrier mobility is so low that the dynamics of the local magnetic hyperfine field can be related to macroscopic transport properties. The temperature dependence of the magnetic contribu7 Tight-binding calculations of Matthiess show that the 3dxz – 3dxz interaction (b ¼ Eddp ¼ 9:45 meV) is the strongest Cu–Cu interaction. The next strongest is that of 3dz2 – 3dz2 (b ¼ 0:25Edds þ 0:75Eddd ¼ 6:14 meV).
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tion to spin–lattice relaxation correlates well with the DC conductivity and an analysis of the correlation leads to the conclusion that the carrier concentration is thermally activated. The mobility is essentially independent of temperature above 200 K with a value of approximately 0.7 cm2/Vs inferred from the conductivity and relaxation rates. We have argued that this relatively low mobility results from weak overlap of d-states on neighboring Cu ions in the Cu plane of the delafossite structure. The strong temperature dependence of the inferred carrier concentration suggests that a significant fraction of the potential carriers are trapped in deep states. This is a major factor influencing the DC conductivity. Although there is an advantage to be expected from the use of compounds with reduced Cu–Cu distances, and hence higher mobilities, the present results suggest that the search for more highly conducting p-type delafossite transparent conductors may be aided by the identification of dopants with relatively shallow acceptor levels.
Acknowledgments This work was supported in part by National Science Foundation Grants DMR-0071898 and DMR-0071727. We are indebted to L.F. Matthiess who provided his unpublished tight-binding results for the Cu–Cu overlap integrals. We also wish to thank A.W. Sleight for use of sample preparation and characterization facilities, and for constructive criticism of this manuscript. The scientific life of one of us (WWW) has benefited from many years of collaboration and informal discussions with Prof. Ray Dupree. The author’s understanding of issues such as those described in this paper has been enriched and sharpened by these interactions and he wishes to express his appreciation on the occasion of Prof. Dupree’s retirement.
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