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Manifestation of a pseudogap in the raman spectra of underdoped YBa2Cu3O6.5?
Pergamon
PII: S0022-3697(98)00151-6
J. Phys. Chem Solids Vol 59, No. 10–12, pp. 1968–1971, 1998 0022-3697/98/$ - see front matter 䉷 1998 Elsevier Science Ltd. All rights reserved
MANIFESTATION OF A PSEUDOGAP IN THE RAMAN SPECTRA OF UNDERDOPED YBa 2Cu 3O 6.5? X. K. CHEN a, J. G. NAEINI a, J. C. IRWIN a ,*, R. LIANG b and W. N. HARDY b a
Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 b Department of Physics, University of B.C., Vancouver, British Columbia, Canada V6T 1Z1
Abstract—Raman scattering experiments have been carried out on single crystals of underdoped YBa 2Cu 3O 6.5 and optimally doped YBa 2Cu 3O 6.95. The B 2g spectra of the underdoped samples are comparable in strength to those from optimally doped compounds while the B 1g continua in the underdoped samples are much weaker than they are in optimally doped compounds. The loss of spectral weight in the B 1g channel in the underdoped compounds may be associated with the presence of a normal state pseudogap which masks the transition to the superconducting state. There is however, no definitive indication in the spectra of either an onset temperature T*, or a feature that could be used to estimate an upper energy limit, or gap energy, for the spectral weight depletion. Assuming weighted distributions for the degree of depletion a simple model is used to calculate a schematic representation of the spectra in the B 1g and B 2g channels. The results imply that the observed spectral weight depletion is localized to Fermi surface regions near the (p, 0) points of the Brillouin zone. 䉷 1998 Elsevier Science Ltd. All rights reserved
It now appears that the normal state electronic properties of the underdoped cuprates are strongly influenced [1–7] by the presence of a pseudogap. Although the nature of this pseudogap (PG) is not well understood its existence has been inferred from the results of a large number of experiments. Warren et al. [1] found that a sharp decrease of the 63Cu nuclear relaxation rate occurred at temperatures well above T c and attributed it to the onset of precursor spin pairing. Evidence for the suppression of low frequency spectral weight has also been obtained from specific heat measurements [2–4], transport measurements [5] and optical measurements [6, 7]. The specific heat data have been used to obtain estimates for the magnitude and symmetry of the normal state gap and its variation with doping. Recently angle resolved photoemission spectroscopy (ARPES) experiments [8–11] have provided a much clearer picture of a highly anisotropic pseudogap that exists in a temperature range T c ⬍ T ⬍ T* and has a d-wave angular dependence, and energy, similar to those found for the superconducting gap. Raman scattering also allows one to probe the nature of the electronic excitations in selected regions of the Brillouin zone and should thus be able to provide valuable and complementary information concerning the nature of the PG. However, the onset of the PG appears to have relatively minor influence on the Raman spectra obtained from underdoped cuprates and the relatively few results that have been published to date [12–15] have been somewhat contradictory in nature. We have therefore searched for features in the spectra that appear to be *Corresponding author.
connected with the PG and which can be interpreted in an unambiguous manner. This in turn will hopefully lead to a useful technique that can be used to enhance our understanding of the origin of the PG and the role it plays, if any, in determining the superconducting properties of the hole-doped cuprates. We have carried out Raman scattering experiments on two different underdoped YBa 2Cu 3O x(Y123{x}) single crystals with x ⬇ 6.5 and an optimally doped Y123{6.95} single crystal. The underdoped crystals had critical temperatures of T c ¼ 60 and 61 K and for the optimally doped crystal T c ¼ 93 K. The spectra were excited with the 514.5 or 488.0 nm lines of an Ar þ laser with an incident power level of less than 15 W/cm 2 which limited local heating to less than 20 K. The sample temperatures quoted in this paper are the estimated temperature in the excited region (ambient plus 20 K). Spectra were obtained in a quasi-backscattering geometry with the incident light travelling parallel to the c or z axis of the crystal and polarized either parallel to x(100) or x⬘(110). Then for example one could couple to B 1g(x⬘y⬘ channel) excitations by also selecting scattered light polarized along the y⬘ axes. Similarly the xy scattering geometry allows coupling to B 2g excitations. Spectra obtained in the B 1g channel are shown in Fig. 1 for several different temperatures. The spectra are displayed on the same scale so that one can see that the B 1g intensity increases slightly as the temperature is increased from 100 to 200 K and then decreases as the temperature is increased further to room temperature. In addition as the sample was cooled to about 200 K a broad maximum was observed to form near 1200 cm ¹1 in some spectra. However, further work is required to establish the
1968
Pseudogap in the Raman spectra of underdoped YBa 2Cu 3O 6.5?
Fig. 1. The B 1g response functions obtained from an underdoped (x ¼ 6.5) sample at several different temperatures.
1969
reproducibility of this feature. To within our experimental accuracy (⫾20%) the strength of the B 2g response function remains constant between 100 K and 300 K and the 120 K spectrum is shown in Fig. 2. Perhaps the most interesting feature of the data, as shown in Fig. 2, is that the B 1g intensity in the underdoped sample is much weaker than it is in optimally doped samples, while the intensity in the B 2g channel is about the same for both doping levels. Thus, as shown in Fig. 2, in optimally doped compounds the intensity in the B 1g channel is much greater than it is in the B 2g channel, but they become roughly equal in the underdoped samples. Since the B 1g spectrum primarily probes excitations located near the axes our results imply that the spectral weight is significantly depleted on regions of the Fermi Surface (FS) located near (p, 0) and related points. A depletion of spectral weight near the (p, 0) regions of the zone has been observed [8–10] in ARPES experiments on underdoped samples and is attributed to the formation of a PG below about 200 K. In addition they use the leading edge shift of their signal to assign an energy of about 30 meV to the PG. In contrast, however, our results do not provide any clear indication of an onset temperature T* and there is no feature in the spectra that provides an unambiguous indication of the energy of the PG. The ratios shown in Fig. 2 with the 120 K spectra are essentially identical to those obtained [13] using spectra obtained at 35 K (in the superconducting state). Thus to gain additional insight into the nature of the spectral
Fig. 2. A comparison of the Raman spectra of Y123 measured in the B 1g (thin lines) and B 2g (thick lines) geometries of (a) optimally doped and (b) underdoped samples.
1970
X. K. CHEN et al.
Fig. 3. Calculated B 1g and B 2g Raman response functions obtained by integrating over the whole FS and the modified response functions obtained by restricting the integration to a region of the FS defined by 20⬚ ⬍ J ⬍ 70⬚ in each quadrant (see [13]).
Fig. 4. The B 1g and B 2g response functions calculated using eqn (3) and integrating over the complete FS. The four curves shown correspond (in decreasing amplitude) to b ¼ 0, 1, 10 and 100.
Pseudogap in the Raman spectra of underdoped YBa 2Cu 3O 6.5?
depletion that could lead to the observed changes in the spectra with doping we can carry out a crude calculation of the spectra. The unscreened response is given by [16–18] * + (gij )2 lD(k)l2 ⬘⬘ q (1) xij (q, q→0)⬀ q q2 ¹ 4lD(k)l2 where the triangular brackets indicate an average over the FS (with q ⬎ 2lD(k)l) and gij is a cartesian component of the Raman tensor which, if one is far from resonance, is closely related to the reciprocal effective mass: gij ⬀
2 E(k) ki kj
(2)
A tight binding model has been used [13] to represent the band structure and the B 1g and B 2g spectra have been calculated using eqn (1) and (a) integrating over the whole FS, then (b) integration with a region defined by an angle of 20 degrees on either side of the k x and k y axes excluded from the integration. This latter configuration is intended to simulate a loss of spectral weight from the regions of the FS near (p,0) and equivalent points. It is assumed that the FS, although perhaps smeared out, is still large and intact, as found in photoemission experiments. The results are shown in Fig. 3 and it is clear that a loss of spectral weight near (p,0) drastically reduces the B 1g spectrum but has little effect on the B 2g spectrum. It is also clear that there is qualitative agreement between these results and the changes that actually occur in the spectra in going from optimally doped to the underdoped region (Fig. 2). The results of ARPES experiments also suggest that the PG in Bi2212 has d-wave symmetry. In an attempt to compare our results to a scenario in which the spectral weight depletion can be represented by a d-wave type distribution we have calculated the spectra using: * + (gij )2 lD(k)l2 ⬘⬘ q (3) xij ⬀ [1 þ b(k2x ¹ k2y )]q q2 ¹ 4lD(k)l2 The results are shown in Fig. 4 for the cases b ¼ 0, 1, 10 and 100. With this distribution of depletion, both spectra are diminished in a very similar manner. This feature is in obvious disagreement with our results. In conclusion, the B 1g Raman spectra of underdoped Y123(6.5) are much weaker than those obtained from the optimally doped compound (x ¼ 6.95) which suggests a significant depletion of spectral weight on regions of the FS located near the (p,0) points. This result is in accord with ARPES measurements, but in contrast to these measurements, the Raman results do not provide any indication of the magnitude of the PG or clear evidence of an onset temperature T*. Finally the relative strengths of
1971
the B 1g and B 2g Raman spectra from the underdoped compounds suggest a spectral depletion that is quite localised to regions of the FS near the (p,0) points, and not a conventional d-wave distribution as found in ARPES experiments. These contrasting features suggest that the B 1g spectral depletion that we have observed does not constitute direct evidence of the low energy PG observed using other techniques [5–11]. That is the B 1g spectra in underdoped compounds may arise from excitations that interact with the charge carriers but which are not themselves directly involved in transport. Acknowledgements—The financial support of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.
REFERENCES 1. Warren, W. W., Walstedt, R. E., Brennert, G. F., Cava, R. J., Tycko, R., Bell, R. F. and Dabbagh, G., Phys. Rev. Lett., 1989, 62, 1193. 2. Loram, J. W., Mirza, K. A., Cooper, J. R., Liang, W. Y., J. Supercond., 1994, 7, 243. 3. Loram, J. W., Mirza, K. A., Wade, J. M., Cooper, J. R. and Liang, W. Y., Physica C, 1994, 235–240, 135. 4. Gurvitch, M. and Fiory, A. T., Phys. Rev. Lett., 1987, 59, 1337. 5. Batlogg, B., Hwang, H. Y., Takagi, H., Cava, R. J., Kao, H. L., Kwo, J., Physica C, 1994, 235–240, 130. 6. Puchkov, A. V., Fournier, P., Timusk, T. and Kolesnikov, N. N., Phys. Rev. Lett., 1996, 77, 1853. 7. Puchkov, A. V., Fournier, P., Basov, D. N., Timusk, T., Kapitulnik, A. and Kolesnikov, N. N., Phys. Rev. Lett., 1996, 77, 3212. 8. Loeser, A. G., Shen, Z.-X., Dessau, D. S., Marshall, D. S., Park, C-H., Fournier, P. and Kapitulnik, A., Science, 1996, 273, 325. 9. Marshall, D. S., Dessau, D. S., Loeser, A. G., Park, C-H., Matsuura, A. Y., Eckstein, J. N., Bozovic, I., Fournier, P., Kapitulnik, A., Spicer, W. E. and Shen, Z.-X., Phys. Rev. Lett., 1996, 76, 4841. 10. Ding, H., Yokoya, T., Campuzano, J. C., Takahashi, T., Randeria, M., Norman, M. R., Mochiku, T., Kadowaki, K. and Giapintzakis, J., Nature, 1996, 382, 51. 11. Ding, H., Norman, M. R., Yokoya, T., Takeuchi, T., Randeria, M., Campuzano, J. C., Takahashi, T., Mochiku, T. and Kadowaki, K., Phys. Rev. Lett., 1997, 78, 2628. 12. Slakey, F., Klein, M. V., Rice, J. P. and Ginsberg, D. M., Phys. Rev. B, 1990, 42, 2643. 13. Chen, X. K., Naeini, J. G., Hewitt, K. C., Irwin, J. C., Liang, R. and Hardy, W. N., Phys. Rev. B, 1997, 56, R513. 14. Nemetschek, R., Opel, M., Hoffmann, C., Muller, P. F., Hackl, R., Berger, H., Forro, L., Erb, A., Walker, E., Phys. Rev. Lett., 1997, 78, 4873. 15. Blumberg, G., Klein, M. V., Kadowaki, K., Kendziora, C., Guptasarma, P. and Hinks, D., J. Phys. Chem. Solids, 1998, these proceedings. 16. Klein, M. V. and Dierker, S. B., Phys. Rev. B, 1984, 29, 4976. 17. Devereaux, T. P., Einzel, D., Stadlober, B., Hackl, R., Leach, D. H. and Neumeler, J. J., Phys. Rev. Lett., 1994, 72, 396. 18. Chen, X. K., Irwin, J. C., Trodahl, H. J., Kimura, T. and Kishio, K., Phys. Rev. Lett., 1994, 73, 3290.
PII: S0022-3697(98)00151-6
J. Phys. Chem Solids Vol 59, No. 10–12, pp. 1968–1971, 1998 0022-3697/98/$ - see front matter 䉷 1998 Elsevier Science Ltd. All rights reserved
MANIFESTATION OF A PSEUDOGAP IN THE RAMAN SPECTRA OF UNDERDOPED YBa 2Cu 3O 6.5? X. K. CHEN a, J. G. NAEINI a, J. C. IRWIN a ,*, R. LIANG b and W. N. HARDY b a
Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 b Department of Physics, University of B.C., Vancouver, British Columbia, Canada V6T 1Z1
Abstract—Raman scattering experiments have been carried out on single crystals of underdoped YBa 2Cu 3O 6.5 and optimally doped YBa 2Cu 3O 6.95. The B 2g spectra of the underdoped samples are comparable in strength to those from optimally doped compounds while the B 1g continua in the underdoped samples are much weaker than they are in optimally doped compounds. The loss of spectral weight in the B 1g channel in the underdoped compounds may be associated with the presence of a normal state pseudogap which masks the transition to the superconducting state. There is however, no definitive indication in the spectra of either an onset temperature T*, or a feature that could be used to estimate an upper energy limit, or gap energy, for the spectral weight depletion. Assuming weighted distributions for the degree of depletion a simple model is used to calculate a schematic representation of the spectra in the B 1g and B 2g channels. The results imply that the observed spectral weight depletion is localized to Fermi surface regions near the (p, 0) points of the Brillouin zone. 䉷 1998 Elsevier Science Ltd. All rights reserved
It now appears that the normal state electronic properties of the underdoped cuprates are strongly influenced [1–7] by the presence of a pseudogap. Although the nature of this pseudogap (PG) is not well understood its existence has been inferred from the results of a large number of experiments. Warren et al. [1] found that a sharp decrease of the 63Cu nuclear relaxation rate occurred at temperatures well above T c and attributed it to the onset of precursor spin pairing. Evidence for the suppression of low frequency spectral weight has also been obtained from specific heat measurements [2–4], transport measurements [5] and optical measurements [6, 7]. The specific heat data have been used to obtain estimates for the magnitude and symmetry of the normal state gap and its variation with doping. Recently angle resolved photoemission spectroscopy (ARPES) experiments [8–11] have provided a much clearer picture of a highly anisotropic pseudogap that exists in a temperature range T c ⬍ T ⬍ T* and has a d-wave angular dependence, and energy, similar to those found for the superconducting gap. Raman scattering also allows one to probe the nature of the electronic excitations in selected regions of the Brillouin zone and should thus be able to provide valuable and complementary information concerning the nature of the PG. However, the onset of the PG appears to have relatively minor influence on the Raman spectra obtained from underdoped cuprates and the relatively few results that have been published to date [12–15] have been somewhat contradictory in nature. We have therefore searched for features in the spectra that appear to be *Corresponding author.
connected with the PG and which can be interpreted in an unambiguous manner. This in turn will hopefully lead to a useful technique that can be used to enhance our understanding of the origin of the PG and the role it plays, if any, in determining the superconducting properties of the hole-doped cuprates. We have carried out Raman scattering experiments on two different underdoped YBa 2Cu 3O x(Y123{x}) single crystals with x ⬇ 6.5 and an optimally doped Y123{6.95} single crystal. The underdoped crystals had critical temperatures of T c ¼ 60 and 61 K and for the optimally doped crystal T c ¼ 93 K. The spectra were excited with the 514.5 or 488.0 nm lines of an Ar þ laser with an incident power level of less than 15 W/cm 2 which limited local heating to less than 20 K. The sample temperatures quoted in this paper are the estimated temperature in the excited region (ambient plus 20 K). Spectra were obtained in a quasi-backscattering geometry with the incident light travelling parallel to the c or z axis of the crystal and polarized either parallel to x(100) or x⬘(110). Then for example one could couple to B 1g(x⬘y⬘ channel) excitations by also selecting scattered light polarized along the y⬘ axes. Similarly the xy scattering geometry allows coupling to B 2g excitations. Spectra obtained in the B 1g channel are shown in Fig. 1 for several different temperatures. The spectra are displayed on the same scale so that one can see that the B 1g intensity increases slightly as the temperature is increased from 100 to 200 K and then decreases as the temperature is increased further to room temperature. In addition as the sample was cooled to about 200 K a broad maximum was observed to form near 1200 cm ¹1 in some spectra. However, further work is required to establish the
1968
Pseudogap in the Raman spectra of underdoped YBa 2Cu 3O 6.5?
Fig. 1. The B 1g response functions obtained from an underdoped (x ¼ 6.5) sample at several different temperatures.
1969
reproducibility of this feature. To within our experimental accuracy (⫾20%) the strength of the B 2g response function remains constant between 100 K and 300 K and the 120 K spectrum is shown in Fig. 2. Perhaps the most interesting feature of the data, as shown in Fig. 2, is that the B 1g intensity in the underdoped sample is much weaker than it is in optimally doped samples, while the intensity in the B 2g channel is about the same for both doping levels. Thus, as shown in Fig. 2, in optimally doped compounds the intensity in the B 1g channel is much greater than it is in the B 2g channel, but they become roughly equal in the underdoped samples. Since the B 1g spectrum primarily probes excitations located near the axes our results imply that the spectral weight is significantly depleted on regions of the Fermi Surface (FS) located near (p, 0) and related points. A depletion of spectral weight near the (p, 0) regions of the zone has been observed [8–10] in ARPES experiments on underdoped samples and is attributed to the formation of a PG below about 200 K. In addition they use the leading edge shift of their signal to assign an energy of about 30 meV to the PG. In contrast, however, our results do not provide any clear indication of an onset temperature T* and there is no feature in the spectra that provides an unambiguous indication of the energy of the PG. The ratios shown in Fig. 2 with the 120 K spectra are essentially identical to those obtained [13] using spectra obtained at 35 K (in the superconducting state). Thus to gain additional insight into the nature of the spectral
Fig. 2. A comparison of the Raman spectra of Y123 measured in the B 1g (thin lines) and B 2g (thick lines) geometries of (a) optimally doped and (b) underdoped samples.
1970
X. K. CHEN et al.
Fig. 3. Calculated B 1g and B 2g Raman response functions obtained by integrating over the whole FS and the modified response functions obtained by restricting the integration to a region of the FS defined by 20⬚ ⬍ J ⬍ 70⬚ in each quadrant (see [13]).
Fig. 4. The B 1g and B 2g response functions calculated using eqn (3) and integrating over the complete FS. The four curves shown correspond (in decreasing amplitude) to b ¼ 0, 1, 10 and 100.
Pseudogap in the Raman spectra of underdoped YBa 2Cu 3O 6.5?
depletion that could lead to the observed changes in the spectra with doping we can carry out a crude calculation of the spectra. The unscreened response is given by [16–18] * + (gij )2 lD(k)l2 ⬘⬘ q (1) xij (q, q→0)⬀ q q2 ¹ 4lD(k)l2 where the triangular brackets indicate an average over the FS (with q ⬎ 2lD(k)l) and gij is a cartesian component of the Raman tensor which, if one is far from resonance, is closely related to the reciprocal effective mass: gij ⬀
2 E(k) ki kj
(2)
A tight binding model has been used [13] to represent the band structure and the B 1g and B 2g spectra have been calculated using eqn (1) and (a) integrating over the whole FS, then (b) integration with a region defined by an angle of 20 degrees on either side of the k x and k y axes excluded from the integration. This latter configuration is intended to simulate a loss of spectral weight from the regions of the FS near (p,0) and equivalent points. It is assumed that the FS, although perhaps smeared out, is still large and intact, as found in photoemission experiments. The results are shown in Fig. 3 and it is clear that a loss of spectral weight near (p,0) drastically reduces the B 1g spectrum but has little effect on the B 2g spectrum. It is also clear that there is qualitative agreement between these results and the changes that actually occur in the spectra in going from optimally doped to the underdoped region (Fig. 2). The results of ARPES experiments also suggest that the PG in Bi2212 has d-wave symmetry. In an attempt to compare our results to a scenario in which the spectral weight depletion can be represented by a d-wave type distribution we have calculated the spectra using: * + (gij )2 lD(k)l2 ⬘⬘ q (3) xij ⬀ [1 þ b(k2x ¹ k2y )]q q2 ¹ 4lD(k)l2 The results are shown in Fig. 4 for the cases b ¼ 0, 1, 10 and 100. With this distribution of depletion, both spectra are diminished in a very similar manner. This feature is in obvious disagreement with our results. In conclusion, the B 1g Raman spectra of underdoped Y123(6.5) are much weaker than those obtained from the optimally doped compound (x ¼ 6.95) which suggests a significant depletion of spectral weight on regions of the FS located near the (p,0) points. This result is in accord with ARPES measurements, but in contrast to these measurements, the Raman results do not provide any indication of the magnitude of the PG or clear evidence of an onset temperature T*. Finally the relative strengths of
1971
the B 1g and B 2g Raman spectra from the underdoped compounds suggest a spectral depletion that is quite localised to regions of the FS near the (p,0) points, and not a conventional d-wave distribution as found in ARPES experiments. These contrasting features suggest that the B 1g spectral depletion that we have observed does not constitute direct evidence of the low energy PG observed using other techniques [5–11]. That is the B 1g spectra in underdoped compounds may arise from excitations that interact with the charge carriers but which are not themselves directly involved in transport. Acknowledgements—The financial support of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.
REFERENCES 1. Warren, W. W., Walstedt, R. E., Brennert, G. F., Cava, R. J., Tycko, R., Bell, R. F. and Dabbagh, G., Phys. Rev. Lett., 1989, 62, 1193. 2. Loram, J. W., Mirza, K. A., Cooper, J. R., Liang, W. Y., J. Supercond., 1994, 7, 243. 3. Loram, J. W., Mirza, K. A., Wade, J. M., Cooper, J. R. and Liang, W. Y., Physica C, 1994, 235–240, 135. 4. Gurvitch, M. and Fiory, A. T., Phys. Rev. Lett., 1987, 59, 1337. 5. Batlogg, B., Hwang, H. Y., Takagi, H., Cava, R. J., Kao, H. L., Kwo, J., Physica C, 1994, 235–240, 130. 6. Puchkov, A. V., Fournier, P., Timusk, T. and Kolesnikov, N. N., Phys. Rev. Lett., 1996, 77, 1853. 7. Puchkov, A. V., Fournier, P., Basov, D. N., Timusk, T., Kapitulnik, A. and Kolesnikov, N. N., Phys. Rev. Lett., 1996, 77, 3212. 8. Loeser, A. G., Shen, Z.-X., Dessau, D. S., Marshall, D. S., Park, C-H., Fournier, P. and Kapitulnik, A., Science, 1996, 273, 325. 9. Marshall, D. S., Dessau, D. S., Loeser, A. G., Park, C-H., Matsuura, A. Y., Eckstein, J. N., Bozovic, I., Fournier, P., Kapitulnik, A., Spicer, W. E. and Shen, Z.-X., Phys. Rev. Lett., 1996, 76, 4841. 10. Ding, H., Yokoya, T., Campuzano, J. C., Takahashi, T., Randeria, M., Norman, M. R., Mochiku, T., Kadowaki, K. and Giapintzakis, J., Nature, 1996, 382, 51. 11. Ding, H., Norman, M. R., Yokoya, T., Takeuchi, T., Randeria, M., Campuzano, J. C., Takahashi, T., Mochiku, T. and Kadowaki, K., Phys. Rev. Lett., 1997, 78, 2628. 12. Slakey, F., Klein, M. V., Rice, J. P. and Ginsberg, D. M., Phys. Rev. B, 1990, 42, 2643. 13. Chen, X. K., Naeini, J. G., Hewitt, K. C., Irwin, J. C., Liang, R. and Hardy, W. N., Phys. Rev. B, 1997, 56, R513. 14. Nemetschek, R., Opel, M., Hoffmann, C., Muller, P. F., Hackl, R., Berger, H., Forro, L., Erb, A., Walker, E., Phys. Rev. Lett., 1997, 78, 4873. 15. Blumberg, G., Klein, M. V., Kadowaki, K., Kendziora, C., Guptasarma, P. and Hinks, D., J. Phys. Chem. Solids, 1998, these proceedings. 16. Klein, M. V. and Dierker, S. B., Phys. Rev. B, 1984, 29, 4976. 17. Devereaux, T. P., Einzel, D., Stadlober, B., Hackl, R., Leach, D. H. and Neumeler, J. J., Phys. Rev. Lett., 1994, 72, 396. 18. Chen, X. K., Irwin, J. C., Trodahl, H. J., Kimura, T. and Kishio, K., Phys. Rev. Lett., 1994, 73, 3290.