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Inelastic neutron scattering study of Tl2Ba2CuO6+δ
Journal of Physics and Chemistry of Solids 63 (2002) 2243–2246 www.elsevier.com/locate/jpcs
Inelastic neutron scattering study of Tl2Ba2CuO6þd B. Keimera,*, H. Hea, P. Bourgesb, Y. Sidisb, C. Ulricha, L.P. Regnaultc, S. Pailhe`sb, N.S. Berzigiarovad, N.N. Kolesnikovd a
Max-Planck-Institut fu¨r Festko¨rperforschung, 70569 Stuttgart, Germany Laboratoire Le´on Brillouin, CEA-CNRS, CE Saclay, 91191 Gif sur Yvette, France c CEA Grenoble, De´partement de Recherche Fondamentale sur la Matie`re Condense´e, 38054 Grenoble Cedex 9, France d Institute of Solid State Physics, Russian Academy of Science, Chernogolovka 142432, Russian Federation b
Abstract We present inelastic neutron scattering data on optimally doped Tl2Ba2CuO6þd ðTc ¼ 92 KÞ; a single-layer copper oxide with undistorted copper oxide planes. The data indicate a magnetic resonant mode below Tc, as previously observed in YBa2Cu3O6þd and Bi2Sr2CaCu2O8þd. The mode is thus a generic feature of the copper oxide superconductors. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: D. Superconductivity; C. Neutron scattering; A. Superconductors
Since the discovery of high temperature superconductivity, neutron scattering measurements have provided crucial clues to the origin of this phenomenon. Neutron scattering is the only technique capable of determining the spin susceptibility in a model-free manner over the entire Brillouin zone. Since large single crystals are needed, however, only two materials have so far been investigated in detail: La22xSrxCuO4þd and YBa2Cu3O6þd. The phenomena that were discovered now figure prominently in current theories of high temperature superconductivity, and at least some of the current disputes among theorists can be traced back to the fact that the magnetic dynamics in these two materials do not show a uniform picture. In particular, a sharp, strongly temperature dependent resonant mode at the commensurate wave vector Q ¼ ðp; pÞ dominates the spectrum in YBa2Cu3O6þd [1– 3]. The mode has not been found in La22xSrxCuO4þd despite much experimental effort [4]; if present in this material, its spectral weight must be substantially smaller than in YBa2Cu3O6þd. Conversely, pronounced incommensurate spin excitations are seen in La22xSrxCuO4þd over a wide range of energies [4]. They extend to very low energies at all doping levels x, and around x , 1=8 they become Goldstone modes of a magnetically ordered state, often termed the ‘striped phase’ [5,6]. From x , 1=8 and above, it thus appears * Corresponding author. E-mail address: [email protected] (B. Keimer).
reasonable to think of the incommensurate magnetic excitations as a signature of fluctuating stripes. Weak incommensurate excitations are also seen in YBa2Cu3O6þd [7– 9], but only over a very limited energy range below the resonant mode. They are closely related to the commensurate resonant mode, and at optimum doping both types of excitation appear only below Tc [9]. This observation is difficult to reconcile with a picture in which stripes form at high temperatures and superconductivity occurs at lower temperatures on a background of fluctuating stripes. Indeed, the incommensurate modes in YBa2Cu3O6þd are well described as part of a continuously dispersing resonant mode [10 – 12]. This leaves us with two classes of materials with disparate (though certainly somehow related) features in their magnetic spectra. There are several possible reasons for these discrepancies, such as disorder and soft lattice modes in La22xSrxCuO4þd, or magnetic interactions within a ‘bilayer’ of YBa2Cu3O6þd which are known to be substantial [13]. In order to elucidate the materials physics responsible for the discrepancies among these compounds and to bring out the underlying commonality that can then be related to the mechanism of high temperature superconductivity, it is imperative to investigate the magnetic spectra of copper oxides with different crystal structures and doping mechanisms. We have started a systematic investigation of other cuprate families by a series of experiments on optimally doped [14] and overdoped [15] Bi2Sr2CaCu2
0022-3697/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 3 6 9 7 ( 0 2 ) 0 0 2 5 6 - 1
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B. Keimer et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2243–2246
Fig. 1. (a) Crystal structure of Tl2Ba2CuO6þd, (b) photograph of the array of co-oriented Tl2Ba2CuO6þd single crystals. The crystals are glued onto Al plates of which only two are shown.
O8þd, where we observed a resonant mode akin to that in YBa2Cu3O6þd, albeit somewhat broadened by disorder. While these studies are important for comparison with the results obtained by other experimental techniques, such as tunneling [16] and photoemission [17,18], they do not provide an explanation for the puzzling disparity of the neutron scattering results. Since the superconducting transition temperature and crystal structure of Bi2Sr2CaCu2 O8þd (in particular the bilayer arrangement) are very similar to YBa2Cu3O6þd, it is not surprising to find similar spin excitations spectra. The purpose of the present study was to clarify the role of interlayer interactions by establishing the existence (or lack thereof) of the resonant mode in the Tl2Ba2CuO6þd system (Fig. 1(a)) where the layer spacing is much larger (and the
interlayer interactions hence much weaker) than in YBa2 Cu3O6þd and Bi2Sr2CaCu2O8þd. Together with HgBa2 CuO4þd, this material holds the Tc record for single layer materials (about 92 K), indicating that disorder effects (which are presumably at least in part responsible for depressing Tc in La22xSrxCuO4þd) are minimal in Tl2Ba2 CuO6þd. Finally, whereas different types of buckling distortions are present in the copper oxide planes of most of the high-Tc compounds, the layers in Tl2Ba2CuO6þd are unbuckled and the crystal structure is perfectly tetragonal. Unfortunately, the volume of the largest Tl2Ba2CuO6þd crystals currently available [20] is more than two orders of magnitude too small for inelastic neutron scattering, a situation that is unlikely to improve anytime soon because of difficulties associated with the toxicity of thallium. We therefore assembled a multicrystal array containing about 300 individual crystals of optimally doped Tl2Ba2CuO6þd, a section of which is shown in Fig. 1(b). The rocking curve of the array had a full width at half maximum of 1.58. The quality of the alignment was confirmed by studying selected acoustic phonons, which were used for a calibration of the magnetic cross-section. The experiments were carried out on the IN22 triple axis spectrometers at the Institut LaueLangevin in Grenoble, France, and at the 2T1 triple axis spectrometer at the Laboratoire Le´on Brillouin in Saclay, France, with fixed final energies of 14.7 and 30.5 meV, respectively. Both instruments use beam focusing techniques that ensure efficient beam delivery onto small samples. Some of our data will be published separately [19]. Although the sample volume was comparable to that of the Bi2Sr2CaCu2O8þd specimens studied before, the experiment was considerably more difficult because of the lower density of copper oxide layers and the increased background due to the aluminum plates and adhesive in the sample mount. The signal-to-background ratio was therefore poor, and a variety of cross-checks was performed in order to rule out spurious effects. It is well known, for instance, that accidental Bragg scattering can give rise to sharp extraneous features in the recorded spectrum [21]. Such processes depend sensitively on the final energy and are therefore ruled out if a given feature is independent of the final energy. The representative raw data shown in Figs. 2 and 3 were taken with the same energy transfer (47 meV) but different final neutron energies (14.7 and 30.5 meV, respectively). The peak around Q ¼ ðp; pÞ appears at low temperature in both data sets and therefore has to be of intrinsic origin. This is confirmed by its temperature dependence: While spurious processes are at most weakly temperature dependent, the observed peak disappears entirely upon heating (Fig. 2). A strongly temperature dependent intrinsic signal can arise either from magnetic scattering or from phonon scattering, and both possibilities have to be carefully considered. As for phonon scattering, the intensity at a given energy transfer could change due to a superconductivity-induced phonon shift, but this would require a shift in
B. Keimer et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2243–2246
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Fig. 2. Constant-energy scans along Q ¼ ðH; H; LÞ with (a and b) L ¼ 10:7 and (c and d) L ¼ 12:25 at an energy of 47.5 meV. The data were taken on the 2T1 spectrometer with a final neutron energy of 14.7 meV. The wave vector Q is given in reciprocal lattice units (r.l.u.).
Fig. 3. Constant-energy scans at (a) 47 and (b) 40 meV, taken on IN22 where the final energy was 30.5 meV. The wave vector Q is given in reciprocal lattice units (r.l.u.).
the order of the energy resolution of our experiment (about 5 meV full width at half maximum). Such a large shift has so far been observed only at one instance (HgBa2Ca3Cu4O10þd with four consecutive copper oxide layers) [22]. As for magnetic scattering, an intensity enhancement around Q ¼ ðp; pÞ below Tc is one of the signatures of the resonant mode in YBa2Cu3O6þd and Bi2Sr2CaCu2O8þd. In order to further discriminate between these two possibilities, constant-energy scans were carried out for different wave vector components, L, perpendicular to the copper oxide sheets (Fig. 2). Whereas at least for c-axis polarized phonons the intensity is expected to be strongly Ldependent [21], the magnetic intensity is expected to depend weakly on L due to the weak interactions between neighboring layers. Fig. 2 shows that the intensity is indeed identical at two different values of L, within the error, as expected for magnetic scattering. Further, we carried out constant-energy scans at different energy transfers (Fig. 3) as well as constant-Q scans around the in-plane wave vector ðp; pÞ: While strong phonon features are not present in the normal-state background around 47 meV, the results are fully consistent with a single resolution-limited magnetic mode that appears below Tc, as in optimally doped YBa2Cu3O6þd and Bi2Sr2CaCu2O8þd. The energy-integrated spectral weight of the mode at Q ¼ ðp; pÞ was obtained by normalizing the measured intensity to acoustic phonons. The result, 0:7 ^ 0:25m2B, is also consistent with the other
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B. Keimer et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2243–2246
two materials [2,14]. At present, the large background and small signal precludes ‘acid tests’ of the magnetic origin of the peak, such as a set of scans in higher Brillouin zones or an analysis of the spin polarization of incident and scattered neutrons. Such measurements have been carried out for YBa2Cu3O7 [21], and we hope to repeat them on a larger array in the future. However, the circumstantial evidence we have collected so far (energy, wave vector and temperature dependence of the intensity as well as the spectral weight) clearly speaks in favor of a magnetic assignment of the mode; any phonon scenario would be highly contrived. We therefore conclude that the magnetic resonant mode is indeed present in optimally doped Tl2Ba2CuO6þd, and that it is comparable in energy and spectral weight to the magnetic modes previously studied in the bilayer systems. This implies that it is a feature of a single copper oxide layer that is only weakly influenced by interactions with other layers. As the mode has now been observed in three materials whose crystals structures are quite different and whose most salient common feature is their high transition temperature Tc, it is tempting to correlate its apparent absence in La22xSrxCuO4þd with the intrinsically low Tc of that system. This conjecture could be tested through further work on other systems with low maximum Tc (such as Bi2Sr2CuO6þd, the single-layer version of Bi2Sr2CaCu2 O8þd). On the other hand, neither Tl2Ba2CuO6þd nor the bilayer materials studied with neutrons exhibit the pronounced low energy incommensurate spin excitations characteristic of La22xSrxCuO4þd; a search for such excitations in Tl2Ba2CuO6þd has so far remained fruitless. The incommensurate low energy fluctuations are thus weak in those materials in which superconductivity is most robust. They appear to originate from the proximity of the competing stripe instability that is most prominent in La22xSrxCuO4þd and its derivatives. In summary, we have taken another step in a program to develop a comprehensive experimental description of the spin dynamics of the copper oxide superconductors. This study demonstrates that inelastic neutron scattering experiments can be performed on materials of which only mm3sized single crystals are available. With time, other copper oxide families so far not studied with neutrons may also become accessible to this technique. So far, only unpolarizedbeam data are available on Tl2Ba2CuO6þd, and the data analysis relies to some degree on knowledge gained from other cuprate systems. With larger multicrystal arrays and further advances in neutron scattering instrumentation, it may become possible to perform polarized-beam experi-
ments in which the spin susceptibility can be extracted without interference from phonon scattering.
Acknowledgments We would like to thank Bernard Hennion for his support during the LLB experiment and Patrick Baroni for technical assistance. The work at the Institute of Solid State Physics was supported in part by the Russian Foundation for Basic Research. The work at the MPI-FKF was supported in part by the German Federal Ministry of Research and Technology (BMFT).
References [1] P. Bourges, in: J. Bok, G. Deutscher, D. Pavuna, S.A. Wolf (Eds.), The Gap Symmetry and Fluctuations in High Temperature Superconductors, vol. 349, Plenum Press, New York, 1998, and references therein. [2] H.F. Fong, et al., Phys. Rev. B 61 (2000) 14773 and references therein. [3] P. Dai, H.A. Mook, R.D. Hunt, F. Dogan, Phys. Rev. B 63 (2000) 054525 and references therein. [4] M.A. Kastner, R.J. Birgeneau, G. Shirane, Y. Endoh, Rev. Mod. Phys. 70 (1998) 897 and references therein. [5] J.M. Tranquada, et al., Phys. Rev. B 54 (1996) 7489. [6] J.M. Tranquada, et al., Phys. Rev. B 59 (1999) 14712. [7] H.A. Mook, et al., Nature 395 (1998) 580. [8] M. Arai, et al., Phys. Rev. Lett. 83 (1999) 608. [9] P. Bourges, et al., Science 288 (2000) 1234. [10] F. Onufrieva, P. Pfeuty, preprint cond-mat/9903097, unpublished. [11] M.R. Norman, Phys. Rev. B 63 (2001) 092509. [12] A.V. Chubukov, B. Janko, O. Tchernyshyov, Phys. Rev. B 63 (2001) 180507. [13] D. Reznik, et al., Phys. Rev. B 53 (1996) R14741. [14] H.F. Fong, et al., Nature 398 (1999) 588. [15] H. He, et al., Phys. Rev. Lett. 86 (2001) 1610. [16] J.F. Zasadzinski, et al., Phys. Rev. Lett. 87 (2001) 067005. [17] M. Eschrig, M.R. Norman, Phys. Rev. Lett. 85 (2000) 3261. [18] A. Abanov, A.V. Chubukov, Phys. Rev. Lett. 83 (1999) 1652. [19] H. He, P. Bourges, Y. Sidis, C. Ulrich, L.P. Regnault, S. Pailhes, N.S. Berzigiarova, N.N. Kolesnikov, B. Keimer, Science 295 (2002) 1047. [20] N.N. Kolesnikov, et al., Physica C 242 (1995) 385. [21] H.F. Fong, B. Keimer, D. Reznik, D.L. Milius, I.A. Aksay, Phys. Rev. B 54 (1996) 6708. [22] V.G. Hadjiev, et al., Phys. Rev. B 58 (1998) 1043.
Inelastic neutron scattering study of Tl2Ba2CuO6þd B. Keimera,*, H. Hea, P. Bourgesb, Y. Sidisb, C. Ulricha, L.P. Regnaultc, S. Pailhe`sb, N.S. Berzigiarovad, N.N. Kolesnikovd a
Max-Planck-Institut fu¨r Festko¨rperforschung, 70569 Stuttgart, Germany Laboratoire Le´on Brillouin, CEA-CNRS, CE Saclay, 91191 Gif sur Yvette, France c CEA Grenoble, De´partement de Recherche Fondamentale sur la Matie`re Condense´e, 38054 Grenoble Cedex 9, France d Institute of Solid State Physics, Russian Academy of Science, Chernogolovka 142432, Russian Federation b
Abstract We present inelastic neutron scattering data on optimally doped Tl2Ba2CuO6þd ðTc ¼ 92 KÞ; a single-layer copper oxide with undistorted copper oxide planes. The data indicate a magnetic resonant mode below Tc, as previously observed in YBa2Cu3O6þd and Bi2Sr2CaCu2O8þd. The mode is thus a generic feature of the copper oxide superconductors. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: D. Superconductivity; C. Neutron scattering; A. Superconductors
Since the discovery of high temperature superconductivity, neutron scattering measurements have provided crucial clues to the origin of this phenomenon. Neutron scattering is the only technique capable of determining the spin susceptibility in a model-free manner over the entire Brillouin zone. Since large single crystals are needed, however, only two materials have so far been investigated in detail: La22xSrxCuO4þd and YBa2Cu3O6þd. The phenomena that were discovered now figure prominently in current theories of high temperature superconductivity, and at least some of the current disputes among theorists can be traced back to the fact that the magnetic dynamics in these two materials do not show a uniform picture. In particular, a sharp, strongly temperature dependent resonant mode at the commensurate wave vector Q ¼ ðp; pÞ dominates the spectrum in YBa2Cu3O6þd [1– 3]. The mode has not been found in La22xSrxCuO4þd despite much experimental effort [4]; if present in this material, its spectral weight must be substantially smaller than in YBa2Cu3O6þd. Conversely, pronounced incommensurate spin excitations are seen in La22xSrxCuO4þd over a wide range of energies [4]. They extend to very low energies at all doping levels x, and around x , 1=8 they become Goldstone modes of a magnetically ordered state, often termed the ‘striped phase’ [5,6]. From x , 1=8 and above, it thus appears * Corresponding author. E-mail address: [email protected] (B. Keimer).
reasonable to think of the incommensurate magnetic excitations as a signature of fluctuating stripes. Weak incommensurate excitations are also seen in YBa2Cu3O6þd [7– 9], but only over a very limited energy range below the resonant mode. They are closely related to the commensurate resonant mode, and at optimum doping both types of excitation appear only below Tc [9]. This observation is difficult to reconcile with a picture in which stripes form at high temperatures and superconductivity occurs at lower temperatures on a background of fluctuating stripes. Indeed, the incommensurate modes in YBa2Cu3O6þd are well described as part of a continuously dispersing resonant mode [10 – 12]. This leaves us with two classes of materials with disparate (though certainly somehow related) features in their magnetic spectra. There are several possible reasons for these discrepancies, such as disorder and soft lattice modes in La22xSrxCuO4þd, or magnetic interactions within a ‘bilayer’ of YBa2Cu3O6þd which are known to be substantial [13]. In order to elucidate the materials physics responsible for the discrepancies among these compounds and to bring out the underlying commonality that can then be related to the mechanism of high temperature superconductivity, it is imperative to investigate the magnetic spectra of copper oxides with different crystal structures and doping mechanisms. We have started a systematic investigation of other cuprate families by a series of experiments on optimally doped [14] and overdoped [15] Bi2Sr2CaCu2
0022-3697/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 3 6 9 7 ( 0 2 ) 0 0 2 5 6 - 1
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B. Keimer et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2243–2246
Fig. 1. (a) Crystal structure of Tl2Ba2CuO6þd, (b) photograph of the array of co-oriented Tl2Ba2CuO6þd single crystals. The crystals are glued onto Al plates of which only two are shown.
O8þd, where we observed a resonant mode akin to that in YBa2Cu3O6þd, albeit somewhat broadened by disorder. While these studies are important for comparison with the results obtained by other experimental techniques, such as tunneling [16] and photoemission [17,18], they do not provide an explanation for the puzzling disparity of the neutron scattering results. Since the superconducting transition temperature and crystal structure of Bi2Sr2CaCu2 O8þd (in particular the bilayer arrangement) are very similar to YBa2Cu3O6þd, it is not surprising to find similar spin excitations spectra. The purpose of the present study was to clarify the role of interlayer interactions by establishing the existence (or lack thereof) of the resonant mode in the Tl2Ba2CuO6þd system (Fig. 1(a)) where the layer spacing is much larger (and the
interlayer interactions hence much weaker) than in YBa2 Cu3O6þd and Bi2Sr2CaCu2O8þd. Together with HgBa2 CuO4þd, this material holds the Tc record for single layer materials (about 92 K), indicating that disorder effects (which are presumably at least in part responsible for depressing Tc in La22xSrxCuO4þd) are minimal in Tl2Ba2 CuO6þd. Finally, whereas different types of buckling distortions are present in the copper oxide planes of most of the high-Tc compounds, the layers in Tl2Ba2CuO6þd are unbuckled and the crystal structure is perfectly tetragonal. Unfortunately, the volume of the largest Tl2Ba2CuO6þd crystals currently available [20] is more than two orders of magnitude too small for inelastic neutron scattering, a situation that is unlikely to improve anytime soon because of difficulties associated with the toxicity of thallium. We therefore assembled a multicrystal array containing about 300 individual crystals of optimally doped Tl2Ba2CuO6þd, a section of which is shown in Fig. 1(b). The rocking curve of the array had a full width at half maximum of 1.58. The quality of the alignment was confirmed by studying selected acoustic phonons, which were used for a calibration of the magnetic cross-section. The experiments were carried out on the IN22 triple axis spectrometers at the Institut LaueLangevin in Grenoble, France, and at the 2T1 triple axis spectrometer at the Laboratoire Le´on Brillouin in Saclay, France, with fixed final energies of 14.7 and 30.5 meV, respectively. Both instruments use beam focusing techniques that ensure efficient beam delivery onto small samples. Some of our data will be published separately [19]. Although the sample volume was comparable to that of the Bi2Sr2CaCu2O8þd specimens studied before, the experiment was considerably more difficult because of the lower density of copper oxide layers and the increased background due to the aluminum plates and adhesive in the sample mount. The signal-to-background ratio was therefore poor, and a variety of cross-checks was performed in order to rule out spurious effects. It is well known, for instance, that accidental Bragg scattering can give rise to sharp extraneous features in the recorded spectrum [21]. Such processes depend sensitively on the final energy and are therefore ruled out if a given feature is independent of the final energy. The representative raw data shown in Figs. 2 and 3 were taken with the same energy transfer (47 meV) but different final neutron energies (14.7 and 30.5 meV, respectively). The peak around Q ¼ ðp; pÞ appears at low temperature in both data sets and therefore has to be of intrinsic origin. This is confirmed by its temperature dependence: While spurious processes are at most weakly temperature dependent, the observed peak disappears entirely upon heating (Fig. 2). A strongly temperature dependent intrinsic signal can arise either from magnetic scattering or from phonon scattering, and both possibilities have to be carefully considered. As for phonon scattering, the intensity at a given energy transfer could change due to a superconductivity-induced phonon shift, but this would require a shift in
B. Keimer et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2243–2246
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Fig. 2. Constant-energy scans along Q ¼ ðH; H; LÞ with (a and b) L ¼ 10:7 and (c and d) L ¼ 12:25 at an energy of 47.5 meV. The data were taken on the 2T1 spectrometer with a final neutron energy of 14.7 meV. The wave vector Q is given in reciprocal lattice units (r.l.u.).
Fig. 3. Constant-energy scans at (a) 47 and (b) 40 meV, taken on IN22 where the final energy was 30.5 meV. The wave vector Q is given in reciprocal lattice units (r.l.u.).
the order of the energy resolution of our experiment (about 5 meV full width at half maximum). Such a large shift has so far been observed only at one instance (HgBa2Ca3Cu4O10þd with four consecutive copper oxide layers) [22]. As for magnetic scattering, an intensity enhancement around Q ¼ ðp; pÞ below Tc is one of the signatures of the resonant mode in YBa2Cu3O6þd and Bi2Sr2CaCu2O8þd. In order to further discriminate between these two possibilities, constant-energy scans were carried out for different wave vector components, L, perpendicular to the copper oxide sheets (Fig. 2). Whereas at least for c-axis polarized phonons the intensity is expected to be strongly Ldependent [21], the magnetic intensity is expected to depend weakly on L due to the weak interactions between neighboring layers. Fig. 2 shows that the intensity is indeed identical at two different values of L, within the error, as expected for magnetic scattering. Further, we carried out constant-energy scans at different energy transfers (Fig. 3) as well as constant-Q scans around the in-plane wave vector ðp; pÞ: While strong phonon features are not present in the normal-state background around 47 meV, the results are fully consistent with a single resolution-limited magnetic mode that appears below Tc, as in optimally doped YBa2Cu3O6þd and Bi2Sr2CaCu2O8þd. The energy-integrated spectral weight of the mode at Q ¼ ðp; pÞ was obtained by normalizing the measured intensity to acoustic phonons. The result, 0:7 ^ 0:25m2B, is also consistent with the other
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B. Keimer et al. / Journal of Physics and Chemistry of Solids 63 (2002) 2243–2246
two materials [2,14]. At present, the large background and small signal precludes ‘acid tests’ of the magnetic origin of the peak, such as a set of scans in higher Brillouin zones or an analysis of the spin polarization of incident and scattered neutrons. Such measurements have been carried out for YBa2Cu3O7 [21], and we hope to repeat them on a larger array in the future. However, the circumstantial evidence we have collected so far (energy, wave vector and temperature dependence of the intensity as well as the spectral weight) clearly speaks in favor of a magnetic assignment of the mode; any phonon scenario would be highly contrived. We therefore conclude that the magnetic resonant mode is indeed present in optimally doped Tl2Ba2CuO6þd, and that it is comparable in energy and spectral weight to the magnetic modes previously studied in the bilayer systems. This implies that it is a feature of a single copper oxide layer that is only weakly influenced by interactions with other layers. As the mode has now been observed in three materials whose crystals structures are quite different and whose most salient common feature is their high transition temperature Tc, it is tempting to correlate its apparent absence in La22xSrxCuO4þd with the intrinsically low Tc of that system. This conjecture could be tested through further work on other systems with low maximum Tc (such as Bi2Sr2CuO6þd, the single-layer version of Bi2Sr2CaCu2 O8þd). On the other hand, neither Tl2Ba2CuO6þd nor the bilayer materials studied with neutrons exhibit the pronounced low energy incommensurate spin excitations characteristic of La22xSrxCuO4þd; a search for such excitations in Tl2Ba2CuO6þd has so far remained fruitless. The incommensurate low energy fluctuations are thus weak in those materials in which superconductivity is most robust. They appear to originate from the proximity of the competing stripe instability that is most prominent in La22xSrxCuO4þd and its derivatives. In summary, we have taken another step in a program to develop a comprehensive experimental description of the spin dynamics of the copper oxide superconductors. This study demonstrates that inelastic neutron scattering experiments can be performed on materials of which only mm3sized single crystals are available. With time, other copper oxide families so far not studied with neutrons may also become accessible to this technique. So far, only unpolarizedbeam data are available on Tl2Ba2CuO6þd, and the data analysis relies to some degree on knowledge gained from other cuprate systems. With larger multicrystal arrays and further advances in neutron scattering instrumentation, it may become possible to perform polarized-beam experi-
ments in which the spin susceptibility can be extracted without interference from phonon scattering.
Acknowledgments We would like to thank Bernard Hennion for his support during the LLB experiment and Patrick Baroni for technical assistance. The work at the Institute of Solid State Physics was supported in part by the Russian Foundation for Basic Research. The work at the MPI-FKF was supported in part by the German Federal Ministry of Research and Technology (BMFT).
References [1] P. Bourges, in: J. Bok, G. Deutscher, D. Pavuna, S.A. Wolf (Eds.), The Gap Symmetry and Fluctuations in High Temperature Superconductors, vol. 349, Plenum Press, New York, 1998, and references therein. [2] H.F. Fong, et al., Phys. Rev. B 61 (2000) 14773 and references therein. [3] P. Dai, H.A. Mook, R.D. Hunt, F. Dogan, Phys. Rev. B 63 (2000) 054525 and references therein. [4] M.A. Kastner, R.J. Birgeneau, G. Shirane, Y. Endoh, Rev. Mod. Phys. 70 (1998) 897 and references therein. [5] J.M. Tranquada, et al., Phys. Rev. B 54 (1996) 7489. [6] J.M. Tranquada, et al., Phys. Rev. B 59 (1999) 14712. [7] H.A. Mook, et al., Nature 395 (1998) 580. [8] M. Arai, et al., Phys. Rev. Lett. 83 (1999) 608. [9] P. Bourges, et al., Science 288 (2000) 1234. [10] F. Onufrieva, P. Pfeuty, preprint cond-mat/9903097, unpublished. [11] M.R. Norman, Phys. Rev. B 63 (2001) 092509. [12] A.V. Chubukov, B. Janko, O. Tchernyshyov, Phys. Rev. B 63 (2001) 180507. [13] D. Reznik, et al., Phys. Rev. B 53 (1996) R14741. [14] H.F. Fong, et al., Nature 398 (1999) 588. [15] H. He, et al., Phys. Rev. Lett. 86 (2001) 1610. [16] J.F. Zasadzinski, et al., Phys. Rev. Lett. 87 (2001) 067005. [17] M. Eschrig, M.R. Norman, Phys. Rev. Lett. 85 (2000) 3261. [18] A. Abanov, A.V. Chubukov, Phys. Rev. Lett. 83 (1999) 1652. [19] H. He, P. Bourges, Y. Sidis, C. Ulrich, L.P. Regnault, S. Pailhes, N.S. Berzigiarova, N.N. Kolesnikov, B. Keimer, Science 295 (2002) 1047. [20] N.N. Kolesnikov, et al., Physica C 242 (1995) 385. [21] H.F. Fong, B. Keimer, D. Reznik, D.L. Milius, I.A. Aksay, Phys. Rev. B 54 (1996) 6708. [22] V.G. Hadjiev, et al., Phys. Rev. B 58 (1998) 1043.