H. He, C. Ulrich, and B. Keimer; Y. Sidis, P. Bourges, and L.P. Regnault (CEA, France);
N.S. Berzigiarova and N.N. Kolesnikov (Russian Academy of Sciences) Electronic conduction in the copper oxide high
temperature superconductors takes place pre-dominantly in structural units of chemical com-position CuO2, in which copper and oxy-gen atoms form an approximately square pla-nar arrangement. Most theoretical models of high temperature superconductivity are there-fore based on a two-dimensional square lat-tice. In real materials, however, deviations from this simple situation are nearly always present. For instance, buckling distortions of the CuO2 layers that are found in many cop-per oxides are thought to have a significant in-fluence on the electronic structure and on the superconducting transition temperature Tc. In-terlayer interactions in materials with closely
spaced CuO2 layers (forming bi- or trilayer units) or additional copper oxide chains in the crystal structure present further complications whose influence on the superconducting prop-erties remains a subject of debate. Experiments on Tl2Ba2CuO6δ, a material with unbuckled, widely spaced CuO2layers and a maximum Tc
around 90 K, have therefore played a pivotal role in resolving some issues central to our un-derstanding of these materials.
We have performed inelastic neutron scattering measurements of Tl2Ba2CuO6δnear optimum doping (Tc90 K) that provide evidence of a sharp magnetic resonant mode below Tc. A res-onant spin excitation of this kind has been
ex-tensively characterized by neutron scattering in the bilayer copper oxide YBa2Cu3O6δand was recently also observed in Bi2Sr2CaCu2O8δ, another bilayer compound. At all doping lev-els, strong line shape anomalies of this collec-tive spin excitation below Tc bear witness to a substantial interaction with charged ticles. Conversely, anomalies in the quasipar-ticle spectra observed by a variety of charge spectroscopies (including in particular angle re-solved photoemission, optical conductivity, and tunneling) have been interpreted as evidence of coupling to the neutron mode.
The correspondence between anomalous fea-tures in the spectra of spin and charge excita-tions has stimulated much theoretical work on the role of spin excitations in high temperature superconductivity. It is therefore of great inter-est to inter-establish whether the resonant spin exci-tation is a general feature of the various crys-tallographically distinct families of supercon-ducting copper oxides. The failure to detect such an excitation in the single-layer compound La2xSrxCuO4δ, despite much experimental effort, has hampered a unified phenomenology of the copper oxides, and it has left us with two distinct classes of high-Tcoxides with very dif-ferent spin excitation spectra. This
unsatisfac-tory situation provided the motivation for our experiment on a material with an ‘ideal’ crystal structure and low intrinsic disorder.
Together with HgBa2CuO4
δ, Tl2Ba2CuO6δ
holds the Tc record for single layer materials (about 92 K), indicating that disorder effects (which are presumably at least in part respon-sible for depressing Tcin La2xSrxCuO4δ) are minimal in this material. Unfortunately, the vol-ume of the largest Tl2Ba2CuO6δ crystals cur-rently available is more than two orders of mag-nitude 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 individ-ual crystals of optimally doped Tl2Ba2CuO6δ, a section of which is shown in Fig. 69(a). The rocking curve of the array had a full width at half maximum of 1.5Æ (Fig. 69(b)). The quality of the alignment was confirmed by studying se-lected acoustic phonons, which were used for a calibration of the magnetic cross section. The experiments were carried out on neutron triple axis spectrometers that use beam focusing tech-niques to ensure efficient beam delivery onto small samples.
Figure 69: (a) Photograph of the array of co-orientedTl2Ba2CuO6δsingle crystals. The crystals are glued onto Al plates only two of which is shown. (b) Rocking curve of the entire multicrystal array around the (1,1,0) Bragg reflection. The line is a Gaussian with a full width at half maximum of 1.5Æ.
Figure 70: (a), (b) Constant-energy scans alongQ= (H,H,L) with L = 10.7 at an energy of 47.5 meV at temperatures above and belowTc. The components of the wave vector are given in reciprocal lattice units (r.l.u.), that is, in units of the reciprocal lattice vectorsa=b= 1.62 ˚A1andc= 0.27 ˚A1of the tetragonal structure. The in-plane component1212corresponds to the antiferromagnetic wave vectorQAF= (π,πin a notation where the lattice parameter is set to unity. (c), (d) Constant-energy scans at different excitation energies belowTc.
Figures 70 and 71 show constant-energy and constant-Q scans, respectively, on the multi-crystal array. An enhancement of the intensity sharply concentrated around the in-plane wave vector Q = (π,π(that is, the wave vector char-acteristic of antiferromagnetic order in undoped copper oxides) and excitation energy 47 meV is observed below Tc. This is precisely the signa-ture of the resonant mode in YBa2Cu3O6δand Bi2Sr2CaCu2O8δ. When normalized per cop-per oxide layer, the spectral weight of the mode is comparable to that in the bilayer systems.
The intensity is independent of the momen-tum transfer perpendicular to the layers, as ex-pected for weak interlayer exchange
interac-tions. These and other data provide persua-sive evidence that the resonant mode is indeed present in Tl2Ba2CuO6δand must hence be re-garded as a property of a single, isolated cop-per oxide layer. Interestingly, the mode energy found in Tl2Ba2CuO6δ exceeds the ones in both YBa2Cu3O7and Bi2Sr2CaCu2O8δ. This is in agreement with models according to which the resonant mode is a collective excitation pulled below the quasiparticle pair production continuum by exchange interactions. The lower mode energy in the bilayer materials could thus be a consequence of the strong interactions be-tween the two CuO2 layers that form a bilayer unit.
Figure 71: Difference between constant-Qscans at T = 99 K(Tc) and T = 27 K (Tc), at wave vector Q= (0.5, 0.5, 12.25). The line is a Gaussian profile of width equal to the instrumental resolution. The constant negative offset arises from temperature de-pendent phonon scattering.
In summary, we have taken another step in a program to develop a comprehensive exper-imental 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 mm3-sized single crystals are avail-able. With time, other copper oxide families thus far not studied with neutrons may also be-come accessible to this technique.
The most important implication of our findings regards the unified phenomenological picture recently developed for spin and charge spec-troscopies of the copper oxides. The spectral anomalies that have been interpreted as evi-dence of coupling to the collective spin excita-tion are also present in optical conductivity and tunneling data on single-layer Tl2Ba2CuO6δ, and equally pronounced as in analogous data on bilayer materials. If the mode had turned out to be absent (or its spectral weight substan-tially diminished) in Tl2Ba2CuO6δ, this gen-eral approach would have become untenable. It is now time to further refine the description of the coupled spin and charge excitations in the cuprates, and to fully evaluate its implications for the mechanism of high temperature super-conductivity.