In order to better understand the nature of excitation spectra in Sr₁₄Cu₂₄O₄₁, we recently performed accurate polarimetric inelastic-neutron-scattering studies of the chain and ladder excitations in this compound. By measuring the spin-flip and non spin-flip contributions for the incident polarisation applied parallel and perpendicular to the scattering vector Q we have been able to separate the nuclear and the various magnetic components. Quite unexpectedly, our results reveal the existence of a strong anisotropy of the magnetic inelastic structure factors, which could be the signature of orbital effects predicted theoretically.

The understanding of high-T_c superconductivity in cuprates leads physicists to study materials with related crystallographic structures or showing similar electronic processes. Among those materials, the spin-ladder compound Sr₁₄Cu₂₄O₄₁ (SCO) is a good candidate to investigate. Its crystallographic structure is a misfit stacking of layers of two distinct quantumspin systems: linear edge-sharing CuO₂ chains and 2-leg Cu₂O₃ spin-ladders (figure 1). The pure compound naturally contains hole carriers which are mainly located in the chains and by substitution of Ca for Sr, some holes are transfered from the chains to the ladders and an insulator-to-metal transition appears. Furthermore, by applying a high pressure (3GPa) on a highly Cadoped compound, superconductivity is observed with a critical temperature of the order of 10K. Thus, this holetransfer mechanism leading to superconductivity is very similar to the one observed in the high-T_c superconductors YBa₂Cu₃O_6+δ and the characterisation of magnetic excitations in this spin-ladder compound may provide a better understanding of the role of magnetism in the pairing mechanism. In the two sub-systems, the existence of magnetic dimers leads to the opening of magnetic gaps in the inelastic spectra. In order to probe the exact nature of elementary excitations in the chain and ladder sub-systems of SCO (in particular the possible existence of hybride modes), we have recently performed longitudinal polarisation analysis experiments on the CRG three-axis spectrometer IN22. Figure 2 shows a typical constant-Q scan performed at the scattering vector Q = (-3, 0, 0.8), characteristic of the chain sub-system, with the incident polarisation kept parallel to Q during the scan. Within this configuration, one is able to separate unambiguously the magnetic (all spin- flip) and structural (all non spin-flip) contributions. At the accuracy of the measurements, no structural components could be detected, thus confirming the purely magnetic nature of both modes at 11 meV and 12.2 meV. Interestingly, the peaks are resolution-limited, implying a very weak intrinsic splitting of the triplet modes.

From the structural point of view, the octahedral environment of a single copper ion (see pink squares in figure 1) is similar in the ladder and in the chain sub-system, so the anisotropy of the Landé g-factor is expected to be similar in both systems. It is not possible to perform measurements of the gtensor in the ladder sub-system due to the high value of the magnetic gap. However, in the chain sub-system, applying a strong magnetic field perpendicular to the (a, c) plane , we were able to left the degeneracy of the triplet state and to determine the Landé g-factor.
Due to crossing of the dispersion curves of magnetic excitations in the chain sub-system, the two triplet states are superimposed at Q = (2.5, 0, 0.25) and we can observe from the scan depicted in figure 3 that the triplet states are well-defined and resolutionlimited in zero field (blue curve). The inelastic scan under a strong magnetic field of 11.5 Tesla is also shown in the same figure (red curve) and we clearly observe the splitting of the triplet state into three modes with a splitting of 1.5 meV = g_bµ_βH. From our measurements, we determine that g-tensor component along the direction perpendicular to the plane of chains is g_b = 2.31 ± 0.06. This value is very close to the value found recently by ESR [1] and confirms the rather strong anisotropy previously found by magnetic susceptibility measurements on single crystals [2], signature of strong spin-orbit couplings.

Such an anisotropy is in contradiction with the absence of splitting in the zero field data. In order to understand this paradoxical situation, we have used the LPA to determine separately the in-plane and the out-of-plane dynamical structure factors, by measuring the polarization dependence of the scattering cross-sections with the incident polarization applied successively along the scattering vector Q, perpendicular to Q in the CuO₂ planes, and perpendicular to these planes. Similar measurements have been performed on the ladder contribution and quite surprisingly, we observe in both cases a strong anisotropy =1.4 ± 0.15, which means that the two-point correlation functions are much better established for the components perpendicular to the CuO₂ or Cu₂O₃ planes. To conclude, the strong anisotropy observed in the dynamical correlation functions together with the absence of a gap splitting in zero-field, lead us to believe that in SCO the hamiltonian should not be a simple Heisenberg one, but should contains more complicated terms. Indeed, the paradoxical situation could very likely be understood by taking into account the orbital degrees of freedom and the spin-orbit couplings, expected to be strong in Sr₁₄Cu₂₄O₄₁.