In the early days of high temperature superconductivity it was already recognised that magnetic properties of these materials are intimately related to the superconducting ones. When doped, the long-range ordered antiferromagnetic background of pristine copper oxide insulators gets frustrated leading to short range antiferromagnetic fluctuations and superconductivity. That is why the magnetic properties of parent compounds have attracted so much attention since the discovery of superconductivity in cuprates. The spin dynamics of cuprates has been studied up to now mostly with neutron inelastic scattering.

Recently Hill et al. [1] have found that Cu K edge resonant inelastic X-ray scattering (RIXS) spectra of undoped antiferromagnetic cuprates at 20 K show a sizable peak around 500 meV when the transferred momentum q corresponds to the (,0) point of the reciprocal space. This feature, suppressed by doping, has been assigned to the simultaneous excitation of two magnons. Magnons are collective excitations of a lattice presenting a long range magnetic order and they correspond to changing by one unit the magnetic moment of the system. Their non-local nature manifests itself in a dispersive behaviour, i.e. a non-constant relation between momentum and energy. Following that first indication, we have employed the same technique in the soft X-ray range, working at the L3 edge (2p 3d transition) of Cu. We have seen that Cu L3 RIXS is an ideal technique to determine magnon dispersion in cuprates. In La2CuO4 and CaCuO2 we have found dispersing spectral features both at room temperature and at 30 K.

Figure 110 shows how Cu L3 RIXS works in undoped cuprates, where all Cu sites are divalent (3d9 configuration) and how two magnons can be thereby excited simultaneously. In undoped cuprates, a two-dimensional antiferromagnetic order of the spin 1/2 Cu2+ sites always characterises the ground state. In the intermediate state, the 3d10 configuration (spin zero) makes the scattering site act as a magnetic impurity that quenches the super-exchange locally in the antiferromagnetic lattice. The screening by neighbouring sites can result in the generation of a couple of magnons. Similarly to optical Raman scattering, the total spin moment of the system is conserved, but finite energy and momentum have been transferred from the scattered photon to the system [2]. As opposed to K edge RIXS, a single magnon can also be excited in L3 RIXS due to the strong spin-orbit interaction in the 2p core hole present in the intermediate state.

Fig. 110: Schematics of RIXS at the Cu L3 edge and RIXS excitation of bi-magnons.

The measurements made at beamline ID08 with the AXES spectrometer have a combined energy resolution of 400 meV, sufficient to resolve the magnetic excitation in the 100-400 meV energy range. We are working at present on the problem of separating single from mutliple magnons. The results, summarised in Figure 111, show a clear dispersive behaviour already in the raw data (left panel). The spectra are labelled as function of qn = qII x a; qII is the transferred momentum component in the ab plane and a is the in plane lattice parameter, so qn is adimensional and equals at the zone boundary. In the right hand panel, the experimental data-points are compared to the single magnon results obtained on the same compound by inelastic neutron scattering and to the theoretical prediction for bi-magnons according to ref. [2].

Fig. 111: Cu L3 RIXS results of La2CuO4. The peak dispersion curve was extracted from the raw data (left panel) corresponding to the given dots in the Brillouin zone.

These results provide the first direct measurement of the magnon dispersion made with inelastic X-ray scattering. As the peak position exceeds the energy of a single magnon excitation measured with neutrons, an important contribution has to come from two magnon excitations. A theoretical calculation for bi-magnons, after broadening for inclusion into the experimental resolution, agrees very well with the experimental data points. Nevertheless a contribution from single magnons cannot be excluded. In the doped La1.85Sr0.15CuO4 sample we have measured a different dispersion curve, presenting a finite energy at qn = 0. In the doped compounds the measured excitations might have mixed spin-charge character.


Principal publication and authors

L. Braicovich (a), L.J.P. Ament (b), V. Bisogni (c), F. Forte (b,d), C. Aruta (e), G. Balestrino (f), N.B. Brookes (c), G.M. De Luca (e), P.G. Medaglia (f), F. Miletto Granozio (e), M. Radovic (e), M. Salluzzo (e), J. van den Brink (b,g), and G. Ghiringhelli (a), arXiv:0807:1140v1, (2008).
(a) CNR/INFM and Politecnico di Milano (Italy)
(b) Universiteit Leiden (The Netherlands)
(c) ESRF
(d) CNR/INFM and Università di Salerno (Italy)
(e) CNR/INFM and Università Federico II, Napoli (Italy)
(f) CNR/INFM and Università di Roma Tor Vergata (Italy)
(g) Radboud Universiteit Nijmegen (The Netherlands)


[1] J.P. Hill, G. Blumberg, Y.-J. Kim, D.S. Ellis, S. Wakimoto, R.J. Birgeneau, S. Komiya, Y. Ando, B. Liang, R.L. Greene, D. Casa, and T. Gog, Phys. Rev. Lett. 100, 097001 (2008).
[2] F. Forte, L.J.P. Ament and J. van den Brink, Phys. Rev. B 77, 134428 (2008).