Spin-wave dispersion in antiferromagnetic cuprates mapped with soft X-rays


In magnetically-ordered systems the inversion of one atomic spin leads to a collective excited state called a magnon or spin-wave that travels along the magnetic lattice. The relation between energy and momentum (dispersion) of spin waves has been measured for the first time with X-rays. Scientists working at the ESRF made this discovery using the technique of resonant soft X-ray inelastic scattering.

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In the early days of high-temperature superconductivity it was already recognised that the magnetic properties of high-temperature superconducting materials are intimately related to their superconducting properties. When doped, the long-range ordered antiferromagnetic background of pristine copper oxide insulators disappears, leading to short range antiferromagnetic fluctuations and superconductivity. For this reason the magnetic properties of parent compounds have attracted so much attention since the discovery of superconductivity in cuprates. To date, inelastic neutron scattering has practically been the only experimental technique available for studying the spin dynamics of cuprates and of most of the ferromagnetic and antiferromagnetic systems. Nevertheless neutrons suffer from the very small scattering cross sections, which impose the use of big single-crystals, not always available, and are difficult to use for high-energy excitations such as those in layered cuprates. These difficulties are overcome by resonant inelastic X-ray scattering (RIXS) which can be performed on cubic micrometre volumes and can profit from strong resonant enhancements mainly in the soft X-ray range (400 – 1000 eV). Thus we have used high resolution RIXS at the Cu 2p → 3d resonance to study the spin-wave dispersion in the antiferromagnetic insulating La2CuO4 and CaCuO2 compounds, where single and multiple magnon excitations are expected up to 500 meV.

Previously Hill et al. [1] found that Cu K edge RIXS spectra of undoped antiferromagnetic cuprates at 20 K show a sizable peak around 500 meV when the transferred momentum q corresponds to the (PI.gif,0) point of the 2D 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 the magnetic moment of the system by one unit. 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 employed the same technique in the soft X-ray range, working at the L3 edge (2p3/2 → 3d transition) of Cu. We found that Cu L3 RIXS is an ideal technique to determine magnon dispersion in cuprates. In La2CuO4 and CaCuO2 we saw dispersing spectral features both at room temperature and at 30 K.

Figure 1 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 (central panel), in addition to single magnons (bottom panel). In undoped cuprates, a two-dimensional antiferromagnetic order of the spin ½ Cu2+ sites always characterises the ground state. In the intermediate state the 3d10 configuration (spin zero) makes the scattering site act as a “non-magnetic” impurity which 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 [3].

Schematics of RIXS at the Cu L3 edge and how RIXS can excite bi-magnons and single magnons.

Figure 1. Schematics of RIXS at the Cu L3 edge (top panel) and how RIXS can excite bi-magnons (central panel) and single magnons (bottom panel).

 The measurements at beamline ID08 with the AXES spectrometer have a combined energy resolution of 400 meV, sufficient to resolve the magnetic excitations in the 100-400 meV energy range by exploiting the fact that the elastic peak is very weak. We are working at present on the problem of separating single from multiple magnons. The results, summarised in Figure 2, show a clear dispersive behaviour already in the raw data (left panel). The spectra are labelled as function of qn = q|| × a; q|| is the transferred momentum component in the ab plane and a is the in-plane lattice parameter, so qn is adimensional and equals PI.gif 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 accordingly to ref. [2].

Cu L3 RIXS results of La2CuO4: From the raw RIXS data corresponding to the given dots in the Brillouin zone, we have extracted the peak dispersion curve which is compared with the RIXS theory and neutron scattering.

Figure 2. Cu L3 RIXS results of La2CuO4: From the raw RIXS data (left and middle panel) corresponding to the given dots in the Brillouin zone (top right panel), we have extracted the peak dispersion curve which is compared with the RIXS theory and neutron scattering in the bottom right panel.

 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 including the experimental resolution, agrees very well with the experimental data points. Nevertheless a contribution from single magnons is present too. These results demonstrate that RIXS can be a powerful complement to inelastic neutron scattering in the study of collective excitations in general, having magnetic character or not. Until now RIXS has been limited by energy resolution, particularly difficult to achieve with soft x-rays. These limitations have eventually been overcome thanks to the work done over the last 15 years at the ESRF by the AXES group (Politecnico di Milano, Italy) in collaboration with the ID08 team, leading to crucial advances both in the instrumentation and in the understanding of RIXS. That experience has also greatly contributed to some recent results [4,5] in collaboration with the Swiss Light Source, and provides motivation for the new RIXS beamline for the ESRF, aimed at gaining an order of magnitude in resolution with respect to the data presented here, i.e. 30 meV at Cu L3.

[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).
[3] L.J.P. Ament, G. Ghiringhelli, M. Moretti Sala, L. Braicovich and J. van den Brink, arXiv:0903.3021v1 (2009).
[4] G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, N.V. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, Rev. Sci. Instrum. 77, 113108 (2006).
[5] G. Ghiringhelli, A. Piazzalunga, C. Dallera, T. Schmitt, V. N. Strocov, J. Schlappa, L. Patthey, X. Wang, H. Berger, and M. Grioni, Phys. Rev. Lett. 102, 027401 (2009).

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), Dispersion of magnetic excitations in the cuprate La2CuO4 and CaCuO2 compounds measured using resonant X-ray scattering, Phys. Rev. Lett. 102, 167401 (2009).
(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)


Top image: Magnons studied with RIXS