In the past decade, Resonant Inelastic X-ray Scattering (RIXS) has made remarkable progress as a spectroscopic technique. This is a direct result of the availability of highbrilliance synchrotron X-ray radiation sources and of advanced photon detection instrumentation. The technique's unique capability to probe elementary excitations in complex materials by measuring their energy-, momentum-, and polarization-dependence has brought RIXS to the forefront of experimental photon science. We review both the experimental and theoretical RIXS investigations of the past decade, focusing on those determining the low-energy charge, spin, orbital and lattice excitations of solids. We present the fundamentals of RIXS as an experimental method and then review the theoretical state of affairs, its recent developments and discuss the different (approximate) methods to compute the dynamical RIXS response. The last decade's body of experimental RIXS data and its interpretation is surveyed, with an emphasis on RIXS studies of correlated electron systems, especially transition metal compounds. Finally, we discuss the promise that RIXS holds for the near future, particularly in view of the advent of x-ray laser photon sources.

We probe the collective magnetic modes of La2CuO4 and underdoped La2-xSrxCuO4 (LSCO) by momentum resolved resonant inelastic x-ray scattering (RIXS) at the Cu L3 edge. For the undoped antiferromagnetic sample, we show that the single magnon dispersion measured with RIXS coincides with the one determined by inelastic neutron scattering, thus demonstrating that x rays are an alternative to neutrons in this field. In the spin dynamics of LSCO, we find a branch dispersing up to approximately 400 meV coexisting with one at lower energy. The high-energy branch has never been seen before. It indicates that underdoped LSCO is in a dynamic inhomogeneous spin state.

By resonant inelastic x-ray scattering in the soft x-ray regime we probe the dynamical multiple-spin correlations in the antiferromagnetic cuprates La2CuO4 and CaCuO2. High resolution measurements at the copper L3 edge allow the clear observation of dispersing bimagnon excitations. Theory based on the ultrashort core-hole lifetime expansion fits the data on these coherent spin excitations without free parameters.

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We measured the momentum dependence of magnetic excitations in the model spin-1=2 2D antiferromagnetic insulator Sr 2 CuO 2 Cl 2 (SCOC). We identify a single-spin-wave feature and a multimagnon continuum, with different polarization dependences. The spin waves display a large (70 meV) dispersion between the zone-boundary points (, 0) and (=2, =2). Employing an extended t-t 0 -t 00 -U one-band Hubbard model, we find significant electronic hopping beyond nearest-neighbor Cu ions, indicative of extended magnetic interactions. The spectral line shape at (, 0) indicates sizable quantum effects in SCOC and probably more generally in the cuprates. DOI: 10.1103/PhysRevLett.105.157006 PACS numbers: 74.72.Cj, 75.30.Ds, 78.70.Ck Magnetism in low-dimensional cuprates remains of considerable interest, in relation both to the fundamental quest to understand strong electron correlation and quantum spin effects in Mott insulators, and to the search for the mechanism of high-T c superconductivity. To lowest order, the undoped cuprate superconductors can be described by the spin 1=2 two-dimensional (2D) square-lattice nearestneighbor (NN) Heisenberg antiferromagnet, which is among the simplest and most studied models in magnetism [1]. The ground state displays classical order, reduced by quantum fluctuations at zero temperature and destroyed by thermal fluctuations at finite temperature. A possible crossover between renormalized classical [2] and quantum critical [3] scaling was tested experimentally in the undoped cuprates Sr 2 CuO 2 Cl 2 (SCOC) [4] and La 2 CuO 4 (LCO) [5], and in the organometallic salt CuðDCOOÞ 2 Á 4D 2 O (CFTD) [6]. However, while the latter shows only nearest-neighbor coupling, high-energy inelastic neutron scattering (INS) data on LCO [7] suggest that further-neighbor magnetic interactions influence the scaling measurements. Frustrated further-neighbor interactions could also bring the undoped cuprates closer to the valence bond liquid proposed as mechanism for superconductivity [8].It is therefore timely to investigate the excitation spectrum of SCOC, as an important model system. Inelastic neutron scattering (INS) measurements of SCOC have been limited to low energies and small momenta around the ordering wave vector [4]. In this Letter we report the full magnetic excitation spectrum measured by resonant inelastic x-ray scattering (RIXS). We discover a surprisingly large dispersion along the magnetic Brillouin zone boundary (ZB). An analysis of the data in terms of an extended Hubbard model yields a quantitative estimation of sizable further-neighbor electronic hopping. The resulting series of longer-ranged magnetic interactions enhance quantum fluctuations, in agreement with the reduced ordered moment. The importance of quantum fluctuations is further revealed by differences in the spectral line shapes at the (À, 0) and (À=2, =2) ZB points.SCOC is an insulating single-layer parent compound of the high-T c superconducting (SC) materials. It is isostructural to the high-temperature tetragonal phase of...

We show that, contrary to common lore, in resonant inelastic x-ray scattering (RIXS) at the copper L-and M-edge direct spin-flip scattering is in principle allowed. We demonstrate how this possibility can be exploited to probe the momentum dependent magnetic properties of cuprates such as the high Tc superconductors and compute in detail the relevant local and momentum dependent magnetic scattering amplitudes, which we compare to the elastic and dd-excitation scattering intensities. For cuprates these results put RIXS as a technique on the same footing as neutron scattering.Introduction. In recent years the experimental technique of resonant inelastic x-ray scattering (RIXS) has made tremendous progress in terms of energy and momentum resolution [1,2,3,4,5,6,7,8,9,10,11]. RIXS is particularly apt to probe the properties of strongly correlated electrons, for instance the ones of the transition metal oxides [1,2]. With an incoming x-ray of energy ω in first an electron is resonantly excited from a core level into the valence shell. Subsequently one measures the energy ω out of the outgoing x-ray resulting from the recombination of the core hole with a valence electron. Depending on the resonance that the experiment is performed at, ω in corresponds to the transition metal K-edge (1s → 4p), L-edge (2p → 3d) or M-edge (3p → 3d). Compared to the many other photon scattering techniques, RIXS has the advantage that there is no core hole present in the final state, so that the energy lost by the scattered photon at a transition metal L-or M-edge is directly related to electronic excitations within the strongly correlated 3d valence bands. The chemical selectivity and bulk sensitivity of RIXS allows the study of the electronic and magnetic properties of, for example, complex and nanostructured materials that might be inaccessible with non-resonant techniques.

We show that high resolution Resonant Inelastic X-ray Scattering (RIXS) provides direct, elementspecific and momentum-resolved information on the electron-phonon (e-p) coupling strength. Our theoretical analysis demonstrates that the e-p coupling can be extracted from RIXS spectra by determining the differential phonon scattering cross section. An alternative, very direct manner to extract the coupling is to use the one and two-phonon loss ratio, which is governed by the e-p coupling strength and the core-hole life-time. This allows measurement of the e-p coupling on an absolute energy scale. PACS numbers: 78.70.CkOften novel electronic properties of a material can be understood by systematically unravelling the interaction between its electrons and phonons. Tunable electric transport properties in molecular crystals, for instance, are explained by the presence of a strong electronphonon (e-p) coupling [1]. The dressing of electrons by phonons is also responsible for the colossal magnetoresistance effect in manganites [2]. More delicate is the role that the e-p interaction plays in high T c superconducting cuprates -topic of a persisting debate [3][4][5]. The lack of a technique to measure the e-p coupling strength perpetuates this controversy. Here we show that high resolution Resonant Inelastic X-ray Scattering (RIXS) can fill this void as it gives direct, element-specific and momentumresolved information on the coupling between electrons and phonons. We provide the theoretical framework required to distill e-p interaction strengths from RIXS, particularly in strongly correlated transition metal oxides such as the High T c cuprates.In RIXS experiments one scatters high energy, x-ray photons inelastically off a material [6]. The energy of the incident photons is chosen such that it coincides, and thus resonates, with an intrinsic electronic excitation of the material under study -one of the materials' x-ray absorption edges. At present the highest energy resolutions are reached at the L-edge of transition metal oxides, where an incident photon launches a 2p electron out of the atomic core into an empty 3d state around the Fermi-level. This highly unstable intermediate state decays rapidly, typically within 1-2 femtoseconds, so that the 2p core-state is refilled and an outgoing photon emitted. The state-of-the-art resolution is such that photon energy loss features on an energy scale of 25 meV can be distinguished at a copper or nickel L 3 -edge [7-9].This resolution has brought phonons within the energy window of observation and indeed last year for the first time phonon loss features were resolved in RIXS [8-10].To put this achievement in perspective, one should realize that the incident photons at the Cu L-edge have an energy of around 930 eV, implying experiments have a resolving power better than 10 4 . Advanced instrumentation will drive this up further. Here we show how the progress in accuracy allows the extraction of a number of characteristics of the e-p interaction directly from RIXS, including spatial...

Recent experiments on La 2 CuO 4 suggest that indirect resonant inelastic x-ray scattering ͑RIXS͒ might provide a probe for transversal spin dynamics. We present in detail a systematic expansion of the relevant magnetic RIXS cross section by using the ultrashort core-hole lifetime ͑UCL͒ approximation. We compute the scattering intensity and its momentum dependence in leading order of the UCL expansion. The scattering is due to two-magnon processes and is calculated within a linear spin-wave expansion of the Heisenberg spin model for this compound, including longer range and cyclic spin interactions. We observe that the latter terms in the Hamiltonian enhance the first moment of the spectrum if they strengthen the antiferromagnetic ordering. The theoretical spectra agree very well with experimental data, including the observation that scattering intensity vanishes for the transferred momenta q = ͑0,0͒ and q = ͑ , ͒. We show that at finite temperature, there is an additional single-magnon contribution to the scattering with a spectral weight proportional to T 3 . We also compute the leading corrections to the UCL approximation and find them to be small, setting the UCL results on a solid basis. All this univocally points to the conclusion that the observed low temperature RIXS intensity in La 2 CuO 4 is due to two-magnon scattering.