Dispersion of magnetic excitations in the cuprate La2CuO4 and CaCuO2 compounds measured using resonant x-ray scattering

A setup for hard x-ray time-resolved resonant inelastic x-ray scattering at SwissFEL

We present a new setup for resonant inelastic hard x-ray scattering at the Bernina beamline of SwissFEL with energy, momentum, and temporal resolution. The compact R = 0.5 m Johann-type spectrometer can be equipped with up to three crystal analyzers and allows efficient collection of RIXS spectra. Optical pumping for time-resolved studies can be realized with a broad span of optical wavelengths. We demonstrate the performance of the setup at an overall ∼180 meV resolution in a study of ground-state and photoexcited (at 400 nm) honeycomb 5d iridate α-Li2IrO3. Steady-state RIXS spectra at the iridium L3-edge (11.214 keV) have been collected and are in very good agreement with data collected at synchrotrons. The time-resolved RIXS transients exhibit changes in the energy loss region <2 eV, whose features mostly result from the hopping nature of 5d electrons in the honeycomb lattice. These changes are ascribed to modulations of the Ir-to-Ir inter-site transition scattering efficiency, which we associate to a transient screening of the on-site Coulomb interaction.

Angle-resolved X-ray emission spectroscopy facility realized by an innovative spectrometer rotation mechanism at SPring-8 BL07LSU

The X-ray emission spectrometer at SPring-8 BL07LSU has recently been upgraded with advanced modifications that enable the rotation of the spectrometer with respect to the scattering angle. This major upgrade allows the scattering angle to be flexibly changed within the range of 45-135°, which considerably simplifies the measurement of angle-resolved X-ray emission spectroscopy. To accomplish the rotation system, a sophisticated sample chamber and a highly precise spectrometer rotation mechanism have been developed. The sample chamber has a specially designed combination of three rotary stages that can smoothly move the connection flange along the wide scattering angle without breaking the vacuum. In addition, the spectrometer is rotated by sliding on a flat metal surface, ensuring exceptionally high accuracy in rotation and eliminating the need for any further adjustments during rotation. A control system that integrates the sample chamber and rotation mechanism to automate the measurement of angle-resolved X-ray emission spectroscopy has also been developed. This automation substantially streamlines the process of measuring angle-resolved spectra, making it far easier than ever before. Furthermore, the upgraded X-ray emission spectrometer can now also be utilized in diffraction experiments, providing even greater versatility to our research capabilities.

Resonant inelastic X-ray scattering endstation at the 1C beamline of Pohang Light Source II

An endstation for resonant inelastic X-ray scattering (RIXS), dedicated to operations in the hard X-ray regime, has been constructed at the 1C beamline of Pohang Light Source II. At the Ir L₃-edge, a total energy resolution of 34.2 meV was achieved, close to the theoretical estimation of 34.0 meV, which considers factors such as the incident energy bandpass, intrinsic analyzer resolution, geometrical broadening of the spectrometer, finite beam-size effect and Johann aberration. The performance of the RIXS instrument is demonstrated by measuring the RIXS spectra of Sr₂IrO₄. The endstation can be easily reconfigured to measure energy-integrated intensities with very low background for diffuse scattering and diffraction experiments.

I21: an advanced high-resolution resonant inelastic X-ray scattering beamline at Diamond Light Source

The I21 beamline at Diamond Light Source is dedicated to advanced resonant inelastic X-ray scattering (RIXS) for probing charge, orbital, spin and lattice excitations in materials across condensed matter physics, applied sciences and chemistry. Both the beamline and the RIXS spectrometer employ divergent variable-line-spacing gratings covering a broad energy range of 280-3000 eV. A combined energy resolution of ∼35 meV (16 meV) is readily achieved at 930 eV (530 eV) owing to the optimized optics and the mechanics. Considerable efforts have been paid to the design of the entire beamline, particularly the implementation of the collection mirrors, to maximize the X-ray photon throughput. The continuous rotation of the spectrometer over 150° under ultra high vacuum and a cryogenic manipulator with six degrees of freedom allow accurate mappings of low-energy excitations from solid state materials in momentum space. Most importantly, the facility features a unique combination of the high energy resolution and the high photon throughput vital for advanced RIXS applications. Together with its stability and user friendliness, I21 has become one of the most sought after RIXS beamlines in the world.

Superconductivity in nickel-based 112 systems

Superconductivity has been discovered recently in infinite-layer nickel-based 112 thin films R_1−xA_xNiO₂ (R = La, Nd, Pr and A = Sr, Ca). They are isostructural to the infinite-layer cuprate (Ca,Sr)CuO₂ and are supposed to have a formal Ni 3d⁹ valence, thus providing a new platform to study the unconventional pairing mechanism of high-temperature superconductors. This important discovery immediately triggers a huge amount of innovative scientific curiosity in the field. In this paper, we try to give an overview of the recent research progress on the newly found superconducting nickelate systems, both from experimental and theoretical aspects. We mainly focus on the electronic structures, magnetic excitations, phase diagrams and superconducting gaps, and finally make some open discussions for possible pairing symmetries in Ni-based 112 systems.

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The infinite-layer nickel-based 112 thin films R_1−xA_xNiO₂ can host superconductivity up to 15 K

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R_1−xA_xNiO₂ is a multiband system, in which the short-range antiferromagnetic fluctuations can be detected

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R_1−xA_xNiO₂ has an unconventional superconducting pairing sate with a robust d-wave gap and a full gap without unified understanding

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The nickelate system provides a new platform for researching unconventional superconductivity

IRIXS Spectrograph: an ultra high-resolution spectrometer for tender RIXS

The IRIXS Spectrograph represents a new design of an ultra-high-resolution resonant inelastic X-ray scattering (RIXS) spectrometer that operates at the Ru L3-edge (2840 eV). First proposed in the field of hard X-rays by Shvyd'ko [(2015), Phys. Rev. A, 91, 053817], the X-ray spectrograph uses a combination of laterally graded multilayer mirrors and collimating/dispersing Ge(111) crystals optics in a novel spectral imaging approach to overcome the energy resolution limitation of a traditional Rowland-type spectrometer [Gretarsson et al. (2020), J. Synchrotron Rad. 27, 538-544]. In combination with a dispersionless nested four-bounce high-resolution monochromator design that utilizes Si(111) and Al2O3(110) crystals, an overall energy resolution better than 35 meV full width at half-maximum has been achieved at the Ru L3-edge, in excellent agreement with ray-tracing simulations.

Time-resolved RIXS experiment with pulse-by-pulse parallel readout data collection using X-ray free electron laser

Time-resolved resonant inelastic X-ray scattering (RIXS) is one of the developing techniques enabled by the advent of X-ray free electron laser (FEL). It is important to evaluate how the FEL jitter, which is inherent in the self-amplified spontaneous emission process, influences the RIXS measurement. Here, we use a microchannel plate (MCP) based Timepix soft X-ray detector to conduct a time-resolved RIXS measurement at the Ti L₃-edge on a charge-density-wave material TiSe₂. The fast parallel Timepix readout and single photon sensitivity enable pulse-by-pulse data acquisition and analysis. Due to the FEL jitter, low detection efficiency of spectrometer, and low quantum yield of RIXS process, we find that less than 2% of the X-ray FEL pulses produce signals, preventing acquiring sufficient data statistics while maintaining temporal and energy resolution in this measurement. These limitations can be mitigated by using future X-ray FELs with high repetition rates, approaching MHz such as the European XFEL in Germany and LCLS-II in the USA, as well as by utilizing advanced detectors, such as the prototype used in this study.

Magnetic Contrast at Spin-Flip Excitations: An Advanced X-Ray Spectroscopy Tool to Study Magnetic-Ordering

The determination of the local orientation and magnitude of the magnetization in spin textures plays a pivotal role in understanding and harnessing magnetic properties for technological applications. Here, we show that by employing the polarization dependence of resonant inelastic X-ray scattering (RIXS), we can directly probe the spin ordering with chemical and site selectivity. Applied on the prototypical ferrimagnetic mixed-valence system, magnetite ([Fe³⁺]_A[Fe³⁺,Fe²⁺]_BO₄), we can distinguish spin-flip excitations at the A and B antiferromagnetically coupled Fe³⁺ sublattices and quantify the exchange field. Furthermore, it is possible to determine the orbital contribution to the magnetic moment from detailed angular dependence measurements. RIXS dichroism measurements performed at spin-flip excitations with nanometer spatial resolution will offer a powerful mapping contrast suitable for the characterization of magnetic ordering at interfaces and engineered spin textures.

Detecting Crystallographic Lattice Chirality using Resonant Inelastic X-ray Scattering

The control and detection of crystallographic chirality is an important and challenging scientific problem. Chirality has wide ranging implications from medical physics to cosmology including an intimate but subtle connection in magnetic systems, for example Mn1-xFexSi. X-ray diffraction techniques with resonant or polarized variations of the experimental setup are currently utilized to characterize lattice chirality. We demonstrate using theoretical calculations the feasibility of indirect K -edge bimagnon resonant inelastic X-ray scattering (RIXS) spectrum as a viable experimental technique to distinguish crystallographic handedness. We apply spin wave theory to the recently discovered √5 × √5 vacancy ordered chalcogenide Rb0.89Fe1.58Se2 for realistic X-ray experimental set up parameters (incoming energy, polarization, Bragg angle, and experimental resolution) to show that the computed RIXS spectrum is sensitive to the underlying handedness (right or left) of the lattice. A Flack parameter definition that incorporates the right- and left- chiral lattice RIXS response is introduced. It is shown that the RIXS response of the multiband magnon system RbFeSe arises both from inter- and intra- band scattering processes. The extinction or survival of these RIXS peaks are sensitive to the underlying chiral lattice orientation. This in turn allows for the identification of the two chiral lattice orientations.

Spin waves and spin-state transitions in a ruthenate high-temperature antiferromagnet

Ruthenium compounds serve as a platform for fundamental concepts such as spin-triplet superconductivity¹, Kitaev spin liquids^2-5 and solid-state analogues of the Higgs mode in particle physics^6,7. However, basic questions about the electronic structure of ruthenates remain unanswered, because several key parameters (including Hund's coupling, spin-orbit coupling and exchange interactions) are comparable in magnitude and their interplay is poorly understood, partly due to difficulties in synthesizing large single crystals for spectroscopic experiments. Here we introduce a resonant inelastic X-ray scattering (RIXS)^8,9 technique capable of probing collective modes in microcrystals of 4d electron materials. We observe spin waves and spin-state transitions in the honeycomb antiferromagnet SrRu₂O₆ (ref. ¹⁰) and use the extracted exchange interactions and measured magnon gap to explain its high Néel temperature^11-16. We expect that the RIXS method presented here will enable momentum-resolved spectroscopy of a large class of 4d transition-metal compounds.

Continuum Charge Excitations in High-Valence Transition-Metal Oxides Revealed by Resonant Inelastic X-Ray Scattering

We present a theoretical investigation of the origin of Raman-like and fluorescencelike (FL) features of resonant inelastic x-ray scattering (RIXS) spectra. Using a combination of local-density approximation+dynamical mean-field theory and a configuration interaction solver for Anderson impurity model, we calculate the L-edge RIXS and x-ray absorption spectra of high-valence transition-metal oxides LaCuO_{3} and NaCuO_{2}. We analyze in detail the behavior of the FL feature and show how it is connected to the details of electronic and crystal structure. On the studied compounds we demonstrate how material details determine whether the electron-hole continuum can be excited in the L-edge RIXS process.

Magnon Splitting Induced by Charge Transfer in the Three-Orbital Hubbard Model

Understanding spin excitations and their connection to unconventional superconductivity have remained central issues since the discovery of cuprates. Direct measurement of the dynamical spin structure factor in the parent compounds can provide key information on important interactions relevant in the doped regime, and variations in the magnon dispersion have been linked closely to differences in crystal structure between families of cuprate compounds. Here, we elucidate the relationship between spin excitations and various controlling factors thought to be significant in high-T_{c} materials by systematically evaluating the dynamical spin structure factor for the three-orbital Hubbard model, revealing differences in the spin dispersion along the Brillouin zone axis and the diagonal. Generally, we find that the absolute energy scale and momentum dependence of the excitations primarily are sensitive to the effective charge-transfer energy, while changes in the on-site Coulomb interactions have little effect on the details of the dispersion. In particular, our result highlights the splitting between spin excitations along the axial and diagonal directions in the Brillouin zone. This splitting decreases with increasing charge-transfer energy and correlates with changes in the apical oxygen position, and general structural variations, for different cuprate families.

Quartz-based flat-crystal resonant inelastic x-ray scattering spectrometer with sub-10 meV energy resolution

Continued improvement of the energy resolution of resonant inelastic x-ray scattering (RIXS) spectrometers is crucial for fulfilling the potential of this technique in the study of electron dynamics in materials of fundamental and technological importance. In particular, RIXS is the only alternative tool to inelastic neutron scattering capable of providing fully momentum resolved information on dynamic spin structures of magnetic materials, but is limited to systems whose magnetic excitation energy scales are comparable to the energy resolution. The state-of-the-art spherical diced crystal analyzer optics provides energy resolution as good as 25 meV but has already reached its theoretical limit. Here, we demonstrate a novel sub-10 meV RIXS spectrometer based on flat-crystal optics at the Ir-L3 absorption edge (11.215 keV) that achieves an analyzer energy resolution of 3.9 meV, very close to the theoretical value of 3.7 meV. In addition, the new spectrometer allows efficient polarization analysis without loss of energy resolution. The performance of the instrument is demonstrated using longitudinal acoustical and optical phonons in diamond, and magnon in Sr₃Ir₂O₇. The novel sub-10 meV RIXS spectrometer thus provides a window into magnetic materials with small energy scales.

Indirect K-edge bimagnon resonant inelastic x-ray scattering spectrum of α-FeTe

We calculate the K-edge indirect bimagnon resonant inelastic x-ray scattering (RIXS) intensity spectra of the bicollinear antiferromagnetic order known to occur in the α-FeTe chalcogenide system. Utilizing linear spin wave theory for this large-S spin system we find that the bimagnon spectrum contains four scattering channels (two intraband and two interband). We find from our calculations that for suitable energy-momentum combination the RIXS spectra can exhibit a one-, two- or three- peak structure. The number of peaks provides a clue on the various bimagnon excitation processes that can be supported both in and within the acoustic and optical magnon branches of the bicollinear antiferromagnet. Unlike the RIXS response of the antiferromagnetic or the collinear antiferromagnetic spin ordering, the RIXS intensity spectrum of the bicollinear antiferromagnet does not vanish at the magnetic ordering wave vector [Formula: see text]. It is also sensitive to next-next nearest neighbor and biquadratic coupling interactions. Our predicted RIXS spectrum can be utilized to understand the role of multi-channel bimagnon spin excitations present in the α-FeTe chalcogenide.

Orbital breathing effects in the computation of x-ray d-ion spectra in solids by ab initio wave-function-based methods

In existing theoretical approaches to core-level excitations of transition-metal ions in solids relaxation and polarization effects due to the inner core hole are often ignored or described phenomenologically. Here we set up an ab initio computational scheme that explicitly accounts for such physics in the calculation of x-ray absorption and resonant inelastic x-ray scattering spectra. Good agreement is found with experimental transition-metal L-edge data for the strongly correlated d ⁹ cuprate Li₂CuO₂, for which we determine the absolute scattering intensities. The newly developed methodology opens the way for the investigation of even more complex d ⁿ electronic structures of group VI B to VIII B correlated oxide compounds.

Quenched Magnon excitations by oxygen sublattice reconstruction in (SrCuO2)n/(SrTiO3)2 superlattices

The recently discovered structural reconstruction in the cuprate superlattice (SrCuO2)n/(SrTiO3)2 has been investigated across the critical value of n = 5 using resonant inelastic x-ray scattering (RIXS). We find that at the critical value of n, the cuprate layer remains largely in the bulk-like two-dimensional structure with a minority of Cu plaquettes being reconstructed. The partial reconstruction leads to quenching of the magnons starting at the Γ-point due to the minority plaquettes acting as scattering points. Although comparable in relative abundance, the doped charge impurities in electron-doped cuprate superconductors do not show this quenching of magnetic excitations.

Theoretical approach to resonant inelastic x-ray scattering in iron-based superconductors at the energy scale of the superconducting gap

We develop a phenomenological theory to predict the characteristic features of the momentum-dependent scattering amplitude in resonant inelastic x-ray scattering (RIXS) at the energy scale of the superconducting gap in iron-based super-conductors. Taking into account all relevant orbital states as well as their specific content along the Fermi surface we evaluate the charge and spin dynamical structure factors for the compounds LaOFeAs and LiFeAs, based on tight-binding models which are fully consistent with recent angle-resolved photoemission spectroscopy (ARPES) data. We find a characteristic intensity redistribution between charge and spin dynamical structure factors which discriminates between sign-reversing and sign-preserving quasiparticle excitations. Consequently, our results show that RIXS spectra can distinguish between s± and s++ wave gap functions in the singlet pairing case. In addition, we find that an analogous intensity redistribution at small momenta can reveal the presence of a chiral p-wave triplet pairing.

Raman and fluorescence characteristics of resonant inelastic X-ray scattering from doped superconducting cuprates

Measurements of spin excitations are essential for an understanding of spin-mediated pairing for superconductivity; and resonant inelastic X-ray scattering (RIXS) provides a considerable opportunity to probe high-energy spin excitations. However, whether RIXS correctly measures the collective spin excitations of doped superconducting cuprates remains under debate. Here we demonstrate distinct Raman- and fluorescence-like RIXS excitations of Bi_1.5Pb_0.6Sr_1.54CaCu₂O_8+δ. Combining photon-energy and momentum dependent RIXS measurements with theoretical calculations using exact diagonalization provides conclusive evidence that the Raman-like RIXS excitations correspond to collective spin excitations, which are magnons in the undoped Mott insulators and evolve into paramagnons in doped superconducting compounds. In contrast, the fluorescence-like shifts are due primarily to the continuum of particle-hole excitations in the charge channel. Our results show that under the proper experimental conditions RIXS indeed can be used to probe paramagnons in doped high-T_c cuprate superconductors.

Effect of broken symmetry on resonant inelastic x-ray scattering from undoped cuprates

We study the magnetic excitation spectra of resonant inelastic x-ray scattering (RIXS) at the L-edge from undoped cuprates beyond the fast collision approximation. We analyse the effect of the symmetry breaking ground state on the RIXS process of the Heisenberg model by using a projection procedure. We derive the expressions of the scattering amplitude in both one-magnon and two-magnon excitation channels. Each of them consists of the isotropic and anisotropic contributions. The latter is a new finding and attributed to the long range order of the ground state. The presence of anisotropic terms is supported by numerical calculations on a two-dimensional spin cluster. We express the RIXS spectra in the form of spin-correlation functions with the coefficients evaluated on the cluster, and calculate the function in a two dimensional system within the 1/S expansion. Due to the anisotropic terms, the spectral intensities are considerably enhanced around momentum transfer q = 0 in both one-magnon and two-magnon excitation channels. This finding may be experimentally confirmed by examining carefully the q-dependence of the spectra.

Orbital control of effective dimensionality: from spin-orbital fractionalization to confinement in the anisotropic ladder system CaCu(2)O(3)

Fractionalization of an electronic quasiparticle into spin, charge, and orbital parts is a fundamental and characteristic property of interacting electrons in one dimension. However, real materials are never strictly one dimensional and the fractionalization phenomena are hard to observe. Here we studied the spin and orbital excitations of the anisotropic ladder material CaCu_{2}O_{3}, whose electronic structure is not one dimensional. Combining high-resolution resonant inelastic x-ray scattering experiments with theoretical model calculations, we show that (i) spin-orbital fractionalization occurs in CaCu_{2}O_{3} along the leg direction x through the xz orbital channel as in a 1D system, and (ii) no fractionalization is observed for the xy orbital, which extends in both leg and rung direction, contrary to a 1D system. We conclude that the directional character of the orbital hopping can select different degrees of dimensionality. Using additional model calculations, we show that spin-orbital separation is generally far more robust than the spin-charge separation. This is not only due to the already mentioned selection realized by the orbital hopping, but also due to the fact that spinons are faster than the orbitons.

Low-energy V t2g orbital excitations in NdVO3

The electronic structure of NdVO(3) and YVO(3) has been investigated as a function of sample temperature using resonant inelastic soft x-ray scattering at the V L(3)-edge. Most of the observed spectral features are in good agreement with an atomic crystal-field multiplet model. However, a low energy feature is observed at ∼ 0.4 eV that cannot be explained by crystal-field arguments. The resonant behaviour of this feature establishes it as due to excitations of the V t(2g) states. Moreover, this feature exhibits a strong sample temperature dependence, reaching maximum intensity in the orbitally-ordered phase of NdVO(3), before becoming suppressed at low temperatures. This behaviour indicates that the origin of this feature is a collective orbital excitation, i.e. the bi-orbiton.

The simultaneous measurement of energy and linear polarization of the scattered radiation in resonant inelastic soft x-ray scattering

Resonant Inelastic X-ray Scattering (RIXS) in the soft x-ray range is an element-specific energy-loss spectroscopy used to probe the electronic and magnetic excitations in strongly correlated solids. In the recent years, RIXS has been progressing very quickly in terms of energy resolution and understanding of the experimental results, but the interpretation of spectra could further improve, sometimes decisively, from a full knowledge of the polarization of incident and scattered photons. Here we present the first implementation, in a high resolution soft-RIXS spectrometer used to analyze the scattered radiation, of a device allowing the measurement of the degree of linear polarization. The system, based on a graded W/B4C multilayer mirror installed in proximity of the CCD detector, has been installed on the AXES spectrometer at the ESRF (European Synchrotron Radiation Facility); it has been fully characterized and it has been used for a demonstration experiment at the Cu L3 edge on a high-Tc superconducting cuprate. The loss in efficiency suffered by the spectrometer equipped with this test facility was a factor 17.5. We propose also a more advanced version, suitable for a routine use on the next generation of RIXS spectrometers and with an overall efficiency up to 10%.

Real-space visualization of remnant Mott gap and magnon excitations

We demonstrate the ability to visualize real-space dynamics of charge gap and magnon excitations in the Mott phase of the single-band Hubbard model and the remnants of these excitations with hole or electron doping. At short times, the character of magnetic and charge excitations is maintained even for large doping away from the Mott and antiferromagnetic phases. Doping influences both the real-space patterns and long timescales of these excitations with a clear carrier asymmetry attributable to particle-hole symmetry breaking in the underlying model. Further, a rapidly oscillating charge-density-wave-like pattern weakens, but persists as a visible demonstration of a subleading instability at half-filling which remains upon doping. The results offer an approach to analyzing the behavior of systems where momentum space is either inaccessible or poorly defined.

Femtosecond dynamics of momentum-dependent magnetic excitations from resonant inelastic X-ray scattering in CaCu2O3

Taking spinon excitations in the quantum antiferromagnet CaCu2O3 as an example, we demonstrate that femtosecond dynamics of magnetic electronic excitations can be probed by direct resonant inelastic x-ray scattering (RIXS). To this end, we isolate the contributions of single and double spin-flip excitations in experimental RIXS spectra, identify the physical mechanisms that cause them, and determine their respective time scales. By comparing theory and experiment, we find that double spin flips need a finite amount of time to be generated, rendering them sensitive to the core-hole lifetime, whereas single spin flips are, to a very good approximation, independent of it. This shows that RIXS can grant access to time-domain dynamics of excitations and illustrates how RIXS experiments can distinguish between excitations in correlated electron systems based on their different time dependence.

Persistence of magnetic excitations in La(2-x)Sr(x)CuO4 from the undoped insulator to the heavily overdoped non-superconducting metal

One of the most intensely studied scenarios of high-temperature superconductivity (HTS) postulates pairing by exchange of magnetic excitations. Indeed, such excitations have been observed up to optimal doping in the cuprates. In the heavily overdoped regime, neutron scattering measurements indicate that magnetic excitations have effectively disappeared, and this has been argued to cause the demise of HTS with overdoping. Here we use resonant inelastic X-ray scattering, which is sensitive to complementary parts of reciprocal space, to measure the evolution of the magnetic excitations in La(2-x)Sr(x)CuO4 across the entire phase diagram, from a strongly correlated insulator (x = 0) to a non-superconducting metal (x = 0.40). For x = 0, well-defined magnon excitations are observed. These magnons broaden with doping, but they persist with a similar dispersion and comparable intensity all the way to the non-superconducting, heavily overdoped metallic phase. The destruction of HTS with overdoping is therefore caused neither by the general disappearance nor by the overall softening of magnetic excitations. Other factors, such as the redistribution of spectral weight, must be considered.

High-energy magnetic excitations in the cuprate superconductor Bi(2)Sr(2)CaCu(2)O(8+δ): towards a unified description of its electronic and magnetic degrees of freedom

We investigate the high-energy magnetic excitation spectrum of the high-T(c) cuprate superconductor Bi(2)Sr(2)CaCu(2)O(8+δ) (Bi-2212) using Cu L(3) edge resonant inelastic x-ray scattering. Broad, dispersive magnetic excitations are observed, with a zone boundary energy of ∼ 300 meV and a weak dependence on doping. These excitations are strikingly similar to the bosons proposed to explain the high-energy "kink" observed in photoemission. A phenomenological calculation of the spin response, based on a parametrization of the the angle-resolved photoemission spectroscopy derived electronic structure and Yang-Rice-Zhang quasiparticles, provides a reasonable prediction of the energy dispersion of the observed magnetic excitations. These results indicate a possible unified framework to reconcile the magnetic and electronic properties of the cuprates and we discuss the advantages and disadvantages of such an approach.

Resonant inelastic x-ray scattering as a probe of the phase and excitations of the order parameter of superconductors

The capability to probe the dispersion of elementary spin, charge, orbital, and lattice excitations has positioned resonant inelastic x-ray scattering (RIXS) at the forefront of photon science. Here we develop the scattering theory for RIXS on superconductors, calculating its momentum-dependent scattering amplitude. Considering superconductors with different pairing symmetries, we show that the low-energy scattering is strongly affected by the superconducting gap and coherence factors. This establishes RIXS as a tool to disentangle pairing symmetries and to probe the elementary excitations of unconventional superconductors.

Crystal-field splitting and correlation effect on the electronic structure of A2IrO3

The electronic structure of the honeycomb lattice iridates Na(2)IrO(3) and Li(2)IrO(3) has been investigated using resonant inelastic x-ray scattering (RIXS). Crystal-field-split d-d excitations are resolved in the high-resolution RIXS spectra. In particular, the splitting due to noncubic crystal fields, derived from the splitting of j(eff)=3/2 states, is much smaller than the typical spin-orbit energy scale in iridates, validating the applicability of j(eff) physics in A(2)IrO(3). We also find excitonic enhancement of the particle-hole excitation gap around 0.4 eV, indicating that the nearest-neighbor Coulomb interaction could be large. These findings suggest that both Na(2)IrO(3) and Li(2)IrO(3) can be described as spin-orbit Mott insulators, similar to the square lattice iridate Sr(2)IrO(4).

Unraveling orbital correlations with magnetic resonant inelastic x-ray scattering

Although orbital degrees of freedom are a factor of fundamental importance in strongly correlated transition-metal compounds, orbital correlations and dynamics remain very difficult to access, in particular by neutron scattering. Via a direct calculation of scattering amplitudes we show that instead magnetic resonant inelastic x-ray scattering (RIXS) does reveal orbital correlations. In contrast to neutron scattering, the intensity of the magnetic excitations in RIXS depends very sensitively on the symmetry of the orbitals that spins occupy and on photon polarizations. We show in detail how this effect allows magnetic RIXS to distinguish between alternating orbital-ordered and ferro-orbital (or orbital liquid) states.

Two-spinon and orbital excitations of the spin-Peierls system TiOCl

We combine high-resolution resonant inelastic x-ray scattering with cluster calculations utilizing a recently derived effective magnetic scattering operator to analyze the polarization, excitation energy, and momentum-dependent excitation spectrum of the low-dimensional quantum magnet TiOCl in the range expected for orbital and magnetic excitations (0-2.5 eV). Ti 3d orbital excitations yield complete information on the temperature-dependent crystal-field splitting. In the spin-Peierls phase we observe a dispersive two-spinon excitation and estimate the inter- and intradimer magnetic exchange coupling from a comparison to cluster calculations.

Ab Initio determination of Cu 3d orbital energies in layered copper oxides

It has long been argued that the minimal model to describe the low-energy physics of the high T(c) superconducting cuprates must include copper states of other symmetries besides the canonical [see text] one, in particular the [see text] orbital. Experimental and theoretical estimates of the energy splitting of these states vary widely. With a novel ab initio quantum chemical computational scheme we determine these energies for a range of copper-oxides and -oxychlorides, determine trends with the apical Cu-ligand distances and find excellent agreement with recent Resonant Inelastic X-ray Scattering measurements, available for La(2)CuO(4), Sr(2)CuO(2)Cl(2), and CaCuO(2).

Spin-exchange dynamical structure factor of the S=1/2 Heisenberg chain

We determine the spin-exchange dynamical structure factor of the Heisenberg spin chain, as is measured by indirect resonant inelastic x-ray scattering (RIXS). We find that two-spin RIXS excitations nearly entirely fractionalize into two-spinon states. These share the same continuum lower bound as single-spin neutron scattering excitations, even if the relevant final states belong to orthogonal symmetry sectors. The RIXS spectral weight is mainly carried by higher-energy excitations, and is beyond the reach of the low-energy effective theories of Luttinger liquid type.

Theory of resonant inelastic x-ray scattering by collective magnetic excitations

I present a tractable theory for the resonant inelastic x-ray scattering (RIXS) of magnons. The low-energy transition operator is written as a product of local spin operators and fundamental x-ray absorption spectral functions. This leads to simple selection rules. The scattering cross section linear (quadratic) in spin operators is proportional to the fundamental magnetic circular (linear) dichroic spectral function. RIXS is a novel tool to measure magnetic quasiparticles (magnons) and the incoherent spectral weight, as well as multiple magnons up to very high energy losses, in small samples, thin films, and multilayers, complementary to neutron scattering.

Measurement of magnetic excitations in the two-dimensional antiferromagnetic Sr₂CuO₂Cl₂ insulator using resonant x-ray scattering: evidence for extended interactions

We measured the momentum dependence of magnetic excitations in the model spin-1/2 2D antiferromagnetic insulator Sr2CuO2Cl2 (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 (π, 0) and (π/2, π/2). Employing an extended t-t'-t''-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 (π, 0) indicates sizable quantum effects in SCOC and probably more generally in the cuprates.

Magnetic excitations and phase separation in the underdoped La2-xSrxCuO4 superconductor measured by resonant inelastic X-ray scattering

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.

Theoretical demonstration of how the dispersion of magnetic excitations in cuprate compounds can be determined using resonant inelastic X-ray scattering

We show that 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 dispersion of magnetic excitations, for instance magnons, of cuprates such as the high T(c) superconductors. We compute the relevant local and momentum dependent magnetic scattering amplitudes, which we compare to the elastic and dd-excitation scattering intensities. For cuprates these theoretical results put RIXS as a technique on the same footing as neutron scattering.

Momentum dependence of orbital excitations in Mott-insulating titanates

High-resolution resonant inelastic x-ray scattering has been used to determine the momentum dependence of orbital excitations in Mott-insulating LaTiO(3) and YTiO(3) over a wide range of the Brillouin zone. The data are compared to calculations in the framework of lattice-driven and superexchange-driven orbital ordering models. A superexchange model in which the experimentally observed modes are attributed to two-orbiton excitations yields the best description of the data.

Collective magnetic excitations in the spin ladder Sr14Cu24O41 measured using high-resolution resonant inelastic x-ray scattering

We investigate magnetic excitations in the spin-ladder compound Sr_{14}Cu_{24}O_{41} using high-resolution Cu L_{3} edge resonant inelastic x-ray scattering (RIXS). Our findings demonstrate that RIXS couples to two-triplon collective excitations. In contrast to inelastic neutron scattering, the RIXS cross section changes only moderately over the entire Brillouin zone, revealing high sensitivity also at small momentum transfers, allowing determination of the two-triplon energy gap as 100 +/- 30 meV. Our results are backed by calculations within an effective Hubbard model for a finite-size cluster, and confirm that optical selection rules are obeyed for excitations from this spherically symmetric quantum spin-liquid ground state.