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We use Resonant Inelastic X-ray Scattering (RIXS) to compare the doping dependence of magnetic excitations of an Infinite-Layer nickelate to those of a prototypical superconducting cuprate. The polarization analysis of RIXS spectra establishes the dominant spin-flip nature of the mid-infrared peak in both cases. Hole doping leads to opposite behavior of the magnetic energy in the two materials. By fitting the data with an original Hubbard-based model for dynamic susceptibility, we find that t is comparable in the two materials while U is about twice larger in the nickelate. This finding accounts for the smaller magnetic bandwidth of nickelates and for its decrease upon doping., Comment: 7 pages with bibliography, 4 figures

In strongly correlated systems the complete determination of the dynamical susceptibility $\chi(\textbf{q}, \omega)$ is of special relevance because of the entwinement of the spin and charge components. Although Resonant Inelastic X-Ray Scattering (RIXS) spectra are directly related to both the charge ($\chi''_c(\textbf{q}, \omega)$) and the spin ($\chi''_s(\textbf{q}, \omega)$) contributions, only the latter has been extensively studied with RIXS so far. Here we show how to extract from RIXS spectra of high-$T_c$ superconducting cuprates relevant properties of $\chi''_c$, such as the presence of the superconducting gap and of the pseudogap. In particular, we exploit the temperature dependence of the Cu L$_3$ edge RIXS spectra of underdoped YBa$_2$Cu$_3$O$_{7-\delta}$ at specific wave-vectors q. The signature of the two gaps is in the departure of the low energy Bosonic excitation continuum from the statistical temperature-dependence. This approach can be immediately used to investigate systematically the nature of the pseudogap in cuprates, thereby taking advantage of the RIXS technique that does not suffer the limitations of surface-sensitive electron spectroscopies. Its extension to other interesting materials is foreseen., Comment: 14 pages, 12 figures

We have investigated the 3d orbital excitations in CaCuO2 (CCO), Nd2CuO4 (NCO), and La2CuO4 (LCO) using high-resolution resonant inelastic x-ray scattering. In LCO they behave as well-localized excitations, similarly to several other cuprates. On the contrary, in CCO and NCO the dxy orbital clearly disperse, pointing to a collective character of this excitation (orbiton) in compounds without apical oxygen. We ascribe the origin of the dispersion as stemming from a substantial next-nearest-neighbor (NNN) orbital superexchange. Such an exchange leads to the liberation of orbiton from its coupling to magnons, which is associated with the orbiton hopping between nearest neighbor copper sites. We show that the exceptionally large NNN orbital superexchange can be traced back to the absence of apical oxygens suppressing the charge transfer energy., Comment: 24 pages, 10 figures

Identifying quantum critical points (QCPs) and their associated fluctuations may hold the key to unraveling the unusual electronic phenomena observed in cuprate superconductors. Recently, signatures of quantum fluctuations associated with charge order (CO) have been inferred from the anomalous enhancement of CO excitations that accompany the reduction of the CO order parameter in the superconducting state. To gain more insight about the interplay between CO and superconductivity, here we investigate the doping dependence of this phenomenon throughout the Bi-2212 cuprate phase diagram using resonant inelastic x-ray scattering (RIXS) at the Cu L3- edge. As doping increases, the CO wavevector decreases, saturating at a commensurate value of 0.25 r.l.u. beyond a characteristic doping pc, where the correlation length becomes shorter than the apparent periodicity (4a0). Such behavior is indicative of the fluctuating nature of the CO; and the proliferation of CO excitations in the superconducting state also appears strongest at pc, consistent with expected behavior at a CO QCP. Intriguingly, pc appears to be near optimal doping, where the superconducting transition temperature Tc is maximal., Comment: This is a submitted version of the manuscript. The revised manuscript is now published on Physical Review B

While electron-phonon coupling (EPC) is crucial for Cooper pairing in conventional superconductors, its role in high-$T_c$ superconducting cuprates is debated. Using resonant inelastic x-ray scattering at the oxygen $K$-edge, we studied the EPC in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) and Nd$_{1+x}$Ba$_{2-x}$Cu$_3$O$_{7-\delta}$ (NBCO) at different doping levels ranging from heavily underdoped ($p =0.07$) to overdoped ($p=0.21$). We analyze the data with a localized Lang-Firsov model that allows for the coherent excitations of two phonon modes. While electronic band dispersion effects are non-negligible, we are able to perform a study of the relative values of EPC matrix elements in these cuprate families. In the case of NBCO, the choice of the excitation energy allows us to disentangle modes related to the CuO$_3$ chains and the CuO$_2$ planes. Combining the results from the two families, we find the EPC strength decreases with doping at $\mathbf{q_\parallel}=(-0.25, 0)$ r.l.u., but has a non-monotonic trend as a function of doping at smaller momenta. This behavior is attributed to the screening effect of charge carriers. We also find that the phonon intensity is enhanced in the vicinity of the charge-density-wave (CDW) excitations while the extracted EPC strength appears to be less sensitive to their proximity. By performing a comparative study of two cuprate families, we are able to identify general trends in the EPC for the cuprates and provide experimental input to theories invoking a synergistic role for this interaction in $d$-wave pairing., Comment: 10 pages, 5 figures

We use resonant inelastic x-ray scattering (RIXS) to investigate the magnetic dynamics of the infinite-layer cuprate CaCuO2. We find that close to the (1/2,0) point the single magnon decays into a broad continuum of excitations accounting for 80% of the total magnetic spectral weight. Polarization resolved RIXS spectra reveal the overwhelming dominance of spin-flip ($\Delta S = 1$) characterof this continuum with respect to the $\Delta S= 0$ multimagnon contributions. Moreover, its incident energy dependence is identical to that of the magnon, supporting a common physical origin. We propose that the continuum originates from the decay of the magnon into spinon pairs, and we relate it to the exceptionally high ring exchange $J_\mathrm{c} \sim J_1$ of CaCuO2. In the infinite layer cuprates long-range and multi-site hopping integrals are pivotal and amplify the 2D quantum magnetism effects in spite the 3D antiferromagnetic N\'eel order., Comment: 10 pages, 6 figures

Thanks to high resolution and polarization analysis, resonant inelastic x-ray scattering (RIXS) magnetic spectra of La2CuO4, Sr2CuO2Cl2 and CaCuO2 reveal a rich set of properties of the spin 1/2 antiferromagnetic square lattice of cuprates. The leading single-magnon peak energy dispersion is in excellent agreement with the corresponding inelastic neutron scattering measurements. However, the RIXS data unveil an asymmetric lineshape possibly due to odd higher order terms. Moreover, a sharp bimagnon feature emerges from the continuum at (1/2,0), coincident in energy with the bimagnon peak detected in optical spectroscopy. These findings show that the inherently complex spin spectra of cuprates, an exquisite manifestation of quantum magnetism, can be effectively explored by exploiting the richness of RIXS cross sections., Comment: 7 pages, 3 figures

Despite its simple structure and low degree of electronic correlation, SrTiO$_3$ (STO) features collective phenomena linked to charge transport and, ultimately, superconductivity, that are not yet fully explained. Thus, a better insight in the nature of the quasiparticles shaping the electronic and conduction properties of STO is needed. We studied the low energy excitations of bulk STO and of the LaAlO$_{3}$/SrTiO$_{3}$ two dimensional electron gas (2DEG) by Ti L$_3$ edge resonant inelastic x-ray scattering. In all samples, we find the hallmark of polarons in the form of intense $dd$+phonon excitations, and a decrease of the LO3-mode electron-phonon coupling when going from insulating to highly conducting STO single crystals and heterostructures. Both results are attributed to the dynamic screening of the large polaron self-induced polarization, showing that the low temperature physics of STO and STO-based 2DEGs is dominated by large polaron quasiparticles., Comment: 5 pages, 4 figures

Motivated by the recent synthesis of Ba$_2$CuO$_{3+\delta}$ (BCO), a high temperature superconducting cuprate with putative $d_{3z^2-r^2}$ ground state symmetry, we investigated its electronic structure by means of Cu $L_3$ x-ray absorption (XAS) and resonant inelastic x-ray scattering (RIXS) at the Cu $L_3$ edge on a polycrystalline sample. We show that the XAS profile of BCO is characterised by two peaks associated to inequivalent Cu sites, and that its RIXS response features a single, sharp peak associated to crystal-field excitations. We argue that these observations are only partially compatible with the previously proposed crystal structure of BCO. Based on our spectroscopic results and on previously published powder diffraction measurements, we propose a crystalline structure characterized by two inequivalent Cu sites located at alternated planes along the $c$ axis: nominally trivalent Cu(1) belonging to very short Cu-O chains, and divalent Cu(2) in the oxygen deficient CuO$_ {1.5}$ planes. We also analyze the low-energy region of the RIXS spectra to estimate the magnitude of the magnetic interactions in BCO and find that in-plane nearest neighbor superexchange exceeds 120~meV, similarly to that of other layered cuprates. Although these results do not support the pure $d_{3z^2-r^2}$ ground state scenario, they hint at a significant departure from the common quasi-2D electronic structure of superconducting cuprates of pure $d_{x^2-y^2}$ symmetry.

We investigate the Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS) spectra of a quasi-1D antiferromagnet Ca$_2$CuO$_3$. In addition to the magnetic excitations, which are well-described by the two-spinon continuum, we observe two dispersive orbital excitations, the $3d_{xy}$ and the $3d_{yz}$ orbitons. We carry out a quantitative comparison of the RIXS spectra, obtained with two distinct incident polarizations, with a theoretical model. We show that any realistic spin-orbital model needs to include a finite, but realistic, Hund's exchange $J_H \approx 0.5$ eV. Its main effect is an increase in orbiton velocities, so that their theoretically calculated values match those observed experimentally. Even though Hund's exchange also mediates some interaction between spinon and orbiton, the picture of spin-orbit separation remains intact and describes orbiton motion in this compound., Comment: 13 pages, 10 figures

The coupling between lattice vibration quanta and valence electrons can induce charge density modulations and decisively influence the transport properties of materials, e.g. leading to conventional superconductivity. In high critical temperature superconductors, where electronic correlation is the main actor, the actual role of electron-phonon coupling (EPC) is being intensely debated theoretically and investigated experimentally. We present an in-depth study of how the EPC strength can be obtained directly from resonant inelastic x-ray scattering (RIXS) data through the theoretical approach derived by Ament et al. [EPL 95, 27008 (2011)]. The role of the model parameters (e.g. phonon energy $\omega_0$, intermediate state lifetime $1/\Gamma$, EPC matrix element $M$, and detuning energy $\Omega$) is thoroughly analyzed, providing general relations among them that can be used to make quantitative estimates of the dimensionless EPC $g = (M/\omega_0)^2$ without detailed microscopic modeling. We then apply these methods to very high resolution Cu $L_3$ edge RIXS spectra of three Nd$_{1+x}$Ba$_{2-x}$Cu$_3$O$_{7-\delta}$ films. For the insulating antiferromagnetic parent compound the value of $M$ as a function of the in-plane momentum transfer is obtained for Cu-O bond-stretching (breathing) and bond-bending (buckling) phonon branches. For the underdoped and the nearly optimally doped samples, the effects of Coulomb screening and of charge-density-wave correlations on $M$ are assessed. In light of the anticipated further improvements of the RIXS experimental resolution, this work provides a solid framework for an exhaustive investigation of the EPC in cuprates and other quantum materials., Comment: 21 pages, 16 figures

We provide a novel experimental method to quantitatively estimate the electron-phonon coupling and its momentum dependence from resonant inelastic x-ray scattering (RIXS) spectra based on the detuning of the incident photon energy away from an absorption resonance. We apply it to the cuprate parent compound NdBa$_2$Cu$_3$O$_6$ and find that the electronic coupling to the oxygen half-breathing phonon mode is strongest at the Brillouin zone boundary, where it amounts to $\sim 0.17$ eV, in agreement with previous studies. In principle, this method is applicable to any absorption resonance suitable for RIXS measurements and will help to define the contribution of lattice vibrations to the peculiar properties of quantum materials., Comment: 6 pages, 3 figures

We demonstrate that combining standing-wave (SW) excitation with resonant inelastic x-ray scattering (RIXS) can lead to depth resolution and interface sensitivity for studying orbital and magnetic excitations in correlated oxide heterostructures. SW-RIXS has been applied to multilayer heterostructures consisting of a superconductor La$_{1.85}$Sr$_{0.15}$CuO$_{4}$(LSCO) and a half-metallic ferromagnet La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ (LSMO). Easily observable SW effects on the RIXS excitations were found in these LSCO/LSMO multilayers. In addition, we observe different depth distribution of the RIXS excitations. The magnetic excitations are found to arise from the LSCO/LSMO interfaces, and there is also a suggestion that one of the dd excitations comes from the interfaces. SW-RIXS measurements of correlated-oxide and other multilayer heterostructures should provide unique layer-resolved insights concerning their orbital and magnetic excitations, as well as a challenge for RIXS theory to specifically deal with interface effects., Comment: 18 pages, 3 figures, plus supplemental materials (14 pages)

Experimental evidence on high-Tc cuprates reveals ubiquitous charge density wave (CDW) modulations, which coexist with superconductivity. Although the CDW had been predicted by theory, important questions remain about the extent to which the CDW influences lattice and charge degrees of freedom and its characteristics as functions of doping and temperature. These questions are intimately connected to the origin of the CDW and its relation to the mysterious cuprate pseudogap. Here, we use ultrahigh resolution resonant inelastic x-ray scattering (RIXS) to reveal new CDW character in underdoped Bi2Sr2CaCu2O8+{\delta} (Bi2212). At low temperature, we observe dispersive excitations from an incommensurate CDW that induces anomalously enhanced phonon intensity, unseen using other techniques. Near the pseudogap temperature T*, the CDW persists, but the associated excitations significantly weaken and the CDW wavevector shifts, becoming nearly commensurate with a periodicity of four lattice constants. The dispersive CDW excitations, phonon anomaly, and temperature dependent commensuration provide a comprehensive momentum space picture of complex CDW behavior and point to a closer relationship with the pseudogap state.

In Charge Coupled Device (CCD) detectors the electrons excited upon absorption of a single x-ray photon quickly diffuse and generate charge-spots often larger than pixel dimensions. In the soft x-ray range this phenomenon drastically limits the effective spatial resolution to approximately 25\mu m, irrespective of the pixel size. For very low fluence the charge-cloud centroid determination can be used, on each individual spot, to estimate the actual photon impact position with sub-pixel precision. The readout noise and speed, together with the charge and spatial undersampling, are the main factors limiting the accuracy of this procedure in commercial devices. We have developed and extensively tested an algorithm for efficient centroid reconstruction on images acquired by low noise detectors not designed for single photon counting. We have thus measured a position uncertainty of 6-7\mu m in CCDs with 13.5\mu m and 20.0\mu m pixel size, around 1 keV photon energy. We have analyzed the centroid calculation performances by modelling the spot generation process. We show how the resolution is affected by both random uncertainty, mainly ascribed to the readout noise, and systematic error, due to the undersampling of the charge spot. This study was motivated by the growing need of of high-resolution high-sensitivity 2D position sensitive detectors in resonant inelastic (soft) x-ray scattering (RIXS), an emergent synchrotron radiation based spectroscopy., Comment: 8 pages, 7 figures

Taking spinon excitations in the quantum antiferromagnet CaCu2O3 as an example, we demonstrate that femtosecond dynamics of magnetic 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 timescales. 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.