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Although entanglement is both a central ingredient in our understanding of quantum many-body systems and an essential resource for quantum technologies, we only have a limited ability to quantify entanglement in real quantum materials. Thus far, entanglement metrology in quantum materials has been limited to measurements involving Hermitian operators, such as the detection of spin entanglement using inelastic neutron scattering. Here, we devise a method to extract the quantum Fisher information (QFI) from non-Hermitian operators and formulate an entanglement witness for resonant inelastic x-ray scattering (RIXS). Our approach is then applied to the model iridate dimer system Ba$_3$CeIr$_2$O$_9$ and used to directly test for entanglement of the electronic orbitals between neighboring Ir sites. We find that entanglement is challenging to detect under standard conditions, but that it could be achieved by analyzing the outgoing x-ray polarization or via specific choices of momentum and energy. Our protocol provides a new handle for entanglement detection, which offers routes to related types of entanglement witness (such as orbitally-resolved measurements) and to the generalization to out-of-equilibrium settings accessed in ultrafast settings., Comment: 10 pages, 8 figures

The $5d^1$ ordered double perovskites present an exotic playground for studying novel multi-polar physics due to large spin-orbit coupling. We present Re L3 edge resonant inelastic X-ray scattering (RIXS) results that reveal the presence of the dynamic Jahn-Teller effect in the A$_2$MgReO$_6$ (A = Ca, Sr, Ba) family of $5d^1$ double perovskites. The spin-orbit excitations in these materials show a strongly asymmetric lineshape and exhibit substantial temperature dependence, indicating that they are dressed with lattice vibrations. Our experimental results are explained quantitatively through a RIXS calculation based on a spin-orbit-lattice entangled electronic ground state with the dynamic Jahn-Teller effect taken into consideration. We find that the spin-orbit-lattice entangled state is robust against magnetic and structural phase transitions as well as against significant static Jahn-Teller distortions. Our results illustrate the importance of including vibronic coupling for a complete description of the ground state physics of $5d^1$ double perovskites. Usage: Secondary publications and information retrieval purposes.

We reveal in this study the fundamental low-energy landscape in the ferrimagnetic Sr2CrReO6 double perovskite and describe the underlying mechanisms responsible for the three low-energy excitations below 1.4 eV. Based on resonant inelastic x-ray scattering and magnetic dynamics calculations, and experiments collected from both Sr2CrReO6 powders and epitaxially strained thin films, we reveal a strong competition between spin-orbit coupling, Hund's coupling, and the strain-induced tetragonal crystal field. We also demonstrate that a spin-flip process is at the origin of the lowest excitation at 200 meV, and we bring insights into the predicted presence of orbital ordering in this material. We study the nature of the magnons through a combination of ab initio and spin-wave theory calculations, and show that two nondegenerate magnon bands exist and are dominated either by rhenium or chromium spins. The rhenium band is found to be flat at about 200 meV ($\pm$25 meV) through X-L-W-U high-symmetry points and is dispersive toward $\Gamma$, Comment: 6 figures

A comparative resonant inelastic x-ray scattering (RIXS) study of three well-known Kitaev materials is presented: $\alpha$-Li$_2$IrO$_3$, Na$_2$IrO$_3$, and $\alpha$-RuCl$_3$. Despite similar low-energy physics, these materials show distinct electronic properties, such as the large difference in the size of the charge gap. The RIXS spectra of the spin-orbit exciton for these materials show remarkably similar three-peak features, including sharp low energy peak (peak A) as well as transitions between $j_{\text{eff}}=1/2$ and $j_{\text{eff}}=3/2$ states. Comparison of experimental spectra with cluster calculations reveals that the observed three-peak structure reflects the significant role that non-local physics plays in the electronic structure of these materials. In particular, the low-energy peak A arises from a holon-doublon pair rather than a conventional particle-hole exciton as proposed earlier. Our study suggests that while spin-orbit assisted Mott insulator is still the best description for these materials, electron itinerancy cannot be ignored when formulating low-energy Hamiltonian of these materials.

We use resonant inelastic x-ray scattering (RIXS) at the O $K$- and Cu $K$-edges to investigate the doping- and temperature dependence of low-energy plasmon excitations in La$_{2-x}$Sr$_{x}$CuO$_4$. We observe a monotonic increase of the energy scale of the plasmons with increasing doping $x$ in the underdoped regime, whereas a saturation occurs above optimal doping $x \gtrsim 0.16$ and persists at least up to $x = 0.4$. Furthermore, we find that the plasmon excitations show only a marginal temperature dependence, and possible effects due to the superconducting transition and the onset of strange metal behavior are either absent or below the detection limit of our experiment. Taking into account the strongly correlated character of the cuprates, we show that layered $t$-$J$-$V$ model calculations accurately capture the increase of the plasmon energy in the underdoped regime. However, the computed plasmon energy continues to increase even for doping levels above $x \gtrsim 0.16$, which is distinct from the experimentally observed saturation, and reaches a broad maximum around $x = 0.55$. We discuss whether possible lattice disorder in overdoped samples, a renormalization of the electronic correlation strength at high dopings, or an increasing relevance of non-planar Cu and O orbitals could be responsible for the discrepancy between experiment and theory for doping levels above $x = 0.16$., Comment: 19 pages, 11 figures

We investigate the electronic structure of two Ir$^{5+}$ honeycomb iridates, Sr$_3$CaIr$_2$O$_9$ and NaIrO$_3$, by means of resonant x-ray techniques. We confirm that Sr$_3$CaIr$_2$O$_9$ realizes a large spin-orbit driven non-magnetic $J = 0$ singlet ground state despite sizable tetragonal distortions of Ir coordinating octahedra. On the other hand, the resonant inelastic x-ray spectra of NaIrO$_3$ are drastically different from expectations for a Mott insulator with octahedrally coordinated Ir$^{5+}$. We find that the data for NaIrO$_3$ can be best interpreted as originating from a narrow gap non-magnetic $S = 0$ band insulating ground state. Our results highlight the complex role of the ligand environment in the electronic structure of honeycomb iridates and the essential role of x-ray spectroscopy to characterize electronic ground states of insulating materials.

By performing resonant inelastic x-ray scattering (RIXS) measurements at the Ir $\mathit{L_{\mathrm{3}}}$ edge, we have investigated the low-energy elementary excitations in a series of double perovskite iridate single crystals, La$_{2}$$\mathit{M}$IrO$_{6}$ ($\mathit{M}$ = Co, Ni, and Zn). Almost dispersionless magnetic excitations at $\sim$ 42(6) meV and $\sim$ 35(5) meV have been observed in crystals containing magnetic 3$\mathit{d}$ ions, La$_{2}$CoIrO$_{6}$ and La$_{2}$NiIrO$_{6}$, respectively. In contrast, this low-energy magnetic excitation is absent in La$_{2}$ZnIrO$_{6}$ in which the 3$\mathit{d}$ ions are non-magnetic, suggesting the importance of 3$\mathit{d}$-5$\mathit{d}$ hybridization in the magnetic properties of these double perovskite iridates. The magnetic excitation is suppressed completely above the magnetic ordering temperature, suggesting the inadequacy of using a simple spin Hamiltonian to describe magnetism of these materials., Comment: 8 pages, 4 figures, accepted for publication in Physical Review B

Excitonic insulators are usually considered to form via the condensation of a soft charge mode of bound electron-hole pairs. This, however, presumes that the soft exciton is of spin-singlet character. Early theoretical considerations have also predicted a very distinct scenario, in which the condensation of magnetic excitons results in an antiferromagnetic excitonic insulator state. Here we report resonant inelastic x-ray scattering (RIXS) measurements of Sr3Ir2O7. By isolating the longitudinal component of the spectra, we identify a magnetic mode that is well-defined at the magnetic and structural Brillouin zone centers, but which merges with the electronic continuum in between these high-symmetry points and which decays upon heating concurrent with a decrease in the material's resistivity. We show that a bilayer Hubbard model, in which electron-hole pairs are bound by exchange interactions, consistently explains all the electronic and magnetic properties of Sr3Ir2O7 indicating that this material is a realization of the long-predicted antiferromagnetic excitonic insulators phase., Comment: accepted in Nature Communications; 6 pages main materials

Spinons are well-known as the elementary excitations of one-dimensional antiferromagnetic chains, but means to realize spinons in higher dimensions is the subject of intense research. Here, we use resonant x-ray scattering to study the layered trimer iridate Ba4Ir3O10, which shows no magnetic order down to 0.2 K. An emergent one-dimensional spinon continuum is observed that can be well-described by XXZ spin-1/2 chains with magnetic exchange of ~55 meV and a small Ising-like anisotropy. With 2% isovalent Sr doping, magnetic order appears below TN=130 K along with sharper excitations, indicating that the spinons become more confined in (Ba1-xSrx)4Ir3O10. We propose that the frustrated intra-trimer interactions effectively reduce the system into decoupled spin chains, the subtle balance of which can be easily tipped by perturbations such as chemical doping. Our results put Ba4Ir3O10 between the one-dimensional chain and two-dimensional quantum spin liquid scenarios, illustrating a new way to suppress magnetic order and realize fractional spinons., Comment: Accepted in Physical Review Letters; 5 pages not including references or supplementary

We use x-ray spectroscopy at Ir L$_3$/L$_2$ absorption edge to study powder samples of the intercalated honeycomb magnet Ag$_3$LiIr$_2$O$_6$. Based on x-ray absorption and resonant inelastic x-ray scattering measurements, and exact diagonalization calculations including next-neighbour Ir-Ir electron hoping integrals, we argue that the intercalation of Ag atoms results in a nearly itinerant electronic structure with enhanced Ir-O hybridization. As a result of the departure from the local relativistic $j_{\rm eff}\! = \!1/2$ state, we find that the relative orbital contribution to the magnetic moment is increased, and the magnetization density is spatially extended and asymmetric. Our results confirm the importance of metal - ligand hybridazation in the magnetism of transition metal oxides and provide empirical guidance for understanding the collective magnetism in intercalated honeycomb iridates.

The family of edge-sharing tri-coordinated iridates and ruthenates has emerged in recent years as a major platform for Kitaev spin liquid physics, where spins fractionalize into emergent magnetic fluxes and Majorana fermions with Dirac-like dispersions. While such exotic states are usually pre-empted by long-range magnetic order at low temperatures, signatures of Majorana fermions with long coherent times have been predicted to manifest at intermediate and higher energy scales, similar to the observation of spinons in quasi-1D spin chains. Here we present a Resonant Inelastic X-ray Scattering study of the magnetic excitations of the hyperhoneycomb iridate $\beta$-Li$_2$IrO$_3$ under a magnetic field with a record-high-resolution spectrometer. At low-temperatures, dispersing spin waves can be resolved around the predicted intertwined incommensurate spiral and field-induced zigzag orders, whose excitation energy reaches a maximum of 16meV. A 2T magnetic field softens the dispersion around ${\bf Q}=0$. The behavior of the spin waves under magnetic field is consistent with our semiclassical calculations for the ground state and the dynamical spin structure factor, which further predicts that the ensued intertwined uniform states remain robust up to very high fields (100 T). Most saliently, the low-energy magnon-like mode is superimposed by a broad continuum of excitations, centered around 35meV and extending up to 100meV. This high-energy continuum survives up to at least 300K -- well above the ordering temperature of 38K -- and gives evidence for pairs of long-lived Majorana fermions of the proximate Kitaev spin liquid., Comment: 8 pages, 4 figures

In the high spin-orbit coupled Sr2IrO4, the high sensitivity of the ground state to the details of the local lattice structure shows a large potential for the manipulation of the functional properties by inducing local lattice distortions. We use epitaxial strain to modify the Ir-O bond geometry in Sr2IrO4 and perform momentum-dependent Resonant Inelastic X-ray Scattering (RIXS) at the metal and at the ligand sites to unveil the response of the low energy elementary excitations. We observe that the pseudospin-wave dispersion for tensile-strained Sr2IrO4 films displays large softening along the [h,0] direction, while along the [h,h] direction it shows hardening. This evolution reveals a renormalization of the magnetic interactions caused by a strain-driven crossover from anisotropic to isotropic interactions between the magnetic moments. Moreover, we detect dispersive electron-hole pair excitations which shift to lower (higher) energies upon compressive (tensile) strain, manifesting a reduction (increase) in the size of the charge gap. This behavior shows an intimate coupling between charge excitations and lattice distortions in Sr2IrO4, originating from the modified hopping elements between the t2g orbitals. Our work highlights the central role played by the lattice degrees of freedom in determining both the pseudospin and charge excitations of Sr2IrO4 and provides valuable information towards the control of the ground state of complex oxides in the presence of high spin-orbit coupling., Comment: Published in Proceedings of the National Academy of Sciences, September 2020

Although ultrafast manipulation of magnetism holds great promise for new physical phenomena and applications, targeting specific states is held back by our limited understanding of how magnetic correlations evolve on ultrafast timescales. Using ultrafast resonant inelastic x-ray scattering we demonstrate that femtosecond laser pulses can excite transient magnons at large wavevectors in gapped antiferromagnets, and that they persist for several picoseconds which is opposite to what is observed in nearly gapless magnets. Our work suggests that materials with isotropic magnetic interactions are preferred to achieve rapid manipulation of magnetism., Comment: 6 pages, 4 figures, not including supplemental material; accepted in PNAS

We present a study of resonant inelastic X-ray scattering (RIXS) spectra collected at the rare-earth $L$ edges of divalent hexaborides YbB$_6$ and EuB$_6$. In both systems, RIXS-active features are observed at two distinct resonances separated by $\sim10$ eV in incident energy, with angle-dependence suggestive of distinct photon scattering processes. RIXS spectra collected at the divalent absorption peak strongly resemble the unoccupied 5$d$ density of states calculated using density functional theory, an occurrence we ascribe to transitions between weakly-dispersing 4$f$ and strongly dispersing 5$d$ states. In addition, anomalous resonant scattering is observed at higher incident energy, where no corresponding absorption feature is present. Our results suggest the far-reaching utility of $L$-edge RIXS in determining the itinerant-state properties of $f$-electron materials.

The electronic states of many Mott insulators, including iridates, are often conceptualized in terms of localized atomic states such as the famous "$J_\text{eff}=1/2$ state". Although, orbital hybridization can strongly modify such states and dramatically change the electronic properties of materials, probing this process is highly challenging. In this work, we directly detect and quantify the formation of dimer orbitals in an iridate material Ba$_5$AlIr$_2$O$_{11}$ using resonant inelastic x-ray scattering (RIXS). Sharp peaks corresponding to the excitations of dimer orbitals are observed and analyzed by a combination of density functional theory (DFT) calculations and theoretical simulations based on a Ir-Ir cluster model. Such partially delocalized dimer states lead to a re-definition of the angular momentum of the electrons and changes in the magnetic and electronic behaviors of the material. We use this to explain the reduction of the observed magnetic moment with respect to prediction based on atomic states. This study opens new directions to study dimerization in a large family of materials including solids, heterostructures, molecules and transient states., Comment: 7 pages, 3 figures

Spin-orbit entangled magnetic dipoles, often referred to as pseudospins, provide a new avenue to explore novel magnetism inconceivable in the weak spin-orbit coupling limit, but the nature of their low-energy interactions remains to be understood. We present a comprehensive study of the static magnetism and low-energy pseudospin dynamics in the archetypal spin-orbit Mott insulator Sr2IrO4. We find that in order to understand even basic magnetization measurements, a formerly overlooked in-plane anisotropy is fundamental. In addition to magnetometry, we use neutron diffraction, inelastic neutron scattering and resonant elastic and inelastic x-ray scattering to identify and quantify the interactions that determine the global symmetry of the system and govern the linear responses of pseudospins to external magnetic felds and their low-energy dynamics. We find that a pseudospin-only Hamiltonian is insufficient for an accurate description of the magnetism in Sr2IrO4 and that pseudospin-lattice coupling is essential. This finding should be generally applicable to other pseudospin systems with sizable orbital moments sensitive to anisotropic crystalline environments., Comment: Main text:11 pages, 12 figures Supplementary Material: 3 pages, 2 figures, 1 table

We report a comprehensive resonant inelastic x-ray scattering (RIXS) study of various iridate materials focusing on core-level excitations and transitions between crystal-field split d-levels. The 2p core hole created at the Ir $L_3$ absorption edge has a very short lifetime giving rise to a broad absorption width ($\sim 5$~eV). This absorption linewidth broadening can be overcome by studying the resonant x-ray emission spectroscopy (RXES) map, which is a two-dimensional intensity map of the Ir L$\alpha_2$ emission obtained with high energy-resolution monochromator and analyzer. By limiting the emitted photon energy to a narrow range, one can obtain x-ray absorption spectra in the high energy-resolution fluorescence detection (HERFD) mode, while one can also simulate quasi-$M_4$-edge absorption spectra by integrating over incident photon energies. Both methods improve the absorption line width significantly, allowing detailed studies of unoccupied electronic structure in iridates and other $5d$ transition metal compounds. On the other hand, the short lifetime of the 2p core hole benefits the study of excitations of valence electrons. We show that the incident energy dependence of the RIXS spectra for $d-d$ transitions is simple to understand due to the short core-hole lifetime, which validates ultra-short core-hole lifetime approximation used widely in theoretical calculations. We compared $d-d$ excitations in various iridates and found that the excitations between the t$_{2g}$ and e$_g$ states share many similarities among different materials. However, the RIXS spectra due to the transitions between the spin-orbit-split t$_{2g}$ levels vary widely depending on the oxidation state and electronic bandwidths., Comment: 13 pages, 9 figures

Motivated by RIXS experiments on a wide range of complex heavy oxides, including rhenates, osmates, and iridates, we discuss the theory of RIXS for site-localized $t_{2g}$ orbital systems with strong spin-orbit coupling. For such systems, we present exact diagonalization results for the spectrum at different electron fillings, showing that it accesses "single-particle" and "multi-particle" excitations. This leads to a simple picture for the energies and intensities of the RIXS spectra in Mott insulators such as double perovskites which feature highly localized electrons, and yields estimates of the spin-orbit coupling and Hund's coupling in correlated $5d$ oxides. We present new higher resolution RIXS data at the Re-L$_3$ edge in Ba$_2$YReO$_6$ which finds a previously unresolved peak splitting, providing further confirmation of our theoretical predictions. Using ab initio electronic structure calculations on Ba$_2$${\cal M}$ReO$_6$ (with ${\cal M}$=Re, Os, Ir) we show that while the atomic limit yields a reasonable effective Hamiltonian description of the experimental observations, effects such as $t_{2g}$-$e_g$ interactions and hybridization with oxygen are important. Our ab initio estimate for the strength of the intersite exchange coupling shows that, compared to the osmates, the exchange is one or two orders of magnitude weaker in the rhenates and iridates, which may partly explain the suppression of long-range magnetic order in the latter compounds. As a way to interpolate between the site-localized picture and our electronic structure band calculations, we discuss the spin-orbital levels of the ${\cal M}$O$_6$ cluster. This suggests a possible role for non-dispersive intra-cluster excitons in Ba$_2$YIrO$_6$ which may lead to a weak breakdown of the atomic $J_{\rm eff}=0$ picture and to small magnetic moments., Comment: 11 pages, 6 figs, added experimental coauthors, revised following referee comments, published in PRB

The electronic ground state in many iridate materials is described by a complex wave-function in which spin and orbital angular momenta are entangled due to relativistic spin-orbit coupling (SOC). Such a localized electronic state carries an effective total angular momentum of $J_{eff}=1/2$. In materials with an edge-sharing octahedral crystal structure, such as the honeycomb iridates Li2IrO3 and Na2IrO3, these $J_{eff}=1/2$ moments are expected to be coupled through a special bond-dependent magnetic interaction, which is a necessary condition for the realization of a Kitaev quantum spin liquid. However, this relativistic electron picture is challenged by an alternate description, in which itinerant electrons are confined to a benzene-like hexagon, keeping the system insulating despite the delocalized nature of the electrons. In this quasi-molecular orbital (QMO) picture, the honeycomb iridates are an unlikely choice for a Kitaev spin liquid. Here we show that the honeycomb iridate Li2IrO3 is best described by a $J_{eff}=1/2$ state at ambient pressure, but crosses over into a QMO state under the application of small (~ 0.1 GPa) hydrostatic pressure. This result illustrates that the physics of iridates is extremely rich due to a delicate balance between electronic bandwidth, spin-orbit coupling, crystal field, and electron correlation., Comment: 7 pages, 5 figures, additional supplemental material included

We report Resonant Inelastic X-ray Scattering (RIXS) study of the magnetic excitation spectrum in a highly insulating Eu$_{2}$Ir$_{2}$O$_{7}$ single crystal that exhibits a metal-insulator transition at $T_{MI}$ = 111(7) K. A propagating magnon mode with 20 meV bandwidth and 28 meV magnon gap is found in the excitation spectrum at 7 K, which is expected in the all-in-all-out (AIAO) magnetically ordered state. This magnetic excitation exhibits substantial softening as temperature is raised towards $T_{MI}$, and turns into highly damped excitation in the paramagnetic phase. Remarkably, the softening occurs throughout the whole Brillouin zone including the zone boundary. This observation is inconsistent with magnon renormalization expected in a local moment system, and indicates that the strength of electron correlation in Eu$_{2}$Ir$_{2}$O$_{7}$ is only moderate, so that electron itinerancy should be taken into account in describing its magnetism., Comment: 5 pages, 3 figures

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-10meV RIXS spectrometer based on flat-crystal optics at the Ir-L$_3$ absorption edge (11.215$\sim$ keV) that achieves an analyzer energy resolution of 3.9$\sim$meV, very close to the theoretical value of 3.7$\sim$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 Sr$_3$Ir$_2$O$_7$. The novel sub-10$\sim$meV RIXS spectrometer thus provides a window into magnetic materials with small energy scales.

Strong spin-orbit coupling lifts the degeneracy of t2g orbitals in 5d transition-metal systems, leaving a Kramers doublet and quartet with effective angular momentum of Jeff = 1/2 and 3/2, respectively. These spin-orbit entangled states can host exotic quantum phases such as topological Mott state, unconventional superconductivity, and quantum spin liquid. The lacunar spinel GaTa4Se8 was theoretically predicted to form the molecular Jeff = 3/2 ground state. Experimental verification of its existence is an important first step to exploring the consequences of the Jeff = 3/2 state. Here, we report direct experimental evidence of the Jeff = 3/2 state in GaTa4Se8 by means of excitation spectra of resonant inelastic x-rays scattering at the Ta L3 and L2 edges. We found that the excitations involving the Jeff = 1/2 molecular orbital were suppressed only at the Ta L2 edge, manifesting the realization of the molecular Jeff = 3/2 ground state in GaTa4Se8., Comment: 25 pages, 5 figures + Supplementary Materials [10 pages, 5 figures]

We report on the tuning of magnetic interactions in superlattices composed of single and bilayer SrIrO$_3$ inter-spaced with SrTiO$_3$. Magnetic scattering shows predominately $c$-axis antiferromagnetic orientation of the magnetic moments for the bilayer justifying these systems as viable artificial analogues of the bulk Ruddlesden-Popper series iridates. Magnon gaps are observed in both superlattices, with the magnitude of the gap in the bilayer being reduced to nearly half that in its bulk structural analogue, Sr$_3$Ir$_2$O$_7$. We assign this to modifications in the anisotropic exchange driven by bending of the $c$-axis Ir-O-Ir bond and subsequent local environment changes, as detected by x-ray diffraction and modeled using spin wave theory. These findings explain how even subtle structural modulations driven by heterostructuring in iridates are leveraged by spin orbit coupling to drive large changes in the magnetic interactions., Comment: 5 pages, 4 figures

We report resonant inelastic X-ray scattering (RIXS) measurements on ordered double perovskite samples containing Re$^{5+}$ and Ir$^{5+}$ with $5d^2$ and $5d^4$ electronic configurations respectively. In particular, the observed RIXS spectra of Ba$_2$YReO$_6$ and Sr$_2$MIrO$_6$ (M=Y, Gd) show sharp intra-t$_{2g}$ transitions, which can be quantitatively understood using a minimal `atomic' Hamiltonian incorporating spin-orbit coupling ($\lambda$) and Hund's coupling ($J_H$). Our analysis yields $\lambda=0.38(2)$eV with $J_H=0.26(2)$eV for Re$^{5+}$, and $\lambda=0.42(2)$eV with $J_H=0.25(4)$eV for Ir$^{5+}$. Our results provide the first sharp estimates for the Hund's coupling in $5d$ oxides, and suggest that it should be treated on equal footing with spin-orbit interaction in multi-orbital $5d$ transition metal compounds., Comment: Added theoretical RIXS spectrum + expanded. To appear in PRB

The dispersive magnetic excitations in Sr2IrO4 have previously been well described within an isospin-1/2 Heisenberg model on a square lattice that revealed parallels with La2CuO4. Here we investigate the inelastic spectra of Sr2Ir0.8Ru0.2O4 with resonant inelastic x-ray scattering (RIXS) at the Ir L3-edge. The results are well described using linear spin-wave theory within a similar Heisenberg model applicable to Sr2IrO4, however the disorder induced by the substitution of 20% Ir4+ ions for Ru4+ removes longer range exchange interactions. A large spin-gap (40 meV) is measured indicating strong anisotropy from spin-orbit coupling that is manifest due to the altered magnetic structure in Sr2Ir0.8Ru0.2O4 with c-axis aligned moments compared to the basal plane moments in the parent. Collectively the results indicate the robustness of a Heisenberg model description even when the magnetic structure is altered and the J=1/2 moments diluted.

NaOsO3 hosts a rare manifestation of a metal-insulator transition driven by magnetic correlations, placing the magnetic exchange interactions in a central role. We use resonant inelastic x-ray scattering to directly probe these magnetic exchange interactions. A dispersive and strongly gapped (58 meV) excitation is observed indicating appreciable spin-orbit coupling in this 5d3 system. The excitation is well described within a minimal model Hamiltonian with strong anisotropy and Heisenberg exchange (J1=J2=13.9 meV). The observed behavior places NaOsO3 on the boundary between localized and itinerant magnetism.

We use resonant elastic and inelastic X-ray scattering at the Ir-$L_3$ edge to study the doping-dependent magnetic order, magnetic excitations and spin-orbit excitons in the electron-doped bilayer iridate (Sr$_{1-x}$La$_{x}$)$_3$Ir$_2$O$_7$ ($0 \leq x \leq 0.065$). With increasing doping $x$, the three-dimensional long range antiferromagnetic order is gradually suppressed and evolves into a three-dimensional short range order from $x = 0$ to $0.05$, followed by a transition to two-dimensional short range order between $x = 0.05$ and $0.065$. Following the evolution of the antiferromagnetic order, the magnetic excitations undergo damping, anisotropic softening and gap collapse, accompanied by weakly doping-dependent spin-orbit excitons. Therefore, we conclude that electron doping suppresses the magnetic anisotropy and interlayer couplings and drives (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ into a correlated metallic state hosting two-dimensional short range antiferromagnetic order and strong antiferromagnetic fluctuations of $J_{\text{eff}} = \frac{1}{2}$ moments, with the magnon gap strongly suppressed., Comment: 6 Pages, 3 Figures, with supplementary in Source

We study the evolution of magnetic excitations in the disordered two-dimensional antiferromagnet Sr2Ir1-xRuxO4. A gigantic magnetic gap greater than 40 meV opens at x = 0.27 and increases with Ru concentration, rendering the dispersive magnetic excitations in Sr2IrO4 almost momentum independent. Up to a Ru concentration of x = 0.77, both experiments and first-principles calculations show the Ir Jeff = 1/2 state remains intact. The magnetic gap arises from the local interaction anisotropy in the proximity of the Ru disorder. Under the coherent potential approximation, we reproduce the experimental magnetic excitations using the disordered Heisenberg antiferromagnetic model with suppressed next-nearest neighbor ferromagnetic coupling., Comment: 6 pages, 4 figures

The spin-orbit Mott insulator Sr3Ir2O7 provides a fascinating playground to explore insulator-metal transition driven by intertwined charge, spin, and lattice degrees of freedom. Here, we report high pressure electric resistance and resonant inelastic x ray scattering measurements on single crystal Sr3Ir2O7 up to 63 65 GPa at 300 K. The material becomes a confined metal at 59.5 GPa, showing metallicity in the ab plane but an insulating behavior along the c axis. Such an unusual phenomenon resembles the strange metal phase in cuprate superconductors. Since there is no sign of the collapse of spin orbit or Coulomb interactions in x-ray measurements, this novel insulator metal transition is potentially driven by a first-order structural change at nearby pressures. Our discovery points to a new approach for synthesizing functional materials., Comment: 4-page 3-figure

Measuring how the magnetic correlations throughout the Brillouin zone evolve in a Mott insulator as charges are introduced dramatically improved our understanding of the pseudogap, non-Fermi liquids and high $T_C$ superconductivity. Recently, photoexcitation has been used to induce similarly exotic states transiently. However, understanding how these states emerge has been limited because of a lack of available probes of magnetic correlations in the time domain, which hinders further investigation of how light can be used to control the properties of solids. Here we implement magnetic resonant inelastic X-ray scattering at a free electron laser, and directly determine the magnetization dynamics after photo-doping the Mott insulator Sr$_2$IrO$_4$. We find that the non-equilibrium state 2~ps after the excitation has strongly suppressed long-range magnetic order, but hosts photo-carriers that induce strong, non-thermal magnetic correlations. The magnetism recovers its two-dimensional (2D) in-plane N\'eel correlations on a timescale of a few ps, while the three-dimensional (3D) long-range magnetic order restores over a far longer, fluence-dependent timescale of a few hundred ps. The dramatic difference in these two timescales, implies that characterizing the dimensionality of magnetic correlations will be vital in our efforts to understand ultrafast magnetic dynamics., Comment: 7 page, 4 figures; to appear in Nature Materials

We have investigated the structural, electronic, and magnetic properties of the pyrochlore iridates Eu2Ir2O7 and Pr2Ir2O7 using a combination of resonant elastic x-ray scattering, x-ray powder diffraction, and resonant inelastic x-ray scattering (RIXS). The structural parameters of Eu2Ir2O7 have been examined as a function of temperature and applied pressure, with a particular emphasis on regions of the phase diagram where electronic and magnetic phase transitions have been reported. We find no evidence of crystal symmetry change over the range of temperatures (~6 to 300 K) and pressures (~0.1 to 17 GPa) studied. We have also investigated the electronic and magnetic excitations in single crystal samples of Eu2Ir2O7 and Pr2Ir2O7 using high resolution Ir L3-edge RIXS. In spite of very different ground state properties, we find these materials exhibit qualitatively similar excitation spectra, with crystal field excitations at ~3-5 eV, spin-orbit excitations at ~0.5-1 eV, and broad low-lying excitations below ~0.15 eV. In Eu2Ir2O7 we observe highly damped magnetic excitations at ~45 meV, which display significant momentum dependence. We compare these results with recent dynamical structure factor calculations., Comment: 14 pages, 13 figures (including supplemental material)

The rich physics manifested by 5d oxides falls outside the Mott-Hubbard paradigm used to successfully explain the electronic and magnetic properties of 3d oxides. Much consideration has been given to the extent to which strong spin-orbit coupling (SOC), in the limit of increased bandwidth and reduced electron correlation, drives the formation of novel electronic states, as manifested through the existence of metal-insulator transitions (MITs). SOC is believed to play a dominant role in 5d5 systems such as iridates (Ir4+), undergoing MITs which may or may not be intimately connected to magnetic order, with pyrochlore and perovksite systems being examples of the former and latter, respectively. However, the role of SOC for other 5d configurations is less clear. For example, 5d3 (e.g Os5+) systems are expected to have an orbital singlet and consequently a reduced effect of SOC in the groundstate. The pyrochlore osmate Cd2Os2O7 nonetheless exhibits a MIT intimately entwined with magnetic order with phenomena similar to pyrochlore iridates. Here we report the first resonant inelastic X-ray scattering (RIXS) measurements on an osmium compound, allowing us to determine the salient electronic and magnetic energy scales controlling the MIT in Cd2Os2O7, which we benchmark against detailed quantum chemistry calculations. In particular, we reveal the emergence at the MIT of a magnetic excitation corresponding to a superposition of multiple spin-flip processes from an Ising-like all-in/all-out magnetic groundstate. We discuss our results with respect to the role of SOC in magnetically mediated MITs in 5d systems

We present a refined and improved study of the influence of screening on the effective fine structure constant of graphene, $\alpha^*$, as measured in graphite using inelastic x-ray scattering. This follow-up to our previous study [J. P. Reed, et al., Science 330, 805 (2010)] was carried out with two times better energy resolution, five times better momentum resolution, and improved experimental setup with lower background. We compare our results to RPA calculations and evaluate the relative importance of interlayer hopping, excitonic corrections, and screening from high energy excitations involving the $\sigma$ bands. We find that the static, limiting value of $\alpha^*$ falls in the range 0.25 to 0.35, which is higher than our previous result of 0.14, but still below the value expected from RPA. We show the reduced value is not a consequence of interlayer hopping effects, which were ignored in our previous analysis, but of a combination of excitonic effects in the $\pi \rightarrow \pi^*$ particle-hole continuum, and background screening from the $\sigma$-bonded electrons. We find that $\sigma$-band screening is extremely strong at distances of the order of a few nm, and should be highly effective at screening out short-distance, Hubbard-like interactions in graphene, as well as other carbon allotropes., Comment: 23 pages, 5 figures

We report x-ray resonant magnetic scattering (XRMS) and resonant inelastic x-ray scattering (RIXS) studies of epitaxially-strained $\mathrm{Sr_2IrO_4}$ thin films. The films were grown on $\mathrm{SrTiO_3}$ and $\mathrm{(LaAlO_3)_{0.3}(Sr_2AlTaO_6)_{0.7}}$ substrates, under slight tensile and compressive strains, respectively. Although the films develop a magnetic structure reminiscent of bulk $\mathrm{Sr_2IrO_4}$, the magnetic correlations are extremely anisotropic, with in-plane correlation lengths significantly longer than the out-of-plane correlation lengths. In addition, the compressive (tensile) strain serves to suppress (enhance) the magnetic ordering temperature $\mathrm{T_N}$, while raising (lowering) the energy of the zone boundary magnon. Quantum chemical calculations show that the tuning of magnetic energy scales can be understood in terms of strain-induced change in bond lengths., Comment: 5 pages, 4 figures

We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We make use of different adaptations of the strong-disorder renormalization-group (SDRG) scheme of Ma, Dasgupta and Hu, widely employed in the study of random spin chains, supplemented by quantum Monte Carlo and density-matrix renormalization-group numerical calculations, to study the nature of the ground state as the coupling modulation is increased. We find no phase transition for the Fibonacci chain, while we show that the 6-3 chain exhibits a phase transition to a gapless, aperiodicity-dominated phase similar to the one found for the aperiodic spin-1/2 XXZ chain. Contrary to what is verified for random spin-1 chains, we show that different adaptations of the SDRG scheme may lead to different qualitative conclusions about the nature of the ground state in the presence of aperiodic coupling modulations., Comment: Accepted for publication in Physical Review B

We have used a combination of resonant magnetic x-ray scattering (RMXS) and x-ray absorption spectroscopy (XAS) to investigate the properties of the doped spin-orbital Mott insulator Sr2Ir(1-x)Rh(x)O4 (0.07 < x < 0.70). We show that Sr2Ir(1-x)Rh(x)O4 represents a unique model system for the study of dilute magnetism in the presence of strong spin-orbit coupling, and provide evidence of a doping-induced change in magnetic structure and a suppression of magnetic order at x_c ~ 0.17. We demonstrate that Rh-doping introduces Rh3+/Ir5+ ions which effectively hole-dope this material. We propose that the magnetic phase diagram for this material can be understood in terms of a novel spin-orbital percolation picture., Comment: 9 pages, 7 figures

The low energy excitations in Na2IrO3 have been investigated using resonant inelastic x-ray scattering (RIXS). A magnetic excitation branch can be resolved, whose dispersion reaches a maximum energy of about 35 meV at the \Gamma-point. The momentum dependence of the excitation energy is much larger along the \Gamma-X direction compared to that along the \Gamma-Y direction. The observed dispersion relation is consistent with a recent theoretical prediction based on Heisenberg-Kitaev model. At high temperatures, we find large contributions from lattice vibrational modes to our RIXS spectra, suggesting that a strong electron-lattice coupling is present in Na2IrO3., Comment: 5 pages, 3 figures

We report a combined experimental and theoretical study of the unusual ferromagnetism in the one-dimensional copper-iridium oxide Sr$_3$CuIrO$_6$. Utilizing Ir $L_3$ edge resonant inelastic x-ray scattering, we reveal a large gap magnetic excitation spectrum. We find that it is caused by an unusual exchange anisotropy generating mechanism, namely, strong ferromagnetic anisotropy arising from antiferromagnetic superexchange, driven by the alternating strong and weak spin-orbit coupling on the $5d$ Ir and 3d Cu magnetic ions, respectively. From symmetry consideration, this novel mechanism is generally present in systems with edge-sharing Cu$^{2+}$O$_4$ plaquettes and Ir$^{4+}$O$_6$ octahedra. Our results point to unusual magnetic behavior to be expected in mixed 3d-5d transition-metal compounds via exchange pathways that are absent in pure 3d or 5d compounds., Comment: 5 pages, 4 figures

We report a Fe K\beta x-ray emission spectroscopy study of local magnetic moments in the rare-earth doped iron pnictide Ca_{1-x}RE_xFe_2As_2 (RE=La, Pr, and Nd). In all samples studied the size of the Fe local moment is found to decrease significantly with temperature and goes from ~0.9 \mu_B at T = 300 K to ~0.45 \mu_B at T = 70 K. In the collapsed tetragonal (cT) phase of Nd- and Pr-doped samples (T<70K) the local moment is quenched, while the moment remains unchanged for the La-doped sample, which does not show lattice collapse. Our results show that Ca_{1-x}RE_xFe_2As_2 (RE= Pr and Nd) exhibits a spin-state transition and provide direct evidence for a non-magnetic Fe^{2+} ion in the cT-phase, as predicted by Yildirim. We argue that the gradual change of the the spin-state over a wide temperature range reveals the importance of multiorbital physics, in particular the competition between the crystal field split Fe 3d orbitals and the Hund's rule coupling., Comment: 5 pages and 3 figures. To be published in PRL

We report strongly momentum-dependent local charge screening dynamics in CE-type charge, orbital, and spin ordered La$_{0.5}$Sr$_{1.5}$MnO$_4$, based on Mn K-edge resonant inelastic x-ray scattering data. Through a comparison with theoretical calculations, we show that the observed momentum dependence reflects highly localized, nearest neighbor screening of the transient local charge perturbation in this compound with an exciton-like screening cloud, rather than delocalized screening. The size of the screening cloud is estmated to be about 0.4-0.5 interatomic distances.

The electronic structure of Sr$_3$CuIrO$_6$, a model system for the 5d Ir ion in an octahedral environment, is studied through a combination of resonant inelastic x-ray scattering (RIXS) and theoretical calculations. RIXS spectra at the Ir L$_3$-edge reveal an Ir $t_{2g}$ manifold that is split into three levels, in contrast to the expectations of the strong spin-orbit-coupling limit. Effective Hamiltonian and $ab inito$ quantum chemistry calculations find a strikingly large non-cubic crystal field splitting comparable to the spin-orbit coupling, which results in a strong mixing of the $j_{\mathsf{eff}}=1/2$ and $j_{\mathsf{eff}}=3/2$ states and modifies the isotropic wavefunctions on which many theoretical models are based., Comment: to appear in phys. Rev. Lett

The electronic structure of the honeycomb lattice iridates Na2IrO3 and Li2IrO3 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 non-cubic 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 A2IrO3. 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 Na2IrO3 and Li2IrO3 can be described as spin-orbit Mott insulators, similar to the square lattice iridate Sr2IrO4.

Using resonant inelastic x-ray scattering, we observe in the bilayer iridate Sr3Ir2O7, a spin-orbit coupling driven magnetic insulator with a small charge gap, a magnon gap of ~92 meV for both acoustic and optical branches. This exceptionally large magnon gap exceeds the total magnon bandwidth of ~70 meV and implies a marked departure from the Heisenberg model, in stark contrast to the case of the single-layer iridate Sr2IrO4. Analyzing the origin of these observations, we find that the giant magnon gap results from bond-directional pseudo-dipolar interactions that are strongly enhanced near the metal-insulator transition boundary. This suggests that novel magnetism, such as that inspired by the Kitaev model built on the pseudo-dipolar interactions, may emerge in small charge-gap iridates.

We used resonant inelastic x-ray scattering to reveal the nature of magnetic interactions in Sr2IrO4, a 5d transition-metal oxide with a spin-orbit entangled ground state and Jeff=1/2 magnetic momemts, referred to as 'isospins'. The magnon dispersion in Sr2IrO4 is well described by an antiferromagnetic Heisenberg model with isospin one-half moments on a square lattice, which renders the low-energy effective physics of Sr2IrO4 much akin to that in superconducting cuprates. This is further supported by the observation of exciton modes in Sr2IrO4 whose dispersion is strongly renormalized by magnons, which can be understood by analogy to the hole propagation in the background of antiferromagnetically ordered spins in the cuprates.

We give a brief summary of the current status of the electron many-body problem in graphene. We claim that graphene has intrinsic dielectric properties which should dress the interactions among the quasiparticles, and may explain why the observation of electron-electron renormalization effects has been so elusive in the recent experiments. We argue that the strength of Coulomb interactions in graphene may be characterized by an effective fine structure constant given by $\alpha^{\star}(\mathbf{k},\omega)\equiv2.2/\epsilon(\mathbf{k},\omega)$, where $\epsilon(\mathbf{k},\omega)$ is the dynamical dielectric function. At long wavelengths, $\alpha^{\star}(\mathbf{k},\omega)$ appears to have its smallest value in the static regime, where $\alpha^{\star}(\mathbf{k}\to0,0)\approx1/7$ according to recent inelastic x-ray measurements, and the largest value in the optical limit, where $\alpha^{\star}(0,\omega)\approx2.6$. We conclude that the strength of Coulomb interactions in graphene is not universal, but depends highly on the scale of the phenomenon of interest. We propose a prescription in order to reconcile different experiments., Comment: 7pages, 3 Figures. Contribution to the Proceedings of the Nobel symposium on graphene and quantum matter

We report Fe K beta x-ray emission spectroscopy study of local magnetic moments in various iron based superconductors in their paramagnetic phases. Local magnetic moments are found in all samples studied: PrFeAsO, Ba(Fe,Co)2As2, LiFeAs, Fe1+x(Te,Se), and A2Fe4Se5 (A=K, Rb, and Cs). The moment size varies significantly across different families. Specifically, all iron pnictides samples have local moments of about 1 $\mu_B$/Fe, while FeTe and K2Fe4Se5 families have much larger local moments of ~2$\mu_B$/Fe, ~3.3$\mu_B$/Fe, respectively. In addition, we find that neither carrier doping nor temperature change affects the local moment size., Comment: 5 pages, 3 figures

The electronic structure of CuIr$_2$S$_4$ has been investigated using various bulk-sensitive x-ray spectroscopic methods near the Ir $L_3$-edge: resonant inelastic x-ray scattering (RIXS), x-ray absorption spectroscopy in the partial fluorescence yield (PFY-XAS) mode, and resonant x-ray emission spectroscopy (RXES). A strong RIXS signal (0.75 eV) resulting from a charge-density-wave gap opening is observed below the metal-insulator transition temperature of 230 K. The resultant modification of electronic structure is consistent with the density functional theory prediction. In the spin- and charge- dimer disordered phase induced by x-ray irradiation below 50 K, we find that a broad peak around 0.4 eV appears in the RIXS spectrum., Comment: 4 pages and 4 figures

We report a comprehensive Cu $K$-edge RIXS investigation of $\rm La_{2-x}Sr_xCuO_4$ (LSCO) for 0$\leq$x$\leq$0.35, stripe-ordered $\rm La_{1.875}Ba_{0.125}CuO_4$ (LBCO), and $\rm La_{2}Cu_{0.96}Ni_{0.04}O_4$ (LCNO) crystals. The RIXS spectra measured at three high-symmetry momentum transfer (\textbf{q}) positions are compared as a function of doping and for the different dopants. The spectra in the energy range 1-6 eV can be described with three broad peaks, which evolve systematically with increased doping. The most systematic trend was observed for \textbf{q}=($\pi$, 0) corresponding to the zone boundary. As hole doping increased, the spectral weight transfer from high energies to low energies is nearly linear with \emph{x} at this \textbf{q}. We interpret the peaks as interband transitions in the context of existing band models for this system, assigning them to Zhang-Rice band$\rightarrow$upper Hubbard band, lower-lying band$\rightarrow$upper Hubbard band, and lower-lying band$\rightarrow$Zhang-Rice band transitions. The spectrum of stripe-ordered LBCO was also measured, and found to be identical to the correspondingly doped LSCO, except for a relative enhancement of the near-infrared peak intensity around 1.5-1.7 eV. The temperature dependence of this near-infrared peak in LBCO was more pronounced than for other parts of the spectrum, continuously decreasing in intensity as the temperature was raised from 25 K to 300 K. Finally, we find that 4\% Ni substitution in the Cu site has a similar effect on the spectra as does Sr substitution in the La site., Comment: 10 pages (according to my pdf), 8 figures. Was accepted for publication in PRB. When I did the preview in the previous step, somehow figure 2 looked very broken into pieces ?

Electrons in graphene behave like Dirac fermions, permitting phenomena from high energy physics to be studied in a solid state setting. A key question is whether or not these Fermions are critically influenced by Coulomb correlations. We performed inelastic x-ray scattering experiments on crystals of graphite, and applied reconstruction algorithms to image the dynamical screening of charge in a freestanding, graphene sheet. We found that the polarizability of the Dirac fermions is amplified by excitonic effects, improving screening of interactions between quasiparticles. The strength of interactions is characterized by a scale-dependent, effective fine structure constant, \alpha *(k,\omega), whose value approaches \alpha * ~ 1/7 at low energy and large distances. This value is substantially smaller than the nominal \alpha = 2.2, suggesting that, on the whole, graphene is more weakly interacting than previously believed., Comment: 28 pages, 10 figures, 2 animations

We report a high resolution resonant inelastic x-ray scattering investigation of the bilayer manganites La$_{2-2x}$Sr$_{1+2x}$Mn$_2$O$_7$ with $x = 0.36$ and $0.5$. The momentum dependence along the crystallographic $(110)$ direction for energy losses $1\,\rm{eV} \leq \Delta E \leq 15\,\rm{eV}$ has been measured in detail with the data analysis focusing on the energy loss region $1\,\rm{eV} \leq \Delta E \leq 5\,\rm{eV}$, which includes a strong peak located at $\Delta E \approx 2\,\rm{eV}$. We observe a clear dispersion of up to $0.5\,\rm{eV}$ in the measured $\textbf{q}$ range, which is direct evidence of the non-local character of this excitation. Further, we found that the intensity in this low energy region strongly depends on both the reduced wave vector $\textbf{q} = (h, h, 0)$, $h = 0.1 - 0.5$, and temperature, i.e. different ordered phases. Results can be explained via an intersite $d-d$ charge transfer excitation, proposed for pseudo-cubic manganites, where the hopping rate is strongly increased (decreased) by ferromagnetic (antiferromagnetic) alignment of neighboring in-plane Mn ion core spins.