Investigation of elementary excitations has advanced our understanding of many-body physics governing most physical properties of matter. Recently spin-orbit excitons have drawn much attention, whose condensates near phase transitions exhibit Higgs m
ode oscillations, a long-sought physical phenomenon [Nat. Phys. {bf 13}, 633 (2017)]. These critical transition points resulting from competing spin-orbit coupling (SOC), local crystalline symmetry and exchange interactions, are not obvious in Iridium based materials, where SOC prevails in general. Here, we present results of resonant inelastic x-ray scattering on a spin-orbital liquid Ba$_3$ZnIr$_2$O$_9$ and three other 6H-hexagonal perovskite iridates which show magnetism, contrary to non-magnetic singlet ground state expected due to strong SOC. Our results show that substantial hopping between closely placed Ir$^{5+}$ ions within Ir$_2$O$_9$ dimers in these 6H-iridates, modifies spin-orbit coupled states and reduces spin-orbit excitation energies. Here, we are forced to use at least a two-site model, to match the excitation spectrum going in line with the strong intra-dimer hopping. Apart from SOC, low energy physics of iridates is thus critically dependent on hopping, and may not be ignored even for systems having moderate hopping, where the excitation spectra can be explained using an atomic model. SOC which is generally found to be 0.4-0.5~eV in iridates, is scaled in effect down to $sim$0.26~eV for the 6H-systems, sustaining the hope to achieve quantum criticality by tuning Ir-Ir separation.
In the quest for realizations of quantum spin liquids, the exploration of Kitaev materials - spin-orbit entangled Mott insulators with strong bond-directional exchanges - has taken center stage. However, in these materials the local spin-orbital j=1/
2 moments typically show long-range magnetic order at low temperature, thus defying the formation of a spin-liquid ground state. Using resonant inelastic x-ray scattering (RIXS), we here report on a proximate spin liquid regime with clear fingerprints of Kitaev physics in the magnetic excitations of the honeycomb iridates alpha-Li2IrO3 and Na2IrO3. We observe a broad continuum of magnetic excitations that persists up to at least 300K, more than an order of magnitude larger than the magnetic ordering temperatures. We prove the magnetic character of this continuum by an analysis of the resonance behavior. RIXS measurements of the dynamical structure factor for energies within the continuum show that dynamical spin-spin correlations are restricted to nearest neighbors. Notably, these spectroscopic observations are also present in the magnetically ordered state for excitation energies above the conventional magnon excitations. Phenomenologically, our data agree with inelastic neutron scattering results on the related honeycomb compound RuCl3, establishing a common ground for a proximate Kitaev spin-liquid regime in these materials.
Youngs archetypal double-slit experiment forms the basis for modern diffraction techniques: the elastic scattering of waves yields an interference pattern that captures the real-space structure. Here, we report on an inelastic incarnation of Youngs e
xperiment and demonstrate that resonant inelastic x-ray scattering (RIXS) measures interference patterns which reveal the symmetry and character of electronic excited states in the same way as elastic scattering does for the ground state. A prototypical example is provided by the quasi-molecular electronic structure of insulating Ba3CeIr2O9 with structural Ir dimers and strong spin-orbit coupling. The double slits in this resonant experiment are the highly localized core levels of the two Ir atoms within a dimer. The clear double-slit-type sinusoidal interference patterns that we observe allow us to characterize the electronic excitations, demonstrating the power of RIXS interferometry to unravel the electronic structure of solids containing, e.g., dimers, trimers, ladders, or other superstructures.
We have investigated the electronic structure of Sr2IrO4 using core level resonant inelastic x-ray scattering. The experimental spectra can be well reproduced using ab initio density functional theory based multiplet ligand field theory calculations,
thereby validating these calculations. We found that the low-energy, effective Ir t2g orbitals are practically degenerate in energy. We uncovered that covalency in Sr2IrO4, and generally in iridates, is very large with substantial oxygen ligand hole character in the Ir t2g Wannier orbitals. This has far reaching consequences, as not only the onsite crystal-field energies are determined by the long range crystal-structure, but, more significantly, magnetic exchange interactions will have long range distance dependent anisotropies in the spin direction. These findings set constraints and show pathways for the design of d^5 materials that can host compass-like magnetic interactions.
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.
Magnetic excitations in the optimally doped high-$T_mathrm{c}$ superconductor Bi$_{1.5}$Pb$_{0.55}$Sr$_{1.6}$La$_{0.4}$CuO$_{6+delta}$ (OP-Bi2201, $T_mathrm{c}simeq 34$ K) are investigated by Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS),
below and above the pseudogap opening temperature. At both temperatures the broad spectral distribution disperses along the (1,0) direction up to $sim$350~meV at zone boundary, similarly to other hole-doped cuprates. However, above $sim$0.22 reciprocal lattice units, we observe a concurrent intensity decrease for magnetic excitations and quasi-elastic signals with weak temperature dependence. This anomaly seems to indicate a coupling between magnetic, lattice and charge modes in this compound. We also compare the magnetic excitation spectra near the anti-nodal zone boundary in the single layer OP-Bi2201 and in the bi-layer optimally doped Bi$_{1.5}$Pb$_{0.6}$Sr$_{1.54}$CaCu$_2$O$_{8+delta}$ (OP-Bi2212, $T_mathrm{c}simeq96$ K). The strong similarities in the paramagnon dispersion and in their energy at zone boundary indicate that the strength of the super-exchange interaction and the short-range magnetic correlation cannot be directly related to $T_mathrm{c}$, not even within the same family of cuprates.
We have studied local magnetic moment and electronic phase separation in superconducting K$_{x}$Fe$_{2-y}$Se$_2$ by x-ray emission and absorption spectroscopy. Detailed temperature dependent measurements at the Fe K-edge have revealed coexisting elec
tronic phases and their correlation with the transport properties. By cooling down, the local magnetic moment of Fe shows a sharp drop across the superconducting transition temperature (T$_c$) and the coexisting phases exchange spectral weights with the low spin state gaining intensity at the expense of the higher spin state. After annealing the sample across the iron-vacancy order temperature, the system does not recover the initial state and the spectral weight anomaly at T$_c$ as well as superconductivity disappear. The results clearly underline that the coexistence of the low spin and high spin phases and the transitions between them provide unusual magnetic fluctuations and have a fundamental role in the superconducting mechanism of electronically inhomogeneous K$_{x}$Fe$_{2-y}$Se$_2$ system.
In CaIrO3 electronic correlation, spin-orbit coupling, and tetragonal crystal field splitting are predicted to be of comparable strength. However, the nature of its ground state is still object of debate, with contradictory experimental and theoretic
al results. We probe the ground state of CaIrO3 and assess the effective tetragonal crystal field splitting and spin-orbit coupling at play in this system by means of resonant inelastic x-ray scattering. We conclude that insulating CaIrO3 is not a jeff = 1/2 iridate and discuss the consequences of our finding to the interpretation of previous experiments. In particular, we clarify how the Mott insulating state in iridates can be readily extended beyond the jeff = 1/2 ground state.
We present RIXS data at O K edge from La2-xSrxCuO4 vs. doping between x=0.10 and x=0.22 with attention to the magnetic excitations in the Mid-Infrared region. The sampling done by RIXS is the same as in the undoped cuprates provided the excitation is
at the first pre-peak induced by doping. Note that this excitation energy is about 1.5 eV lower than that needed to see bimagnons in the parent compound. This approach allows the study of the upper region of the bimagnon continuum around 450 meV within about one third of the Brilluoin Zone around Gamma. The results show the presence of damped bimagnons and of higher even order spin excitations with almost constant spectral weight at all the dopings explored here. The implications on high Tc studies are briefly addressed.
We measured high resolution Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS) of the undoped cuprates La$_2$CuO$_4$, Sr$_2$CuO$_2$Cl$_2$, CaCuO$_2$ and NdBa$_2$Cu$_3$O$_6$. The dominant spectral features were assigned to $dd$ excitations and w
e extensively studied their polarization and scattering geometry dependence. In a pure ionic picture, we calculated the theoretical cross sections for those excitations and used them to fit the experimental data with excellent agreement. By doing so, we were able to determine the energy and symmetry of Cu-3$d$ states for the four systems with unprecedented accuracy and confidence. The values of the effective parameters could be obtained for the single ion crystal field model but not for a simple two-dimensional cluster model. The firm experimental assessment of $dd$ excitation energies carries important consequences for the physics of high $T_c$ superconductors. On one hand, having found that the minimum energy of orbital excitation is always $geq 1.4$ eV, i.e., well above the mid-infrared spectral range, leaves to magnetic excitations (up to 300 meV) a major role in Cooper pairing in cuprates. On the other hand, it has become possible to study quantitatively the effective influence of $dd$ excitations on the superconducting gap in cuprates.
