Large spin-wave energy gap in the bilayer iridate Sr3Ir2O7: evidence for enhanced dipolar interactions near the mott metal-insulator transition

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.

Reconciling Monolayer and Bilayer J_{eff}=1/2 Square Lattices in Hybrid Oxide Superlattice

The number of atomic layers confined in a two-dimensional structure is crucial for the electronic and magnetic properties. Single-layer and bilayer J_{eff}=1/2 square lattices are well-known examples where the presence of the extra layer turns the XY anisotropy to the c-axis anisotropy. We report on experimental realization of a hybrid SrIrO_{3}/SrTiO_{3} superlattice that integrates monolayer and bilayer square lattices in one layered structure. By synchrotron x-ray diffraction, resonant x-ray magnetic scattering, magnetization, and resistivity measurements, we found that the hybrid superlattice exhibits properties that are distinct from both the single-layer and bilayer systems and cannot be explained by a simple addition of them. In particular, the entire hybrid superlattice orders simultaneously through a single antiferromagnetic transition at temperatures similar to the bilayer system but with all the J_{eff}=1/2 moments mainly pointing in the ab plane similar to the single-layer system. The results show that bringing monolayer and bilayer with orthogonal properties in proximity to each other in a hybrid superlattice structure is a powerful way to stabilize a unique state not obtainable in a uniform structure.

Antiferromagnetic excitonic insulator state in Sr3Ir2O7

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 insulator phase.

Antiferromagnetic excitonic insulators are a distinct form of excitonic insulator, in which electrons and holes are bound by magnetic exchange rather than Coulomb attraction. Here, Mazzone et al. show, using X-ray scattering, that Sr3Ir2O7 realizes this particular state.

Enhancement of Photoresponse on Narrow-Bandgap Mott Insulator α-RuCl3 via Intercalation

Charge doping to Mott insulators is critical to realize high-temperature superconductivity, quantum spin liquid state, and Majorana fermion, which would contribute to quantum computation. Mott insulators also have a great potential for optoelectronic applications; however, they showed insufficient photoresponse in previous reports. To enhance the photoresponse of Mott insulators, charge doping is a promising strategy since it leads to effective modification of electronic structure near the Fermi level. Intercalation, which is the ion insertion into the van der Waals gap of layered materials, is an effective charge-doping method without defect generation. Herein, we showed significant enhancement of optoelectronic properties of a layered Mott insulator, α-RuCl₃, through electron doping by organic cation intercalation. The electron-doping results in substantial electronic structure change, leading to the bandgap shrinkage from 1.2 eV to 0.7 eV. Due to localized excessive electrons in RuCl₃, distinct density of states is generated in the valence band, leading to the optical absorption change rather than metallic transition even in substantial doping concentration. The stable near-infrared photodetector using electronic modulated RuCl₃ showed 50 times higher photoresponsivity and 3 times faster response time compared to those of pristine RuCl₃, which contributes to overcoming the disadvantage of a Mott insulator as a promising optoelectronic device and expanding the material libraries.

Electronic band structure of iridates

In this review, an attempt has been made to compare the electronic structures of various 5d iridates (iridium oxides), with an effort to note the common features and differences. Both experimental studies, especially angle-resolved photoemission spectroscopy (ARPES) results, and first-principles band structure calculations have been discussed. This brings to focus the fact that the electronic structures and magnetic properties of the high-Z 5d transition iridates depend on the intricate interplay of strong electron correlation, strong (relativistic) spin-orbit coupling, lattice distortion, and the dimensionality of the system. For example, in the thin film limit, SrIrO₃ exhibits a metal-insulator transition that corresponds to the dimensionality crossover, with the band structure resembling that of bulk Sr₂IrO₄.

Laser-induced transient magnons in Sr3Ir2O7 throughout the Brillouin zone

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.

Strain engineering of the charge and spin-orbital interactions in Sr2IrO4

Understanding the relationship between entangled degrees of freedom (DOF) is a central problem in correlated materials and the possibility to influence their balance is promising toward realizing novel functionalities. In Sr₂IrO₄, the interaction between spin–orbit coupling and electron correlations induces an exotic ground state with magnetotransport properties promising for antiferromagnetic spintronics applications. Moreover, the coupling between orbital and spin DOF renders the magnetic structure sensitive to the Ir–O bond environment. To date, a detailed understanding of the microscopic spin-lattice and electron–phonon interactions is still lacking. Here, we use strain engineering to perturb the local lattice environment and, by tracking the response of the low-energy elementary excitations, we unveil the response of the microscopic spin and charge interactions.

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 cross-over 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 t_2g 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 toward the control of the ground state of complex oxides in the presence of high spin–orbit coupling.

Symmetry-Resolved Two-Magnon Excitations in a Strong Spin-Orbit-Coupled Bilayer Antiferromagnet

We used a combination of polarized Raman spectroscopy and spin wave calculations to study magnetic excitations in the strong spin-orbit-coupled bilayer perovskite antiferromagnet Sr_{3}Ir_{2}O_{7}. We observed two broad Raman features at ∼800 and ∼1400  cm^{-1} arising from magnetic excitations. Unconventionally, the ∼800  cm^{-1} feature is fully symmetric (A_{1g}) with respect to the underlying tetragonal (D_{4h}) crystal lattice which, together with its broad line shape, definitively rules out the possibility of a single magnon excitation as its origin. In contrast, the ∼1400  cm^{-1} feature shows up in both the A_{1g} and B_{2g} channels. From spin wave and two-magnon scattering cross-section calculations of a tetragonal bilayer antiferromagnet, we identified the ∼800  cm^{-1} (1400  cm^{-1}) feature as two-magnon excitations with pairs of magnons from the zone-center Γ point (zone-boundary van Hove singularity X point). We further found that this zone-center two-magnon scattering is unique to bilayer perovskite magnets which host an optical branch in addition to the acoustic branch, as compared to their single layer counterparts. This zone-center two-magnon mode is distinct in symmetry from the time-reversal symmetry broken "spin wave gap" and "phase mode" proposed to explain the ∼92  meV (742  cm^{-1}) gap in resonant inelastic x-ray spectroscopy magnetic excitation spectra of Sr_{3}Ir_{2}O_{7}.

Montel mirror based collimating analyzer system for high-pressure resonant inelastic X-ray scattering experiments

Resonant inelastic X-ray scattering (RIXS) is increasingly playing a significant role in studying highly correlated systems, especially since it was proven capable of measuring low-energy magnetic excitations. However, despite high expectations for experimental evidence of novel magnetic phases at high pressure, unequivocal low-energy spectral signatures remain obscured by extrinsic scattering from material surrounding the sample in a diamond anvil cell (DAC): pressure media, Be gasket and the diamond anvils themselves. A scattered X-ray collimation based medium-energy resolution (∼100 meV) analyzer system for a RIXS spectrometer at the Ir L₃-absorption edge has been designed and built to remediate these difficulties. Due to the confocal nature of the analyzer system, the majority of extrinsic scattering is rejected, yielding a clean low-energy excitation spectrum of an iridate Sr₂IrO₄ sample in a DAC cell. Furthermore, the energy resolution of different configurations of the collimating and analyzing optics are discussed.

Magnetic fluctuations and the spin-orbit interaction in Mott insulating CoO

Motivated by the presence of an unquenched orbital angular momentum in CoO, a team at Chalk River, including a recently hired research officer Roger Cowley, performed the first inelastic neutron scattering experiments on the classic Mott insulator [Sakuraiet al1968Phys. Rev.167510]. Despite identifying two magnon modes at the zone boundary, the team was unable to parameterise the low energy magnetic excitation spectrum belowTNusing conventional pseudo-bosonic approaches, instead achieving only qualitative agreement. It would not be for another 40 years that Roger, now at Oxford and motivated by the discovery of the high-Tccuprate superconductors [Bednorz and Muller 1986Z. Phys. B64189], would make another attempt at the parameterisation of the magnetic excitation spectrum that had previously alluded him at the start of his career. Upon his return to CoO, Roger found a system embroiled in controversy, with some of its most fundamental parameters still remaining undetermined. Faced with such a formidable task, Roger performed a series of inelastic neutron scattering experiments in the early 2010s on both CoO and a magnetically dilute structural analogue Mg0.97Co0.03O. These experiments would prove instrumental in the determination of both single-ion [Cowleyet al2013Phys. Rev. B88205117] and cooperative magnetic parameters [Sarteet al2018Phys. Rev. B98024415] for CoO. Both these sets of parameters would eventually be used in a spin-orbit exciton model [Sarteet al2019Phys. Rev. B100075143], developed by his longtime friend and collaborator Bill Buyers, to successfully parameterise the complex spectrum that both measured at Chalk River almost 50 years prior. The story of CoO is of one that has come full circle, one filled with both spectacular failures and intermittent, yet profound, little victories.

Magnetic Anisotropy of a Quasi Two-Dimensional Canted Antiferromagnet

We report the control of the interplane magnetic exchange coupling in CaIrO₃ perovskite thin films and superlattices with SrTiO₃. By analyzing the anisotropic magneto-transport data, we demonstrate that a semimetallic paramagnetic CaIrO₃ turns into a canted antiferromagnetic Mott insulator at reduced dimensions. The emergence of a biaxial magneto-crystalline anisotropy indicates the canted moment responding to the cubic symmetry. Extending to superlattices and probing oxygen octahedral rotation by half-integer X-ray Braggs diffraction, a more complete picture about the canted moment evolution with interplane coupling can be understood. Remarkably, a rotation of the canted moments' easy axes by 45° is also observed by a sign reversal of the in-plane strain. These results demonstrate the robustness of anisotropic magnetoresistance in revealing quasi two-dimensional canted antiferromagnets, as well as valuable insights about quadrupolar magnetoelastic coupling, relevant for designing future antiferromagnetic spintronic devices.

Anomalous magnetoresistance due to longitudinal spin fluctuations in a Jeff = 1/2 Mott semiconductor

As a hallmark of electronic correlation, spin-charge interplay underlies many emergent phenomena in doped Mott insulators, such as high-temperature superconductivity, whereas the half-filled parent state is usually electronically frozen with an antiferromagnetic order that resists external control. We report on the observation of a positive magnetoresistance that probes the staggered susceptibility of a pseudospin-half square-lattice Mott insulator built as an artificial SrIrO₃/SrTiO₃ superlattice. Its size is particularly large in the high-temperature insulating paramagnetic phase near the Néel transition. This magnetoresistance originates from a collective charge response to the large longitudinal spin fluctuations under a linear coupling between the external magnetic field and the staggered magnetization enabled by strong spin-orbit interaction. Our results demonstrate a magnetic control of the binding energy of the fluctuating particle-hole pairs in the Slater-Mott crossover regime analogous to the Bardeen-Cooper-Schrieffer-to-Bose-Einstein condensation crossover of ultracold-superfluids.

Spin-charge interactions are at the core of electronic correlation phenomena in Mott insulators. Here, the authors observe a positive anomalous magnetoresistance in a SrIrO₃/SrTiO₃ superlattice, indicative of strong spin-charge fluctuations in this pseudospin-half square-lattice Mott insulator.

Resonant inelastic X-ray scattering of magnetic excitations under pressure

Resonant inelastic X-ray scattering (RIXS) is an extremely valuable tool for the study of elementary, including magnetic, excitations in matter. The latest developments of this technique have mostly been aimed at improving the energy resolution and performing polarization analysis of the scattered radiation, with a great impact on the interpretation and applicability of RIXS. Instead, this article focuses on the sample environment and presents a setup for high-pressure low-temperature RIXS measurements of low-energy excitations. The feasibility of these experiments is proved by probing the magnetic excitations of the bilayer iridate Sr₃Ir₂O₇ at pressures up to 12 GPa.

Preferential quenching of 5d antiferromagnetic order in Sr3(Ir1-x Mn x )2O7

The breakdown of [Formula: see text] antiferromagnetism in the limit of strong disorder is studied in Sr₃(Ir_1-x Mn _x )₂O₇. Upon Mn-substitution, antiferromagnetic ordering of the Ir cations becomes increasingly two-dimensional, resulting in the complete suppression of long-range Ir magnetic order above [Formula: see text]. Long-range antiferromagnetism however persists on the Mn sites to higher Mn concentrations (x  >  0.25) and is necessarily mediated via a random network of majority Ir sites. Our data suggest a shift in the Mn valence from Mn⁴⁺ to Mn³⁺ at intermediate doping levels, which in turn generates nonmagnetic Ir⁵⁺ sites and suppresses long-range order within the Ir network. The collapse of long-range [Formula: see text] antiferromagnetism and the survival of percolating antiferromagnetic order on Mn-sites demonstrates a complex 3d-5d exchange process that surprisingly enables minority Mn spins to order far below the conventional percolation threshold for a bilayer square lattice.

Ultrafast dynamics of spin and orbital correlations in quantum materials: an energy- and momentum-resolved perspective

Many remarkable properties of quantum materials emerge from states with intricate coupling between the charge, spin and orbital degrees of freedom. Ultrafast photo-excitation of these materials holds great promise for understanding and controlling the properties of these states. Here, we introduce time-resolved resonant inelastic X-ray scattering (tr-RIXS) as a means of measuring the charge, spin and orbital excitations out of equilibrium. These excitations encode the correlations and interactions that determine the detailed properties of the states generated. After outlining the basic principles and instrumentations of tr-RIXS, we review our first observations of transient antiferromagnetic correlations in quasi two dimensions in a photo-excited Mott insulator and present possible future routes of this fast-developing technique. The increasing number of X-ray free electron laser facilities not only enables tackling long-standing fundamental scientific problems, but also promises to unleash novel inelastic X-ray scattering spectroscopies. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Critical fluctuations in the spin-orbit Mott insulator Sr3Ir2O7

X-ray magnetic critical scattering measurements and specific heat measurements were performed on the perovskite iridate [Formula: see text]. We find that the magnetic interactions close to the Néel temperature [Formula: see text] are three-dimensional. This contrasts with previous studies which suggest two-dimensional behaviour like Sr₂IrO₄. Violation of the Harris criterion ([Formula: see text]) means that weak disorder becomes relevant. This leads a rounding of the antiferromagnetic phase transition at [Formula: see text], and modifies the critical exponents relative to the clean system. Specifically, we determine that the critical behaviour of [Formula: see text] is representative of the diluted 3D Ising universality class.

Overdamped Antiferromagnetic Strange Metal State in Sr_{3}IrRuO_{7}

The unconventional electronic ground state of Sr_{3}IrRuO_{7} is explored via resonant x-ray scattering techniques and angle-resolved photoemission measurements. As the Ru content approaches x=0.5 in Sr_{3}(Ir_{1-x}Ru_{x})_{2}O_{7}, intermediate to the J_{eff}=1/2 Mott state in Sr_{3}Ir_{2}O_{7} and the quantum critical metal in Sr_{3}Ru_{2}O_{7}, a thermodynamically distinct metallic state emerges. The electronic structure of this intermediate phase lacks coherent quasiparticles, and charge transport exhibits a linear temperature dependence over a wide range of temperatures. Spin dynamics associated with the long-range antiferromagnetism of this phase show nearly local, overdamped magnetic excitations and an anomalously large energy scale of 200 meV-an energy far in excess of exchange energies present within either the Sr_{3}Ir_{2}O_{7} or Sr_{3}Ru_{2}O_{7} solid-solution end points. Overdamped quasiparticle dynamics driven by strong spin-charge coupling are proposed to explain the incoherent spectral features of the strange metal state in Sr_{3}IrRuO_{7}.

Nuclear resonant scattering from 193Ir as a probe of the electronic and magnetic properties of iridates

The high brilliance of modern synchrotron radiation sources facilitates experiments with high-energy x-rays across a range of disciplines, including the study of the electronic and magnetic correlations using elastic and inelastic scattering techniques. Here we report on Nuclear Resonance Scattering at the 73 keV nuclear level in ¹⁹³Ir. The transitions between the hyperfine split levels show an untypically high E2/M1 multi-polarity mixing ratio combined with an increased sensitivity to certain changes in the hyperfine field direction compared to non-mixing transitions. The method opens a new way for probing local magnetic and electronic properties of correlated materials containing iridium and provides novel insights into anisotropic magnetism in iridates. In particular, unexpected out-of-plane components of magnetic hyperfine fields and non-zero electric field gradients in Sr₂IrO₄ have been detected and attributed to the strong spin-orbit interaction in this iridate. Due to the high, 62% natural abundance of the ¹⁹³Ir isotope, no isotopic enrichment of the samples is required, qualifying the method for a broad range of applications.

Magnetism in iridate heterostructures leveraged by structural distortions

Fundamental control of magnetic coupling through heterostructure morphology is a prerequisite for rational engineering of magnetic ground states. We report the tuning of magnetic interactions in superlattices composed of single and bilayers of SrIrO₃ inter-spaced with SrTiO₃ in analogy to the Ruddlesden-Popper series iridates. Magnetic scattering shows predominately c-axis antiferromagnetic orientation of the magnetic moments for the bilayer, as in Sr₃Ir₂O₇. However, the magnetic excitation gap, measured by resonant inelastic x-ray scattering, is quite different between the two structures, evidencing a significant change in the stability of the competing magnetic phases. In contrast, the single layer iridate hosts a more bulk-like gap. We find these changes are driven by bending of the c-axis Ir-O-Ir bond, which is much weaker in the single layer, and subsequent local environment changes, evidenced through x-ray diffraction and magnetic excitation modeling. Our findings demonstrate how large changes in the magnetic interactions can be tailored and probed in spin-orbit coupled heterostructures by engineering subtle structural modulations.

The challenge of spin-orbit-tuned ground states in iridates: a key issues review

Effects of spin-orbit interactions in condensed matter are an important and rapidly evolving topic. Strong competition between spin-orbit, on-site Coulomb and crystalline electric field interactions in iridates drives exotic quantum states that are unique to this group of materials. In particular, the 'J _eff  =  ½' Mott state served as an early signal that the combined effect of strong spin-orbit and Coulomb interactions in iridates has unique, intriguing consequences. In this Key Issues Review, we survey some current experimental studies of iridates. In essence, these materials tend to defy conventional wisdom: absence of conventional correlations between magnetic and insulating states, avoidance of metallization at high pressures, 'S-shaped' I-V characteristic, emergence of an odd-parity hidden order, etc. It is particularly intriguing that there exist conspicuous discrepancies between current experimental results and theoretical proposals that address superconducting, topological and quantum spin liquid phases. This class of materials, in which the lattice degrees of freedom play a critical role seldom seen in other materials, evidently presents some profound intellectual challenges that call for more investigations both experimentally and theoretically. Physical properties unique to these materials may help unlock a world of possibilities for functional materials and devices. We emphasize that, given the rapidly developing nature of this field, this Key Issues Review is by no means an exhaustive report of the current state of experimental studies of iridates.

A high-energy-resolution resonant inelastic X-ray scattering spectrometer at ID20 of the European Synchrotron Radiation Facility

An end-station for resonant inelastic X-ray scattering and (resonant) X-ray emission spectroscopy at beamline ID20 of ESRF - The European Synchrotron is presented. The spectrometer hosts five crystal analysers in Rowland geometry for large solid angle collection and is mounted on a rotatable arm for scattering in both the horizontal and vertical planes. The spectrometer is optimized for high-energy-resolution applications, including partial fluorescence yield or high-energy-resolution fluorescence detected X-ray absorption spectroscopy and the study of elementary electronic excitations in solids. In addition, it can be used for non-resonant inelastic X-ray scattering measurements of valence electron excitations.

High-energy-resolution diced spherical quartz analyzers for resonant inelastic X-ray scattering

A novel diced spherical quartz analyzer for use in resonant inelastic X-ray scattering (RIXS) is introduced, achieving an unprecedented energy resolution of 10.53 meV at the Ir L₃ absorption edge (11.215 keV). In this work the fabrication process and the characterization of the analyzer are presented, and an example of a RIXS spectrum of magnetic excitations in a Sr₃Ir₂O₇ sample is shown.

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.

Coulomb correlations in 4d and 5d oxides from first principles-or how spin-orbit materials choose their effective orbital degeneracies

The interplay of spin-orbit coupling and Coulomb correlations has become a hot topic in condensed matter theory and is especially important in 4d and 5d transition metal oxides, like iridates or rhodates. Here, we review recent advances in dynamical mean-field theory (DMFT)-based electronic structure calculations for treating such compounds, introducing all necessary implementation details. We also discuss the evaluation of Hubbard interactions in spin-orbit materials. As an example, we perform DMFT calculations on insulating strontium iridate (Sr₂IrO₄) and its 4d metallic counterpart, strontium rhodate (Sr₂RhO₄). While a Mott-insulating state is obtained for Sr₂IrO₄ in its paramagnetic phase, the spectral properties and Fermi surfaces obtained for Sr₂RhO₄ show excellent agreement with available experimental data. Finally, we discuss the electronic structure of these two compounds by introducing the notion of effective spin-orbital degeneracy as the key quantity that determines the correlation strength. We stress that effective spin-orbital degeneracy introduces an additional axis into the conventional picture of a phase diagram based on filling and on the ratio of interactions to bandwidth, analogous to the degeneracy-controlled Mott transition in d¹ perovskites.

A charge density wave-like instability in a doped spin-orbit-assisted weak Mott insulator

Layered perovskite iridates realize a rare class of Mott insulators that are predicted to be strongly spin-orbit coupled analogues of the parent state of cuprate high-temperature superconductors. Recent discoveries of pseudogap, magnetic multipolar ordered and possible d-wave superconducting phases in doped Sr₂IrO₄ have reinforced this analogy among the single layer variants. However, unlike the bilayer cuprates, no electronic instabilities have been reported in the doped bilayer iridate Sr₃Ir₂O₇. Here we show that Sr₃Ir₂O₇ realizes a weak Mott state with no cuprate analogue by using ultrafast time-resolved optical reflectivity to uncover an intimate connection between its insulating gap and antiferromagnetism. However, we detect a subtle charge density wave-like Fermi surface instability in metallic electron doped Sr₃Ir₂O₇ at temperatures (T_DW) close to 200 K via the coherent oscillations of its collective modes, which is reminiscent of that observed in cuprates. The absence of any signatures of a new spatial periodicity below T_DW from diffraction, scanning tunnelling and photoemission based probes suggests an unconventional and possibly short-ranged nature of this density wave order.

Doping Evolution of Magnetic Order and Magnetic Excitations in (Sr_{1-x}La_{x})_{3}Ir_{2}O_{7}

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≤x≤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 across the insulator-to-metal transition from x=0 to 0.05, followed by a transition to two-dimensional short range order between x=0.05 and 0.065. Because of the interactions between the J_{eff}=1/2 pseudospins and the emergent itinerant electrons, 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 with two-dimensional short range antiferromagnetic order. Strong antiferromagnetic fluctuations of the J_{eff}=1/2 moments persist deep in this correlated metallic state, with the magnon gap strongly suppressed.

Collimating Montel mirror as part of a multi-crystal analyzer system for resonant inelastic X-ray scattering

Advances in resonant inelastic X-ray scattering (RIXS) have come in lockstep with improvements in energy resolution. Currently, the best energy resolution at the Ir L3-edge stands at ∼25 meV, which is achieved using a diced Si(844) spherical crystal analyzer. However, spherical analyzers are limited by their intrinsic reflection width. A novel analyzer system using multiple flat crystals provides a promising way to overcome this limitation. For the present design, an energy resolution at or below 10 meV was selected. Recognizing that the angular acceptance of flat crystals is severely limited, a collimating element is essential to achieve the necessary solid-angle acceptance. For this purpose, a laterally graded, parabolic, multilayer Montel mirror was designed for use at the Ir L3-absorption edge. It provides an acceptance larger than 10 mrad, collimating the reflected X-ray beam to smaller than 100 µrad, in both vertical and horizontal directions. The performance of this mirror was studied at beamline 27-ID at the Advanced Photon Source. X-rays from a diamond (111) monochromator illuminated a scattering source of diameter 5 µm, generating an incident beam on the mirror with a well determined divergence of 40 mrad. A flat Si(111) crystal after the mirror served as the divergence analyzer. From X-ray measurements, ray-tracing simulations and optical metrology results, it was established that the Montel mirror satisfied the specifications of angular acceptance and collimation quality necessary for a high-resolution RIXS multi-crystal analyzer system.

Spin-orbit-driven magnetic structure and excitation in the 5d pyrochlore Cd2Os2O7

Much consideration has been given to the role of spin-orbit coupling (SOC) in 5d oxides, particularly on the formation of novel electronic states and manifested metal-insulator transitions (MITs). SOC plays a dominant role in 5d⁵ iridates (Ir⁴⁺), undergoing MITs both concurrent (pyrochlores) and separated (perovskites) from the onset of magnetic order. However, the role of SOC for other 5d configurations is less clear. For example, 5d³ (Os⁵⁺) systems are expected to have an orbital singlet with reduced effective SOC. The pyrochlore Cd₂Os₂O₇ nonetheless exhibits a MIT entwined with magnetic order phenomenologically similar to pyrochlore iridates. Here, we resolve the magnetic structure in Cd₂Os₂O₇ with neutron diffraction and then via resonant inelastic X-ray scattering determine the salient electronic and magnetic energy scales controlling the MIT. In particular, SOC plays a subtle role in creating the electronic ground state but drives the magnetic order and emergence of a multiple spin-flip magnetic excitation.

Strong electronic correlations in 5d materials such as osmates may combine with spin-orbit coupling to yield novel order. Here, the authors demonstrate how spin-orbit coupling in pyrochlore Cd₂Os₂O₇ generates magnetic order and excitations associated with a magnetic metal-insulator transition.

Pressure-Induced Confined Metal from the Mott Insulator Sr_{3}Ir_{2}O_{7}

The spin-orbit Mott insulator Sr_{3}Ir_{2}O_{7} 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 Sr_{3}Ir_{2}O_{7} 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.

Two-Magnon Raman Scattering and Pseudospin-Lattice Interactions in Sr_{2}IrO_{4} and Sr_{3}Ir_{2}O_{7}

We have used Raman scattering to investigate the magnetic excitations and lattice dynamics in the prototypical spin-orbit Mott insulators Sr_{2}IrO_{4} and Sr_{3}Ir_{2}O_{7}. Both compounds exhibit pronounced two-magnon Raman scattering features with different energies, line shapes, and temperature dependencies, which in part reflect the different influence of long-range frustrating exchange interactions. Additionally, we find strong Fano asymmetries in the line shapes of low-energy phonon modes in both compounds, which disappear upon cooling below the antiferromagnetic ordering temperatures. These unusual phonon anomalies indicate that the spin-orbit coupling in Mott-insulating iridates is not sufficiently strong to quench the orbital dynamics in the paramagnetic state.

Probing single magnon excitations in Sr₂IrO₄ using O K-edge resonant inelastic x-ray scattering

Resonant inelastic x-ray scattering (RIXS) at the L-edge of transition metal elements is now commonly used to probe single magnon excitations. Here we show that single magnon excitations can also be measured with RIXS at the K-edge of the surrounding ligand atoms when the center heavy metal elements have strong spin-orbit coupling. This is demonstrated with oxygen K-edge RIXS experiments on the perovskite Sr2IrO4, where low energy peaks from single magnon excitations were observed. This new application of RIXS has excellent potential to be applied to a wide range of magnetic systems based on heavy elements, for which the L-edge RIXS energy resolution in the hard x-ray region is usually poor.

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.

Linear spin wave theory for single-Q incommensurate magnetic structures

Linear spin wave theory provides the leading term in the calculation of the excitation spectra of long-range ordered magnetic systems as a function of 1/√S. This term is acquired using the Holstein-Primakoff approximation of the spin operator and valid for small δS fluctuations of the ordered moment. We propose an algorithm that allows magnetic ground states with general moment directions and single-Q incommensurate ordering wave vector using a local coordinate transformation for every spin and a rotating coordinate transformation for the incommensurability. Finally we show, how our model can determine the spin wave spectrum of the magnetic C-site langasites with incommensurate order.

J(eff)=1/2 Mott-insulating state in Rh and Ir fluorides

Discovery of new transition metal compounds with large spin orbit coupling coexisting with strong electron-electron correlation among the d electrons is essential for understanding the physics that emerges from the interplay of these two effects. In this study, we predict a novel class of J_{eff}=1/2 Mott insulators in a family of fluoride compounds that are previously synthesized, but not characterized extensively. First principles calculations in the level of all electron density functional theory+dynamical mean field theory indicate that these compounds have large Mott gaps and some of them exhibit unprecedented proximity to the ideal, SU(2) symmetric J_{eff}=1/2 limit.

Coherent quasiparticles with a small fermi surface in lightly doped Sr(3)Ir(2)O(7)

We characterize the electron doping evolution of (Sr_{1-x}La_{x})_{3}Ir_{2}O_{7} by means of angle-resolved photoemission. Concomitant with the metal insulator transition around x≈0.05 we find the emergence of coherent quasiparticle states forming a closed small Fermi surface of volume 3x/2, where x is the independently measured La concentration. The quasiparticle weight Z remains large along the entire Fermi surface, consistent with the moderate renormalization of the low-energy dispersion, and no pseudogap is observed. This indicates a conventional, weakly correlated Fermi liquid state with a momentum independent residue Z≈0.5 in lightly doped Sr_{3}Ir_{2}O_{7}.

Persistent non-metallic behavior in Sr2IrO4 and Sr3Ir2O7 at high pressures

Iridium-based 5d transition-metal oxides are attractive candidates for the study of correlated electronic states due to the interplay of enhanced crystal-field, Coulomb and spin-orbit interaction energies. At ambient pressure, these conditions promote a novel Jeff = 1/2 Mott-insulating state, characterized by a gap of the order of ~0.1 eV. We present high-pressure electrical resistivity measurements of single crystals of Sr2IrO4 and Sr3Ir2O7. While no indications of a pressure-induced metallic state up to 55 GPa were found in Sr2IrO4, a strong decrease of the gap energy and of the resistance of Sr3Ir2O7 between ambient pressure and 104 GPa confirm that this compound is in the proximity of a metal-insulator transition.

CaIrO3: a spin-orbit Mott insulator beyond the j(eff) ground state

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 an object of debate, with contradictory experimental and theoretical 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 j(eff) = 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 j(eff) = 1/2 ground state.

Resonant x-ray scattering and the j(eff) = 1/2 electronic ground state in iridate perovskites

The resonant x-ray scattering (magnetic elastic, RXMS, and inelastic, RIXS) of Ir4+ at the L2,3 edges relevant to spin-orbit Mott insulators A(n+1)Ir(n)O(3n+1) (A = Sr, Ba, etc.) are calculated using a single-ion model which treats the spin-orbit and tetragonal crystal-field terms on an equal footing. Both RXMS and RIXS in the spin-flip channel are found to display a nontrivial dependence on the direction of the magnetic moment, μ. Crucially, we show that for μ in the ab plane, RXMS in the cross-polarized channel at the L2 edge is zero irrespective of the tetragonal crystal field; spin-flip RIXS, relevant to measurements of magnons, behaves reciprocally, being zero at L2 when μ is perpendicular to the ab plane. Our results have important implications for the assignment of a j(eff) = 1/2 ground state on the basis of resonant x-ray experiments.

Effective J=1/2 insulating state in Ruddlesden-Popper iridates: an LDA+DMFT study

Using ab initio methods for correlated electrons in solids, we investigate the metal-insulator transition across the Ruddlesden-Popper (RP) series of iridates and explore the robustness of the Jeff=1/2 state against band effects due to itineracy, tetragonal distortion, octahedral rotation, and Coulomb interaction. We predict the effects of epitaxial strain on the optical conductivity, magnetic moments, and Jeff=1/2 ground-state wave functions in the RP series. To describe the solution of the many-body problem in an intuitive picture, we introduce a concept of energy-dependent atomic states, which strongly resemble the atomic Jeff=1/2 states but with coefficients that are energy or time dependent. We demonstrate that the deviation from the ideal Jeff=1/2 state is negligible at short time scales for both single- and double-layer iridates, while it becomes quite significant for Sr3Ir2O7 at long times and low energy. Interestingly, Sr2IrO4 is positioned very close to the SU(2) limit, with only ∼3% deviation from the ideal Jeff=1/2 situation.

Locking of iridium magnetic moments to the correlated rotation of oxygen octahedra in Sr₂IrO₄ revealed by x-ray resonant scattering

Sr2IrO4 is a prototype of the class of Mott insulators in the strong spin-orbit interaction (SOI) limit described by a Jeff = 1/2 ground state. In Sr2IrO4, the strong SOI is predicted to manifest itself in the locking of the canting of the magnetic moments to the correlated rotation by 11.8(1)° of the oxygen octahedra that characterizes its distorted layered perovskite structure. Using x-ray resonant scattering at the Ir L3 edge we have measured accurately the intensities of Bragg peaks arising from different components of the magnetic structure. From a careful comparison of integrated intensities of peaks due to basal-plane antiferromagnetism, with those due to b-axis ferromagnetism, we deduce a canting of the magnetic moments of 12.2(8)°. We thus confirm that in Sr2IrO4 the magnetic moments rigidly follow the rotation of the oxygen octahedra, indicating that, even in the presence of significant non-cubic structural distortions, it is a close realization of the Jeff = 1/2 state.

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.

Zigzag magnetic order in the iridium oxide Na2IrO3

We explore the phase diagram of spin-orbit Mott insulators on a honeycomb lattice, within the Kitaev-Heisenberg model extended to its full parameter space. Zigzag-type magnetic order is found to occupy a large part of the phase diagram of the model, and its physical origin is explained as due to interorbital t(2g)-e(g) hopping. The magnetic susceptibility, spin wave spectra, and zigzag order parameter are calculated and compared to the experimental data, obtaining thereby the spin coupling constants in Na(2)IrO(3) and Li(2)IrO(3).

Spherical analyzers and monochromators for resonant inelastic hard X-ray scattering: a compilation of crystals and reflections

Resonant inelastic X-ray scattering (RIXS) experiments require special sets of near-backscattering spherical diced analyzers and high-resolution monochromators for every distinct absorption-edge energy and emission line. For the purpose of aiding the design and planning of efficient RIXS experiments, comprehensive lists of suitable analyzer reflections for silicon, germanium, α-quartz, sapphire and lithium niobate crystals were compiled for a multitude of absorption edges and emission lines. Analyzers made from lithium niobate, sapphire or α-quartz offer many choices of reflections with intrinsic resolutions currently unattainable from silicon or germanium. In some cases these materials offer higher intensities at comparable resolutions. While lithium niobate, sapphire or α-quartz analyzers are still in an early stage of development, the present compilation can serve as a computational basis for assessing expected and actual performance. With regard to high-resolution monochromators, bandpass and throughput calculations for combinations of double-crystal, high-heat-load and near-backscattering high-resolution channel-cuts were assembled. The compilation of these analyzer and monochromator data is publicly available on a website.