All-in-all-Out Magnetic Order and Propagating Spin Waves in Sm_{2}Ir_{2}O_{7}

Identifying and Constructing Complex Magnon Band Topology

Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path toward coherent spin transport for spintronics applications. In this work we explore the variety of topological magnon band structures and provide insight into how to efficiently identify topological magnon bands in materials. We do this by adapting the topological quantum chemistry approach that has used constraints imposed by time reversal and crystalline symmetries to enumerate a large class of topological electronic bands. We show how to identify physically relevant models of gapped magnon band topology by using so-called decomposable elementary band representations, and in turn discuss how to use symmetry data to infer the presence of exotic symmetry enforced nodal topology.

Giant stress response of terahertz magnons in a spin-orbit Mott insulator

Magnonic devices operating at terahertz frequencies offer intriguing prospects for high-speed electronics with minimal energy dissipation However, guiding and manipulating terahertz magnons via external parameters present formidable challenges. Here we report the results of magnetic Raman scattering experiments on the antiferromagnetic spin-orbit Mott insulator Sr2IrO4 under uniaxial stress. We find that the energies of zone-center magnons are extremely stress sensitive: lattice strain of 0.1% increases the magnon energy by 40%. The magnon response is symmetric with respect to the sign of the applied stress (tensile or compressive), but depends strongly on its direction in the IrO2 planes. A theory based on coupling of the spin-orbit-entangled iridium magnetic moments to lattice distortions provides a quantitative explanation of the Raman data and a comprehensive framework for the description of magnon-lattice interactions in magnets with strong spin-orbit coupling. The possibility to efficiently manipulate the propagation of terahertz magnons via external stress opens up multifold design options for reconfigurable magnonic devices.

Magnetic monopole density and antiferromagnetic domain control in spin-ice iridates

Magnetically frustrated systems provide fertile ground for complex behaviour, including unconventional ground states with emergent symmetries, topological properties, and exotic excitations. A canonical example is the emergence of magnetic-charge-carrying quasiparticles in spin-ice compounds. Despite extensive work, a reliable experimental indicator of the density of these magnetic monopoles is yet to be found. Using measurements on single crystals of Ho2Ir2O7 combined with dipolar Monte Carlo simulations, we show that the isothermal magnetoresistance is highly sensitive to the monopole density. Moreover, we uncover an unexpected and strong coupling between the monopoles on the holmium sublattice and the antiferromagnetically ordered iridium ions. These results pave the way towards a quantitative experimental measure of monopole density and demonstrate the ability to control antiferromagnetic domain walls using a uniform external magnetic field, a key goal in the design of next-generation spintronic devices.

Pyrochlore oxide Hg2Os2O7on verge of metal-insulator boundary

Semimetallic osmium pyrochlore oxide Cd₂Os₂O₇undergoes a magnetic transition to an all-in-all-out (AIAO)-type order at 227 K, followed by a crossover to an AIAO insulator at around 210 K. Here, we studied the isostructural and isoelectronic compound Hg₂Os₂O₇through thermodynamic measurements, muon spin rotation (μSR) spectroscopy and neutron diffraction experiments. A similar magnetic transition, probably to an AIAO-type order, was observed at 88 K, while the resistivity showed a decrease at the transition and remained metallic down to 2 K. Thus, the ground state of Hg₂Os₂O₇is most likely an AIAO semimetal, which is analogous to the intermediate-temperature state of Cd₂Os₂O₇. Hg₂Os₂O₇exists on the verge of the metal-insulator boundary on the metal side and provides an excellent platform for studying the electronic instability of 5delectrons with moderate electron correlations and strong spin-orbit interactions.

Magnetic Weyl Semimetallic Phase in Thin Films of Eu_{2}Ir_{2}O_{7}

The interplay between electronic interactions and strong spin-orbit coupling is expected to create a plethora of fascinating correlated topological states of quantum matter. Of particular interest are magnetic Weyl semimetals originally proposed in the pyrochlore iridates, which are only expected to reveal their topological nature in thin film form. To date, however, direct experimental demonstrations of these exotic phases remain elusive, due to the lack of usable single crystals and the insufficient quality of available films. Here, we report on the discovery of signatures for the long-sought magnetic Weyl semimetallic phase in (111)-oriented Eu_{2}Ir_{2}O_{7} high-quality epitaxial thin films. We observed an intrinsic anomalous Hall effect with colossal coercivity but vanishing net magnetization, which emerges right below the onset of a peculiar magnetic phase with all-in-all-out (AIAO) antiferromagnetic ordering. The anomalous Hall conductivity obtained experimentally is consistent with the theoretical prediction, likely arising from the nonzero Berry curvature emanated by Weyl node pairs near the Fermi level that act as sources and sinks of Berry flux, activated by broken cubic crystal symmetry at the top and bottom terminations of the thin film.

Topological Magnon Band Crossing in Y_{2}Ir_{2}O_{7}

Topological magnonic materials have attracted much interest because of the potential for dissipationless spintronic applications. Pyrochlore iridates are theoretically regarded as good candidates for designing topological magnon bands. However, experimental identification of topological magnon bands in pyrochlore iridates remains elusive. We explored this possibility in Y_{2}Ir_{2}O_{7} using Raman spectroscopy to measure both the single-magnon excitations and anomalous phonon shifts. From the single-magnon energies and tight-binding model calculations concerning the phonons, we determined the key parameters in the spin Hamiltonian. These confirm that Y_{2}Ir_{2}O_{7} hosts a nontrivial magnon band topology distinct from other pyrochlore iridate compounds. Our work demonstrates that pyrochlore iridates constitute a system in which the magnon band topology can be tailored and that Raman spectroscopy is a powerful technique to explore magnon band topology.

Revisiting Sodium Hexafluoroiridates: Perspective Precursors for Electronic, Quantum, and Related Materials

The following salts have been synthesized and structurally characterized: Na₂[IrF₆]·2H₂O (C2/m, a = 6.6327(4), b = 10.0740(6), c = 5.9283(5) Å, β = 122.3880(10)°) and Na₃[IrF₆]·2H₂O (R-3, a = 7.5963(3), b = 7.5963(3), c = 9.8056(4) Å) (for the first time) by single-crystal X-ray diffraction; the unit cell parameters of a tetragonal phase (P4 ₂/mnm, a = 5.005(2), c = 10.074(4) Å) of the stable α-Na₂[IrF₆] were determined for the first time; and the unit cell parameters of β-Na₂[IrF₆] (P321, a = 9.332(4), c = 5.136(2) Å) and Na₃[IrF₆] (P2₁/n, a = 5.567(4), b = 5.778(4), c = 8.017(2) Å, β = 90.41(2)°) were determined using powder X-ray diffraction (PXRD). The data of the thermal stability was obtained by differential thermal analysis (DTA) for all substances. The presence of Na₃[IrF₆]·H₂O monohydrate is predicted. H₂[IrF₆] was prepared in a solution and was demonstrated to behave as a strong dibasic acid.

Topological Magnons with Nodal-Line and Triple-Point Degeneracies: Implications for Thermal Hall Effect in Pyrochlore Iridates

We analyze the magnon excitations in pyrochlore iridates with all-in-all-out (AIAO) antiferromagnetic order, focusing on their topological features. We identify the magnetic point group symmetries that protect the nodal-line band crossings and triple-point degeneracies that dominate the Berry curvature. We find three distinct regimes of magnon band topology, as a function of the ratio of Dzyaloshinskii-Moriya interaction to the antiferromagnetic exchange. We show how the thermal Hall response provides a unique probe of the topological magnon band structure in AIAO systems.

Design and Synthesis of Ir/Ru Pyrochlore Catalysts for the Oxygen Evolution Reaction Based on Their Bulk Thermodynamic Properties

Density functional theory (DFT) has proven to be an invaluable and effective tool for identifying highly active electrocatalysts for the oxygen evolution reaction (OER). Herein, we take a computational approach to first identify a series of rare-earth pyrochlore oxides based on Ir and Ru as potential OER catalysts. The DFT-based phase diagrams, Pourbaix diagrams (E vs pH), projected density of states, and band energy diagrams were used to identify prospective OER catalysts based on rare-earth Ir and Ru pyrochlores. The predicted materials were synthesized using the spray-freeze freeze-drying approach to afford nanoparticulate oxides conforming to the pyrochlore structural type A₂B₂O₇ where A = Nd, Gd, or Yb and B = Ir or Ru. In agreement with the computed Pourbaix diagrams, the materials were found to be moderately stable under OER conditions. All prepared materials show higher stability as compared to the benchmark IrO₂ catalyst, and the OER mass activity of Yb₂Ir₂O₇ and the ruthenate pyrochlores (Nd₂Ru₂O₇, Gd₂Ru₂O₇, and Yb₂Ru₂O₇) were also found to exceed those of the benchmark IrO₂ catalyst. We find that the OER activity of each pyrochlore series (i.e., iridate or ruthenate) generally improves as the size of the A-site cation decreases, indicating that maintaining control over the structure can be used to influence the electrocatalytic properties.

Selective probing of magnetic order on Tb and Ir sites in stuffed Tb2Ir2O7 using resonant x-ray scattering

We study the magnetic structure of the 'stuffed' (Tb-rich) pyrochlore iridate Tb_2+x Ir_2-x O_7-y (x ∼ 0.18), using resonant elastic x-ray scattering (REXS). In order to disentangle contributions from Tb and Ir magnetic sublattices, experiments were performed at the Ir L ₃ and Tb M ₅ edges, which provide selective sensitivity to Ir 5d and Tb 4f  magnetic moments, respectively. At the Ir L ₃ edge, we found the onset of long-range [Formula: see text] magnetic order below [Formula: see text] K, consistent with the expected signal of all-in all-out (AIAO) magnetic order. Using a single-ion model to calculate REXS cross-sections, we estimate an ordered magnetic moment of [Formula: see text] at 5 K. At the Tb M ₅ edge, long-range [Formula: see text] magnetic order appeared below  ∼[Formula: see text] K, also consistent with an AIAO magnetic structure on the Tb site. Additional insight into the magnetism of the Tb sublattice is gleaned from measurements at the M ₅ edge in applied magnetic fields up to 6 T, which is found to completely suppress the Tb AIAO magnetic order. In zero applied field, the observed gradual onset of the Tb sublattice magnetisation with temperature suggests that it is induced by the magnetic order on the Ir site. The persistence of AIAO magnetic order, despite the greatly reduced ordering temperature and moment size compared to stoichiometric Tb₂Ir₂O₇, for which [Formula: see text] K and [Formula: see text], indicates that stuffing could be a viable means of tuning the strength of electronic correlations, thereby potentially offering a new strategy to achieve topologically non-trivial band crossings in pyrochlore iridates.

X-ray magnetic diffraction under high pressure

Advances in both non-resonant and resonant X-ray magnetic diffraction since the 1980s have provided researchers with a powerful tool for exploring the spin, orbital and ion degrees of freedom in magnetic solids, as well as parsing their interplay. Here, we discuss key issues for performing X-ray magnetic diffraction on single-crystal samples under high pressure (above 40 GPa) and at cryogenic temperatures (4 K). We present case studies of both non-resonant and resonant X-ray magnetic diffraction under pressure for a spin-flip transition in an incommensurate spin-density-wave material and a continuous quantum phase transition of a commensurate all-in-all-out antiferromagnet. Both cases use diamond-anvil-cell technologies at third-generation synchrotron radiation sources. In addition to the exploration of the athermal emergence and evolution of antiferromagnetism discussed here, these techniques can be applied to the study of the pressure evolution of weak charge order such as charge-density waves, antiferro-type orbital order, the charge anisotropic tensor susceptibility and charge superlattices associated with either primary spin order or softened phonons.

Experimental station Bernina at SwissFEL: condensed matter physics on femtosecond time scales investigated by X-ray diffraction and spectroscopic methods

The Bernina instrument at the SwissFEL Aramis hard X-ray free-electron laser is designed for studying ultrafast phenomena in condensed matter and material science. Ultrashort pulses from an optical laser system covering a large wavelength range can be used to generate specific non-equilibrium states, whose subsequent temporal evolution can be probed by selective X-ray scattering techniques in the range 2-12 keV. For that purpose, the X-ray beamline is equipped with optical elements which tailor the X-ray beam size and energy, as well as with pulse-to-pulse diagnostics that monitor the X-ray pulse intensity, position, as well as its spectral and temporal properties. The experiments can be performed using multiple interchangeable endstations differing in specialization, diffractometer and X-ray analyser configuration and load capacity for specialized sample environment. After testing the instrument in a series of pilot experiments in 2018, regular user operation begins in 2019.

Strain-induced spontaneous Hall effect in an epitaxial thin film of a Luttinger semimetal

Pyrochlore iridates have provided a plethora of novel phenomena owing to the combination of topology and correlation. Among them, much attention has been paid to [Formula: see text], as it is known as a Luttinger semimetal characterized by quadratic band touching at the Brillouin zone center, suggesting that the topology of its electronic states can be tuned by a moderate lattice strain and external magnetic field. Here, we report that our epitaxial [Formula: see text] thin films grown by solid-state epitaxy exhibit a spontaneous Hall effect that persists up to 50 K without having spontaneous magnetization within our experimental accuracy. This indicates that the system breaks the time reversal symmetry at a temperature scale that is too high for the magnetism to be due to Pr 4f moments and must be related to magnetic order of the iridium 5d electrons. Moreover, our analysis finds that the chiral anomaly induces the negative contribution to the magnetoresistance only when a magnetic field and the electric current are parallel to each other. Our results indicate that the strained part of the thin film forms a magnetic Weyl semimetal state.

Direct Detection of Dimer Orbitals in Ba_{5}AlIr_{2}O_{11}

The electronic states of many Mott insulators, including iridates, are often conceptualized in terms of localized atomic states such as the famous "J_{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 Letter, 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. Sharp peaks corresponding to the excitations of dimer orbitals are observed and analyzed by a combination of density functional theory calculations and theoretical simulations based on an Ir-Ir cluster model. Such partially delocalized dimer states lead to a redefinition 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 predictions 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.

Strongly-coupled quantum critical point in an all-in-all-out antiferromagnet

Dimensionality and symmetry play deterministic roles in the laws of Nature. They are important tools to characterize and understand quantum phase transitions, especially in the limit of strong correlations between spin, orbit, charge, and structural degrees of freedom. Here, using newly-developed, high-pressure resonant X-ray magnetic and charge diffraction techniques, we have discovered a quantum critical point in Cd₂Os₂O₇ as the all-in-all-out antiferromagnetic order is continuously suppressed to zero temperature and, concomitantly, the cubic lattice structure continuously changes from space group Fd-3m to F-43m. Surrounded by three phases of different time reversal and spatial inversion symmetries, the quantum critical region anchors two phase lines of opposite curvature, with striking departures from a mean-field form at high pressure. As spin fluctuations, lattice breathing modes, and quasiparticle excitations interact in the quantum critical region, we argue that they present the necessary components for strongly-coupled quantum criticality in this three-dimensional compound.

The critical behavior of a continuous phase transition is determined by both symmetry and dimensionality. Wang et al. present evidence that the cubic all-in-all-out spin order in Cd₂Os₂O₇ leads to a realization of a non-mean-field strongly-coupled quantum phase transition in three dimensions.

Universal geometric frustration in pyrochlores

Materials with the pyrochlore/fluorite structure have diverse technological applications, from magnetism to nuclear waste disposal. Here we report the observation of structural instability present in the pyrochlores A₂Zr₂O₆Oʹ (A = Pr, La) and Yb₂Ti₂O₆Oʹ, that exists despite ideal stoichiometry, ideal cation-ordering, the absence of lone pair effects, and a lack of magnetic order. Though these materials appear to have good long-range order, local structure probes find displacements, of the order of 0.01 nm, within the pyrochlore framework. The pattern of displacements of the A₂Oʹ sublattice mimics the entropically-driven fluxional motions characteristic of and well-known in the silica mineral β-cristobalite. The universality of such displacements within the pyrochlore structure adds to the known structural diversity and explains the extreme sensitivity to composition found in quantum spin ices and the lack of ferroelectric behavior in pyrochlores.

The family of pyrochlore complex oxides includes many materials of fundamental or practical interest, such as spin ices and dielectrics. Trump et al. show that flexibility of the pyrochlores’ structure leads to local displacements that explain some of their unusual physical properties.

Magnetic Excitations across the Metal-Insulator Transition in the Pyrochlore Iridate Eu_{2}Ir_{2}O_{7}

We report a resonant inelastic x-ray scattering 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 a 20 meV bandwidth and a 28 meV magnon gap is found in the excitation spectrum at 7 K, which is expected in the all-in-all-out magnetically ordered state. This magnetic excitation exhibits substantial softening as the temperature is raised towards T_{MI} and turns into a 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 the magnon renormalization expected in a local moment system and indicates that the strength of the 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.

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.

Two-magnon scattering in the 5d all-in-all-out pyrochlore magnet Cd2Os2O7

5d pyrochlore oxides with all-in-all-out magnetic order are prime candidates for realizing strongly correlated, topological phases of matter. Despite significant effort, a full understanding of all-in-all-out magnetism remains elusive as the associated magnetic excitations have proven difficult to access with conventional techniques. Here we report a Raman spectroscopy study of spin dynamics in the all-in-all-out magnetic state of the 5d pyrochlore Cd2Os2O7. Through a comparison between the two-magnon scattering and spin-wave theory, we confirm the large single ion anisotropy in this material and show that the Dzyaloshinskii-Moriya and exchange interactions play a significant role in the spin-wave dispersions. The Raman data also reveal complex spin-charge-lattice coupling and indicate that the metal-insulator transition in Cd2Os2O7 is Lifshitz-type. Our work establishes Raman scattering as a simple and powerful method for exploring the spin dynamics in 5d pyrochlore magnets.Pyrochlore 5d transition metal oxides are expected to have interesting forms of magnetic order but are hard to study with conventional probes. Here the authors show that Raman scattering can be used to measure magnetic excitations in Cd2Os2O7 and that it exhibits complex spin-charge-lattice coupling.

Magnetic-field induced multiple topological phases in pyrochlore iridates with Mott criticality

The interplay between electron correlation and spin–orbit coupling in solids has been proven to be an abundant gold mine for emergent topological phases. Here we report the results of systematic magnetotransport study on bandwidth-controlled pyrochlore iridates R₂Ir₂O₇ near quantum metal-insulator transition (MIT). The application of a magnetic field along [001] crystallographic direction (H//[001]) significantly decreases resistivity while producing a unique Hall response, which indicates the emergence of the novel semi-metallic state in the course of the magnetic transformation from all-in all-out (AIAO, 4/0) to 2-in 2-out (2/2) spin configuration. For H//[111] that favours 3-in 1-out (3/1) configuration, by contrast, the resistivity exhibits saturation at a relatively high value typical of a semimetal. The observed properties can be identified to reflect the emergence of multiple Weyl semimetal states with varying numbers of Weyl points and line nodes in respective spin configurations. With tuning effective bandwidth, all these states appear to concentrate around the quantum MIT region, which may open a promising venue for topological phenomena and functions.

The interplay between multiple electronic interactions in solid promotes the emergence of exotic phases. Here, Ueda et al. report magnetotransport study on pyrochlore iridates R₂Ir₂O₇ near quantum metal-insulator transition reflecting the emergence of multiple Weyl semimetal states.

Topological Magnon Bands and Unconventional Superconductivity in Pyrochlore Iridate Thin Films

We theoretically study the magnetic properties of pyrochlore iridate bilayer and trilayer thin films grown along the [111] direction using a strong coupling approach. We find the ground state magnetic configurations on a mean field level and carry out a spin-wave analysis about them. In the trilayer case the ground state is found to be the all-in-all-out (AIAO) state, whereas the bilayer has a deformed AIAO state. For all parameters of the spin-orbit coupled Hamiltonian we study, the lowest magnon band in the trilayer case has a nonzero Chern number. In the bilayer case we also find a parameter range with nonzero Chern numbers. We calculate the magnon Hall response for both geometries, finding a striking sign change as a function of temperature. Using a slave-boson mean-field theory we study the doping of the trilayer system and discover an unconventional time-reversal symmetry broken d+id superconducting state. Our study complements prior work in the weak coupling limit and suggests that the [111] grown thin film pyrochlore iridates are a promising candidate for topological properties and unconventional orders.