Phase-sensitive observation of a spin-orbital Mott state in Sr2IrO4

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.

Engineering 1D Quantum Stripes from Superlattices of 2D Layered Materials

Dimensional tunability from two dimensions to one dimension is demonstrated for the first time using an artificial superlattice method in synthesizing 1D stripes from 2D layered materials. The 1D confinement of layered Sr₂ IrO₄ induces distinct 1D quantum-confined electronic states, as observed from optical spectroscopy and resonant inelastic X-ray scattering. This 1D superlattice approach is generalizable to a wide range of layered materials.

Reentrant spin glass behavior and magnetodielectric coupling of an Ir-based double perovskite compound, La2CoIrO6

The spin glass behavior and the magnetodielectric coupling effect of an Ir-based double perovskite compound, La₂CoIrO₆.

OER activity manipulated by IrO6 coordination geometry: an insight from pyrochlore iridates

The anodic reaction of oxygen evolution reaction (OER), an important point for electrolysis, however, remains the obstacle due to its complicated reaction at electrochemical interfaces. Iridium oxide (IrO₂) is the only currently known 5d transition metal oxide possessing admirable OER activity. Tremendous efforts have been carried out to enhance the activity of iridium oxides. Unfortunately there lies a gap in understanding what factors responsible for the activity in doped IrO₂ or the novel crystal structure. Based on two metallic pyrochlores (Bi₂Ir₂O₇ and Pb₂Ir₂O_6.5) and IrO₂. It has been found that there exists a strong correlation between the specific OER activity and IrO₆ coordination geometry. The more distortion in IrO₆ geometry ascends the activity of Ir sites, and generates activity order of Pb-Ir > IrO₂ > Bi-Ir. Our characterizations reveal that distorted IrO₆ in Pb-Ir induces a disappearance of J = 1/2 subbands in valence band, while Bi-Ir and IrO₂ resist this nature probe. The performed DFT calculations indicated the distortion in IrO₆ geometry can optimize binding strength between Ir-5d and O-2p due to broader d band width. Based on this insight, enhancement in OER activity is obtained by effects that change IrO₆ octahedral geometry through doping or utilizing structural manipulation with nature of distorted octahedral coordination.

From a Quasimolecular Band Insulator to a Relativistic Mott Insulator in t_{2g}^{5} Systems with a Honeycomb Lattice Structure

The t_{2g} orbitals of an edge-shared transition-metal oxide with a honeycomb lattice structure form dispersionless electronic bands when only hopping mediated by the edge-sharing oxygens is accessible. This is due to the formation of isolated quasimolecular orbitals (QMOs) in each hexagon, introduced recently by Mazin et al. [Phys. Rev. Lett. 109, 197201 (2012)], which stabilizes a band insulating phase for t_{2g}^{5} systems. However, with the help of the exact diagonalization method to treat the electron kinetics and correlations on an equal footing, we find that the QMOs are fragile against not only the spin-orbit coupling (SOC) but also the Coulomb repulsion. We show that the electronic phase of t_{2g}^{5} systems can vary from a quasimolecular band insulator to a relativistic J_{eff}=1/2 Mott insulator with increasing the SOC as well as the Coulomb repulsion. The different electronic phases manifest themselves in electronic excitations observed in optical conductivity and resonant inelastic x-ray scattering. Based on our calculations, we assert that the currently known Ru^{3+} and Ir^{4+} based honeycomb systems are far from the quasimolecular band insulator but rather the relativistic Mott insulator.

Slater Insulator in Iridate Perovskites with Strong Spin-Orbit Coupling

The perovskite SrIrO_{3} is an exotic narrow-band metal owing to a confluence of the strengths of the spin-orbit coupling (SOC) and the electron-electron correlations. It has been proposed that topological and magnetic insulating phases can be achieved by tuning the SOC, Hubbard interactions, and/or lattice symmetry. Here, we report that the substitution of nonmagnetic, isovalent Sn^{4+} for Ir^{4+} in the SrIr_{1-x}Sn_{x}O_{3} perovskites synthesized under high pressure leads to a metal-insulator transition to an antiferromagnetic (AF) phase at T_{N}≥225  K. The continuous change of the cell volume as detected by x-ray diffraction and the λ-shape transition of the specific heat on cooling through T_{N} demonstrate that the metal-insulator transition is of second order. Neutron powder diffraction results indicate that the Sn substitution enlarges an octahedral-site distortion that reduces the SOC relative to the spin-spin exchange interaction and results in the type-G AF spin ordering below T_{N}. Measurement of high-temperature magnetic susceptibility shows the evolution of magnetic coupling in the paramagnetic phase typical of weak itinerant-electron magnetism in the Sn-substituted samples. A reduced structural symmetry in the magnetically ordered phase leads to an electron gap opening at the Brillouin zone boundary below T_{N} in the same way as proposed by Slater.

Absence of localization in disordered two-dimensional electron gas at weak magnetic field and strong spin-orbit coupling

The one-parameter scaling theory of localization predicts that all states in a disordered two-dimensional system with broken time reversal symmetry are localized even in the presence of strong spin-orbit coupling. While at constant strong magnetic fields this paradigm fails (recall the quantum Hall effect), it is believed to hold at weak magnetic fields. Here we explore the nature of quantum states at weak magnetic field and strongly fluctuating spin-orbit coupling, employing highly accurate numerical procedure based on level spacing distribution and transfer matrix technique combined with one parameter finite-size scaling hypothesis. Remarkably, the metallic phase, (known to exist at zero magnetic field), persists also at finite (albeit weak) magnetic fields, and eventually crosses over into a critical phase, which has already been confirmed at high magnetic fields. A schematic phase diagram drawn in the energy-magnetic field plane elucidates the occurrence of localized, metallic and critical phases. In addition, it is shown that nearest-level statistics is determined solely by the symmetry parameter β and follows the Wigner surmise irrespective of whether states are metallic or critical.

Dynamical Effects in Resonant X-Ray Diffraction

Using resonant magnetic diffraction at the Ni L_{2,3} edge in a LaNiO_{3} superlattice, we show that dynamical effects beyond the standard kinematic approximation can drastically modify the resonant scattering cross section. In particular, the combination of extinction and refraction convert maxima to minima in the azimuthal-angle dependence of the diffracted intensity, which is commonly used to determine orbital and magnetic structures by resonant x-ray diffraction. We provide a comprehensive theoretical description of these effects by numerically solving Maxwell's equations in three dimensions. The understanding and description of dynamical diffraction enhances the capabilities of resonant x-ray scattering as a probe of electronic ordering phenomena in solids.

Infrared Spectroscopic Evidences of Strong Electronic Correlations in (Sr1-xLax)3Ir2O7

We report on infrared spectroscopic studies of the electronic response of the (Sr1-xLax)3Ir2O7 system. Our experiments revealed hallmarks of strong electronic correlations in the evolution of the electronic response across the filling-controlled insulator-metal transition. We observed a collapse of the Jeff = 1/2 Mott gap accompanying the transfer of the spectral weight from the high-energy region to the gap region with electron doping. The intraband conductivity at the metallic side of the transition was found to consist of coherent Drude-like and incoherent responses. The sum rule and the extended Drude model analyses further indicated a large mass enhancement. Our results demonstrate a critical role of the electronic correlations in the charge dynamics of the (Sr1-xLax)3Ir2O7 system.

Persistent Paramagnons Deep in the Metallic Phase of Sr_{2-x}La_{x}IrO_{4}

We have studied the magnetic excitations of electron-doped Sr_{2-x}La_{x}IrO_{4} (0≤x≤0.10) using resonant inelastic x-ray scattering at the Ir L_{3} edge. The long-range magnetic order is rapidly lost with increasing x, but two-dimensional short-range order (SRO) and dispersive magnon excitations with nearly undiminished spectral weight persist well into the metallic part of the phase diagram. The magnons in the SRO phase are heavily damped and exhibit anisotropic softening. Their dispersions are well described by a pseudospin-1/2 Heisenberg model with exchange interactions whose spatial range increases with doping. We also find a doping-independent high-energy magnetic continuum, which is not described by this model. The spin-orbit excitons arising from the pseudospin-3/2 manifold of the Ir ions broaden substantially in the SRO phase, but remain largely separated from the low-energy magnons. Pseudospin-1/2 models are therefore a good starting point for the theoretical description of the low-energy magnetic dynamics of doped iridates.

Ultrafast dynamics of localized magnetic moments in the unconventional Mott insulator Sr2IrO4

We report a time-resolved study of the ultrafast dynamics of the magnetic moments formed by the [Formula: see text] states in Sr2IrO4 by directly probing the localized iridium 5d magnetic state through resonant x-ray diffraction. Using optical pump-hard x-ray probe measurements, two relaxation time scales were determined: a fast fluence-independent relaxation is found to take place on a time scale of 1.5 ps, followed by a slower relaxation on a time scale of 500 ps-1.5 ns.

Spin orientations of the spin-half Ir(4+) ions in Sr3NiIrO6, Sr2IrO4, and Na2IrO3: Density functional, perturbation theory, and Madelung potential analyses

The spins of the low-spin Ir(4+) (S = 1/2, d(5)) ions at the octahedral sites of the oxides Sr3NiIrO6, Sr2IrO4, and Na2IrO3 exhibit preferred orientations with respect to their IrO6 octahedra. We evaluated the magnetic anisotropies of these S = 1/2 ions on the basis of density functional theory (DFT) calculations including spin-orbit coupling (SOC), and probed their origin by performing perturbation theory analyses with SOC as perturbation within the LS coupling scheme. The observed spin orientations of Sr3NiIrO6 and Sr2IrO4 are correctly predicted by DFT calculations, and are accounted for by the perturbation theory analysis. As for the spin orientation of Na2IrO3, both experimental studies and DFT calculations have not been unequivocal. Our analysis reveals that the Ir(4+) spin orientation of Na2IrO3 should have nonzero components along the c- and a-axis directions. The spin orientations determined by DFT calculations are sensitive to the accuracy of the crystal structures employed, which is explained by perturbation theory analyses when interactions between adjacent Ir(4+) ions are taken into consideration. There are indications implying that the 5d electrons of Na2IrO3 are less strongly localized compared with those of Sr3NiIrO6 and Sr2IrO4. This implication was confirmed by showing that the Madelung potentials of the Ir(4+) ions are less negative in Na2IrO3 than in Sr3NiIrO6 and Sr2IrO4. Most transition-metal S = 1/2 ions do have magnetic anisotropies because the SOC induces interactions among their crystal-field split d-states, and the associated mixing of the states modifies only the orbital parts of the states. This finding cannot be mimicked by a spin Hamiltonian because this model Hamiltonian lacks the orbital degree of freedom, thereby leading to the spin-half syndrome. The spin-orbital entanglement for the 5d spin-half ions Ir(4+) is not as strong as has been assumed.

Slater to Mott Crossover in the Metal to Insulator Transition of Nd_{2}Ir_{2}O_{7}

We present an angle-resolved photoemission study of the electronic structure of the three-dimensional pyrochlore iridate Nd_{2}Ir_{2}O_{7} through its magnetic metal-insulator transition. Our data reveal that metallic Nd_{2}Ir_{2}O_{7} has a quadratic band, touching the Fermi level at the Γ point, similar to that of Pr_{2}Ir_{2}O_{7}. The Fermi node state is, therefore, a common feature of the metallic phase of the pyrochlore iridates. Upon cooling below the transition temperature, this compound exhibits a gap opening with an energy shift of quasiparticle peaks like a band gap insulator. The quasiparticle peaks are strongly suppressed, however, with further decrease of temperature, and eventually vanish at the lowest temperature, leaving a nondispersive flat band lacking long-lived electrons. We thereby identify a remarkable crossover from Slater to Mott insulators with decreasing temperature. These observations explain the puzzling absence of Weyl points in this material, despite its proximity to the zero temperature metal-insulator transition.

Raman spectroscopic signature of fractionalized excitations in the harmonic-honeycomb iridates β- and γ-Li2IrO3

The fractionalization of elementary excitations in quantum spin systems is a central theme in current condensed matter physics. The Kitaev honeycomb spin model provides a prominent example of exotic fractionalized quasiparticles, composed of itinerant Majorana fermions and gapped gauge fluxes. However, identification of the Majorana fermions in a three-dimensional honeycomb lattice remains elusive. Here we report spectroscopic signatures of fractional excitations in the harmonic-honeycomb iridates β- and γ-Li₂IrO₃. Using polarization-resolved Raman spectroscopy, we find that the dynamical Raman response of β- and γ-Li₂IrO₃ features a broad scattering continuum with distinct polarization and composition dependence. The temperature dependence of the Raman spectral weight is dominated by the thermal damping of fermionic excitations. These results suggest the emergence of Majorana fermions from spin fractionalization in a three-dimensional Kitaev–Heisenberg system.

Fractional excitations in quantum spin systems lead to exotic particles predicted in theory but difficult to observe in experiments. Here, Glamazda et al. report the dynamical Raman response of β- and γ-Li₂IrO₃ is dominated by thermal damping of fermionic excitations, suggesting the emergence of Majorana fermions from spin fractionalization.

Direct observation of the Dirac nodes lifting in semimetallic perovskite SrIrO3 thin films

Perovskite SrIrO₃ has long been proposed as an exotic semimetal induced by the interplay between the spin-orbit coupling and electron correlations. However, its low-lying electronic structure is still lacking. We synthesize high-quality perovskite SrIrO₃ (100) films by means of oxide molecular beam epitaxy, and then systemically investigate their low energy electronic structure using in-situ angle-resolved photoemission spectroscopy. We find that the hole-like bands around R and the electron-like bands around U(T) intersect the Fermi level simultaneously, providing the direct evidence of the semimetallic ground state in this compound. Comparing with the density functional theory, we discover that the bandwidth of states near Fermi level is extremely small, and there exists a pronounced mixing between the J_eff = 1/2 and J_eff = 3/2 states. Moreover, our data reveal that the predicted Dirac degeneracy protected by the mirror-symmetry, which was theoretically suggested to be the key to realize the non-trivial topological properties, is actually lifted in perovskite SrIrO₃ thin films. Our findings pose strong constraints on the current theoretical models for the 5d iridates.

Iridates from the molecular side

New exotic phenomena have recently been discovered in oxides of paramagnetic Ir⁴⁺ ions, widely known as ‘iridates'. Their remarkable properties originate from concerted effects of the crystal field, magnetic interactions and strong spin-orbit coupling, characteristic of 5d metal ions. Despite numerous experimental reports, the electronic structure of these materials is still challenging to elucidate, and not attainable in the isolated, but chemically inaccessible, [IrO₆]^8– species (the simplest molecular analogue of the elementary {IrO₆}⁸⁻ fragment present in all iridates). Here, we introduce an alternative approach to circumvent this problem by substituting the oxide ions in [IrO₆]⁸⁻ by isoelectronic fluorides to form the fluorido-iridate: [IrF₆]²⁻. This molecular species has the same electronic ground state as the {IrO₆}⁸⁻ fragment, and thus emerges as an ideal model for iridates. These results may open perspectives for using fluorido-iridates as building-blocks for electronic and magnetic quantum materials synthesized by soft chemistry routes.

Iridates are known to exhibit a range of exotic electronic and magnetic behaviours but it is difficult to prepare isolated [IrO₆]⁸⁻ species via soft chemical routes. Here, the authors isolate the isoelectronic [IrF₆]²⁻ complex, and assess it as a model and for iridate analogues.

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

Using resonant magnetic x-ray scattering we address the unresolved nature of the magnetic ground state and the low-energy effective Hamiltonian of Sm_{2}Ir_{2}O_{7}, a prototypical pyrochlore iridate with a finite temperature metal-insulator transition. Through a combination of elastic and inelastic measurements, we show that the magnetic ground state is an all-in-all-out (AIAO) antiferromagnet. The magnon dispersion indicates significant electronic correlations and can be well described by a minimal Hamiltonian that includes Heisenberg exchange [J=27.3(6)  meV] and Dzyaloshinskii-Moriya interactions [D=4.9(3)  meV], which provides a consistent description of the magnetic order and excitations. In establishing that Sm_{2}Ir_{2}O_{7} has the requisite inversion symmetry preserving AIAO magnetic ground state, our results support the notion that pyrochlore iridates may host correlated Weyl semimetals.

Theory of Multifarious Quantum Phases and Large Anomalous Hall Effect in Pyrochlore Iridate Thin Films

We theoretically investigate emergent quantum phases in the thin film geometries of the pyrochore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases as well as novel quantum states that may arise only in the thin film platforms, are studied via a theoretical model that allows layer-dependent magnetic structures. It is found that the magnetic order develop in inhomogeneous fashions in the thin film geometries. This leads to a variety of magnetic metal phases with modulated magnetic ordering patterns across different layers. Both the bulk and boundary electronic states in these phases conspire to promote unusual electronic properties. In particular, such phases are akin to the Weyl semimetal phase in the bulk system and they would exhibit an unusually large anomalous Hall effect.

Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet

Quantum spin liquids (QSLs) are topological states of matter exhibiting remarkable properties such as the capacity to protect quantum information from decoherence. Whereas their featureless ground states have precluded their straightforward experimental identification, excited states are more revealing and particularly interesting owing to the emergence of fundamentally new excitations such as Majorana fermions. Ideal probes of these excitations are inelastic neutron scattering experiments. These we report here for a ruthenium-based material, α-RuCl3, continuing a major search (so far concentrated on iridium materials) for realizations of the celebrated Kitaev honeycomb topological QSL. Our measurements confirm the requisite strong spin-orbit coupling and low-temperature magnetic order matching predictions proximate to the QSL. We find stacking faults, inherent to the highly two-dimensional nature of the material, resolve an outstanding puzzle. Crucially, dynamical response measurements above interlayer energy scales are naturally accounted for in terms of deconfinement physics expected for QSLs. Comparing these with recent dynamical calculations involving gauge flux excitations and Majorana fermions of the pure Kitaev model, we propose the excitation spectrum of α-RuCl3 as a prime candidate for fractionalized Kitaev physics.

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.

Substrate-tuning of correlated spin-orbit oxides revealed by optical conductivity calculations

We have systematically investigated substrate-strain effects on the electronic structures of two representative Sr-iridates, a correlated-insulator Sr2IrO4 and a metal SrIrO3. Optical conductivities obtained by the ab initio electronic structure calculations reveal that the tensile strain shifts the optical peak positions to higher energy side with altered intensities, suggesting the enhancement of the electronic correlation and spin-orbit coupling (SOC) strength in Sr-iridates. The response of the electronic structure upon tensile strain is found to be highly correlated with the direction of magnetic moment, the octahedral connectivity, and the SOC strength, which cooperatively determine the robustness of Jeff = 1/2 ground states. Optical responses are analyzed also with microscopic model calculation and compared with corresponding experiments. In the case of SrIrO3, the evolution of the electronic structure near the Fermi level shows high tunability of hole bands, as suggested by previous experiments.

Ultrafast energy- and momentum-resolved dynamics of magnetic correlations in the photo-doped Mott insulator Sr2IrO4

Measuring how the magnetic correlations evolve in doped Mott insulators has greatly improved our understanding of the pseudogap, non-Fermi liquids and high-temperature superconductivity. Recently, photo-excitation has been used to induce similarly exotic states transiently. However, the lack of available probes of magnetic correlations in the time domain hinders our understanding of these photo-induced states and how they could be controlled. Here, we implement magnetic resonant inelastic X-ray scattering at a free-electron laser to directly determine the magnetic dynamics after photo-doping the Mott insulator Sr2IrO4. We find that the non-equilibrium state, 2 ps after the excitation, exhibits strongly suppressed long-range magnetic order, but hosts photo-carriers that induce strong, non-thermal magnetic correlations. These two-dimensional (2D) in-plane Néel correlations recover within a few picoseconds, whereas the three-dimensional (3D) long-range magnetic order restores on a fluence-dependent timescale of a few hundred picoseconds. The marked difference in these two timescales implies that the dimensionality of magnetic correlations is vital for our understanding of ultrafast magnetic dynamics.

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.

Atomic-scale control of magnetic anisotropy via novel spin-orbit coupling effect in La2/3Sr1/3MnO3/SrIrO3 superlattices

Magnetic anisotropy (MA) is one of the most important material properties for modern spintronic devices. Conventional manipulation of the intrinsic MA, i.e., magnetocrystalline anisotropy (MCA), typically depends upon crystal symmetry. Extrinsic control over the MA is usually achieved by introducing shape anisotropy or exchange bias from another magnetically ordered material. Here we demonstrate a pathway to manipulate MA of 3d transition-metal oxides (TMOs) by digitally inserting nonmagnetic 5d TMOs with pronounced spin-orbit coupling (SOC). High-quality superlattices comprising ferromagnetic La2/3Sr1/3MnO3 (LSMO) and paramagnetic SrIrO3 (SIO) are synthesized with the precise control of thickness at the atomic scale. Magnetic easy-axis reorientation is observed by controlling the dimensionality of SIO, mediated through the emergence of a novel spin-orbit state within the nominally paramagnetic SIO.

Hallmarks of the Mott-metal crossover in the hole-doped pseudospin-1/2 Mott insulator Sr2IrO4

The physics of doped Mott insulators remains controversial after decades of active research, hindered by the interplay among competing orders and fluctuations. It is thus highly desired to distinguish the intrinsic characters of the Mott-metal crossover from those of other origins. Here we investigate the evolution of electronic structure and dynamics of the hole-doped pseudospin-1/2 Mott insulator Sr₂IrO₄. The effective hole doping is achieved by replacing Ir with Rh atoms, with the chemical potential immediately jumping to or near the top of the lower Hubbard band. The doped iridates exhibit multiple iconic low-energy features previously observed in doped cuprates—pseudogaps, Fermi arcs and marginal-Fermi-liquid-like electronic scattering rates. We suggest these signatures are most likely an integral part of the material's proximity to the Mott state, rather than from many of the most claimed mechanisms, including preformed electron pairing, quantum criticality or density-wave formation.

The physics of Mott insulators is obscured by the interplay between competing orders and fluctuations. Here, the authors track the evolution of the electronic structure of Mott insulator strontium iridate as the iridium atoms are replaced by rhodium, providing insight into this exotic state of matter.

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.

Dynamics of the frustrated spin in the low dimensional magnet Co₃(OH)₂(C₄O₄)₂

We describe powder inelastic neutron scattering experiments on a porous coordination polymer Co3(OH)2(C4O4)2, which has two different ordered magnetic phases known to display spin frustrated behaviour, resulting in an idle-spin phase. The moment on each ion is represented by an effective total angular moment J(eff ) =  ½. A non-dispersive magnetic mode was observed in the idle-spin phase which is described by a simple dimer model that assumes ΔJ  =  0. The excitation was found to persist well above the long range ordering temperature into the paramagnetic region. A combination of frustration, the J(eff)  =  ½ and low dimensionality may induce these quantum phenomena.

Magnetic critical properties and basal-plane anisotropy of Sr₂IrO₄

The anisotropic magnetic properties of Sr2IrO4 are investigated, using longitudinal and torque magnetometry. The critical scaling across T(c) of the longitudinal magnetization is that expected for the 2D XY universality class. Modeling the torque for a magnetic field in the basal plane, and taking into account all in-plane and out-of-plane magnetic couplings, we derive the effective fourfold anisotropy K4 ≈ 1 × 10(5) erg mol(-1). Although larger than for the cuprates, it is found to be too small to account for a significant departure from the isotropic 2D XY model. The in-plane torque also allows us to set an upper bound for the anisotropy of a field-induced shift of the antiferromagnetic ordering temperature.

X-ray Absorption Spectroscopy Study of the Effect of Rh doping in Sr2IrO4

We investigate the effect of Rh doping in Sr2IrO4 using X-ray absorption spectroscopy (XAS). We observed appearance of new electron-addition states with increasing Rh concentration (x in Sr2Ir1-xRhxO4) in accordance with the concept of hole doping. The intensity of the hole-induced state is however weak, suggesting weakness of charge transfer (CT) effect and Mott insulating ground states. Also, Ir Jeff = 1/2 upper Hubbard band shifts to lower energy as x increases up to x = 0.23. Combined with optical spectroscopy, these results suggest a hybridisation-related mechanism, in which Rh doping can weaken the (Ir Jeff = 1/2)-(O 2p) orbital hybridisation in the in-planar Rh-O-Ir bond networks.

Origin of the Spin-Orbital Liquid State in a Nearly J=0 Iridate Ba_{3}ZnIr_{2}O_{9}

We show using detailed magnetic and thermodynamic studies and theoretical calculations that the ground state of Ba_{3}ZnIr_{2}O_{9} is a realization of a novel spin-orbital liquid state. Our results reveal that Ba_{3}ZnIr_{2}O_{9} with Ir^{5+} (5d^{4}) ions and strong spin-orbit coupling (SOC) arrives very close to the elusive J=0 state but each Ir ion still possesses a weak moment. Ab initio density functional calculations indicate that this moment is developed due to superexchange, mediated by a strong intradimer hopping mechanism. While the Ir spins within the structural Ir_{2}O_{9} dimer are expected to form a spin-orbit singlet state (SOS) with no resultant moment, substantial frustration arising from interdimer exchange interactions induce quantum fluctuations in these possible SOS states favoring a spin-orbital liquid phase down to at least 100 mK.

Antiferromagnetic spintronics

Antiferromagnetic materials are internally magnetic, but the direction of their ordered microscopic moments alternates between individual atomic sites. The resulting zero net magnetic moment makes magnetism in antiferromagnets externally invisible. This implies that information stored in antiferromagnetic moments would be invisible to common magnetic probes, insensitive to disturbing magnetic fields, and the antiferromagnetic element would not magnetically affect its neighbours, regardless of how densely the elements are arranged in the device. The intrinsic high frequencies of antiferromagnetic dynamics represent another property that makes antiferromagnets distinct from ferromagnets. Among the outstanding questions is how to manipulate and detect the magnetic state of an antiferromagnet efficiently. In this Review we focus on recent works that have addressed this question. The field of antiferromagnetic spintronics can also be viewed from the general perspectives of spin transport, magnetic textures and dynamics, and materials research. We briefly mention this broader context, together with an outlook of future research and applications of antiferromagnetic spintronics.

Muon-spin relaxation study of the double perovskite insulators Sr2 BOsO6 (B = Fe, Y, ln)

We present the results of zero-field muon-spin relaxation measurements made on the double perovskite insulators Sr2 BOsO6 (B = Fe,Y, In). Spontaneous muon-spin precession indicative of quasistatic long range magnetic ordering is observed in Sr2FeOsO6 within the AF1 antiferromagnetic phase for temperatures below [Formula: see text] K. Upon cooling below T2≈67 K the oscillations cease to be resolvable owing to the coexistence of the AF1 and AF2 phases, which leads to a broader range of internal magnetic fields. Using density functional calculations we identify a candidate muon stopping site within the unit cell, which dipole field simulations show to be consistent with the proposed magnetic structure. The possibility of incommensurate magnetic ordering is discussed for temperatures below TN = 53 K and 25 K for Sr2YOsO6 and Sr2InOsO6, respectively.

Thermoelectric behavior of Ruddlesden-Popper series iridates

The goal of this work is to study the evolution of thermoelectric transport across the members of the Ruddlesden-Popper series iridates [Formula: see text], where a metal-insulator transition driven by bandwidth change occurs, from the strongly insulating Sr2IrO4 to the metallic non Fermi liquid behavior of SrIrO3. Sr2IrO4 ([Formula: see text]), Sr3Ir2O7 ([Formula: see text]) and SrIrO3 ([Formula: see text]) polycrystals are synthesized at high pressure and characterized by structural, magnetic, electric and thermoelectric transport analyses. We find a complex thermoelectric phenomenology in the three compounds. Thermal diffusion of charge carriers accounts for the Seebeck behavior of Sr2IrO4, whereas additional drag mechanisms come into play in determining the Seebeck temperature dependence of Sr3Ir2O7 and SrIrO3. These findings reveal a close relationship between magnetic, electronic and thermoelectric properties, strong coupling of charge carriers with phonons and spin fluctuations as well as the relevance of multiband description in these compounds.

Strong lattice correlation of non-equilibrium quasiparticles in a pseudospin-1/2 Mott insulator Sr2IrO4

In correlated oxides the coupling of quasiparticles to other degrees of freedom such as spin and lattice plays critical roles in the emergence of symmetry-breaking quantum ordered states such as high temperature superconductivity. We report a strong lattice coupling of photon-induced quasiparticles in spin-orbital coupling Mott insulator Sr₂IrO₄ probed via optical excitation. Combining time-resolved x-ray diffraction and optical spectroscopy techniques, we reconstruct a spatiotemporal map of the diffusion of these quasiparticles. Due to the unique electronic configuration of the quasiparticles, the strong lattice correlation is unexpected but extends the similarity between Sr₂IrO₄ and cuprates to a new dimension of electron-phonon coupling which persists under highly non-equilibrium conditions.

Enhanced spin-phonon-electronic coupling in a 5d oxide

Enhanced coupling of material properties offers new fundamental insights and routes to multifunctional devices. In this context 5d oxides provide new paradigms of cooperative interactions that drive novel emergent behaviour. This is exemplified in osmates that host metal–insulator transitions where magnetic order appears intimately entwined. Here we consider such a material, the 5d perovskite NaOsO₃, and observe a coupling between spin and phonon manifested in a frequency shift of 40 cm⁻¹, the largest measured in any material. The anomalous modes are shown to involve solely Os–O interactions and magnetism is revealed as the driving microscopic mechanism for the phonon renormalization. The magnitude of the coupling in NaOsO₃ is primarily due to a property common to all 5d materials: the large spatial extent of the ion. This allows magnetism to couple to phonons on an unprecedented scale and in general offers multiple new routes to enhanced coupled phenomena in 5d materials.

Transition metal oxides with 5d ions present novel emergent behaviour based on the enhanced coupling of material properties compared to those with 3d ions. Here, the authors demonstrate a large spin-phonon coupling in NaOsO₃ which results from a large Os–O electronic orbital overlap.

First-Principles Study of the Magnetic Structure of Na2IrO3

The iridate Na2IrO3 was proposed to be a realization of the Kitaev model with a quantum spin liquid ground state. Experiments have now established that this material hosts a zigzag antiferromagnetic order. However, the previous assignment of the ordered moment direction to the a axis is controversial. We examine the magnetic moment direction of Na2IrO3 using the local spin density approximation plus spin orbit coupling+U calculations. Our calculations reveal that the total energy is minimized when the zigzag-ordered moments are aligned along g≈a+c direction. The dependence of the total energy on moment directions can be explained by adding anisotropic interactions to the nearest-neighbor Kitaev-Heisenberg model, on which the spin-wave spectrum is also calculated. The revision of ordered moments is very important to understanding and achieving possible exotic electronic phases in this compound.

Phase Diagram of Pyrochlore Iridates: All-in-All-out Magnetic Ordering and Non-Fermi-Liquid Properties

We study the prototype 5d pyrochlore iridate Y_{2}Ir_{2}O_{7} from first principles using the local density approximation and dynamical mean-field theory (LDA+DMFT). We map out the phase diagram in the space of temperature, on-site Coulomb repulsion U, and filling. Consistent with experiments, we find that an all-in-all-out ordered insulating phase is stable for realistic values of U. The trigonal crystal field enhances the hybridization between the j_{eff}=1/2 and j_{eff}=3/2 states, and strong interband correlations are induced by the Coulomb interaction, which indicates that a three-band description is important. We demonstrate a substantial band narrowing in the paramagnetic metallic phase and non-Fermi-liquid behavior in the electron- or hole-doped system originating from long-lived quasi-spin-moments induced by nearly flat bands.

Nature of the Insulating Ground State of the 5d Postperovskite CaIrO3

The insulating ground state of the 5d transition metal oxide CaIrO3 has been classified as a Mott-type insulator. Based on a systematic density functional theory (DFT) study with local, semilocal, and hybrid exchange-correlation functionals, we reveal that the Ir t(2g) states exhibit large splittings and one-dimensional electronic states along the c axis due to a tetragonal crystal field. Our hybrid DFT calculation adequately describes the antiferromagnetic (AFM) order along the c direction via a superexchange interaction between Ir^{4+} spins. Furthermore, the spin-orbit coupling (SOC) hybridizes the t(2g) states to open an insulating gap. These results indicate that CaIrO_{3} can be represented as a spin-orbit Slater insulator, driven by the interplay between a long-range AFM order and the SOC. Such a Slater mechanism for the gap formation is also demonstrated by the DFT + dynamical mean field theory calculation, where the metal-insulator transition and the paramagnetic to AFM phase transition are concomitant with each other.

Cooperative effects of lattice and spin-orbit coupling on the electronic structure of orthorhombic SrIrO₃

Orthorhombic SrIrO3 subjected to strain shows tunable transport properties. With underlying symmetry remaining invariant, these properties are associated with IrO6 octahedral tilting. Adopting first-principles methods, the effects of crystal field, spin-orbit coupling (SOC), and Coulomb correlations, on comparable interaction length scales, are discussed. While tilting induces a t(2g) - e(g) crystal-field splitting and band narrowing, SOC induces a partial splitting of the J(eff) bands rendering SrIrO3 a semi-metallic ground state. The SOC enhanced hybridization of Ir-O orbitals serves as an explanation as to why the critical Hubbard correlation strength increases with increasing SOC strength in SrIrO3 to induce an insulating phase.

Anomalous High-Energy Waterfall-Like Electronic Structure in 5 d Transition Metal Oxide Sr2IrO4 with a Strong Spin-Orbit Coupling

The low energy electronic structure of Sr2IrO4 has been well studied and understood in terms of an effective Jeff = 1/2 Mott insulator model. However, little work has been done in studying its high energy electronic behaviors. Here we report a new observation of the anomalous high energy electronic structure in Sr2IrO4. By taking high-resolution angle-resolved photoemission measurements on Sr2IrO4 over a wide energy range, we have revealed for the first time that the high energy electronic structures show unusual nearly-vertical bands that extend over a large energy range. Such anomalous high energy behaviors resemble the high energy waterfall features observed in the cuprate superconductors. While strong electron correlation plays an important role in producing high energy waterfall features in the cuprate superconductors, the revelation of the high energy anomalies in Sr2IrO4, which exhibits strong spin-orbit coupling and a moderate electron correlation, points to an unknown and novel route in generating exotic electronic excitations.

New Insulating Antiferromagnetic Quaternary Iridates MLa10Ir4O24 (M = Sr, Ba)

Recently, oxides of Ir⁴⁺ have received renewed attention in the condensed matter physics community, as it has been reported that certain iridates have a strongly spin-orbital coupled (SOC) electronic state, J_eff = ½, that defines the electronic and magnetic properties. The canonical example is the Ruddlesden-Popper compound Sr₂IrO₄, which has been suggested as a potential route to a new class of high temperature superconductor due to the formal analogy between J_eff = ½ and the S = ½ state of the cuprate superconductors. The quest for other iridium oxides that present tests of the underlying SOC physics is underway. In this spirit, here we report the synthesis and physical properties of two new quaternary tetravalent iridates, MLa₁₀Ir₄O₂₄ (M = Sr, Ba). The crystal structure of both compounds features isolated IrO₆ octahedra in which the electronic configuration of Ir is d⁵. Both compounds order antiferromagnetically despite the lack of obvious superexchange pathways, and resistivity measurement shows that SrLa₁₀Ir₄O₂₄ is an insulator.

Orbital reconstruction in nonpolar tetravalent transition-metal oxide layers

A promising route to tailoring the electronic properties of quantum materials and devices rests on the idea of orbital engineering in multilayered oxide heterostructures. Here we show that the interplay of interlayer charge imbalance and ligand distortions provides a knob for tuning the sequence of electronic levels even in intrinsically stacked oxides. We resolve in this regard the d-level structure of layered Sr₂IrO₄ by electron spin resonance. While canonical ligand-field theory predicts g_||-factors less than 2 for positive tetragonal distortions as present in Sr₂IrO₄, the experiment indicates g_|| is greater than 2. This implies that the iridium d levels are inverted with respect to their normal ordering. State-of-the-art electronic-structure calculations confirm the level switching in Sr₂IrO₄, whereas we find them in Ba₂IrO₄ to be instead normally ordered. Given the nonpolar character of the metal-oxygen layers, our findings highlight the tetravalent transition-metal 214 oxides as ideal platforms to explore d-orbital reconstruction in the context of oxide electronics.

The iridate compounds display interesting physical properties, including quasi-two-dimensional behaviour similar to cuprates. Bogdanov et al. explore the d-level structure of Sr₂IrO₄ using electron spin resonance measurements and detailed calculations and find it is inverted compared to its normal ordering

Weyl spin liquids

The fractionalization of quantum numbers in interacting quantum many-body systems is a central motif in condensed-matter physics with prominent examples including the fractionalization of the electron in quantum Hall liquids or the emergence of magnetic monopoles in spin-ice materials. Here, we discuss the fractionalization of magnetic moments in three-dimensional Kitaev models into Majorana fermions (and a Z_{2} gauge field) and their emergent collective behavior. We analytically demonstrate that the Majorana fermions form a Weyl superconductor for the Kitaev model on the recently synthesized hyperhoneycomb structure of β-Li_{2}IrO_{3} when applying a magnetic field. We characterize the topologically protected bulk and surface features of this state, which we dub a Weyl spin liquid, including thermodynamic and transport signatures.