Novel Jeff=1/2 Mott state induced by relativistic spin-orbit coupling in Sr2IrO4

Superconductivity. Fermi arcs in a doped pseudospin-1/2 Heisenberg antiferromagnet

High-temperature superconductivity in cuprates arises from an electronic state that remains poorly understood. We report the observation of a related electronic state in a noncuprate material, strontium iridate (Sr2IrO4), in which the distinct cuprate fermiology is largely reproduced. Upon surface electron doping through in situ deposition of alkali-metal atoms, angle-resolved photoemission spectra of Sr2IrO4 display disconnected segments of zero-energy states, known as Fermi arcs, and a gap as large as 80 millielectron volts. Its evolution toward a normal metal phase with a closed Fermi surface as a function of doping and temperature parallels that in the cuprates. Our result suggests that Sr2IrO4 is a useful model system for comparison to the cuprates.

Antiferromagnetic Slater insulator phase of Na₂IrO₃

Using a hybrid density-functional theory (DFT) calculation including spin-orbit coupling (SOC), we predict that the zigzag antiferromagnetic (AFM) ground state of the honeycomb layered compound Na₂IrO₃ opens the observed insulating gap through a long-range magnetic order. We show that the effect of SOC and the correction of self-interaction error inherent in previous local or semilocal DFT calculations play crucial roles in predicting the band gap formation in Na₂IrO₃. It is revealed that the itinerant AFM order with a strong suppression of the Ir magnetic moment is attributed to a considerable hybridization of the Ir 5d orbitals with the O 2p orbitals. Thus, our results suggest that the insulating phase of Na₂IrO₃ can be represented as a Slater insulator driven by itinerant magnetism.

Spin-orbital entangled molecular jeff states in lacunar spinel compounds

The entanglement of the spin and orbital degrees of freedom through the spin-orbit coupling has been actively studied in condensed matter physics. In several iridium oxide systems, the spin-orbital entangled state, identified by the effective angular momentum jeff, can host novel quantum phases. Here we show that a series of lacunar spinel compounds, GaM4X8 (M=Nb, Mo, Ta and W and X=S, Se and Te), gives rise to a molecular jeff state as a new spin-orbital composite on which the low-energy effective Hamiltonian is based. A wide range of electron correlations is accessible by tuning the bandwidth under external and/or chemical pressure, enabling us to investigate the cooperation between spin-orbit coupling and electron correlations. As illustrative examples, a two-dimensional topological insulating phase and an anisotropic spin Hamiltonian are investigated in the weak and strong coupling regimes, respectively. Our finding can provide an ideal platform for exploring jeff physics and the resulting emergent phenomena.

Pressure induced second-order structural transition in Sr₃Ir₂O₇

We conducted in situ angle dispersive high pressure x-ray diffraction experiments on Sr3Ir2O7 up to 23.1 GPa at 25 K with neon as the pressure transmitting medium. Pressure induces a highly anisotropic compressional behavior seen where the tetragonal plane is compressed much faster than the perpendicular direction. By analyzing different aspects of the diffraction data, a second-order structural transition is observed at approximately 14 GPa, which is accompanied by the insulating state to nearly metallic state at 13.2 GPa observed previously (Li et al 2013 Phys. Rev. B 87 235127). Our results highlight the coupling between electronic state and lattice structure in Sr3Ir2O7 under pressure.

Dynamical mean field theory-based electronic structure calculations for correlated materials

We give an introduction to dynamical mean field approaches to correlated materials. Starting from the concept of electronic correlation, we explain why a theoretical description of correlations in spectroscopic properties needs to go beyond the single-particle picture of band theory.We discuss the main ideas of dynamical mean field theory and its use within realistic electronic structure calculations, illustrated by examples of transition metals, transition metal oxides, and rare-earth compounds. Finally, we summarise recent progress on the calculation of effective Hubbard interactions and the description of dynamical screening effects in solids.

Electronic structure and magnetic properties of iridate superlattice SrIrO(3)/SrTiO(3)

Motivated by an experimental report of iridate superlattices, we performed first-principle electronic structure calculations for SrIrO3/SrTiO3. Heterostructuring causes SrIrO3 to become Sr2IrO4-like, and the system has the well-defined jeff = 1/2 states near the Fermi level as well as a canted antiferromagnetic order within the quasi-two-dimensional IrO2 plane. In response to a larger tensile strain, the band gap is increased due to the resulting increase in bond length and the bandwidth reduction. The ground state magnetic properties are discussed in comparison to the metastable collinear antiferromagnetic state. Our work sheds new light on understanding the recent experimental results on the iridate heterostructures.

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.

Electronic structure of low-dimensional 4d(5) oxides: interplay of ligand distortions, overall lattice anisotropy, and spin-orbit interactions

The electronic structure of the low-dimensional 4d(5) oxides Sr2RhO4 and Ca3CoRhO6 is herein investigated by embedded-cluster quantum chemistry calculations. A negative tetragonal-like t2g splitting is computed in Sr2RhO4 and a negative trigonal-like splitting is predicted for Ca3CoRhO6, in spite of having positive tetragonal distortions in the former material and cubic oxygen octahedra in the latter. Our findings bring to the foreground the role of longer-range crystalline anisotropy in generating noncubic potentials that compete with local distortions of the ligand cage, an issue not addressed in standard textbooks on crystal-field theory. We also show that sizable t2g(5)-t2g(4)eg(1) couplings via spin-orbit interactions produce in Sr2RhO4 ⟨Z⟩ = ⟨Σ(i)l(i)·s(i)⟩ ground-state expectation values significantly larger than 1, quite similar to theoretical and experimental data for 5d(5) spin-orbit-driven oxides such as Sr2IrO4. On the other hand, in Ca3CoRhO6, the ⟨Z⟩ values are lower because of larger t2g-eg splittings. Future X-ray magnetic circular dichroism experiments on these 4d oxides will constitute a direct test for the ⟨Z⟩ values that we predict here, the importance of many-body t2g-eg couplings mediated by spin-orbit interactions, and the role of low-symmetry fields associated with the extended surroundings.

Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice

We consider a class of d- and f-electron systems in which dipolar-octupolar Kramers doublets arise on the sites of the pyrochlore lattice. For such doublets, two components of the pseudospin transform like a magnetic dipole, while the other transforms like a component of the magnetic octupole tensor. Based on a symmetry analysis, we construct and study models of dipolar-octupolar doublets in itinerant and localized limits. In both limits, the resulting models are of surprisingly simple form. In the itinerant limit, we find topological insulating behavior. In the localized limit, the most general nearest-neighbor spin model is the XYZ model. We show that this XYZ model exhibits two distinct quantum spin ice (QSI) phases, that we dub dipolar QSI, and octupolar QSI. We conclude with a discussion of potential relevance to real material systems.

Tuning magnetic coupling in Sr2IrO4 thin films with epitaxial strain

We report x-ray resonant magnetic scattering and resonant inelastic x-ray scattering studies of epitaxially strained Sr2IrO4 thin films. The films were grown on SrTiO3 and (LaAlO3)0.3(Sr2AlTaO6)0.7 substrates, under slight tensile and compressive strains, respectively. Although the films develop a magnetic structure reminiscent of bulk Sr2IrO4, the magnetic correlations are extremely anisotropic, with in-plane correlation lengths significantly longer than the out-of-plane correlation lengths. In addition, the compressive (tensile) strain serves to suppress (enhance) the magnetic ordering temperature TN, while raising (lowering) the energy of the zone-boundary magnon. Quantum chemical calculations show that the tuning of magnetic energy scales can be understood in terms of strain-induced changes in bond lengths.

Impact of spin-orbit coupling on the magnetism of Sr₃MIrO₆ (M = Ni, Co)

Iridates are of current great interest for their entangled spin-orbital state and possibly exotic properties. In this work, using density functional calculations, we have demonstrated that the hexagonal spin-chain materials Sr₃MIrO₆ (M = Ni, Co) are an iridate system in which the spin-orbit coupling (SOC) tunes the magnetic and electronic properties. The significant SOC alters the orbital state, the exchange pathway, and thus the magnetic structure. This work clarifies the nature and the origin of the intra-chain antiferromagnetism of Sr₃MIrO₆ and well accounts for the most recent experiments.

Carrier localization and electronic phase separation in a doped spin-orbit-driven Mott phase in Sr₃(Ir(1-x)Ru(x))₂O₇

Interest in many strongly spin-orbit-coupled 5d-transition metal oxide insulators stems from mapping their electronic structures to a J(eff)=1/2 Mott phase. One of the hopes is to establish their Mott parent states and explore these systems' potential of realizing novel electronic states upon carrier doping. However, once doped, little is understood regarding the role of their reduced Coulomb interaction U relative to their strongly correlated 3d-electron cousins. Here we show that, upon hole-doping a candidate J(eff)=1/2 Mott insulator, carriers remain localized within a nanoscale phase-separated ground state. A percolative metal-insulator transition occurs with interplay between localized and itinerant regions, stabilizing an antiferromagnetic metallic phase beyond the critical region. Our results demonstrate a surprising parallel between doped 5d- and 3d-electron Mott systems and suggest either through the near-degeneracy of nearby electronic phases or direct carrier localization that U is essential to the carrier response of this doped spin-orbit Mott insulator.

Novel magnetism of Ir5+(5d4) Ions in the double perovskite Sr2YIrO6

We synthesize and study single crystals of a new double-perovskite Sr2YIrO6. Despite two strongly unfavorable conditions for magnetic order, namely, pentavalent Ir5+(5d4) ions which are anticipated to have Jeff=0 singlet ground states in the strong spin-orbit coupling (SOC) limit and geometric frustration in a face-centered cubic structure formed by the Ir5+ ions, we observe this iridate to undergo a novel magnetic transition at temperatures below 1.3 K. We provide compelling experimental and theoretical evidence that the origin of magnetism is in an unusual interplay between strong noncubic crystal fields, local exchange interactions, and "intermediate-strength" SOC. Sr2YIrO6 provides a rare example of the failed dominance of SOC in the iridates.

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.

Spin and orbital contributions to magnetically ordered moments in 5d layered perovskite Sr2IrO4

The ratio of orbital (L) and spin (S) contributions to the magnetically ordered moments of a 5d transition metal oxide, Sr2IrO4 was evaluated by nonresonant magnetic x-ray diffraction. We applied an improved experimental setting that minimized the experimental error, in which we varied only the linear polarization of incident x ray at a fixed scattering angle. Strong polarization dependence of the intensity of magnetic diffraction was observed, from which we conclude that the ordered moments contain substantial contribution from the orbital degree of freedom with the ratio of <L>/<S>∼5.0, evidencing the pronounced effect of spin-orbit coupling. The obtained ratio is close to, but slightly larger than the expected value for the ideal J(eff) = 1/2 moment of a spin-orbital Mott insulator, |<J(1/2)|L(z)|J(1/2)>|/|<J(1/2)|S(z)|J(1/2)>| = 4, which cannot be accounted for by the redistribution of orbital components within the t(2g) bands associated with the elongation of the IrO6 octahedra.

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.

Crystal-chemistry guidelines for noncentrosymmetric A2BO4 Ruddlesden-Popper oxides

Noncentrosymmetric (NCS) phases are seldom seen in layered A2BO4 Ruddlesden-Popper (214 RP) oxides. In this work, we uncover the underlying crystallographic symmetry restrictions that enforce the spatial parity operation of inversion and then subsequently show how to lift them to achieve NCS structures. Simple octahedral distortions alone, while impacting the electronic and magnetic properties, are insufficient. We show using group theory that the condensation of two distortion modes, which describe suitable symmetry unique octahedral distortions or a combination of a single octahedral distortion with a "compositional" A or B cation ordering mode, is able to transform the centrosymmetric aristotype into a NCS structure. With these symmetry guidelines, we formulate a data-driven model founded on Bayesian inference that allows us to rationally search for combinations of A- and B-site elements satisfying the inversion symmetry lifting criterion. We describe the general methodology and apply it to 214 iridates with A(2+) cations, identifying RP-structured Ca2IrO4 as a potential NCS oxide, which we evaluate with density functional theory. We find a strong energetic competition between two closely related polar and nonpolar low-energy crystal structures in Ca2IrO4 and suggest pathways to stabilize the NCS structure.

Non-Fermi-liquid and topological states with strong spin-orbit coupling

We argue that a class of strongly spin-orbit-coupled materials, including some pyrochlore iridates and the inverted band gap semiconductor HgTe, may be described by a minimal model consisting of the Luttinger Hamiltonian supplemented by Coulomb interactions, a problem studied by Abrikosov and collaborators. It contains twofold degenerate conduction and valence bands touching quadratically at the zone center. Using modern renormalization group methods, we update and extend Abrikosov's classic work and show that interactions induce a quantum critical non-Fermi-liquid phase, stable provided time-reversal and cubic symmetries are maintained. We determine the universal power-law exponents describing various observables in this Luttinger-Abrikosov-Beneslavskii state, which include conductivity, specific heat, nonlinear susceptibility, and the magnetic Gruneisen number. Furthermore, we determine the phase diagram in the presence of cubic and/or time-reversal symmetry breaking perturbations, which includes a topological insulator and Weyl semimetal phases. Many of these phases possess an extraordinarily large anomalous Hall effect, with the Hall conductivity scaling sublinearly with magnetization σ(xy)∼M0.51.

Atomically resolved spectroscopic study of Sr2IrO4: experiment and theory

Particularly in Sr2IrO4, the interplay between spin-orbit coupling, bandwidth and on-site Coulomb repulsion stabilizes a J(eff) = 1/2 spin-orbital entangled insulating state at low temperatures. Whether this insulating phase is Mott- or Slater-type, has been under intense debate. We address this issue via spatially resolved imaging and spectroscopic studies of the Sr2IrO4 surface using scanning tunneling microscopy/spectroscopy (STM/S). STS results clearly illustrate the opening of an insulating gap (150 ~ 250 meV) below the Néel temperature (TN), in qualitative agreement with our density-functional theory (DFT) calculations. More importantly, the temperature dependence of the gap is qualitatively consistent with our DFT + dynamical mean field theory (DMFT) results, both showing a continuous transition from a gapped insulating ground state to a non-gap phase as temperatures approach TN. These results indicate a significant Slater character of gap formation, thus suggesting that Sr2IrO4 is a uniquely correlated system, where Slater and Mott-Hubbard-type behaviors coexist.

Possible Kondo physics near a metal-insulator crossover in the a-site ordered perovskite CaCu3Ir4O12

The A-site ordered perovskite (AA(3)')B(4)O(12) can accommodate transition metals on both A' and B sites in the crystal structure. Because of this structural feature, it is possible to have narrow-band electrons interacting with broadband electrons from different sublattices. Here we report a new A-site ordered perovskite (CaCu(3))Ir(4)O(12) synthesized under high pressure. The coupling between localized spins on Cu(2+) and itinerant electrons from the Ir-O sublattice makes Kondo-like physics take place at a temperature as high as 80 K. Results from the local density approximation calculation have confirmed the relevant band structure. The magnetization anomaly found at 80 K can be well rationalized by the two-fluid model.

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.

Topological oxide insulator in cubic perovskite structure

The emergence of topologically protected conducting states with the chiral spin texture is the most prominent feature at the surface of topological insulators. On the application side, large band gap and high resistivity to distinguish surface from bulk degrees of freedom should be guaranteed for the full usage of the surface states. Here, we suggest that the oxide cubic perovskite YBiO₃, more than just an oxide, defines itself as a new three-dimensional topological insulator exhibiting both a large bulk band gap and a high resistivity. Based on first-principles calculations varying the spin-orbit coupling strength, the non-trivial band topology of YBiO₃ is investigated, where the spin-orbit coupling of the Bi 6p orbital plays a crucial role. Taking the exquisite synthesis techniques in oxide electronics into account, YBiO₃ can also be used to provide various interface configurations hosting exotic topological phenomena combined with other quantum phases.

Ferromagnetic exchange anisotropy from antiferromagnetic superexchange in the mixed 3d-5d transition-metal compound Sr3CuIrO6

We report a combined experimental and theoretical study of the unusual ferromagnetism in the one-dimensional copper-iridium oxide Sr(3)CuIrO(6). Utilizing Ir L(3) edge resonant inelastic x-ray scattering, we reveal a large gap magnetic excitation spectrum. We find that it is caused by an unusual exchange anisotropy generating mechanism, namely, strong ferromagnetic anisotropy arising from antiferromagnetic superexchange, driven by the alternating strong and weak spin-orbit coupling on the 5d Ir and 3d Cu magnetic ions, respectively. From symmetry consideration, this novel mechanism is generally present in systems with edge-sharing Cu(2+)O(4) plaquettes and Ir(4+)O(6) octahedra. Our results point to unusual magnetic behavior to be expected in mixed 3d-5d transition-metal compounds via exchange pathways that are absent in pure 3d or 5d compounds.

Imaging the evolution of metallic states in a correlated iridate

The Ruddlesden-Popper series of iridates (Srn+1IrnO3n+1) have been the subject of much recent attention due to the anticipation of emergent phenomena arising from the cooperative action of spin-orbit-driven band splitting and Coulomb interactions. However, an ongoing debate over the role of correlations in the formation of the charge gap and a lack of understanding of the effects of doping on the low-energy electronic structure have hindered experimental progress in realizing many of the predicted states. Using scanning tunnelling spectroscopy we map out the spatially resolved density of states in Sr3Ir2O7 (Ir327). We show that its parent compound, argued to exist only as a weakly correlated band insulator, in fact possesses a substantial ~ 130 meV charge excitation gap driven by an interplay between structure, spin-orbit coupling and correlations. We find that single-atom defects are associated with a strong electronic inhomogeneity, creating an important distinction between the intrinsic and spatially averaged electronic structure. Combined with first-principles calculations, our measurements reveal how defects at specific atomic sites transfer spectral weight from higher energies to the gap energies, providing a possible route to obtaining metallic electronic states from the parent insulating states in the iridates.

Resonant x-ray diffraction study of the strongly spin-orbit-coupled mott insulator CaIrO3

We performed resonant x-ray diffraction experiments at the L absorption edges for the post-perovskite-type compound CaIrO(3) with a (t(2g))^{5} electronic configuration. By observing the magnetic signals, we could clearly see that the magnetic structure was a striped ordering with an antiferromagnetic moment along the c axis and that the wave function of a t(2g) hole is strongly spin-orbit entangled, the J(eff)=1/2 state. The observed spin arrangement is consistent with theoretical work predicting a unique superexchange interaction in the J(eff)=1/2 state and points to the universal importance of the spin-orbit coupling in Ir oxides, independent of the octahedral connectivity and lattice topology. We also propose that nonmagnetic resonant scattering is a powerful tool for unraveling an orbital state even in a metallic iridate.

Mechanism of enhanced optical second-harmonic generation in the conducting pyrochlore-type Pb2Ir2O7-x oxide compound

The structural, electronic, and optical properties of pyrochlore-type Pb(2)Ir(2)O(6)O(0.55)('), which is a metal without spatial inversion symmetry at room temperature, were investigated. Structural analysis revealed that the structural distortion relevant to the breakdown of the inversion symmetry is dominated by the Pb-O' network but is very small in the Ir-O network. At the same time, gigantic second-harmonic generation signals were observed, which can only occur if the local environment of the Ir 5d electrons features broken inversion symmetry. First-principles electronic structure calculations reveal that the underlying mechanism for this phenomenon is the induction of the noncentrosymmetricity in the Ir 5d bands by the strong hybridization with O' 2p orbitals. Our results stimulate theoretical study of inversion-broken iridates, where exotic quantum states such as a topological insulator and Dirac semimetal are anticipated.

Correlation effects in two-dimensional topological insulators

Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlation effects in the two-dimensional case, with a focus on systems with intrinsic spin-orbit coupling and numerical results. Topics addressed include an introduction to the noninteracting case, an overview of theoretical models, correlated topological band insulators, interaction-driven phase transitions, topological Mott insulators and fractional topological states, correlation effects on helical edge states, and topological invariants of interacting systems.

Robustness of basal-plane antiferromagnetic order and the J(eff)=1/2 state in single-layer iridate spin-orbit Mott insulators

The magnetic structure and electronic ground state of the layered perovskite Ba(2)IrO(4) have been investigated using x-ray resonant magnetic scattering. Our results are compared with those for Sr(2)IrO(4), for which we provide supplementary data on its magnetic structure. We find that the dominant, long-range antiferromagnetic order is remarkably similar in the two compounds and that the electronic ground state in Ba(2)IrO(4), deduced from an investigation of the x-ray resonant magnetic scattering L(3)/L(2) intensity ratio, is consistent with a J(eff)=1/2 description. The robustness of these two key electronic properties to the considerable structural differences between the Ba and Sr analogues is discussed in terms of the enhanced role of the spin-orbit interaction in 5d transition metal oxides.

Crystal-field splitting and correlation effect on the electronic structure of A2IrO3

The electronic structure of the honeycomb lattice iridates Na(2)IrO(3) and Li(2)IrO(3) has been investigated using resonant inelastic x-ray scattering (RIXS). Crystal-field-split d-d excitations are resolved in the high-resolution RIXS spectra. In particular, the splitting due to noncubic crystal fields, derived from the splitting of j(eff)=3/2 states, is much smaller than the typical spin-orbit energy scale in iridates, validating the applicability of j(eff) physics in A(2)IrO(3). We also find excitonic enhancement of the particle-hole excitation gap around 0.4 eV, indicating that the nearest-neighbor Coulomb interaction could be large. These findings suggest that both Na(2)IrO(3) and Li(2)IrO(3) can be described as spin-orbit Mott insulators, similar to the square lattice iridate Sr(2)IrO(4).

Doped Mott insulators in (111) bilayers of perovskite transition-metal oxides with a strong spin-orbit coupling

The electronic properties of Mott insulators realized in (111) bilayers of perovskite transition-metal oxides are studied. The low-energy effective Hamiltonians for such Mott insulators are derived in the presence of a strong spin-orbit coupling. These models are characterized by the antiferromagnetic Heisenberg interaction and the anisotropic interaction whose form depends on the d orbital occupancy. From exact diagonalization analyses on finite clusters, the ground state phase diagrams are derived, including a Kitaev spin liquid phase in a narrow parameter regime for t(2g) systems. Slave-boson mean-field analyses indicate the possibility of novel superconducting states induced by carrier doping into the Mott-insulating parent systems, suggesting the present model systems as unique playgrounds for studying correlation-induced novel phenomena. Possible experimental realizations are also discussed.

Monte Carlo study of an unconventional superconducting phase in iridium oxide J(eff)=1/2 Mott insulators induced by carrier doping

Based on a microscopic theoretical study, we show that novel superconductivity is induced by carrier doping in layered perovskite Ir oxides where a strong spin-orbit coupling causes an effective total angular momentum J(eff)=1/2 Mott insulator. Using a variational Monte Carlo method, we find an unconventional superconducting state in the ground state phase diagram of a t(2g) three-orbital Hubbard model on the square lattice. This superconducting state is characterized by a d(x(2)-y(2))-wave "pseudospin singlet" formed by the J(eff)=1/2 Kramers doublet, which thus contains interorbital as well as both singlet and triplet components of t(2g) electrons. The superconducting state is found stable only by electron doping, but not by hole doping, for the case of carrier doped Sr2IrO4. We also study an effective single-orbital Hubbard model to discuss the similarities to high-T(c) cuprate superconductors and the multiorbital effects.

Na2IrO3 as a novel relativistic Mott insulator with a 340-meV gap

We study Na2IrO3 by angle-resolved photoemission spectroscopy, optics, and band structure calculations in the local-density approximation (LDA). The weak dispersion of the Ir 5d-t(2g) manifold highlights the importance of structural distortions and spin-orbit (SO) coupling in driving the system closer to a Mott transition. We detect an insulating gap Δ(gap)≃340  meV which, at variance with a Slater-type description, is already open at 300 K and does not show significant temperature dependence even across T(N)≃15  K. An LDA analysis with the inclusion of SO and Coulomb repulsion U reveals that, while the prodromes of an underlying insulating state are already found in LDA+SO, the correct gap magnitude can only be reproduced by LDA+SO+U, with U=3  eV. This establishes Na2IrO3 as a novel type of Mott-like correlated insulator in which Coulomb and relativistic effects have to be treated on an equal footing.

Magnetic symmetries in neutron and resonant x-ray Bragg diffraction patterns of four iridium oxides

The magnetic properties of Sr(2)IrO(4), Na(2)IrO(3), Sr(3)Ir(2)O(7) and CaIrO(3) are discussed, principally in the light of experimental data in recent literature for Bragg intensities measured in x-ray diffraction with enhancement at iridium L-absorption edges. The electronic structure factors we report, which incorporate parity-even and acentric entities, serve the immediate purpose of making full use of crystal and magnetic symmetry to refine our knowledge of the magnetic properties of the four iridates from resonant x-ray diffraction data. They also offer a platform on which to interpret future investigations, using dichroic signals, resonant x-ray diffraction and neutron diffraction, for example, as well as ab initio calculations of electronic structure. Unit-cell structure factors, suitable for x-ray Bragg diffraction enhanced by an electric dipole-electric dipole (E1-E1) event, reveal exactly which iridium multipoles are visible, e.g., a magnetic dipole parallel to the crystal c-axis (z-axis) and an electric quadrupole with yz-like symmetry in the specific case of CaIrO(3). Magnetic space-groups are assigned to Sr(2)IrO(4), Sr(3)Ir(2)O(7) and CaIrO(3), namely, P(I)cca, P(A)ban and Cm'cm', respectively, in the Belov-Neronova-Smirnova notation. The assignment for Sr(2)IrO(4) is possible because of our new high-resolution neutron diffraction data, gathered on a powder sample. In addition, the new data are used to show that the ordered magnetic moment of an Ir(4+) ion in Sr(2)IrO(4) does not exceed 0.29(4) μ(B). Na(2)IrO(3) has two candidate magnetic space-groups that are not resolved with currently available resonant x-ray data.

Magnetic couplings, optical spectra, and spin-orbit exciton in 5d electron Mott insulator Sr2IrO4

Based on the microscopic model including spin-orbit coupling, on-site Coulomb and Hund's interactions, as well as crystal field effects, we investigate the magnetic and optical properties of Sr(2)IrO(4). Taking into account all intermediate state multiplets generated by virtual hoppings of electrons, we calculate the isotropic, pseudodipolar, and Dzyaloshinsky-Moriya coupling constants, which describe the experiment quite well. The optical conductivity σ(ω) evaluated by the exact diagonalization method shows two peaks at ~0.5 and ~1.0 eV in agreement with experiment. The two-peak structure of σ(ω) arises from the unusual Fano-type overlap between the electron-hole continuum of the J(eff)=1/2 band and the intrasite spin-orbit exciton observed recently in Sr(2)IrO(4).

The Jeff = 1/2 insulator Sr3Ir2O7 studied by means of angle-resolved photoemission spectroscopy

The low-energy electronic structure of the J(eff) = 1/2 spin-orbit insulator Sr3Ir2O7 has been studied by means of angle-resolved photoemission spectroscopy. A comparison of the results for bilayer Sr3Ir2O7 with available literature data for the related single-layer compound Sr2IrO4 reveals qualitative similarities and similar J(eff) = 1/2 bandwidths for the two materials, but also pronounced differences in the distribution of the spectral weight. In particular, photoemission from J(eff) = 1/2 the states appears to be suppressed. Yet, it is found that the Sr3Ir2O7 data are in overall better agreement with band-structure calculations than the data for Sr2IrO4.

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

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

Testing the validity of the strong spin-orbit-coupling limit for octahedrally coordinated iridate compounds in a model system Sr3CuIrO6

The electronic structure of Sr3CuIrO6, a model system for the 5d Ir ion in an octahedral environment, is studied through a combination of resonant inelastic x-ray scattering and theoretical calculations. Resonant inelastic x-ray scattering spectra at the Ir L3 edge reveal an Ir t(2g) manifold that is split into three levels, in contrast to the expectations of the strong spin-orbit-coupling limit. Effective Hamiltonian and ab inito quantum chemistry calculations find a strikingly large noncubic crystal field splitting comparable to the spin-orbit coupling, which results in a strong mixing of the j(eff)=1/2 and j(eff)=3/2 states and modifies the isotropic wave functions on which many theoretical models are based.

Magnetic correlations in a layered iridate, Na2IrO3

Analysis of published data gathered on a sample of Na(2)IrO(3), held deep inside the antiferromagnetic phase at 1.58 K, shows that iridium magnetic dipole moments, measured in resonant x-ray Bragg diffraction, lie in the a-c plane of the monoclinic crystal and enclose an angle ≈118° with the c-axis. These findings, together with bulk measurements, are united in a plausible magnetic ground state for an iridium ion constructed from a Kramers doublet. A magnetic space group, derived from the chemical space group C2/m (unique axis b), possesses an anti-translation, to accommodate antiferromagnetic order, and an odd, two-fold axis of rotation symmetry on the b-axis, C'(2b), placing Ir magnetic dipoles perpendicular to the b-axis. Anapoles (toroidal dipoles) are predicted to be likewise confined to the a-c plane, and magnetic charges forbidden.

Strong magnetic instability in correlated metallic Bi2Ir2O7

We report an experimental/theoretical study of single-crystal Bi(2)Ir(2)O(7) that possesses a metallic state with strongly exchange-enhanced paramagnetism. The ground state of Bi(2)Ir(2)O(7) is characterized by the following features: (1) a divergent low-temperature magnetic susceptibility that indicates no long-range order down to 50 mK; (2) strongly field-dependent coefficients of the low-temperature T and T(3) terms of the specific heat; (3) a conspicuously large Wilson ratio R(W) ≈ 53.5; and (4) unusual temperature and field dependences of the Hall resistivity that abruptly change below 80 K, without any clear correlation with the magnetic behavior. All these unconventional properties suggest the existence of an exotic ground state in Bi(2)Ir(2)O(7).

On the magnetic structure of Sr3Ir2O7: an x-ray resonant scattering study

This report presents azimuthal dependent and polarization dependent x-ray resonant magnetic scattering at the Ir L(3) edge for the bilayered iridate compound Sr(3)Ir(2)O(7). The two magnetic wave vectors, k1 = (1/2, 1/2, 0) and k2 = (1/2, -1/2, 0), result in domains of two symmetry-related G-type antiferromagnetic structures, denoted A and B, respectively. These domains are approximately 0.02 mm(2) and are independent of the thermal history. An understanding of this key aspect of the magnetism is necessary for an overall picture of the magnetic behaviour in this compound. The azimuthal and polarization dependence of the magnetic reflections, relating to both magnetic wavevectors, show that the Ir magnetic moments in the bilayer compound are oriented along the c axis. This contrasts with single layer Sr(2)IrO(4) where the moments are confined to the ab plane.

Dimensionality driven spin-flop transition in layered iridates

Using resonant x-ray diffraction, we observe an easy c-axis collinear antiferromagnetic structure for the bilayer Sr3Ir2O7, a significant contrast to the single layer Sr2IrO4 with in-plane canted moments. Based on a microscopic model Hamiltonian, we show that the observed spin-flop transition as a function of number of IrO2 layers is due to strong competition among intra- and interlayer bond-directional pseudodipolar interactions of the spin-orbit entangled J(eff)=1/2 moments. With this we unravel the origin of anisotropic exchange interactions in a Mott insulator in the strong spin-orbit coupling regime, which holds the key to the various types of unconventional magnetism proposed in 5d transition metal oxides.

Pressure tuning of the spin-orbit coupled ground state in Sr2IrO4

X-ray absorption spectroscopy studies of the magnetic-insulating ground state of Sr2IrO4 at ambient pressure show a clear deviation from a strong spin-orbit (SO) limit J(eff)=1/2 state, a result of local exchange interactions and a nonzero tetragonal crystal field mixing SO split J(eff)=1/2, 3/2 states. X-ray magnetic circular dichroism measurements in a diamond anvil cell show a magnetic transition at a pressure of ∼17  GPa, where the "weak" ferromagnetic moment is quenched despite transport measurements showing insulating behavior to at least 40 GPa. The magnetic transition has implications for the origin of the insulating gap and the nature of exchange interactions in this SO coupled system. The expectation value of the angular part of the SO interaction, <L·S>, extrapolates to zero at ∼80-90  GPa where an increased bandwidth strongly mixes J(eff)=1/2, 3/2 states and SO interactions no longer dominate the electronic ground state of Sr2IrO4.

Noncollinear magnetism and spin-orbit coupling in 5d pyrochlore oxide Cd2Os2O7

We investigate the electronic and magnetic properties of the pyrochlore oxide Cd2Os2O7 using the density-functional theory plus on-site repulsion (U) method, and depict the ground-state phase diagram with respect to U. We conclude that the all-in-all-out noncollinear magnetic order is stable in a wide range of U. We also show that the easy-axis anisotropy arising from the spin-orbit coupling plays a significant role in stabilizing the all-in-all-out magnetic order. A pseudogap was observed near the transition between the antiferromagnetic metallic and insulating phases. Finally, we discuss possible origins of the peculiar low-temperature (T) properties observed in experiments.

Two-dimensional Heisenberg behavior of J(eff)=1/2 isospins in the paramagnetic state of the spin-orbital Mott insulator Sr2IrO4

The dynamical correlations of J(eff)=1/2 isospins in the paramagnetic state of spin-orbital Mott insulator Sr2IrO4 were revealed by resonant magnetic x-ray diffuse scattering. We found a two-dimensional antiferromagnetic fluctuation with a large in-plane correlation length exceeding 100 lattice spacings at even 20 K above the magnetic ordering temperature. In marked contrast to the naive expectation of the strong magnetic anisotropy associated with an enhanced spin-orbit coupling, we discovered an isotropic isospin correlation that is well described by the two-dimensional S=1/2 quantum Heisenberg model. The estimated antiferromagnetic coupling constant as large as J∼0.1  eV that is comparable to the small Mott gap (<0.5  eV) points out the weak and marginal Mott character of this spin-orbital entangled system.

Rh2O3 versus IrO2: relativistic effects and the stability of Ir4+

Despite the wide-ranging applications of binary Rh and Ir oxides, their stability and trends in Rh and Ir oxidation states are not fully understood. Using first-principles electronic structure calculations, we demonstrate that the origin of the categorical stability of Ir(4+) is the relativistic contraction of the 6s orbital and, consequently, an expansion of 5d orbitals. Relativistic effects significantly stabilize Ir(4+)-containing metallic rutile IrO(2) over a wide range of O chemical potentials, despite the choice that Ir has of forming semiconducting corundum Ir(2)O(3). In contrast, Rh is found to display a wider stability range for corundum Rh(2)O(3) with Rh(3+) and a greater propensity for multiple oxidation states.

Magnetic excitation spectra of Sr2IrO4 probed by resonant inelastic x-ray scattering: establishing links to cuprate superconductors

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

Spin waves and revised crystal structure of honeycomb iridate Na2IrO3

We report inelastic neutron scattering measurements on Na2IrO3, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zigzag magnetic order. The onset of long-range magnetic order below T(N)=15.3  K is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90° Ir-O-Ir bonds required for dominant Kitaev exchange.