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

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.

Metal-insulator transition in SrIrO3 with strong spin-orbit interaction

The thickness-dependent metal-insulator transition is observed in meta-stable orthorhombic SrIrO3 thin films synthesized by pulsed laser deposition. SrIrO3 films with thicknesses less than 3 nm demonstrate insulating behaviour, whereas those thicker than 4 nm exhibit metallic conductivity at high temperature, and insulating-like behaviour at low temperature. Weak/Anderson localization is mainly responsible for the observed thickness-dependent metal-insulator transition in SrIrO3 films. Temperature-dependent resistance fitting shows that electrical-conductivity carriers are mainly scattered by the electron-boson interaction rather than the electron-electron interaction. Analysis of the magneto-conductance proves that the spin-orbit interaction plays a crucial role in the magneto-conductance property of SrIrO3.

Magnetic state of pyrochlore Cd(2)Os(2)O(7) emerging from strong competition of ligand distortions and longer-range crystalline anisotropy

By many-body quantum-chemical calculations, we investigate the role of two structural effects--local ligand distortions and the anisotropic Cd-ion coordination--on the magnetic state of Cd(2)Os(2)O(7), a spin S = 3/2 pyrochlore. We find that these effects strongly compete, rendering the magnetic interactions and ordering crucially dependent on these geometrical features. Without trigonal distortions, a large easy-plane magnetic anisotropy develops. Their presence, however, reverses the sign of the zero-field splitting and causes a large easy-axis anisotropy (D ≃ -6.8 meV), which in conjunction with the antiferromagnetic exchange interaction (J ≃ 6.4 meV) stabilizes an all-in-all-out magnetic order. The competition uncovered here is a generic feature of pyrochlore magnets.

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.

Theory of high Tc ferrimagnetism in a multiorbital Mott insulator

We propose a model for the multiorbital material Sr(2)CrOsO(6), an insulator with remarkable magnetic properties and the highest T(c) ~/= 725 K among all perovskites with a net moment. We derive a new criterion for the Mott transition (U(1)U(2))(1/2)>2.5W by using slave-rotor mean field theory, where W is the bandwidth and U(1(2)) are the effective Coulomb interactions on Cr(Os) including Hund's coupling. We show that Sr(2)CrOsO(6) is a Mott insulator, where the large Cr U(1) compensates for the small Os U(2). The spin sector is described by a frustrated antiferromagnetic Heisenberg model that naturally explains the net moment arising from canting and also the observed nonmonotonic magnetization M(T). We predict characteristic magnetic structure factor peaks that can be probed by neutron experiments.

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).

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.

The Reference Genome of the Halophytic Plant Eutrema salsugineum

Halophytes are plants that can naturally tolerate high concentrations of salt in the soil, and their tolerance to salt stress may occur through various evolutionary and molecular mechanisms. Eutrema salsugineum is a halophytic species in the Brassicaceae that can naturally tolerate multiple types of abiotic stresses that typically limit crop productivity, including extreme salinity and cold. It has been widely used as a laboratorial model for stress biology research in plants. Here, we present the reference genome sequence (241 Mb) of E. salsugineum at 8× coverage sequenced using the traditional Sanger sequencing-based approach with comparison to its close relative Arabidopsis thaliana. The E. salsugineum genome contains 26,531 protein-coding genes and 51.4% of its genome is composed of repetitive sequences that mostly reside in pericentromeric regions. Comparative analyses of the genome structures, protein-coding genes, microRNAs, stress-related pathways, and estimated translation efficiency of proteins between E. salsugineum and A. thaliana suggest that halophyte adaptation to environmental stresses may occur via a global network adjustment of multiple regulatory mechanisms. The E. salsugineum genome provides a resource to identify naturally occurring genetic alterations contributing to the adaptation of halophytic plants to salinity and that might be bioengineered in related crop species.

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.

Critical properties of the Kitaev-Heisenberg model

We study the critical properties of the Kitaev-Heisenberg model on the honeycomb lattice at finite temperatures that might describe the physics of the quasi-two-dimensional compounds, Na(2)IrO(3) and Li(2)IrO(3). The model undergoes two phase transitions as a function of temperature. At low temperature, thermal fluctuations induce magnetic long-range order by the order-by-disorder mechanism. This magnetically ordered state with a spontaneously broken Z(6) symmetry persists up to a certain critical temperature. We find that there is an intermediate phase between the low-temperature, ordered phase and the high-temperature, disordered phase. Finite-sized scaling analysis suggests that the intermediate phase is a critical Kosterlitz-Thouless phase with continuously variable exponents. We argue that the intermediate phase has been observed above the low-temperature, magnetically ordered phase in Na(2)IrO(3), and also, likely exists in Li(2)IrO(3).

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.

Variation of charge dynamics in the course of metal-insulator transition for pyrochlore-type Nd2Ir2O7

We have spectroscopically investigated the thermally and doping-induced metal-insulator transitions for pyrochlore-type Nd2Ir2O7 as well as its Rh-doped analogs Nd2(Ir(1-x)Rh(x))(2)O(7), where the spin-orbit interaction as well as the electron correlation is effectively tuned by the doping level (x). The charge dynamics dramatically changes on an energy scale of 1 eV in the course of thermally and doping-induced metal-insulator transitions, while the insulating ground state shows a small but well-defined charge gap of 45 meV. Anomalous doping variation of the low-energy (<0.3 eV) optical-conductivity spectra at the ground state can be interpreted in terms of the phase changes among the narrow-gap Mott insulator, Weyl semimetal, and correlated metal.

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).

Correlation effects on 3D topological phases: from bulk to boundary

Topological phases of quantum matter defy characterization by conventional order parameters but can exhibit a quantized electromagnetic response and/or protected surface states. We examine such phenomena in a model for three-dimensional correlated complex oxides, the pyrochlore iridates. The model realizes interacting topological insulators, with and without time-reversal symmetry, and topological Weyl semimetals. We use cellular dynamical mean-field theory, a method that incorporates quantum many-body effects and allows us to evaluate the magnetoelectric topological response coefficient in correlated systems. This invariant is used to unravel the presence of an interacting axion insulator absent within a simple mean-field study. We corroborate our bulk results by studying the evolution of the topological boundary states in the presence of interactions. Consequences for experiments and for the search for correlated materials with symmetry-protected topological order are given.

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.

Magnetically driven metal-insulator transition in NaOsO3

The metal-insulator transition (MIT) is one of the most dramatic manifestations of electron correlations in materials. Various mechanisms producing MITs have been extensively considered, including the Mott (electron localization via Coulomb repulsion), Anderson (localization via disorder), and Peierls (localization via distortion of a periodic one-dimensional lattice) mechanisms. One additional route to a MIT proposed by Slater, in which long-range magnetic order in a three dimensional system drives the MIT, has received relatively little attention. Using neutron and x-ray scattering we show that the MIT in NaOsO(3) is coincident with the onset of long-range commensurate three dimensional magnetic order. While candidate materials have been suggested, our experimental methodology allows the first definitive demonstration of the long predicted Slater MIT.

Tetrahedral magnetic order and the metal-insulator transition in the pyrochlore lattice of Cd2Os2O7

Cd2Os2O7 shows a peculiar metal-insulator transition at 227 K with magnetic ordering in a frustrated pyrochlore lattice, but its magnetic structure in the ordered state and the transition origin are yet uncovered. We observed a commensurate magnetic peak by resonant x-ray scattering in a high-quality single crystal. X-ray diffraction and Raman scattering experiments confirmed that the transition is not accompanied with any spatial symmetry breaking. We propose a noncollinear all-in-all-out spin arrangement on the tetrahedral network made of Os atoms. Based on this we suggest that the transition is not caused by the Slater mechanism as believed earlier but by an alternative mechanism related to the formation of the specific tetrahedral magnetic order on the pyrochlore lattice in the presence of strong spin-orbit interactions.

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.

Computational design of axion insulators based on 5d spinel compounds

Based on density functional calculation using the local density approximation+U method, we predict that osmium compounds such as CaOs(2)O(4) and SrOs(2)O(4) can be stabilized in the geometrically frustrated spinel crystal structure. They show ferromagnetic order in a reasonable range of the on-site Coulomb correlation U and exotic electronic properties, in particular, a large magnetoelectric coupling characteristic of axion electrodynamics. Depending on U, other electronic phases including a 3D Weyl semimetal and Mott insulator are also shown to occur.

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.

Subband structure of a two-dimensional electron gas formed at the polar surface of the strong spin-orbit perovskite KTaO3

We demonstrate the formation of a two-dimensional electron gas (2DEG) at the (100) surface of the 5d transition-metal oxide KTaO3. From angle-resolved photoemission, we find that quantum confinement lifts the orbital degeneracy of the bulk band structure and leads to a 2DEG composed of ladders of subband states of both light and heavy carriers. Despite the strong spin-orbit coupling, our measurements provide a direct upper bound for the potential Rashba spin splitting of only Δk(parallel)}~0.02 Å(-1) at the Fermi level. The polar nature of the KTaO3(100) surface appears to help mediate the formation of the 2DEG as compared to nonpolar SrTiO3(100).

Topological quantum phase transition in 5d transition metal oxide Na2IrO3

We predict a quantum phase transition from normal to topological insulators in the 5d transition metal oxide Na2IrO3, where the transition can be driven by the change of the long-range hopping and trigonal crystal field terms. From the first-principles-derived tight-binding Hamiltonian, we determine the phase boundary through the parity analysis. In addition, our first-principles calculations for Na2IrO3 model structures show that the interlayer distance can be an important parameter for the existence of a three-dimensional strong topological insulator phase. Na2IrO3 is suggested to be a candidate material which can have both a nontrivial topology of bands and strong electron correlations.

Ab initio studies on the interplay between spin-orbit interaction and Coulomb correlation in Sr2IrO4 and Ba2IrO4

Ab initio analyses of A(2)IrO(4) (A=Sr,Ba) are presented. Effective Hubbard-type models for Ir 5d t(2g) manifolds downfolded from the global band structure are solved based on the dynamical mean-field theory. The results for A=Sr and Ba correctly reproduce paramagnetic metals undergoing continuous transitions to insulators below the Néel temperature T(N). These compounds are classified not into Mott insulators but into Slater insulators. However, the insulating gap opens by a synergy of the Néel order and significant band renormalization, which is also manifested by a 2D bad metallic behavior in the paramagnetic phase near the quantum criticality.

X-ray absorption spectroscopy studies of spin-orbit coupling in 5d transition metal oxides

In order to examine the effects of strong valence band spin-orbit coupling (SOC) in 5d transition metal oxides (TMOs), we have investigated the L(2) and L(3) edge white-line intensities of the x-ray absorption spectra of several 5d TMOs. The white-line intensities at both edges are found to decrease monotonously with increasing 5d electron occupancy, while their ratio showed anomalous behavior for late 5d TMOs (IrO(2), PtO(2), and Au(2)O(3)), deviating significantly from the theoretical value of 2 expected for the case of weak SOC. This observation serves as a clear experimental indication of strong SOC effects in 5d TMOs. We also discussed how the 5d TMOs can have charge transfer effects different from their counterpart 5d elemental metals by making comparative studies. Our works demonstrate the importance of j quantum states due to strong SOC in the 5d system.

Reduced effective spin-orbital degeneracy and spin-orbital ordering in paramagnetic transition-metal oxides: Sr2IrO4 versus Sr2RhO4

We discuss the notions of spin-orbital polarization and ordering in paramagnetic materials, and address their consequences in transition-metal oxides. Extending the combined density functional and dynamical mean field theory scheme to the case of materials with large spin-orbit interactions, we investigate the electronic excitations of the paramagnetic phases of Sr(2)IrO(4) and Sr(2)RhO(4). We show that the interplay of spin-orbit interactions, structural distortions and Coulomb interactions suppresses spin-orbital fluctuations. As a result, the room temperature phase of Sr(2)IrO(4) is a paramagnetic spin-orbitally ordered Mott insulator. In Sr(2)RhO(4), the effective spin-orbital degeneracy is reduced, but the material remains metallic, due to both, smaller spin-orbit and smaller Coulomb interactions. The corresponding spectra are in excellent agreement with photoemission data. Finally, we make predictions for the spectra of paramagnetic Sr(2)IrO(4).

Twisted Hubbard model for Sr2IrO4: magnetism and possible high temperature superconductivity

Sr(2)IrO(4) has been suggested as a Mott insulator from a single J(eff)=1/2 band, similar to the cuprates. However, this picture is complicated by the measured large magnetic anisotropy and ferromagnetism. Based on a careful mapping to the J(eff)=1/2 (pseudospin-1/2) space, we propose that the low energy electronic structure of Sr(2)IrO(4) can indeed be described by a SU(2) invariant pseudospin-1/2 Hubbard model very similar to that of the cuprates, but with a twisted coupling to an external magnetic field (a g tensor with a staggered antisymmetric component). This perspective naturally explains the magnetic properties of Sr(2)IrO(4). We also derive several simple facts based on this mapping and the known results about the Hubbard model and the cuprates, which may be tested in future experiments on Sr(2)IrO(4). In particular, we propose that (electron-)doping Sr(2)IrO(4) can potentially realize high-temperature superconductivity.

Topological magnetic insulators with corundum structure

Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap are protected by time-reversal symmetry. When a proper kind of antiferromagnetic long-range order is established in a topological insulator, the system supports axionic excitations. In this Letter, we study theoretically the electronic states in a transition metal oxide of corundum structure, in which both spin-orbit interaction and electron-electron interaction play crucial roles. A tight-binding model analysis predicts that materials with this structure can be strong topological insulators. Because of the electron correlation, an antiferromagnetic order may develop, giving rise to a topological magnetic insulator phase with axionic excitations.

Theory of electric polarization in multiorbital Mott insulators

The interaction between the electric field E and spins in multiorbital Mott insulators is studied theoretically. We find a generic coupling mechanism, which works for all crystal lattices and which does not involve relativistic effects. It couples E to the "internal" electric field e originating from the dynamical Berry phase. We discuss several effects of this interaction: (i) an unusual electron spin resonance, (ii) the displacement of spin textures in an applied electric field, and (iii) the resonant absorption of circularly polarized light by Skyrmions, magnetic bubbles, and magnetic vortices.

Microscopic study of a spin-orbit-induced Mott insulator in Ir oxides

Motivated by recent experiments of a novel 5d Mott insulator in Sr2IrO4, we have studied the two-dimensional three-orbital Hubbard model with a spin-orbit coupling λ. The variational Monte Carlo method is used to obtain the ground state phase diagram with varying an on-site Coulomb interaction U as well as λ. It is found that the transition from a paramagnetic metal to an antiferromagnetic insulator occurs at a finite U=U(MI), which is greatly reduced by a large λ, characteristic of 5d electrons, and leads to the "spin-orbit-induced" Mott insulator. It is also found that the Hund's coupling induces the anisotropic spin exchange and stabilizes the in-plane antiferromagnetic order. We have further studied the one-particle excitations by using the variational cluster approximation and revealed the internal electronic structure of this novel Mott insulator. These findings are in agreement with experimental observations on Sr2IrO4.

Orbital magnetism and spin-orbit effects in the electronic structure of BaIrO3

The electronic structure and magnetism of Ir 5d5 states in nonmetallic, weakly ferromagnetic BaIrO3 are probed with x-ray absorption techniques. Contrary to expectation, the Ir 5d orbital moment is found to be ~1.5 times larger than the spin moment. This unusual, atomiclike nature of the 5d moment is driven by a strong spin-orbit interaction in heavy Ir ions, as confirmed by the nonstatistical large branching ratio at Ir L(2,3) absorption edges. As a consequence, orbital interactions cannot be neglected when addressing the nature of magnetic ordering in BaIrO3. The local moment behavior persists even as the metallic-paramagnetic phase boundary is approached with Sr doping or applied pressure.

Crystal growth and structure and magnetic properties of the 5d oxide Ca3LiOsO6: extended superexchange magnetic interaction in oxide

Crystals of the newly synthesized compound Ca(3)LiOsO(6) were grown by a flux method using LiCl and KCl, followed by single-crystal X-ray diffraction (XRD), low-temperature powder XRD, and measurements of ac and dc magnetic susceptibility and specific heat. The data indicate that Ca(3)LiOsO(6) has a fully opened electronic gap with an antiferromagnetic ordered state, consistent with suggestions from the first-principles study. The observed magnetic transition temperature is 117 K, too high to be caused only by a direct spin-spin interaction. It appears that the original superexchange magnetic path Os-O-Os is absent; thus, the extended superexchange path (Os-O)-(O-Os) can be expected to be responsible for the 117 K magnetic order. If this is true, Ca(3)LiOsO(6) would be highly valuable to study the nature of extended superexchange magnetic interactions in solids.

Electronic structure of double perovskite A2FeReO6 (A = Ba and Ca): interplay between spin-orbit interaction, electron correlation, and lattice distortion

We have investigated the electronic structure of double perovskites, Ba(2)FeReO(6) (metallic) and Ca(2)FeReO(6) (insulating) using optical and x-ray absorption spectroscopy. By comparing the experimental results with the density functional theory calculations, we found that the electronic structure of Ba(2)FeReO(6) could be determined from the interaction of the electron correlation and spin-orbit coupling. On the other hand, for Ca(2)FeReO(6), the lattice distortion and electron correlation are important in determining the electronic structure. Additionally, the insulating gap in Ca(2)FeReO(6) is realized by the spin-orbit coupling. Our work shows that the subtle interplay of the spin-orbit interaction, electron correlation, and lattice distortion should be taken into account to understand the electronic structure of the 5d transition metal oxides.

Kitaev-Heisenberg model on a honeycomb lattice: possible exotic phases in iridium oxides A2IrO3

We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir4+ ions in a family of layered iridates A2IrO3 (A=Li,Na). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Néel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is the exact ground state of the model at the midpoint between two limits.

Three-dimensional topological insulators on the pyrochlore lattice

Electrons hopping on the sites of a three-dimensional pyrochlore lattice are shown to form topologically nontrivial insulating phases when the spin-orbit (SO) coupling and lattice distortions are present. Of 16 possible topological classes 9 are realized for various parameters in this model. Specifically, at half-filling an undistorted pyrochlore lattice with a SO term yields a "pristine" strong topological insulator with a Z(2) index (1;000). At quarter filling various strong and weak topological phases are obtained provided that both SO coupling and uniaxial lattice distortion are present. Our analysis suggests that many of the nonmagnetic insulating pyrochlores could be topological insulators.

Quantum spin Hall effect in a transition metal oxide Na2IrO3

We study theoretically the electronic states in a 5d transition metal oxide Na2IrO3, in which both the spin-orbit interaction and the electron correlation play crucial roles. A tight-binding model analysis together with the first-principles band structure calculation predicts that this material is a layered quantum spin Hall system. Because of the electron correlation, an antiferromagnetic order first develops at the edge, and later inside the bulk at low temperatures.