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

Time-reversal symmetry breaking hidden order in Sr2(Ir,Rh)O4

Layered 5d transition iridium oxides, Sr₂(Ir,Rh)O₄, are described as unconventional Mott insulators with strong spin-orbit coupling. The undoped compound, Sr₂IrO₄, is a nearly ideal two-dimensional pseudospin-1/2 Heisenberg antiferromagnet, similarly to the insulating parent compound of high-temperature superconducting copper oxides. Using polarized neutron diffraction, we here report a hidden magnetic order in pure and doped Sr₂(Ir,Rh)O₄, distinct from the usual antiferromagnetic pseudospin ordering. We find that time-reversal symmetry is broken while the lattice translation invariance is preserved in the hidden order phase. The onset temperature matches that of the odd-parity hidden order recently highlighted using optical second-harmonic generation experiments. The novel magnetic order and broken symmetries can be explained by the loop-current model, previously predicted for the copper oxide superconductors.

Charge Transfer in Iridate-Manganite Superlattices

Charge transfer in superlattices consisting of SrIrO₃ and SrMnO₃ is investigated using density functional theory. Despite the nearly identical work function and nonpolar interfaces between SrIrO₃ and SrMnO₃, rather large charge transfer was experimentally reported at the interface between them. Here, we report a microscopic model that captures the mechanism behind this phenomenon, providing a qualitative understanding of the experimental observation. This leads to unique strain dependence of such charge transfer in iridate-manganite superlattices. The predicted behavior is consistently verified by experiment with soft X-ray and optical spectroscopy. Our work thus demonstrates a new route to control electronic states in nonpolar oxide heterostructures.

Strong Spin-Phonon Coupling Mediated by Single Ion Anisotropy in the All-In-All-Out Pyrochlore Magnet Cd_{2}Os_{2}O_{7}

Spin-phonon coupling mediated by single ion anisotropy was investigated using optical spectroscopy and first-principles calculations in the all-in-all-out pyrochlore magnet Cd_{2}Os_{2}O_{7}. Clear anomalies were observed in both the phonon frequencies and linewidths at the magnetic ordering temperature. The renormalization of the phonon modes was exceptionally large, signifying the presence of an unconventional magnetoelastic term from large spin-orbit coupling. In addition, the relative phonon frequency shifts show a strong correlation with the modulation of noncubic crystal field by the corresponding lattice distortion. Our observation establishes a new type of spin-phonon coupling through single ion anisotropy, a second-order spin-orbit coupling term, in Cd_{2}Os_{2}O_{7}.

Magnetic and electronic properties of La3 MO7 and possible polaron formation in hole-doped La3 MO7 (M = Ru and Os)

Oxides with 4d/5d transition metal ions are physically interesting for their particular crystalline structures as well as the spin-orbit coupled electronic structures. Recent experiments revealed a series of 4d/5d transition metal oxides R ₃ MO₇ (R: rare earth; M: 4d/5d transition metal) with unique quasi-one-dimensional M chains. Here first-principles calculations have been performed to study the electronic structures of La₃OsO₇ and La₃RuO₇. Our study confirm both of them to be Mott insulating antiferromagnets with identical magnetic order. The reduced magnetic moments, which are much smaller than the expected value for ideal high-spin state (3 t _2g orbitals occupied), are attributed to the strong p  -  d hybridization with oxygen ions, instead of the spin-orbit coupling. The Ca-doping to La₃OsO₇ and La₃RuO₇ can not only modulate the nominal carrier density but also affect the orbital order as well as the local distortions. The Coulombic attraction and particular orbital order would prefer to form polarons, which might explain the puzzling insulating behavior of doped 5d transition metal oxides. In addition, our calculations predict that the Ca-doping can trigger ferromagnetism in La₃RuO₇ but not in La₃OsO₇.

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

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

Spin-Glass-Like Behavior and Topological Hall Effect in SrRuO3/SrIrO3 Superlattices for Oxide Spintronics Applications

The heterostructure interface provides a powerful platform for exploring rich emergent phenomena, such as interfacial superconductivity and nontrivial topological surface states. Here, SrRuO₃/SrIrO₃ superlattices were epitaxially synthesized. The magnetic and magneto-transport properties of these superlattices were characterized. A broad cusp-type splitting in the zero-field-cooling/field-cooling temperature-dependent magnetization and magnetization relaxation, which follows the modified stretched function model, accompanied by double hysteresis magnetization loops were demonstrated. These physical effects were modulated by the SrIrO₃ layer thickness, which confirms the coexistence of interfacial spin glass and ferromagnetic ordering in the superlattices. In addition, the topological Hall effect was observed at low temperatures, and it is weakened with the increase of the SrIrO₃ layer thickness. These results suggest that a noncoplanar spin texture is generated at the SrRuO₃/SrIrO₃ interfaces because of the interfacial Dzyaloshinskii-Moriya interaction. This work demonstrates that SrIrO₃ can effectively induce interfacial Dzyaloshinskii-Moriya interactions in superlattices, which would serve as a mechanism to develop spintronic devices with perovskite oxides.

New Class of 3D Topological Insulator in Double Perovskite

We predict a new class of 3D topological insulators (TIs) in which the spin-orbit coupling (SOC) can more effectively generate band gap. Band gap of conventional TI is mainly limited by two factors, the strength of SOC and, from electronic structure perspective, the band gap when SOC is absent. While the former is an atomic property, the latter can be minimized in a generic rock-salt lattice model in which a stable crossing of bands at the Fermi level along with band character inversion occurs in the absence of SOC. Thus large-gap TIs or TIs composed of lighter elements can be expected. In fact, we find by performing first-principles calculations that the model applies to a class of double perovskites A₂BiXO₆ (A = Ca, Sr, Ba; X = Br, I) and the band gap is predicted up to 0.55 eV. Besides, surface Dirac cones are robust against the presence of dangling bond at boundary.

Metal-Insulator Transition and Topological Properties of Pyrochlore Iridates

Combining density functional theory (DFT) and embedded dynamical mean-field theory (DMFT) methods, we study the metal-insulator transition in R_{2}Ir_{2}O_{7} (R=Y, Eu, Sm, Nd, Pr, and Bi) and the topological nature of the insulating compounds. Accurate free energies evaluated using the charge self-consistent DFT+DMFT method reveal that the metal-insulator transition occurs for an A-cation radius between that of Nd and Pr, in agreement with experiments. The all-in-all-out magnetic phase, which is stable in the Nd compound but not the Pr one, gives rise to a small Ir^{4+} magnetic moment of ≈0.4  μ_{B} and opens a sizable correlated gap. We demonstrate that within this state-of-the-art theoretical method, the insulating bulk pyrochlore iridates are topologically trivial.

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.

Ambipolar transport and magneto-resistance crossover in a Mott insulator, Sr2IrO4

Electric field effect (EFE) controlled magnetoelectric transport in thin films of undoped and La-doped Sr₂IrO₄ (SIO) is investigated using ionic liquid gating. The temperature dependent resistance measurements exhibit insulating behavior in chemically and EFE doped samples with the band filling up to 10%. The ambipolar transport across the Mott gap is demonstrated by EFE tuning of the channel resistance and chemical doping. We observe a crossover from high temperature negative to low temperature positive magnetoresistance around  ∼80-90 K, irrespective of the filling. This temperature and magnetic field dependent crossover is discussed in the light of conduction mechanisms of SIO, especially variable range hopping (VRH), and its relevance to the insulating ground state of SIO.

Electronic Structure of the Kitaev Material α-RuCl3 Probed by Photoemission and Inverse Photoemission Spectroscopies

Recently, α-RuCl₃ has attracted much attention as a possible material to realize the honeycomb Kitaev model of a quantum-spin-liquid state. Although the magnetic properties of α-RuCl₃ have been extensively studied, its electronic structure, which is strongly related to its Kitaev physics, is poorly understood. Here, the electronic structure of α-RuCl₃ was investigated by photoemission (PE) and inverse-photoemission (IPE) spectroscopies. The band gap was directly measured from the PE and IPE spectra and was found to be 1.9 eV, much larger than previously estimated values. Local density approximation (LDA) calculations showed that the on-site Coulomb interaction U could open the band gap without spin-orbit coupling (SOC). However, the SOC should also be incorporated to reproduce the proper gap size, indicating that the interplay between U and SOC plays an essential role. Several features of the PE and IPE spectra could not be explained by the results of LDA calculations. To explain such discrepancies, we performed configuration-interaction calculations for a RuCl₆^3- cluster. The experimental data and calculations demonstrated that the 4d compound α-RuCl₃ is a J_eff = 1/2 Mott insulator rather than a quasimolecular-orbital insulator. Our study also provides important physical parameters required for verifying the proposed Kitaev physics in α-RuCl₃.

Orbital-Dependent Band Narrowing Revealed in an Extremely Correlated Hund's Metal Emerging on the Topmost Layer of Sr_{2}RuO_{4}

We use a surface-selective angle-resolved photoemission spectroscopy and unveil the electronic nature on the topmost layer of Sr_{2}RuO_{4} crystal, consisting of slightly rotated RuO_{6} octahedrons. The γ band derived from the 4d_{xy} orbital is found to be about three times narrower than that for the bulk. This strongly contrasts with a subtle variation seen in the α and β bands derived from the one-dimensional 4d_{xz/yz}. This anomaly is reproduced by the dynamical mean-field theory calculations, introducing not only the on-site Hubbard interaction but also the significant Hund's coupling. We detect a coherence-to-incoherence crossover theoretically predicted for Hund's metals, which has been recognized only recently. The crossover temperature in the surface is about half that of the bulk, indicating that the naturally generated monolayer of reconstructed Sr_{2}RuO_{4} is extremely correlated and well isolated from the underlying crystal.

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.

Post-perovskite CaIrO3: a conventional Slater type antiferromagnetic insulator

To resolve the controversy of whether or not the origin of an electronic gap in antiferromagnetic post-perovskite (pPv) CaIrO₃ is due to Coulomb repulsion or spin-orbit coupling, and/or both, we have performed comprehensive full potential density functional theory based calculations. A rather consistent electronic structure, which explains the origin and magnitude of the electronic gap, inter-band d-d transition energies, high thermopower and large magneto-crystalline anisotropy, is obtained with the use of a modified Becke-Johnson (mBJ) exchange potential. Fundamentally, mBJ calculations correctly capture the strong interplay of the crystal field and long range antiferromagnetic ordering of Ir spins as the mechanism that drives pPv-CaIrO₃ to an insulating state. Based on our findings, we propose that pPv-CaIrO₃ is a conventional Slater type antiferromagnetic insulator.

First principles study of the electronic structure and magnetic properties of spin chain compounds: Ca3ZnMnO6 and Ca3ZnCoO6

We have studied the electronic structure and magnetism of the spin chain compounds Ca3ZnMnO6 and Ca3ZnCoO6 using density functional theory with generalised gradient approximation (GGA). In agreement with experiment our calculations reveal that high spin (HS) state for Mn(4+) ion and low spin (LS) state for Co(4+) ion stabilize the magnetic structure of the respective compounds. The magnetic exchange paths, calculated using Nth order muffin-tin orbital downfolding method, shows dominant intra-chain exchange interaction between the magnetic ions (Mn, Co) is antiferromagnetic for Ca3ZnMnO6 and ferromagnetic for Ca3ZnCoO6. The magnetic order of both the compounds is in accordance with the Goodenough-Kanamori-Anderson rules and is consistent with the experimental results. Finally we have investigated the importance of spin-orbit coupling (SOC) in these compounds. While SOC practically has no effect for the Mn system, it is strong enough to favor the spin quantization along the chain direction for the Co system in the LS state.

Covalent bonds against magnetism in transition metal compounds

Magnetism in transition metal compounds is usually considered starting from a description of isolated ions, as exact as possible, and treating their (exchange) interaction at a later stage. We show that this standard approach may break down in many cases, especially in 4d and 5d compounds. We argue that there is an important intersite effect-an orbital-selective formation of covalent metal-metal bonds that leads to an "exclusion" of corresponding electrons from the magnetic subsystem, and thus strongly affects magnetic properties of the system. This effect is especially prominent for noninteger electron number, when it results in suppression of the famous double exchange, the main mechanism of ferromagnetism in transition metal compounds. We study this mechanism analytically and numerically and show that it explains magnetic properties of not only several 4d-5d materials, including Nb2O2F3 and Ba5AlIr2O11, but can also be operative in 3d transition metal oxides, e.g., in CrO2 under pressure. We also discuss the role of spin-orbit coupling on the competition between covalency and magnetism. Our results demonstrate that strong intersite coupling may invalidate the standard single-site starting point for considering magnetism, and can lead to a qualitatively new behavior.

J_{eff} Description of the Honeycomb Mott Insulator α-RuCl_{3}

Novel ground states might be realized in honeycomb lattices with strong spin-orbit coupling. Here we study the electronic structure of α-RuCl_{3}, in which the Ru ions are in a d^{5} configuration and form a honeycomb lattice, by angle-resolved photoemission, x-ray photoemission, and electron energy loss spectroscopy supported by density functional theory and multiplet calculations. We find that α-RuCl_{3} is a Mott insulator with significant spin-orbit coupling, whose low energy electronic structure is naturally mapped onto J_{eff} states. This makes α-RuCl_{3} a promising candidate for the realization of Kitaev physics. Relevant electronic parameters such as the Hubbard energy U, the crystal field splitting 10 Dq, and the charge transfer energy Δ are evaluated.

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.

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.

Emerging magnetism and anomalous Hall effect in iridate-manganite heterostructures

Strong Coulomb repulsion and spin–orbit coupling are known to give rise to exotic physical phenomena in transition metal oxides. Initial attempts to investigate systems, where both of these fundamental interactions are comparably strong, such as 3d and 5d complex oxide superlattices, have revealed properties that only slightly differ from the bulk ones of the constituent materials. Here we observe that the interfacial coupling between the 3d antiferromagnetic insulator SrMnO₃ and the 5d paramagnetic metal SrIrO₃ is enormously strong, yielding an anomalous Hall response as the result of charge transfer driven interfacial ferromagnetism. These findings show that low dimensional spin–orbit entangled 3d–5d interfaces provide an avenue to uncover technologically relevant physical phenomena unattainable in bulk materials.

Whilst superlattices containing thin films of 5d transition metal oxides are expected to yield strong interfacial coupling, only weak effects have been observed. Here, the authors report strong coupling between 3d SrMnO₃ and 5d SrIrO₃ due to the interplay of strong Coulomb and spin orbit interactions.

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.

Recent progress on correlated electron systems with strong spin-orbit coupling

The emergence of novel quantum ground states in correlated electron systems with strong spin-orbit coupling has been a recent subject of intensive studies. While it has been realized that spin-orbit coupling can provide non-trivial band topology in weakly interacting electron systems, as in topological insulators and semi-metals, the role of electron-electron interaction in strongly spin-orbit coupled systems has not been fully understood. The availability of new materials with significant electron correlation and strong spin-orbit coupling now makes such investigations possible. Many of these materials contain 5d or 4d transition metal elements; the prominent examples are iridium oxides or iridates. In this review, we succinctly discuss recent theoretical and experimental progress on this subject. After providing a brief overview, we focus on pyrochlore iridates and three-dimensional honeycomb iridates. In pyrochlore iridates, we discuss the quantum criticality of the bulk and surface states, and the relevance of the surface/boundary states in a number of topological and magnetic ground states, both in the bulk and thin film configurations. Experimental signatures of these boundary and bulk states are discussed. Domain wall formation and strongly-direction-dependent magneto-transport are also discussed. In regard to the three-dimensional honeycomb iridates, we consider possible quantum spin liquid phases and unusual magnetic orders in theoretical models with strongly bond-dependent interactions. These theoretical ideas and results are discussed in light of recent resonant x-ray scattering experiments on three-dimensional honeycomb iridates. We also contrast these results with the situation in two-dimensional honeycomb iridates. We conclude with the outlook on other related systems.

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.

Tuning directional dependent metal-insulator transitions in quasi-1D quantum wires with spin-orbit density wave instability

We study directional dependent band gap evolutions and metal-insulator transitions (MITs) in model quantum wire systems within the spin-orbit density wave (SODW) model. The evolution of MIT is studied as a function of varying anisotropy between the intra-wire hopping ([Formula: see text]) and inter-wire hopping ([Formula: see text]) with Rashba spin-orbit coupling. We find that as long as the anisotropy ratio ([Formula: see text]) remains below 0.5, and the Fermi surface nesting is tuned to [Formula: see text], an exotic SODW induced MIT easily develops, with its critical interaction strength increasing with increasing anisotropy. As [Formula: see text] (2D system), the nesting vector switches to [Formula: see text], making this state again suitable for an isotropic MIT. Finally, we discuss various physical consequences and possible applications of the directional dependent MIT.

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.

Materials design for new superconductors

Since the announcement in 2011 of the Materials Genome Initiative by the Obama administration, much attention has been given to the subject of materials design to accelerate the discovery of new materials that could have technological implications. Although having its biggest impact for more applied materials like batteries, there is increasing interest in applying these ideas to predict new superconductors. This is obviously a challenge, given that superconductivity is a many body phenomenon, with whole classes of known superconductors lacking a quantitative theory. Given this caveat, various efforts to formulate materials design principles for superconductors are reviewed here, with a focus on surveying the periodic table in an attempt to identify cuprate analogues.

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.

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.

Investigations of metastable Ca2IrO4 epitaxial thin-films: systematic comparison with Sr2IrO4 and Ba2IrO4

We have synthesized thermodynamically metastable Ca2IrO4 thin-films on YAlO3 (110) substrates by pulsed laser deposition. The epitaxial Ca2IrO4 thin-films are of K2NiF4-type tetragonal structure. Transport and optical spectroscopy measurements indicate that the electronic structure of the Ca2IrO4 thin-films is similar to that of Jeff = 1/2 spin-orbit-coupled Mott insulator Sr2IrO4 and Ba2IrO4, with the exception of an increased gap energy. The gap increase is to be expected in Ca2IrO4 due to its increased octahedral rotation and tilting, which results in enhanced electron-correlation, U/W. Our results suggest that the epitaxial stabilization growth of metastable-phase thin-films can be used effectively for investigating layered iridates and various complex-oxide systems.

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.

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.

Emerging ferroelectric transistors with nanoscale channel materials: the possibilities, the limitations

Combining the nonvolatile, locally switchable polarization field of a ferroelectric thin film with a nanoscale electronic material in a field effect transistor structure offers the opportunity to examine and control a rich variety of mesoscopic phenomena and interface coupling. It is also possible to introduce new phases and functionalities into these hybrid systems through rational design. This paper reviews two rapidly progressing branches in the field of ferroelectric transistors, which employ two distinct classes of nanoscale electronic materials as the conducting channel, the two-dimensional (2D) electron gas graphene and the strongly correlated transition metal oxide thin films. The topics covered include the basic device physics, novel phenomena emerging in the hybrid systems, critical mechanisms that control the magnitude and stability of the field effect modulation and the mobility of the channel material, potential device applications, and the performance limitations of these devices due to the complex interface interactions and challenges in achieving controlled materials properties. Possible future directions for this field are also outlined, including local ferroelectric gate control via nanoscale domain patterning and incorporating other emergent materials in this device concept, such as the simple binary ferroelectrics, layered 2D transition metal dichalcogenides, and the 4d and 5d heavy metal compounds with strong spin-orbit coupling.