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

Metal-insulator transitions in pyrochlore oxides

Pyrochlore oxides with chemical formula ofA2B2O7exhibit a diverse range of electronic properties as a representative family of quantum materials. These properties mostly stem from strong electron correlations at the transition metalBsite and typical geometrical frustration effects on the pyrochlore lattice. Furthermore, the coupling between the magnetic moments of the rare-earthAsite and the conduction electrons at theBsite, along with the relativistic spin-orbit coupling particularly affecting the 4d/5delectrons at theBsite, gives rise to the topological characteristics of the correlated electrons. This review paper focuses on the metal-insulator transitions in pyrochlore oxides as evidence of the strong electron correlation, which is highlighted as a rich source of intriguing charge dynamics coupled with frustrated spin-orbital entangled magnetism.

Canted antiferromagnetism in a spin-orbit coupled Seff = 3/2 triangular-lattice magnet DyAuGe

The exploration of nontrivial magnetic states induced by strong spin-orbit interaction is a central topic of frustrated magnetism. Numerous studies have been conducted on rare-earth-based magnets and 4d/5d transition metal compounds. These are mostly described by an effective spin Seff  = 1/2 for the Kramers doublet of the lowest crystal-electric-field levels. The variety of magnetic orderings can be greatly enhanced when magnetic dipolar moments intertwined with multipolar degrees of freedom, which are described by higher-rank tensors and often require the magnetic ions to have Seff  > 1/2. Here, using synchrotron x-ray diffraction near the Dy L3 edge, we unveil a canted antiferromagnetic ground state arising from a quasi-quartet (Seff  =  3/2) of 4f electrons in a triangular-lattice (TL) rare-earth intermetallics DyAuGe. The magnetic moment and electric-quadrupole moment are closely interlocked and a noncollinear magnetic-dipole alignment is induced by antiferroic electric-quadrupole (AFQ) ordering in the TL layers. The AFQ order is suppressed by an in-plane magnetic field, leading to the metamagnetic transition to a collinear up-up-down magnetic state. These findings offer insights into the emergence of nontrivial magnetic states in frustrated TL systems with Seff > 1/2.

Liquid-like spin dynamics in a hybrid Heisenberg-Ising antiferromagnet

Two-dimensional (2D) materials and their heterostructures enable unconventional electronic properties and functionalities not accessible in their bulk counterparts. This approach is now being extended to magnetic materials to engineer their spin structures and magnetic fields produced by them. However, spin dynamics of 2D magnetic heterostructures remain largely unexplored. Here, we demonstrate that heterointerfacing Heisenberg square-lattice antiferromagnet (AF) Sr2IrO4 with its bilayer variant Ising AF Sr3Ir2O7 in a superlattice leads to liquid-like spin dynamics in the former, characterized by slow recovery of the AF order after its transient suppression by an optical pump, and complete absence of spin waves except in an immediate vicinity of the ordering wavevector. Instead, the spin excitation spectra are dominated by isotropic continua, which in previous works have been interpreted as fractional spin excitations, or spinons, that extends to unprecedentedly low energies. Thus, our results provide a pathway to frustrated magnetism in square lattices by heterointerfacing two distinct types of AFs.

Evolution of structural, magnetic and transport properties of 3d-5dbased double perovskites Nd2-xSrxCoIrO6

The evolution of the structural, magnetic and transport properties of the intermediate compounds Nd2-xSrxCoIrO6withx= 0.2, 0.4, 0.6, 1 and 1.5 have been studied to establish important roles of sizes and oxidation states of cations on various phases. The replacement of Nd3+by Sr2+primarily influences the oxidation states of Co (Co2+→Co3+) and Ir (Ir4+→Ir5+) ions to maintain the charge neutrality in the entire system. The Sr dopants give rise to an increasing Co/Ir antisite disorder (ASD) to accommodate the variation of charge state and ionic radius of Co and Ir. The nature of magnetic interaction induced by Sr changes from being a ferrimagnetic (FIM) to a more dominant antiferromagnetic. The suppression of the second magnetic transition below 30 K in samples forx>0.2 is entirely due to dilution of the Nd-Nd magnetic interaction. The combined effects of ASD and mixed oxidation state of Co and Ir ions generate various types of magnetic exchange pathways and create competitive magnetic interactions to stabilize a particular magnetic ground state. In the middle compound NdSrCoIrO6, a Griffith like phase in the temperature region 65-150 K and exchange bias field of 658 Oe at 2.3 K under a cooling field of 50 kOe has been observed. The compounds show an insulating kind of behaviour, and with hole doping the value of room temperature resistivity drastically decreases. The nature of conduction is found to follow three dimensional Mott's variable range hopping process.

Flexomagnetoelectric Effect in Sr_{2}IrO_{4} Thin Films

Symmetry engineering is explicitly effective to manipulate and even create phases and orderings in strongly correlated materials. Flexural stress is universally practical to break the space-inversion or time-reversal symmetry. Here, by introducing strain gradient in a centrosymmetric antiferromagnet Sr_{2}IrO_{4}, the space-inversion symmetry is broken accompanying a nonequivalent O p-Ir d orbital hybridization along the z axis. Thus, an emergent polar phase and out-of-plane magnetic moment have been simultaneously observed in these asymmetric Sr_{2}IrO_{4} thin films, which both are absent in its ground state. Furthermore, upon the application of a magnetic field, such polarization can be controlled by modifying the occupied d orbitals through spin-orbit interaction, giving rise to a flexomagnetoelectric effect. This Letter provides a general strategy to artificially design multiple symmetries and ferroic orderings in strongly correlated systems.

Pseudosymmetry in Tetragonal Perovskite SrIrO3 Synthesized under High Pressure

In this study, we report a tetragonal perovskite structure of SrIrO3 (P4/mmm, a = 3.9362(9) Å, c = 7.880(3) Å) synthesized at 6 GPa and 1400 °C, employing the ambient pressure monoclinic SrIrO3 with distorted 6H structure as a precursor. The crystal structure of tetragonal SrIrO3 was evaluated on the basis of single-crystal and powder X-ray diffraction. A cubic indexing was observed, which was attributed to overlooked superlattice reflections. Weak fractional peaks in the H and K dimensions suggest possible structure modulation by oxygen defects. Magnetization study reveals weak paramagnetic behavior down to 2 K, indicative of the interplay between spin-orbit coupling, electron correlations, and the crystal electric field. Additionally, measurements of electrical resistivity display metallic behavior with an upturn at about 54 K, which is ascribed to weak electron localization and possible structural defects.

Origin of Magnetism in a Supposedly Nonmagnetic Osmium Oxide

A supposedly nonmagnetic 5d^{1} double perovskite oxide is investigated by a combination of spectroscopic and theoretical methods, namely, resonant inelastic x-ray scattering, x-ray absorption spectroscopy, magnetic circular dichroism, and multiplet ligand-field calculations. We found that the large spin-orbit coupling admixes the 5d t_{2g} and e_{g} orbitals, covalency raises the 5d population well above the nominal value, and the local symmetry is lower than O_{h}. The obtained electronic interactions account for the finite magnetic moment of Os in this compound and, in general, of 5d^{1} ions. Our results provide direct evidence of elusive Jahn-Teller distortions, hinting at a strong electron-lattice coupling.

Tunable charge transport properties in non-stoichiometric SrIrO3thin films

Delving into the intricate interplay between spin-orbit coupling and Coulomb correlations in strongly correlated oxides, particularly perovskite compounds, has unveiled a rich landscape of exotic phenomena ranging from unconventional superconductivity to the emergence of topological phases. In this study, we have employed pulsed laser deposition technique to grow SrIrO3(SIO) thin films on SrTiO3substrates, systematically varying the oxygen content during the post-deposition annealing. X-ray photoelectron spectroscopy (XPS) provided insights into the stoichiometry and spin-orbit splitting energy of Iridium within the SIO film, while high-resolution x-ray studies meticulously examined the structural integrity of the thin films. Remarkably, our findings indicate a decrease in the metallicity of SIO thin films with reduced annealing O2partial pressure. Furthermore, we carried out magneto-transport studies on the SIO thin films, the results revealed intriguing insights into spin transport as a function of oxygen content. The tunability of the electronic band structure of SIO films with varying oxygen vacancy is correlated with the density functional theory calculations. Our findings elucidate the intricate mechanisms dictating spin transport properties in SIO thin films, offering invaluable guidance for the design and optimization of spintronic devices based on complex oxide materials. Notably, the ability to tune bandwidth by varying post-annealing oxygen partial pressure in iridate-based spintronic materials holds significant promise for advancing technological applications in the spintronics domain.

Light-induced insulator-metal transition in Sr2IrO4 reveals the nature of the insulating ground state

Sr2IrO4 has attracted considerable attention due to its structural and electronic similarities to La2CuO4, the parent compound of high-Tc superconducting cuprates. It was proposed as a strong spin-orbit-coupled Jeff = 1/2 Mott insulator, but the Mott nature of its insulating ground state has not been conclusively established. Here, we use ultrafast laser pulses to realize an insulator-metal transition in Sr2IrO4 and probe the resulting dynamics using time- and angle-resolved photoemission spectroscopy. We observe a gap closure and the formation of weakly renormalized electronic bands in the gap region. Comparing these observations to the expected temperature and doping evolution of Mott gaps and Hubbard bands provides clear evidence that the insulating state does not originate from Mott correlations. We instead propose a correlated band insulator picture, where antiferromagnetic correlations play a key role in the gap opening. More broadly, our results demonstrate that energy-momentum-resolved nonequilibrium dynamics can be used to clarify the nature of equilibrium states in correlated materials.

Perspective: probing elasto-quantum materials with x-ray techniques andin situanisotropic strain

Anisotropic lattice deformation plays an important role in the quantum mechanics of solid state physics. The possibility of mediating the competition and cooperation among different order parameters by applyingin situstrain/stress on quantum materials has led to discoveries of a variety of elasto-quantum effects on emergent phenomena. It has become increasingly critical to have the capability of combining thein situstrain tuning with x-ray techniques, especially those based on synchrotrons, to probe the microscopic elasto-responses of the lattice, spin, charge, and orbital degrees of freedom. Herein, we briefly review the recent studies that embarked on utilizing elasto-x-ray characterizations on representative material systems and demonstrated the emerging opportunities enabled by this method. With that, we further discuss the promising prospect in this rising area of quantum materials research and the bright future of elasto-x-ray techniques.

Re/Ir@Os-doping induced insulator-to-metal transition in Mott-insulator Ca2FeOsO6: octahedral distortion effects

Regardless of several investigations to elucidate the ground state of the strongly correlated electron systems in doped Mott-insulators (MIs), the origin of the doping-induced insulator-to-metal transition (IMT) remains a crucial and debatable subject in solid-state physics. Herein, we explore the consequences of Re/Ir-doping at the Os-site (Re/Ir@Os), on the physical properties of the MI ferrimagnetic (FiM) Ca2FeOsO6 double perovskite oxides using density functional theory calculations. The doped structures' solidity is analyzed by computing the defect formation energies in terms of the dopant-rich situation, which confirms their growth credibility at ambient conditions along with mechanical and dynamical stabilities. Various FiM spin-ordering is taken into account in the doped structures to analyze the magnetic ground state, which is FiM-I/FiM-II in the Re/Ir@Os-doped system. Remarkably, an IMT is predicted in the Re/Ir@Os-doped structures, which is due to the admixture of the partially occupied 5d orbitals of these ions. The calculated partial spin magnetic moments (ms) of +4.12, -1.58, -0.75 and +0.88μB on the Fe, Os, Re, and Ir ions, endorse the +3, +5, +5, and +4 states having electronic configurations of t32g↑t02g↓e2g↑e0g↓, t32g↑t02g↓e0g↑e0g↓, t22g↑t02g↓e0g↑e0g↓, t32g↑t22g↓e0g↑e0g↓, respectively. The "+" and "-" signs on the ions ms values, lead the systems into various FiM magnetic ordering. Moreover, the estimated Curie temperature (TC) using the Heisenberg model in the pristine structure is 334 K, which is close to the experimentally observed value of 320 K along with a colossal uniaxial magneto crystalline anisotropy energy constant (K) of 2.95 × 107 erg cm-3 having the easy magnetic axis of the ac-plane ([101]). It is established that TC/K reduces and enhances to 298 K/1.33 × 107 erg cm-3 and 365 K/4.71 × 107 erg cm-3 for the Re@Os and Ir@Os-doped motif due to an increase and decrease in the octahedral distortions compared to that of the pristine system, respectively.

Probing the Magnetic Ground State of Ba2YIrO6: Impact of Nonmagnetic Dopants and Spin-Orbit Coupling

Strong spin-orbit coupling (SOC) in iridates has long been predicted to lead to exotic electronic and magnetic ground states. Ba2YIrO6 (BYIO) has attracted particular attention due to the expectation of a Jeff = 0 state for Ir5+ ions under the jj-coupling scheme. However, controversies surround the actual realization of this state, as finite magnetic moments are consistently observed experimentally. We present a multi-physics study of this system by progressively introducing nonmagnetic Sb5+ ions in place of Ir5+ (Ba2YIr​1-ySb​yO​6, BYISO). Despite similar charge and ionic radii, Sb​5+ doping appears highly inhomogeneous, coexisting with a fraction of nearly pure BYIO regions, as confirmed by X-ray diffraction (XRD). This aligns with observations in related compounds. While inhomogeneity creates uncertainty, the doped majority phases offer valuable insights. It is relevant that the inclusion of even small amounts of Sb​5+ (10-20%) leads to a rise in magnetization. This strengthens our previous suggestion that magnetic Ir ions form dynamic singlets in BYIO, resulting in a near-nonmagnetic background. The observed moment enhancement with nonmagnetic doping supports the breakdown of these singlets. Furthermore, the magnetization steadily increases with an increasing Sb​5+ content, contradicting the anticipated approach towards the Jeff = 0 state with increased SOC due to reduced hopping between Ir​5+ ions. This reinforces the presence of individual Ir​5+ moments. Overall, our findings suggest that Ba​2YIrO​6 might not possess sufficiently strong SOC to be solely described within the jj-coupling picture, paving the way for further investigation.

Recent progress on topological semimetal IrO2: electronic structures, synthesis, and transport properties

5dtransition metal oxides, such as iridates, have attracted significant interest in condensed matter physics throughout the past decade owing to their fascinating physical properties that arise from intrinsically strong spin-orbit coupling (SOC) and its interplay with other interactions of comparable energy scales. Among the rich family of iridates, iridium dioxide (IrO2), a simple binary compound long known as a promising catalyst for water splitting, has recently been demonstrated to possess novel topological states and exotic transport properties. The strong SOC and the nonsymmorphic symmetry that IrO2possesses introduce symmetry-protected Dirac nodal lines (DNLs) within its band structure as well as a large spin Hall effect in the transport. Here, we review recent advances pertaining to the study of this unique SOC oxide, with an emphasis on the understanding of the topological electronic structures, syntheses of high crystalline quality nanostructures, and experimental measurements of its fundamental transport properties. In particular, the theoretical origin of the presence of the fourfold degenerate DNLs in band structure and its implications in the angle-resolved photoemission spectroscopy measurement and in the spin Hall effect are discussed. We further introduce a variety of synthesis techniques to achieve IrO2nanostructures, such as epitaxial thin films and single crystalline nanowires, with the goal of understanding the roles that each key parameter plays in the growth process. Finally, we review the electrical, spin, and thermal transport studies. The transport properties under variable temperatures and magnetic fields reveal themselves to be uniquely sensitive and modifiable by strain, dimensionality (bulk, thin film, nanowire), quantum confinement, film texture, and disorder. The sensitivity, stemming from the competing energy scales of SOC, disorder, and other interactions, enables the creation of a variety of intriguing quantum states of matter.

Sr4Al2O7: A New Sacrificial Layer with High Water Dissolution Rate for the Synthesis of Freestanding Oxide Membranes

Freestanding perovskite oxide membranes have drawn great attention recently since they offer exceptional structural tunability and stacking ability, providing new opportunities in fundamental research and potential device applications in silicon-based semiconductor technology. Among different types of sacrificial layers, the (Ca, Sr, Ba)3Al2O6 compounds are most widely used since they can be dissolved in water and prepare high-quality perovskite oxide membranes with clean and sharp surfaces and interfaces; However, the typical transfer process takes a long time (up to hours) in obtaining millimeter-size freestanding membranes, let alone realize wafer-scale samples with high yield. Here, a new member of the SrO-Al2O3 family, Sr4Al2O7 is introduced, and its high dissolution rate, ≈10 times higher than that of Sr3Al2O6 is demonstrated. The high-dissolution-rate of Sr4Al2O7 is most likely related to the more discrete Al-O networks and higher concentration of water-soluble Sr-O species in this compound. This work significantly facilitates the preparation of freestanding membranes and sheds light on the integration of multifunctional perovskite oxides in practical electronic devices.

Pinalites: Optical Properties and Quantum Magnetism of Heteroanionic A3MO5X2 Compounds

Heteroanionic compounds, which contain two or more types of anions, have emerged as a promising class of materials with diverse properties and functionalities. In this paper, I review the experimental findings on Ca3ReO5Cl2 and related compounds that exhibit remarkable pleochroism and novel quantum magnetism. I discuss how the heteroanionic coordination affects the optical and magnetic properties by modulating the d-orbital states of the transition metal ions. Subsequently, I compare these materials with other heteroanionic and monoanionic compounds and highlight the potential of A3MO5X2 materials for future exploration of materials and phenomena.

Insulator-to-metal transition, magnetic anisotropy, and improved TC in a ferrimagnetic La2CoIrO6: strain influence

The elegant interactions between Coulomb repulsion and spin-orbit coupling in Ir-based double perovskite oxides (DPO) normally induce peculiar magnetic behavior. Herein, we investigate the effect of the development of biaxial [110] strain on the formation energetics, and electronic and magnetic properties of the La2CoIrO6 DPO employing density functional theory calculations. Our results reveal that the unstrained motif is a Mott-insulator achieving an energy band gap of 0.35 eV with a ferrimagnetic (FiM) ground state, which essentially arises due to anti-ferromagnetic (AFM) coupling between the half-occupied Co t2g and partially occupied Ir t2g/empty eg orbitals via oxygen 2p states. Along with this, it is found that [001] (c-axis) is the easy magnetic axis, which results in 12.5 meV total energy per u.c., obtaining a large anisotropy constant of 0.8 × 108 erg cm-3. The computed partial spin-magnetic moments on the Co/Ir ion are 2.64/-0.46 μB, where the negative sign on the Ir ion moment confirms the AFM interactions between them. Additionally, the t2g/eg and t2g orbital characteristics of Co2+ and Ir4+ ions are visible in the spin-magnetization density isosurfaces plot, respectively. Likewise, the estimated Curie temperature (TC) using the Heisenberg model is 104 K, which is in agreement with the experimentally observed value of 94/97 K. Interestingly, an insulator-to-metal transition is achieved at a critical compressive strain of -6% with a robust FiM state, where the Co 3dxy and Ir 5dx2-y2 orbitals are mainly responsible for metallicity. Simultaneously, the magnetocrystalline anisotropy energy and TC can be sufficiently enhanced by applying compressive strain due to enhancement in the structural distortions. So this work suggested that the strain strategy is an efficient approach to tuning the properties of the compounds for their feasible realization in spintronics.

Quantum spin nematic phase in a square-lattice iridate

Spin nematic is a magnetic analogue of classical liquid crystals, a fourth state of matter exhibiting characteristics of both liquid and solid1,2. Particularly intriguing is a valence-bond spin nematic3-5, in which spins are quantum entangled to form a multipolar order without breaking time-reversal symmetry, but its unambiguous experimental realization remains elusive. Here we establish a spin nematic phase in the square-lattice iridate Sr2IrO4, which approximately realizes a pseudospin one-half Heisenberg antiferromagnet in the strong spin-orbit coupling limit6-9. Upon cooling, the transition into the spin nematic phase at TC ≈ 263 K is marked by a divergence in the static spin quadrupole susceptibility extracted from our Raman spectra and concomitant emergence of a collective mode associated with the spontaneous breaking of rotational symmetries. The quadrupolar order persists in the antiferromagnetic phase below TN ≈ 230 K and becomes directly observable through its interference with the antiferromagnetic order in resonant X-ray diffraction, which allows us to uniquely determine its spatial structure. Further, we find using resonant inelastic X-ray scattering a complete breakdown of coherent magnon excitations at short-wavelength scales, suggesting a many-body quantum entanglement in the antiferromagnetic state10,11. Taken together, our results reveal a quantum order underlying the Néel antiferromagnet that is widely believed to be intimately connected to the mechanism of high-temperature superconductivity12,13.

Extraordinary Magnetic Response of an Anisotropic 2D Antiferromagnet via Site Dilution

A prominent characteristic of 2D magnetic systems is the enhanced spin fluctuations, which reduce the ordering temperature. We report that a magnetic field of only 1000th of the Heisenberg superexchange interaction can induce a crossover, which for practical purposes is the effective ordering transition, at temperatures about 6 times the Néel transition in a site-diluted two-dimensional anisotropic quantum antiferromagnet. Such a strong magnetic response is enabled because the system directly enters the antiferromagnetically ordered state from the isotropic disordered state, skipping the intermediate anisotropic stage. The underlying mechanism is achieved on a pseudospin-half square lattice realized in the [(SrIrO3)1/(SrTiO3)2] superlattice thin film that is designed to linearly couple the staggered magnetization to external magnetic fields by virtue of the rotational symmetry-preserving Dzyaloshinskii-Moriya interaction. Our model analysis shows that the skipping of the anisotropic regime despite finite anisotropy is due to the enhanced isotropic fluctuations under moderate dilution.

Electronic Structures of Kitaev Magnet Candidates RuCl3 and RuI3

Layered honeycomb magnets with strong atomic spin-orbit coupling at transition metal sites have been intensively studied for the search of Kitaev magnetism and the resulting non-Abelian braiding statistics. α-RuCl3 has been the most promising candidate, and there have been several reports on the realization of sibling compounds α-RuBr3 and α-RuI3 with the same crystal structure. Here, we investigate correlated electronic structures of α-RuCl3 and α-RuI3 by employing first-principles dynamical mean-field theory. Our result provides a valuable insight into the discrepancy between experimental and theoretical reports on transport properties of α-RuI3, and suggests a potential realization of correlated flat bands with strong spin-orbit coupling and a quantum spin-Hall insulating phase in α-RuI3.

Coexistence of spin liquid state and magnetic correlations in 3d-5dbased triangular-lattice antiferromagnet Sr3CuIr2O9

Here, we report detailed lattice structure, magnetization (dc and ac) and specific heat measurements on a 3d-5dbased new triple-perovskite material Sr3CuIr2O9. The Sr/Cu forms a layered structure of triangular-lattice while the Ir forms Ir2O9dimers which lie in chain as well as simultaneously makes layered triangular-lattice with neighboring atoms. Due to random site-sharing with Sr2+, the Cu2+(3d9, spin-1/2) forms a diluted magnetic lattice, thus giving a disordered in-plane exchange interaction. Opposed to conventionalJeffmodel, the Ir5+(5d4,Jeff= 0) is believed to be magnetic here which participates both in-chain and in-plane magnetic interactions. This complex lattice structure driven competing exchange interaction leads the ground state to a gapless quantum-spin-liquid state which coexists with (weak) ferromagnetic spin correlations. While underling the importance of spin state (spin-1/2), we believe that the combined effect of lattice structure, geometric frustration, spin-orbit coupling and spin state has given rise this interesting ground state in this material.

Engineering metal oxidation using epitaxial strain

The oxides of platinum group metals are promising for future electronics and spintronics due to the delicate interplay of spin-orbit coupling and electron correlation energies. However, their synthesis as thin films remains challenging due to their low vapour pressures and low oxidation potentials. Here we show how epitaxial strain can be used as a control knob to enhance metal oxidation. Using Ir as an example, we demonstrate the use of epitaxial strain in engineering its oxidation chemistry, enabling phase-pure Ir or IrO2 films despite using identical growth conditions. The observations are explained using a density-functional-theory-based modified formation enthalpy framework, which highlights the important role of metal-substrate epitaxial strain in governing the oxide formation enthalpy. We also validate the generality of this principle by demonstrating epitaxial strain effect on Ru oxidation. The IrO2 films studied in our work further revealed quantum oscillations, attesting to the excellent film quality. The epitaxial strain approach we present could enable growth of oxide films of hard-to-oxidize elements using strain engineering.

Multiorbital Nature of Doped Sr_{2}IrO_{4}

The low-energy j_{eff}=1/2 band of Sr_{2}IrO_{4} bears stark resemblances with the x^{2}-y^{2} band of La_{2}CuO_{4}, and yet no superconductivity has been found so far by doping Sr_{2}IrO_{4}. Behind such a behavior could be inherent failures of the j_{eff}=1/2 picture, in particular when electrons or holes are introduced in the IrO_{2} planes. In view of this, here we reanalyze the j_{eff}=1/2 scenario. By using the local-density approximation plus dynamical mean-field theory approach, we show that the form of the effective j_{eff}=1/2 state is surprisingly stable upon doping. This supports the j_{eff}=1/2 picture. We show that, nevertheless, Sr_{2}IrO_{4} remains in essence a multiorbital system: The hybridization with the j_{eff}=3/2 orbitals sizably reduces the Mott gap by enhancing orbital degeneracy, and part of the holes go into the j_{eff}=3/2 channels. These effects cannot be reproduced by a simple effective screened Coulomb repulsion. In the optical conductivity spectra, multiorbital processes involving the j_{eff}=3/2 states contribute both to the Drude peak and to relatively low-energy features.

Emergent quantum phenomena in atomically engineered iridate heterostructures

Over the last few years, researches in iridates have developed into an exciting field with the discovery of numerous emergent phenomena, interesting physics, and intriguing functionalities. Among the studies, iridate-based artificial structures play a crucial role owing to their extreme flexibility and tunability in lattice symmetry, chemical composition, and crystal dimensionality. In this article, we present an overview of the recent progress regarding iridate-based artificial structures. We first explicitly introduce several essential concepts in iridates. Then, we illustrate important findings on representative SrIrO3/SrTiO3 superlattices, heterostructures comprised of SrIrO3 and magnetic oxides, and their response to external electric-field stimuli. Finally, we comment on existing problems and promising future directions in this exciting field.

In-gap states and strain-tuned band convergence in layered structure trivalent iridate K0.75Na0.25IrO2

Iridium oxides (iridates) provide a good platform to study the delicate interplay between spin-orbit coupling (SOC) interactions, electron correlation effects, Hund's coupling and lattice degrees of freedom. An overwhelming number of investigations primarily focus on tetravalent (Ir⁴⁺, 5d⁵) and pentavalent (Ir⁵⁺, 5d⁴) iridates, and far less attention has been paid to iridates with other valence states. Here, we pay our attention to a less-explored trivalent (Ir³⁺, 5d⁶) iridate, K_0.75Na_0.25IrO₂, crystallizing in a triangular lattice with edge-sharing IrO₆ octahedra and alkali metal ion intercalated [IrO₂]^- layers, offering a good platform to explore the interplay between different degrees of freedom. We theoretically determine the preferred occupied positions of the alkali metal ions from energetic viewpoints and reproduce the experimentally observed semiconducting behavior and nonmagnetic (NM) properties of K_0.75Na_0.25IrO₂. The SOC interactions play a critical role in the band dispersion, resulting in NM J_eff = 0 states. More intriguingly, our electronic structure not only uncovers the presence of intrinsic in-gap states and nearly free electron character for the conduction band minimum, but also explains the abnormally low activation energy in K_0.75Na_0.25IrO₂. Particularly, the band edge can be effectively modulated by mechanical strain, and the in-gap states feature enhanced band-convergence characteristics by 6% compressive strain, which will greatly enhance the electrical conductivity of K_0.75Na_0.25IrO₂. The present work sheds new light on the unconventional electronic structures of trivalent iridates, indicating their promising application as a nanoelectronic and thermoelectric material, which will attract extensive interest and stimulate experimental works to further understand the unprecedented electronic structures and exploit potential applications of the triangular trivalent iridate.

Dressed jeff-1/2 objects in mixed-valence lacunar spinel molybdates

The lacunar-spinel chalcogenides exhibit magnetic centers in the form of transition-metal tetrahedra. On the basis of density-functional computations, the electronic ground state of an Mo₄¹³⁺ tetrahedron has been postulated as single-configuration a₁² e⁴ t₂⁵, where a₁, e, and t₂ are symmetry-adapted linear combinations of single-site Mo t_2g atomic orbitals. Here we unveil the many-body tetramer wave-function: we show that sizable correlations yield a weight of only 62% for the a₁² e⁴ t₂⁵ configuration. While spin-orbit coupling within the peculiar valence orbital manifold is still effective, the expectation value of the spin-orbit operator and the g factors deviate from figures describing nominal t⁵ j_eff = 1/2 moments. As such, our data documents the dressing of a spin-orbit j_eff = 1/2 object with intra-tetramer excitations. Our results on the internal degrees of freedom of these magnetic moments provide a solid theoretical starting point in addressing the intriguing phase transitions observed at low temperatures in these materials.

Non-Centrosymmetric Sr2IrO4 Obtained Under High Pressure

Sr₂IrO₄ with strong spin-orbit coupling and Hubbard repulsion (U) hosts Mott insulating states. The similar crystal structure and magnetic and electronic properties, particularly the d-wave gap observed in Sr₂IrO₄ enhanced the analogies to the cuprate high-T_c superconductor, La₂CuO₄. The incomplete analogy was due to the lack of broken inversion symmetry phases observed in Sr₂IrO₄. Here, under high-pressure and high-temperature conditions, we report a noncentrosymmetric Sr₂IrO₄. The crystal structure and its noncentrosymmetric character were determined by single-crystal X-ray diffraction and high-resolution scanning transmission electron microscopy. The magnetic characterization confirms the Ir⁴⁺ with S = 1/2 at low temperature in Sr₂IrO₄ with magnetic ordering occurring at around 86 K, where a larger moment is observed than the ambient pressure Sr₂IrO₄. Moreover, the resistivity measurement shows three-dimensional Mott variable-range hopping (VRH) existed in the system. This noncentrosymmetric Sr₂IrO₄ phase appears to be a unique material that offers a further understanding of high-T_c superconductivity.

Polar magnetism and chemical bond inα-RuCl3

The micaceous black allotrope of ruthenium trichloride is the subject of many recent experimental and theoretical studies. Even so, its structural and magnetic properties remain undecided; monoclinic, trigonal and rhombohedral space groups for the crystal structure have been proposed on the basis of various types of experiments. The magnetic structure is often discussed in the context of the Kitaev state, but inevitably they are inconclusive discussions in the absence of structural and magnetic space groups. Johnsonet alinfer a candidate for the magnetic structure (C_c2/m) from results gathered in an extensive set of experiments on an untwined sample ofα-RuCl₃(Johnsonet al2015Phys. Rev.B92235119). The proposed zigzag antiferromagnetic ground state of Ru ions does not respond to bulk magnetic probes, with optical rotation and all forms of dichroism prohibited by symmetry. Experimental techniques exploited by Johnsonet alincluded x-ray and magnetic neutron diffraction. Properties of the candidate magnetic structure not previously explored include polar magnetism that supports Ru Dirac multipoles, e.g. a ruthenium anapole that is also known as a toroidal dipole. In a general case, Dirac dipoles are capable of generating interactions between magnetic ions, as in an electrical Dzyaloshinskii-Moryia interaction (Kaplan and Mahanti 2011Phys. Rev.B83174432; Zhaoet al2021Nat. Mater.20341). Notably, the existence of Dirac quadrupoles in the pseudo-gap phases of cuprate superconductors YBCO and Hg1201 account for observed magnetic Bragg diffraction patterns. Dirac multipoles contribute to the diffraction of both x-rays and neutrons, and a stringent test of the magnetic structure C_c2/m awaits future experiments. From symmetry-informed calculations we show that, the magnetic candidate permits Bragg spots that arise solely from Dirac multipoles. Stringent tests of C_c2/m can also be accomplished by performing resonant x-ray diffraction with signal enhancement from the chlorineK-edge. X-ray absorption spectra published forα-RuCl₃possess a significant low-energy feature (Plumbet al2014Phys. Rev.B90041112(R)). Many experimental studies of other Cl-metal compounds concluded that identical features hallmark the chemical bond. Using a monoclinic C_c2/m structure, we predict the contribution to Bragg diffraction at the ClK-edge absorption. Specifically, the variation of intensity of Bragg spots with rotation of the sample about the reflection vector. The two principal topics of our studies, polar magnetism and the chemical bond in the black allotrope of ruthenium trichloride, are brought together in a minimal model of magnetic Ru ions in C_c2/m.

Enhanced Electron Correlation and Significantly Suppressed Thermal Conductivity in Dirac Nodal-Line Metal Nanowires by Chemical Doping

Enhancing electron correlation in a weakly interacting topological system has great potential to promote correlated topological states of matter with extraordinary quantum properties. Here, the enhancement of electron correlation in a prototypical topological metal, namely iridium dioxide (IrO₂ ), via doping with 3d transition metal vanadium is demonstrated. Single-crystalline vanadium-doped IrO₂ nanowires are synthesized through chemical vapor deposition where the nanowire yield and morphology are improved by creating rough surfaces on substrates. Vanadium doping leads to a dramatic decrease in Raman intensity without notable peak broadening, signifying the enhancement of electron correlation. The enhanced electron correlation is further evidenced by transport studies where the electrical resistivity is greatly increased and follows an unusual T $\sqrt T $ dependence on the temperature (T). The lattice thermal conductivity is suppressed by an order of magnitude via doping even at room temperature where phonon-impurity scattering becomes less important. Density functional theory calculations suggest that the remarkable reduction of thermal conductivity arises from the complex phonon dispersion and reduced energy gap between phonon branches, which greatly enhances phase space for phonon-phonon Umklapp scattering. This work demonstrates a unique system combining 3d and 5d transition metals in isostructural materials to enrich the system with various types of interactions.

Controllable Itinerant Ferromagnetism in Weakly Correlated 5d SrIrO3

The weakly correlated nature of 5d oxide SrIrO₃ determines its rare ferromagnetism, and the control of its magnetic order is even less studied. Tailoring structure distortion is currently a main route to tune the magnetic order of 5d iridates, but only for the spatially confined insulating counterparts. Here, we have realized ferromagnetic order in metallic SrIrO₃ by construction of SrIrO₃/ferromagnetic-insulator (LaCoO₃) superlattices, which reveal a giant coercivity of ∼10 T and saturation field of ∼25 T with strong perpendicular magnetic anisotropy. The Curie temperature of SrIrO₃ can be controlled by engineering interface charge transfer, which is confirmed by Hall effect measurements collaborating with EELS and XAS. Besides, the noncoplanar spin texture is captured, which is caused by interfacial Dzyaloshinskii-Moriya interactions as well. These results indicate controllable itinerant ferromagnetism and an emergent topological magnetic state in strong spin-orbit coupled semimetal SrIrO₃, showing great potential to develop efficient spintronic devices.

Effects of the on-site energy on the electronic response of Sr3(Ir1−xMnx)2O7

We investigated the doping and temperature evolutions of the optical response of Sr3(Ir1−xMnx)2O7 single crystals with 0 ≤ x ≤ 0.36 by utilizing infrared spectroscopy. Substitution of 3d transition metal Mn ions into Sr3Ir2O7 is expected to induce an insulator-to-metal transition via the decrease in the magnitude of the spin–orbit coupling and the hole doping. In sharp contrast, our data reveal the resilience of the spin–orbit coupling and the incoherent character of the charge transport. Upon Mn substitution, an incoherent in-gap excitation at about 0.25 eV appeared with the decrease in the strength of the optical transitions between the effective total angular momentum Jeff bands of the Ir ions. The resonance energies of the optical transitions between the Jeff bands which are directly proportional to the magnitude of the spin–orbit coupling hardly varied. In addition to these evolutions of the low-energy response, Mn substitution led to the emergence of a distinct high-energy optical excitation at about 1.2 eV which is larger than the resonance energies of the optical transitions between the Jeff bands. This observation indicates that the Mn 3d states are located away from the Ir 5d states in energy and that the large difference in the on-site energies of the transition metal ions is responsible for the incoherent charge transport and the robustness of the spin–orbit coupling. The effect of Mn substitution was also registered in the temperature dependence of the electronic response. The anomaly in the optical response of the parent compound observed at the antiferromagnetic transition temperature is notably suppressed in the Mn-doped compounds despite the persistence of the long-range antiferromagnetic ordering. The suppression of the spin-charge coupling could be related to charge disproportionation of the Ir ions.

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

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

Reconciling Monolayer and Bilayer J_{eff}=1/2 Square Lattices in Hybrid Oxide Superlattice

The number of atomic layers confined in a two-dimensional structure is crucial for the electronic and magnetic properties. Single-layer and bilayer J_{eff}=1/2 square lattices are well-known examples where the presence of the extra layer turns the XY anisotropy to the c-axis anisotropy. We report on experimental realization of a hybrid SrIrO_{3}/SrTiO_{3} superlattice that integrates monolayer and bilayer square lattices in one layered structure. By synchrotron x-ray diffraction, resonant x-ray magnetic scattering, magnetization, and resistivity measurements, we found that the hybrid superlattice exhibits properties that are distinct from both the single-layer and bilayer systems and cannot be explained by a simple addition of them. In particular, the entire hybrid superlattice orders simultaneously through a single antiferromagnetic transition at temperatures similar to the bilayer system but with all the J_{eff}=1/2 moments mainly pointing in the ab plane similar to the single-layer system. The results show that bringing monolayer and bilayer with orthogonal properties in proximity to each other in a hybrid superlattice structure is a powerful way to stabilize a unique state not obtainable in a uniform structure.

Fluorite-related iridate Pr3IrO7: crystal growth, structure, magnetism, thermodynamic, and optical properties

Spin-orbit coupling in heavy 5dmetal oxides, in particular, iridates have received tremendous interest in recent years due to the realization of exotic electronic and magnetic phases. Here, we report the synthesis, structural, magnetic, thermodynamic, and optical properties of the ternary iridate Pr₃IrO₇. Single crystals of Pr₃IrO₇have been grown by the KF flux method. Structural analysis shows that Pr₃IrO₇crystallizes in an orthorhombic phase withCmcmsymmetry. The electron energy loss spectroscopy study indicates that Pr is in a 3+ valence state, which implies a 5+ oxidation state of Ir. Magnetization data measured at high and low magnetic fields do not exhibit any bifurcation betweenM_ZFCandM_FC, however, a weak hump inM(T) is observed atT∗∼10.4 K. The specific heat data reveal two maxima at ∼253 and ∼4.8 K. The optical conductivityσ1(ω)spectrum shows 24 infrared-active phonon modes and reveals an insulating behavior with an optical gapΔOPof size ∼500 meV. During cooling down, the temperature-dependent reflectivity spectrum reveals eight extra phonon modes below the structural phase transition (∼253 K). An anomaly is observed at aroundT∗in the temperature evolution of infrared-active mode frequencies suggesting the presence of significant spin-phonon coupling in the system.

Electronic and Magnetic Properties of Spin-Orbit-Entangled Honeycomb Lattice Iridates MIrO3 (M = Cd, Zn, and Mg)

By means of density functional theory calculations with the inclusion of spin-orbit coupling, we present a comprehensive investigation of the structural, electronic, and magnetic properties of the novel series of ilmenite-type honeycomb lattice iridates MIrO₃ (M = Cd, Zn, and Mg), the potential candidates for realizing the quantum spin liquid. Our findings are as follows: (i) the structural relaxations could not properly capture the abnormal thin two-dimensional honeycomb IrO₆ layers in CdIrO₃, making the experimentally proposed crystal structure questionable. Furthermore, the calculations within the experimental structure could not correctly determine the magnetic ground state; however, the results within the optimized one rectify this scenario and provide a precise and reasonable description of its electronic and magnetic properties, which is in good agreement with the experimental observations and that of Zn and Mg analogues. In this regard, we hope that our report will inspire additional studies on this issue and eventually resolve the crystal structure of CdIrO₃. (ii) We identified that the magnetic ground state of this series of iridates MIrO₃ is the zigzag antiferromagnetic ordering, where ferromagnetic zigzag chains are coupling antiferromagnetically across the bridging bonds within a hexagon. (iii) Though it is widely assumed that all the iridates can be well described based on the spin-orbit-assisted J_eff = 1/2 Mott insulating state model, detailed analysis of electronic band structures indicates that the formation of quasimolecular orbitals (QMOs) within a hexagon plays a non-negligible role in appropriately depicting the electronic and magnetic properties. Finally, (iv) we found that all the antiferromagnetic patterns are insulating with finite band gaps. Clarifying the effect of magnetic ordering on the electronic structures is important because it reminds us of potential erroneous identification/prediction of the ground state. The results suggest that precisely determining the magnetic ground state and adopting it in the simulations are imperative for faithfully rendering the electronic properties of a compound. Our results underline the importance of structural factor, spin-orbit coupling, correlation correction, the formation of the QMOs within the hexagon, as well as magnetic ordering in elucidating the electronic structure of a series of ilmenite-type honeycomb lattice iridates MIrO₃.

Synthesis and structural link to the electronic and magneto-transport properties of spin-orbit Mott insulator Sr2IrO4

We investigate the effect of sample preparation conditions on the link between the structural and physical properties of polycrystalline spin-orbit Mott insulator, Sr₂IrO₄. The samples were prepared in two batches. With the first batch prepared as per the commonly adopted procedure in literature and the second batch prepared adopting the same procedure as the first batch but with an additional annealing in vacuum. Interestingly, our results show that without change in the value of the Curie temperature (T_C), there occurs increase in the value of magnetization, resistivity, magneto-resistance (MR) and an increase in temperature range of stabilization of the canted antiferromagnetic structure. The temperature behaviour of the difference in the irreversible magnetization between the samples is in line with the difference in the Ir-O-Ir in-plane bond angle. At low temperatures, the conduction mechanism in the first batch of the sample is mainly governed by disorder while in the case of the other sample it is of Arrhenius type. The magneto-transport results have shown its strong link with the disorder and structural results. Although the nature and mechanism of the disorder needs to be investigated further, the present results throw light on the role of disorder and its connectivity between the structure and physical properties to understand its complex behaviours.

Controllable Emergent Spatial Spin Modulation in Sr_{2}IrO_{4} by In Situ Shear Strain

Symmetric anisotropic interaction can be ferromagnetic and antiferromagnetic at the same time but for different crystallographic axes. We show that the competition of anisotropic interactions of orthogonal irreducible representations can be a general route to obtain new exotic magnetic states. We demonstrate it here by observing the emergence of a continuously tunable 12-layer spatial spin modulation when distorting the square-lattice planes in the quasi-two-dimensional antiferromagnetic Sr_{2}IrO_{4} under in situ shear strain. This translation-symmetry-breaking phase is a result of an unusual strain-activated anisotropic interaction which is at the fourth order and competing with the inherent quadratic anisotropic interaction. Such a mechanism of competing anisotropy is distinct from that among the ferromagnetic, antiferromagnetic, and/or the Dzyaloshinskii-Moriya interactions, and it could be widely applicable and highly controllable in low-dimensional magnets.

Nanoscale Antiferromagnetic Domain Imaging using Full-Field Resonant X-ray Magnetic Diffraction Microscopy

The physical properties of magnetic materials frequently depend not only on the microscopic spin and electronic structures, but also on the structures of mesoscopic length scales that emerge, for instance, from domain formations, or chemical and/or electronic phase separations. However, experimental access to such mesoscopic structures is currently limited, especially for antiferromagnets with net zero magnetization. Here, full-field microscopy and resonant magnetic X-ray diffraction are combined to visualize antiferromagnetic (AF) domains of the spin-orbit Mott insulator Sr₂ IrO₄ with area over ≈0.1 mm² and with spatial resolution as high as ≈150 nm. With the unprecedented wide field of views and high spatial resolution, an intertwining of two AF domains on a length comparable to the measured average AF domain wall width of 545 nm is revealed. This mesoscopic structure comprises a substantial portion of the sample surface, and thus can result in a macroscopic response unexpected from its microscopic magnetic structure. In particular, the symmetry analysis presented in this work shows that the inversion symmetry, which is preserved by the microscopic AF order, becomes ill-defined at the mesoscopic length scale. This result underscores the importance of this novel technique for a thorough understanding of the physical properties of antiferromagnets.

Direct Observation of Strong Anomalous Hall Effect and Proximity-Induced Ferromagnetic State in SrIrO3

The 5d iridium-based transition metal oxides have gained broad interest because of their strong spin-orbit coupling, which favors new or exotic quantum electronic states. On the other hand, they rarely exhibit more mainstream orders like ferromagnetism due to generally weak electron-electron correlation strength. Here, a proximity-induced ferromagnetic (FM) state with T_C  ≈ 100 K and strong magnetocrystalline anisotropy is shown in a SrIrO₃ (SIO) heterostructure via interfacial charge transfer by using a ferromagnetic insulator in contact with SIO. Electrical transport allows to selectively probe the FM state of the SIO layer and the direct observation of a strong, intrinsic, and positive anomalous Hall effect (AHE). For T ≤ 20 K, the AHE displays unusually large coercive and saturation field, a fingerprint of a strong pseudospin-lattice coupling. A Hall angle, σ_xy ^AHE /σ_{xx ,} larger by an order of magnitude than in typical 3d metals and an FM net moment of about 0.1 μ_B /Ir, is reported. This emphasizes how efficiently the nontrivial topological band properties of SIO can be manipulated by structural modifications and the exchange interaction with 3d TMOs.

Dimensionality of the Superconductivity in the Transition Metal Pnictide WP

We report theoretical and experimental results on the transition metal pnictide WP. The theoretical outcomes based on tight-binding calculations and density functional theory indicate that WP is a three-dimensional superconductor with an anisotropic electronic structure and nonsymmorphic symmetries. On the other hand, magnetoresistance experimental data and the analysis of superconducting fluctuations of the conductivity in external magnetic field indicate a weakly anisotropic three-dimensional superconducting phase.

Interplay between Spin-Orbital Coupling and Electron-Correlation: Induction of Phase Transitions and Giant Magnetic Anisotropy in Strained LaSr_{1−x}Ca_xNiReO_6

In recent decades, 3d-5d based double perovskite oxides (DPO) have received considerable attention due to the existence of the Mott-insulating (MI) state, which is owing to the spin-orbit coupling (SOC)...

IrOx Nanoclusters Modified by BaCO3 Enable ″Two Birds with One Stone″ in Solar-Driven Direct Unbuffered Seawater Electrolysis

Direct seawater electrolysis (DSE) coupled with renewable energy can maximize the sustainability of hydrogen energy acquisition by effectively alleviating the dependence on pure water resources. In a practical sense, the parallel chlorine evolution reaction (CER) of DSE opens up an opportunity to hit ″two birds with one stone″ by the dual values of anode and cathode. However, the biggest challenge is how to control the selectivity of CER to balance its values and drawbacks. Here, we use the different nucleation rates of iridium and barium ions in a weak basic solution and subsequent acid etching to devise an IrO_x nanocluster (IrO_x-Cs) supported BaCO₃. The catalyst-support interaction between IrO_x-Cs and BaCO₃ enables repelling the Cl^- near the electrode interface layer to achieve a controlled CER selectivity. Additionally, the mass activity of the prepared IrO_x-Cs@BaCO₃ is as high as 1402 A g^-1_Ir, which is 7.12 times higher than that of IrO₂ oxides in unbuffered seawater. The photovoltaic-electrolysis device paired by IrO_x-Cs@BaCO₃ with controlled CER activity and Pt demonstrated that valuable active chlorine and H₂ can be simultaneously obtained, with the flexibility to bind to different ion exchange membranes.

Spin-orbital entangled state and realization of Kitaev physics in 3dcobalt compounds: a progress report

The realization of Kitaev's honeycomb magnetic model in real materials has become one of the most pursued topics in condensed matter physics and materials science. If found, it is expected to host exotic quantum phases of matter and offers potential realizations of fault-tolerant quantum computations. Over the past years, much effort has been made on 4d- or 5d-heavy transition metal compounds because of their intrinsic strong spin-orbit coupling. But more recently, there have been growing shreds of evidence that the Kitaev model could also be realized in 3d-transition metal systems with much weaker spin-orbit coupling. This review intends to serve as a guide to this fast-developing field focusing on systems withd⁷transition metal occupation. It overviews the current theoretical and experimental progress on realizing the Kitaev model in those systems. We examine the recent experimental observations of candidate materials with Co²⁺ions: e.g., CoPS₃, Na₃Co₂SbO₆, and Na₂Co₂TeO₆, followed by a brief review of theoretical backgrounds. We conclude this article by comparing experimental observations with density functional theory calculations. We stress the importance of inter-t_2ghopping channels and Hund's coupling in the realization of Kitaev interactions in Co-based compounds, which has been overlooked in previous studies. This review suggests future directions in the search for Kitaev physics in 3dcobalt compounds and beyond.

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

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

Efficient Method for Prediction of Metastable or Ground Multipolar Ordered States and Its Application in Monolayer α-RuX_{3} (X=Cl, I)

Exotic high-rank multipolar order parameters have been found to be unexpectedly active in more and more correlated materials in recent years. Such multipoles are usually dubbed "hidden orders" since they are insensitive to common experimental probes. Theoretically, it is also difficult to predict multipolar orders via ab initio calculations in real materials. Here, we present an efficient method to predict possible multipoles in materials based on linear response theory under random phase approximation. Using this method, we successfully predict two pure metastable magnetic octupolar states in monolayer α-RuCl_{3}, which is confirmed by self-consistent unrestricted Hartree-Fock calculations. We then demonstrate that these octupolar states can be stabilized in monolayer α-RuI_{3}, one of which becomes the octupolar ground state. Furthermore, we also predict a fingerprint of an orthogonal magnetization pattern produced by the octupole moment that can be easily detected by experiment. The method and the example presented in this Letter serve as a guide for searching multipolar order parameters in other correlated materials.

Magnetoelectric phase transition driven by interfacial-engineered Dzyaloshinskii-Moriya interaction

Strongly correlated oxides with a broken symmetry could exhibit various phase transitions, such as superconductivity, magnetism and ferroelectricity. Construction of superlattices using these materials is effective to design crystal symmetries at atomic scale for emergent orderings and phases. Here, antiferromagnetic Ruddlesden-Popper Sr₂IrO₄ and perovskite paraelectric (ferroelectric) SrTiO₃ (BaTiO₃) are selected to epitaxially fabricate superlattices for symmetry engineering. An emergent magnetoelectric phase transition is achieved in Sr₂IrO₄/SrTiO₃ superlattices with artificially designed ferroelectricity, where an observable interfacial Dzyaloshinskii-Moriya interaction driven by non-equivalent interface is considered as the microscopic origin. By further increasing the polarization namely interfacial Dzyaloshinskii-Moriya interaction via replacing SrTiO₃ with BaTiO₃, the transition temperature can be enhanced from 46 K to 203 K, accompanying a pronounced magnetoelectric coefficient of ~495 mV/cm·Oe. This interfacial engineering of Dzyaloshinskii-Moriya interaction provides a strategy to design quantum phases and orderings in correlated electron systems.

Large Magnetocrystalline Anisotropy and Giant Coercivity in the Ferrimagnetic Double Perovskite Lu2NiIrO6

We discover that large uniaxial magnetocrystalline anisotropy driven by the simultaneous presence of spin-orbit coupling and structural distortions is the origin of the giant coercivity observed experimentally in the double perovskite Lu₂NiIrO₆. The magnetic easy axis turns out to be the monoclinic b-axis with an anisotropy constant as high as 1.9 × 10⁸ erg/cm³. The predicted coercive field of 50 kOe and Curie temperature of 220 K agree with the experimentally observed values and point to potential of Lu₂NiIrO₆ in spintronics applications. We find that the spin-orbit coupling induces a rare Ir⁴⁺ J_eff = 1/2 Mott insulating state, suggesting that Lu₂NiIrO₆ provides a playground to study the interplay between spin-orbit coupling and electronic correlations in a 5d transition metal oxide. The spin-orbit coupling also results in a direct band gap with the valence and conduction states localized on different transition metal sublattices, i.e., efficient electron-hole separation upon photoexcitation and low electron-hole recombination.

Electronic band structure of iridates

In this review, an attempt has been made to compare the electronic structures of various 5d iridates (iridium oxides), with an effort to note the common features and differences. Both experimental studies, especially angle-resolved photoemission spectroscopy (ARPES) results, and first-principles band structure calculations have been discussed. This brings to focus the fact that the electronic structures and magnetic properties of the high-Z 5d transition iridates depend on the intricate interplay of strong electron correlation, strong (relativistic) spin-orbit coupling, lattice distortion, and the dimensionality of the system. For example, in the thin film limit, SrIrO₃ exhibits a metal-insulator transition that corresponds to the dimensionality crossover, with the band structure resembling that of bulk Sr₂IrO₄.

Coupled spin-orbital fluctuations in a three orbital model for 4dand 5doxides with electron fillingsn3, 4, 5-application to NaOsO3, Ca2RuO4and Sr2IrO4

A unified approach is presented for investigating coupled spin-orbital fluctuations within a realistic three-orbital model for strongly spin-orbit coupled systems with electron fillingsn= 3, 4, 5 in thet_2gsector ofd_yz,d_xz,d_xyorbitals. A generalized fluctuation propagator is constructed which is consistent with the generalized self-consistent Hartree-Fock approximation where all Coulomb interaction contributions involving orbital diagonal and off-diagonal spin and charge condensates are included. Besides the low-energy magnon, intermediate-energy orbiton and spin-orbiton, and high-energy spin-orbit exciton modes, the generalized spectral function also shows other high-energy excitations such as the Hund's coupling induced gapped magnon modes. We relate the characteristic features of the coupled spin-orbital excitations to the complex magnetic behavior resulting from the interplay between electronic bands, spin-orbit coupling, Coulomb interactions, and structural distortion effects, as realized in the compounds NaOsO₃, Ca₂RuO₄, and Sr₂IrO₄.

Magnetic and transport properties of the mixed 3d-5d-4fdouble perovskite Sm2CoIrO6

Iridium-based double perovskites having mixed 3d-5d-4fmagnetic sub-lattices are expected to exhibit exotic magnetic phenomenon. In this paper, we report a study of structural, magnetic and transport properties of the mixed 3d-5d-4fdouble perovskite Sm₂CoIrO₆(SMCO), which crystallizes in monoclinic structure with space groupP2₁/nand the crystal symmetry remains same throughout the measured temperature down to 15 K. High resolution synchrotron x-ray diffraction reveals an isostructural phase transition around 104 K. Magnetization measurements on polycrystalline samples indicate that SMCO orders ferrimagnetically atT_FiM= 104 K; while, a second transition is observed below 10 K due to the rare-earth (Sm³⁺) ordering. The ferrimagnetic transition is well-understood by Néel's two-sublattice model, which is primarily ascribed to antiferromagnetic coupling between Co²⁺and Ir⁴⁺sub-lattices. Electronic transport measurement shows the insulting behaviour of SMCO, which follows Mott variable-range hopping conduction mechanism. However, dielectric measurements as a function of temperature rules out the presence of magneto dielectric coupling in this compound.