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

Structural and magnetic studies of KOsO4, a 5d1 quantum magnet oxide

The quantum magnet KOsO₄ has been characterized by a combination of X-ray and neutron diffraction techniques. This represents the first structural and magnetic characterization of a simple Os⁷⁺, S = 1/2 oxide system.

Antiferromagnet-Based Spintronic Functionality by Controlling Isospin Domains in a Layered Perovskite Iridate

The novel electronic state of the canted antiferromagnetic (AFM) insulator strontium iridate (Sr₂ IrO₄ ) is well described by the spin-orbit-entangled isospin J_eff = 1/2, but the role of isospin in transport phenomena remains poorly understood. In this study, antiferromagnet-based spintronic functionality is demonstrated by combining the unique characteristics of the isospin state in Sr₂ IrO₄ . Based on magnetic and transport measurements, a large and highly anisotropic magnetoresistance (AMR) is obtained by manipulating the AFM isospin domains. First-principles calculations suggest that electrons whose isospin directions are strongly coupled to the in-plane net magnetic moment encounter an isospin mismatch when moving across the AFM domain boundaries, which generates a high resistance state. By rotating a magnetic field that aligns in-plane net moments and removes domain boundaries, the macroscopically ordered isospins govern dynamic transport through the system, which leads to the extremely angle-sensitive AMR. As this work establishes a link between isospins and magnetotransport in strongly spin-orbit-coupled AFM Sr₂ IrO₄ , the peculiar AMR effect provides a beneficial foundation for fundamental and applied research on AFM spintronics.

Strong Effect of Hydrogen Order on Magnetic Kitaev Interactions in H_{3}LiIr_{2}O_{6}

Very recently a quantum liquid was reported to form in H_{3}LiIr_{2}O_{6}, an iridate proposed to be a close realization of the Kitaev honeycomb model. To test this assertion we perform detailed quantum chemistry calculations to determine the magnetic interactions between Ir moments. We find that weakly bond dependent ferromagnetic Kitaev exchange dominates over other couplings, but still is substantially lower than in Na_{2}IrO_{3}. This reduction is caused by the peculiar position of the interlayer species: removing hydrogen cations next to a Ir_{2}O_{2} plaquette increases the Kitaev exchange by more than a factor of 3 on the corresponding Ir─Ir link. Consequently, any lack of hydrogen order will have a drastic effect on the magnetic interactions and strongly promote spin disordering.

Disorder induced power-law gaps in an insulator-metal Mott transition

A correlated material in the vicinity of an insulator-metal transition (IMT) exhibits rich phenomenology and a variety of interesting phases. A common avenue to induce IMTs in Mott insulators is doping, which inevitably leads to disorder. While disorder is well known to create electronic inhomogeneity, recent theoretical studies have indicated that it may play an unexpected and much more profound role in controlling the properties of Mott systems. Theory predicts that disorder might play a role in driving a Mott insulator across an IMT, with the emergent metallic state hosting a power-law suppression of the density of states (with exponent close to 1; V-shaped gap) centered at the Fermi energy. Such V-shaped gaps have been observed in Mott systems, but their origins are as-yet unknown. To investigate this, we use scanning tunneling microscopy and spectroscopy to study isovalent Ru substitutions in Sr3(Ir1-xRux)2O7 (0 ≤ x ≤ 0.5) which drive the system into an antiferromagnetic, metallic state. Our experiments reveal that many core features of the IMT, such as power-law density of states, pinning of the Fermi energy with increasing disorder, and persistence of antiferromagnetism, can be understood as universal features of a disordered Mott system near an IMT and suggest that V-shaped gaps may be an inevitable consequence of disorder in doped Mott insulators.

Engineering Carrier Effective Masses in Ultrathin Quantum Wells of IrO_{2}

The carrier effective mass plays a crucial role in modern electronic, optical, and catalytic devices and is fundamentally related to key properties of solids such as the mobility and density of states. Here we demonstrate a method to deterministically engineer the effective mass using spatial confinement in metallic quantum wells of the transition metal oxide IrO_{2}. Using a combination of in situ angle-resolved photoemission spectroscopy measurements in conjunction with precise synthesis by oxide molecular-beam epitaxy, we show that the low-energy electronic subbands in ultrathin films of rutile IrO_{2} have their effective masses enhanced by up to a factor of 6 with respect to the bulk. The origin of this strikingly large mass enhancement is the confinement-induced quantization of the highly nonparabolic, three-dimensional electronic structure of IrO_{2} in the ultrathin limit. This mechanism lies in contrast to that observed in other transition metal oxides, in which mass enhancement tends to result from complex electron-electron interactions and is difficult to control. Our results demonstrate a general route towards the deterministic enhancement and engineering of carrier effective masses in spatially confined systems, based on an understanding of the three-dimensional bulk electronic structure.

Na2IrIVCl6: Spin-Orbital-Induced Semiconductor Showing Hydration-Dependent Structural and Magnetic Variations

Iridium(IV) oxides have gained increased attention in recent years owing to the presence of competing spin-orbit coupling and Coulomb interactions, which facilitate the emergence of novel quantum phenomena. In contrast, the electronic structure and magnetic properties of Ir^IV-based molecular materials remain largely unexplored. In this paper, we take a fresh look at an old but puzzling compound, Na₂IrCl₆, which can be hydrated to form two stable phases with formulas Na₂IrCl₆·2H₂O and Na₂IrCl₆·6H₂O. Their crystal structures are well illustrated based on X-ray powder diffraction data. Magnetic studies reveal that Na₂IrCl₆ and Na₂IrCl₆·2H₂O are canted antiferromagnets with ordering temperatures of 7.4 and 2.7 K, respectively, whereas Na₂IrCl₆·6H₂O is paramagnetic down to 1.8 K. First-principle calculations on Na₂IrCl₆ reveal a J_eff = 1/2 ground state, and the band structures show that Na₂IrCl₆ is a spin-orbital-induced semiconductor with an indirect gap of about 0.18 eV.

Spectroscopic Studies on the Metal-Insulator Transition Mechanism in Correlated Materials

The metal-insulator transition (MIT) in correlated materials is a novel phenomenon that accompanies a large change in resistivity, often many orders of magnitude. It is important in its own right but its switching behavior in resistivity can be useful for device applications. From the material physics point of view, the starting point of the research on the MIT should be to understand the microscopic mechanism. Here, an overview of recent efforts to unravel the microscopic mechanisms for various types of MITs in correlated materials is provided. Research has focused on transition metal oxides (TMOs), but transition metal chalcogenides have also been studied. Along the way, a new class of MIT materials is discovered, the so-called relativistic Mott insulators in 5d TMOs. Distortions in the MO₆ (M = transition metal) octahedron are found to have a large and peculiar effect on the band structure in an orbital dependent way, possibly paving a way to the orbital selective Mott transition. In the final section, the character of the materials suitable for applications is summarized, followed by a brief discussion of some of the efforts to control MITs in correlated materials, including a dynamical approach using light.

Dynamics of a single hole in the Heisenberg-Kitaev model: a self-consistent Born approximation study

The magnetic properties of 4d and 5d transition-metal insulating compounds with the honeycomb structure are believed to be described by the Heisenberg-Kitaev model, which contains both the isotropic Heisenberg interaction J and anisotropic Kitaev interaction K. In this paper, we study the single-hole propagation of the t-J-K model in various magnetically ordered phases by the self-consistent Born approximation. We find that there are low-energy coherent quasiparticle (QP) excitations in all of these phases which appear firstly around the K point in the first Brillouin zone (BZ), but the bandwidths of these QPs are very small due to the hole-magnon coupling. Interestingly, in the zigzag phase relevant to recent experiments, though the QP weights are largely suppressed in the physical spectra in the first BZ, we find that they recover in the extended BZs. Moreover, our results reveal that the low-energy QP spectra are reduced with the increase of K.

Determination of the local structure of Sr2-xMxIrO4 (M = K, La) as a function of doping and temperature

The local structure of correlated spin-orbit insulator Sr2-xMxIrO4 (M = K, La) has been investigated by Ir L3-edge extended X-ray absorption fine structure measurements. The measurements were performed as a function of temperature for different dopings induced by substitution of Sr with La or K. It is found that Ir-O bonds have strong covalency and they hardly show any change across the Néel temperature. In the studied doping range, neither Ir-O bonds nor their dynamics, measured by their mean square relative displacements, show any appreciable change upon carrier doping, indicating the possibility of nanoscale phase separation in the doped system. On the other hand, there is a large increase of the static disorder in Ir-Sr correlation, larger for K doping than La doping. Similarities and differences with respect to the local lattice displacements in cuprates are briefly discussed.

Comparative study of DFT+U functionals for non-collinear magnetism

We performed comparative analysis for DFT+U functionals to better understand their applicability to non-collinear magnetism. Taking LiNiPO₄ and Sr₂IrO₄ as examples, we investigated the results out of two formalisms based on charge-only density and spin density functional plus U calculations. Our results show that the ground state spin order in terms of tilting angle is strongly dependent on Hund J. In particular, the opposite behavior of canting angles as a function of J is found for LiNiPO₄. The dependence on the other physical parameters such as Hubbard U and Slater parameterization [Formula: see text] is investigated. We also discuss the formal aspects of these functional dependences as well as parameter dependences. The current study provides useful information and important intuition for the first-principles calculation of non-collinear magnetic materials.

A Family of A-Site Cation-Deficient Double-Perovskite-Related Iridates: Ln9Sr2Ir4O24 (Ln = La, Pr, Nd, Sm)

The compositions of the general formula Ln_{11- x}Sr _xIr₄O₂₄ (Ln = La, Pr, Nd, Sm; 1.37 ≥ x ≥ 2) belonging to a family of A-site cation-deficient double-perovskite-related oxide iridates were grown as highly faceted single crystals from a molten strontium chloride flux. Their structures were determined by single-crystal X-ray diffraction. On the basis of the single-crystal results, additional compositions, Ln₉Sr₂Ir₄O₂₄ (Ln = La, Pr, Nd, Sm), were prepared as polycrystalline powders via solid-state reactions and structurally characterized by Rietveld refinement. The compositions Ln₉Sr₂Ir₄O₂₄ (Ln = La, Pr, Nd, Sm) contain Ir(V) and Ir(IV) in a 1:3 ratio with an average iridium oxidation state of 4.25. The single-crystal compositions La_9.15Sr_1.85Ir₄O₂₄ and Pr_9.63Sr_1.37Ir₄O₂₄ contain relatively less Ir(V), with the average iridium oxidation states being 4.21 and 4.09, respectively. The magnetic properties of Ln₉Sr₂Ir₄O₂₄ (Ln = La, Pr, Nd, Sm) were measured, and complex magnetic behavior was observed in all cases at temperatures below 30 K.

Enhanced insulating behavior in the Ir-vacant Sr2Ir1-xO4 system dominated by the local structure distortion

Sr₂IrO₄, known as the J_eff = 1/2 Mott insulator, was predicted to be an unconventional superconductor upon doping since it highly resembles the high-temperature cuprates. However, recent work pointed out an enhanced insulating behavior in the Ir-vacant Sr₂Ir_1-xO₄ system. In this contribution, to investigate the microscopic mechanism of its enhanced insulating behavior, X-ray absorption spectroscopy was applied to study the electronic structure and local structure distortion of Sr₂Ir_1-xO₄. Due to the presence of Ir⁵⁺ ions, the preconceived holes are barely doped in the Ir-vacant system. Nevertheless, Ir vacancies finely modulate the local atomic structure, i.e. the topology of IrO₆ octahedra and the in-plane Ir-O1-Ir bond angle. Combined with theoretical calculations, it is demonstrated that both the more distorted IrO₆ octahedra and decreased Ir-O1-Ir angle contribute to the increment of the band gap, and then result in the enhanced insulating state for Sr₂Ir_1-xO₄.

Decoupling of magnetism and electric transport in single-crystal (Sr1-x A x )2IrO4 (A = Ca or Ba)

We report a systematical structural, transport and magnetic study of Ca or Ba doped Sr₂IrO₄ single crystals. Isoelectronically substituting Ca²⁺ (up to 15%) or Ba²⁺ (up to 4%) ion for the Sr²⁺ ion provides no additional charge carriers but effectively changes the lattice parameters in Sr₂IrO₄. In particular, 15% Ca doping considerably reduces the c-axis and the unit cell by nearly 0.45% and 1.00%, respectively. These significant, anisotropic compressions in the lattice parameters conspicuously cause no change in the Néel temperature which remains at 240 K, but drastically reduces the electrical resistivity by up to five orders of magnitude or even precipitates a sharp insulator-to-metal transition at lower temperatures, i.e. the vanishing insulating state accompanies an unchanged Néel temperature in (Sr_1-x A _x )₂IrO₄. This observation brings to light an intriguing difference between chemical pressure and applied pressure, the latter of which does suppress the long-range magnetic order in Sr₂IrO₄. This difference reveals the importance of the Ir1-O2-Ir1 bond angle and homogenous volume compression in determining the magnetic ground state. All results, along with a comparison drawn with results of Tb and La doped Sr₂IrO₄, underscore that the magnetic transition plays a nonessential role in the formation of the charge gap in the spin-orbit-tuned iridate.

Stability of the antiferromagnetic state in the electron doped iridates

Iridates such as Sr₂IrO₄ are of considerable interest owing to the formation of the Mott insulating state driven by a large spin-orbit coupling. However, in contrast to the expectation from the Nagaoka theorem that a single doped hole or electron destroys the anti-ferromagnetic (AFM) state of the half-filled Hubbard model in the large U limit, the anti-ferromagnetism persists in the doped Iridates for a large dopant concentration beyond half-filling. With a tight-binding description of the relevant [Formula: see text] states by the third-neighbor (t ₁, t ₂, t ₃, U) Hubbard model on the square lattice, we examine the stability of the AFM state to the formation of a spin spiral state in the strong coupling limit. The third-neighbor interaction t ₃ is important for the description of the Fermi surface of the electron doped system. A phase diagram in the parameter space is obtained for the regions of stability of the AFM state. Our results qualitatively explain the robustness of the AFM state in the electron doped iridate (such as Sr_2-x La _x IrO₄), observed in many experiments, where the AFM state continues to be stable until a critical dopant concentration.

Unraveling the Nature of Magnetism of the 5d^{4} Double Perovskite Ba_{2}YIrO_{6}

We report electron spin resonance (ESR) spectroscopy results on the double perovskite Ba_{2}YIrO_{6}. On general grounds, this material is expected to be nonmagnetic due to the strong coupling of the spin and orbital momenta of Ir^{5+} (5d^{4}) ions. However, controversial experimental reports on either strong antiferromagnetism with static order at low temperatures or just a weakly paramagnetic behavior have triggered a discussion on the breakdown of the generally accepted scenario of the strongly spin-orbit coupled ground states in the 5d^{4} iridates and the emergence of a novel exotic magnetic state. Our data evidence that the magnetism of the studied material is solely due to a few percent of Ir^{4+} and Ir^{6+} magnetic defects while the regular Ir^{5+} sites remain nonmagnetic. Remarkably, the defect Ir^{6+} species manifest magnetic correlations in the ESR spectra at T≲20  K, suggesting a long-range character of superexchange in the double perovskites as proposed by recent theories.

Magnetic Excitations across the Metal-Insulator Transition in the Pyrochlore Iridate Eu_{2}Ir_{2}O_{7}

We report a resonant inelastic x-ray scattering study of the magnetic excitation spectrum in a highly insulating Eu_{2}Ir_{2}O_{7} single crystal that exhibits a metal-insulator transition at T_{MI}=111(7)  K. A propagating magnon mode with a 20 meV bandwidth and a 28 meV magnon gap is found in the excitation spectrum at 7 K, which is expected in the all-in-all-out magnetically ordered state. This magnetic excitation exhibits substantial softening as the temperature is raised towards T_{MI} and turns into a highly damped excitation in the paramagnetic phase. Remarkably, the softening occurs throughout the whole Brillouin zone including the zone boundary. This observation is inconsistent with the magnon renormalization expected in a local moment system and indicates that the strength of the electron correlation in Eu_{2}Ir_{2}O_{7} is only moderate, so that electron itinerancy should be taken into account in describing its magnetism.

The challenge of spin-orbit-tuned ground states in iridates: a key issues review

Effects of spin-orbit interactions in condensed matter are an important and rapidly evolving topic. Strong competition between spin-orbit, on-site Coulomb and crystalline electric field interactions in iridates drives exotic quantum states that are unique to this group of materials. In particular, the 'J _eff  =  ½' Mott state served as an early signal that the combined effect of strong spin-orbit and Coulomb interactions in iridates has unique, intriguing consequences. In this Key Issues Review, we survey some current experimental studies of iridates. In essence, these materials tend to defy conventional wisdom: absence of conventional correlations between magnetic and insulating states, avoidance of metallization at high pressures, 'S-shaped' I-V characteristic, emergence of an odd-parity hidden order, etc. It is particularly intriguing that there exist conspicuous discrepancies between current experimental results and theoretical proposals that address superconducting, topological and quantum spin liquid phases. This class of materials, in which the lattice degrees of freedom play a critical role seldom seen in other materials, evidently presents some profound intellectual challenges that call for more investigations both experimentally and theoretically. Physical properties unique to these materials may help unlock a world of possibilities for functional materials and devices. We emphasize that, given the rapidly developing nature of this field, this Key Issues Review is by no means an exhaustive report of the current state of experimental studies of iridates.

Negative Longitudinal Magnetoresistance in the Density Wave Phase of Y_{2}Ir_{2}O_{7}

The ground state of nanowires of single-crystalline pyrochlore Y_{2}Ir_{2}O_{7} is a density wave. The application of a transverse magnetic field increases the threshold electric field for the collective depinning of the density wave state at a low temperature, leading to colossal magnetoresistance for voltages around the depinning threshold. This is in striking contrast to the case where even a vanishingly small longitudinal magnetic field sharply reduces the depinning threshold voltage, resulting in negative magnetoresistance. Ruling out several other possibilities, we argue that this phenomenon is likely to be a consequence of the chiral anomaly in the gapped out Weyl semimetal phase in Y_{2}Ir_{2}O_{7}.

Ultralow-Temperature Thermal Conductivity of the Kitaev Honeycomb Magnet α-RuCl_{3} across the Field-Induced Phase Transition

Recently, there have been increasingly hot debates on whether there exists a quantum spin liquid in the Kitaev honeycomb magnet α-RuCl_{3} in a high magnetic field. To investigate this issue, we perform ultralow-temperature thermal conductivity measurements on single crystals of α-RuCl_{3} down to 80 mK and up to 9 T. Our experiments clearly show a field-induced phase transition occurring at μ_{0}H_{c}≈7.5  T, above which the magnetic order is completely suppressed. The minimum of thermal conductivity at 7.5 T is attributed to the strong scattering of phonons by magnetic fluctuations. Most importantly, above 7.5 T, we do not observe any significant contribution of thermal conductivity from gapless magnetic excitations, which puts a strong constraint on the nature of the high-field phase of α-RuCl_{3}.

Unidirectional spin density wave state in metallic (Sr1-xLa x )2IrO4

Materials that exhibit both strong spin–orbit coupling and electron correlation effects are predicted to host numerous new electronic states. One prominent example is the J_eff = 1/2 Mott state in Sr₂IrO₄, where introducing carriers is predicted to manifest high temperature superconductivity analogous to the S = 1/2 Mott state of La₂CuO₄. While bulk superconductivity currently remains elusive, anomalous quasiparticle behaviors paralleling those in the cuprates such as pseudogap formation and the formation of a d-wave gap are observed upon electron-doping Sr₂IrO₄. Here we establish a magnetic parallel between electron-doped Sr₂IrO₄ and hole-doped La₂CuO₄ by unveiling a spin density wave state in electron-doped Sr₂IrO₄. Our magnetic resonant X-ray scattering data reveal the presence of an incommensurate magnetic state reminiscent of the diagonal spin density wave state observed in the monolayer cuprate (La_1−xSr_x)₂CuO₄. This link supports the conjecture that the quenched Mott phases in electron-doped Sr₂IrO₄ and hole-doped La₂CuO₄ support common competing electronic phases.

Electron-doped Sr₂IrO₄ is an intriguing material for searching for an unconventional superconducting state. Here the authors demonstrate that a spin density wave state exists in the metallic phase of electron-doped Sr₂IrO₄ which provides a link between the electronic phase diagrams of the hole-doped cuprates and the electron-doped iridates.

Electrical Control of Structural and Physical Properties via Strong Spin-Orbit Interactions in Sr_{2}IrO_{4}

Electrical control of structural and physical properties is a long-sought, but elusive goal of contemporary science and technology. We demonstrate that a combination of strong spin-orbit interactions (SOI) and a canted antiferromagnetic Mott state is sufficient to attain that goal. The antiferromagnetic insulator Sr_{2}IrO_{4} provides a model system in which strong SOI lock canted Ir magnetic moments to IrO_{6} octahedra, causing them to rigidly rotate together. A novel coupling between an applied electrical current and the canting angle reduces the Néel temperature and drives a large, nonlinear lattice expansion that closely tracks the magnetization, increases the electron mobility, and precipitates a unique resistive switching effect. Our observations open new avenues for understanding fundamental physics driven by strong SOI in condensed matter, and provide a new paradigm for functional materials and devices.

Spin-Orbit Semimetal SrIrO_{3} in the Two-Dimensional Limit

We investigate the thickness-dependent electronic properties of ultrathin SrIrO_{3} and discover a transition from a semimetallic to a correlated insulating state below 4 unit cells. Low-temperature magnetoconductance measurements show that spin fluctuations in the semimetallic state are significantly enhanced while approaching the transition point. The electronic properties are further studied by scanning tunneling spectroscopy, showing that 4 unit cell SrIrO_{3} is on the verge of a gap opening. Our density functional theory calculations reproduce the critical thickness of the transition and show that the opening of a gap in ultrathin SrIrO_{3} requires antiferromagnetic order.

Dimensionality-Driven Metal-Insulator Transition in Spin-Orbit-Coupled SrIrO_{3}

Upon reduction of the film thickness we observe a metal-insulator transition in epitaxially stabilized, spin-orbit-coupled SrIrO_{3} ultrathin films. By comparison of the experimental electronic dispersions with density functional theory at various levels of complexity we identify the leading microscopic mechanisms, i.e., a dimensionality-induced readjustment of octahedral rotations, magnetism, and electronic correlations. The astonishing resemblance of the band structure in the two-dimensional limit to that of bulk Sr_{2}IrO_{4} opens new avenues to unconventional superconductivity by "clean" electron doping through electric field gating.

Structure, magnetism and electronic properties in 3d-5d based double perovskite ([Formula: see text]Y x )2FeIrO6

The 3d-5d based double perovskites are of current interest as they provide model systems to study the interplay between electronic correlation (U) and spin-orbit coupling (SOC). Here, we report detailed structural, magnetic and transport properties of doped double perovskite material ([Formula: see text]Y _x )₂FeIrO₆ with [Formula: see text]. With substitution of Y, the system retains its original crystal structure but structural parameters change with x in nonmonotonic fashion. The magnetization data for Sr₂FeIrO₆ show antiferromagnetic type magnetic transition around 45 K; however, a close inspection of the data indicates a weak magnetic phase transition around 120 K. No change of structural symmetry has been observed down to low temperature, although the lattice parameters show sudden changes around the magnetic transitions. Sr₂FeIrO₆ shows an insulating behavior over the whole temperature range, which nevertheless does not change with Y substitution. The nature of charge conduction is found to follow thermally activated Mott's variable range hopping and power law behavior for parent and doped samples, respectively. Interestingly, evolution of structural, magnetic and transport behavior in ([Formula: see text]Y _x )₂FeIrO₆ is observed to reverse with [Formula: see text], which is believed to arise due to a change in the transition metal ionic state.

Models and materials for generalized Kitaev magnetism

The exactly solvable Kitaev model on the honeycomb lattice has recently received enormous attention linked to the hope of achieving novel spin-liquid states with fractionalized Majorana-like excitations. In this review, we analyze the mechanism proposed by Jackeli and Khaliullin to identify Kitaev materials based on spin-orbital dependent bond interactions and provide a comprehensive overview of its implications in real materials. We set the focus on experimental results and current theoretical understanding of planar honeycomb systems (Na₂IrO₃, α-Li₂IrO₃, and α-RuCl₃), three-dimensional Kitaev materials (β- and γ-Li₂IrO₃), and other potential candidates, completing the review with the list of open questions awaiting new insights.

Charge-Stripe Order and Superconductivity in Ir1-xPtxTe2

A combined resistivity and hard x-ray diffraction study of superconductivity and charge ordering in Ir Ir_1−xPt_xTe₂, as a function of Pt substitution and externally applied hydrostatic pressure, is presented. Experiments are focused on samples near the critical composition x_c ~ 0.045 where competition and switching between charge order and superconductivity is established. We show that charge order as a function of pressure in Ir_0.95Pt_0.05Te₂ is preempted — and hence triggered — by a structural transition. Charge ordering appears uniaxially along the short crystallographic (1, 0, 1) domain axis with a (1/5, 0, 1/5) modulation. Based on these results we draw a charge-order phase diagram and discuss the relation between stripe ordering and superconductivity.

Engineering magnetism at functional oxides interfaces: manganites and beyond

The family of transition metal oxides (TMOs) is a large class of magnetic materials that has been intensively studied due to the rich physics involved as well as the promising potential applications in next generation electronic devices. In TMOs, the spin, charge, orbital and lattice are strongly coupled, and significant advances have been achieved to engineer the magnetism by different routes that manipulate these degrees of freedom. The family of manganites is a model system of strongly correlated magnetic TMOs. In this review, using manganites thin films and the heterostructures in conjunction with other TMOs as model systems, we review the recent progress of engineering magnetism in TMOs. We first discuss the role of the lattice that includes the epitaxial strain and the interface structural coupling. Then we look into the role of charge, focusing on the interface charge modulation. Having demonstrated the static effects, we continue to review the research on dynamical control of magnetism by electric field. Next, we review recent advances in heterostructures comprised of high T _c cuprate superconductors and manganites. Following that, we discuss the emergent magnetic phenomena at interfaces between 3d TMOs and 5d TMOs with strong spin-orbit coupling. Finally, we provide our outlook for prospective future directions.

Cu2IrO3: A New Magnetically Frustrated Honeycomb Iridate

We present the first copper iridium binary metal oxide with the chemical formula Cu₂IrO₃. The material is synthesized from the parent compound Na₂IrO₃ by a topotactic reaction where sodium is exchanged with copper under mild conditions. Cu₂IrO₃ has the same monoclinic space group (C2/c) as Na₂IrO₃ with a layered honeycomb structure. The parent compound Na₂IrO₃ is proposed to be relevant to the Kitaev spin liquid on the basis of having Ir⁴⁺ with an effective spin of 1/2 on a honeycomb lattice. Remarkably, whereas Na₂IrO₃ shows a long-range magnetic order at 15 K and fails to become a true spin liquid, Cu₂IrO₃ remains disordered until 2.7 K, at which point a short-range order develops. Rietveld analysis shows less distortions in the honeycomb structure of Cu₂IrO₃ with bond angles closer to 120° compared to Na₂IrO₃. Thus, the weak short-range magnetism combined with the nearly ideal honeycomb structure places Cu₂IrO₃ closer to a Kitaev spin liquid than its predecessors.

Highly Mobile Two-Dimensional Electron Gases with a Strong Gating Effect at the Amorphous LaAlO3/KTaO3 Interface

Two-dimensional electron gas (2DEG) at the perovskite oxide interface exhibits a lot of exotic properties, presenting a promising platform for the exploration of emergent phenomena. While most of the previous works focused on SrTiO₃-based 2DEG, here we report on the fabrication of high-quality 2DEGs by growing an amorphous LaAlO₃ layer on a (001)-orientated KTaO₃ substrate, which is a 5d metal oxide with a polar surface, at a high temperature that is usually adopted for crystalline LaAlO₃. Metallic 2DEGs with a Hall mobility as high as ∼2150 cm²/(V s) and a sheet carrier density as low as 2 × 10¹² cm^-2 are obtained. For the first time, the gating effect on the transport process is studied, and its influence on spin relaxation and inelastic and elastic scattering is determined. Remarkably, the spin relaxation time can be strongly tuned by a back gate. It is reduced by a factor of ∼69 while the gate voltage is swept from -25 to +100 V. The mechanism that dominates the spin relaxation is elucidated.

Direct experimental observation of the molecular J eff = 3/2 ground state in the lacunar spinel GaTa4Se8

Strong spin–orbit coupling lifts the degeneracy of t_2g orbitals in 5d transition-metal systems, leaving a Kramers doublet and quartet with effective angular momentum of J_eff = 1/2 and 3/2, respectively. These spin–orbit entangled states can host exotic quantum phases such as topological Mott state, unconventional superconductivity, and quantum spin liquid. The lacunar spinel GaTa₄Se₈ was theoretically predicted to form the molecular J_eff = 3/2 ground state. Experimental verification of its existence is an important first step to exploring the consequences of the J_eff = 3/2 state. Here, we report direct experimental evidence of the J_eff = 3/2 state in GaTa₄Se₈ by means of excitation spectra of resonant inelastic X-ray scattering at the Ta L₃ and L₂ edges. We find that the excitations involving the J_eff = 1/2 molecular orbital are absent only at the Ta L₂ edge, manifesting the realization of the molecular J_eff = 3/2 ground state in GaTa₄Se₈.

The strong interaction between electron spin and orbital degrees of freedom in 5d oxides can lead to exotic electronic ground states. Here the authors use resonant inelastic X-ray scattering to demonstrate that the theoretically proposed J_eff = 3/2 state is realised in GaTa₄Se₈.

Correlation induced electron-hole asymmetry in quasi- two-dimensional iridates

The resemblance of crystallographic and magnetic structures of the quasi-two-dimensional iridates Ba₂IrO₄ and Sr₂IrO₄ to La₂CuO₄ points at an analogy to cuprate high-Tc superconductors, even if spin-orbit coupling is very strong in iridates. Here we examine this analogy for the motion of a charge (hole or electron) added to the antiferromagnetic ground state. We show that correlation effects render the hole and electron case in iridates very different. An added electron forms a spin polaron, similar to the cuprates, but the situation of a removed electron is far more complex. Many-body 5d ⁴ configurations form which can be singlet and triplet states of total angular momentum that strongly affect the hole motion. This not only has ramifications for the interpretation of (inverse-)photoemission experiments but also demonstrates that correlation physics renders electron- and hole-doped iridates fundamentally different.Some iridate compounds such as Sr₂IrO₄ have electronic and atomic structures similar to quasi-2D copper oxides, raising the prospect of high temperature superconductivity. Here, the authors show that there is significant electron-hole asymmetry in iridates, contrary to expectations from the cuprates.

Itinerant magnetic metals

In this review, an overview of itinerant magnets without magnetic elements is presented, beginning with a comparison of the local and itinerant moment pictures, the two extremes of magnetism. Then, the theoretical developments leading up to the self-consistent renormalization theory of spin fluctuations will be discussed, followed by an introduction to quantum criticality and the experimental signatures associated with systems near a quantum critical point. Three itinerant magnets without magnetic elements, ZrZn₂, Sc_3.1In, and TiAu are the focus of this review, as their empty d shells set them apart in their purely itinerant character, while several enhanced Pauli paramagnets and intermediate moment magnets are also discussed to put the overall comparison into perspective.

Infrared probe of pseudogap in electron-doped Sr2IrO4

We report on infrared spectroscopy experiments on the electronic response in (Sr_1-x La _x )₂IrO₄ (x = 0, 0.021, and 0.067). Our data show that electron doping induced by La substitution leads to an insulator-to-metal transition. The evolution of the electronic structure across the transition reveals the robustness of the strong electronic correlations against the electron doping. The conductivity data of the metallic compound show the signature of the pseudogap that bears close similarity to the analogous studies of the pseudogap in the underdoped cuprates. While the low energy conductivity of the metallic compound is barely frequency dependent, the formation of the pseudogap is revealed by the gradual suppression of the featureless conductivity below a threshold frequency of about 17 meV. The threshold structure develops below about 100 K which is in the vicinity of the onset of the short-range antiferromagnetic order. Our results demonstrate that the electronic correlations play a crucial role in the anomalous charge dynamics in the (Sr_1-x La _x )₂IrO₄ system.

Two-magnon scattering in the 5d all-in-all-out pyrochlore magnet Cd2Os2O7

5d pyrochlore oxides with all-in-all-out magnetic order are prime candidates for realizing strongly correlated, topological phases of matter. Despite significant effort, a full understanding of all-in-all-out magnetism remains elusive as the associated magnetic excitations have proven difficult to access with conventional techniques. Here we report a Raman spectroscopy study of spin dynamics in the all-in-all-out magnetic state of the 5d pyrochlore Cd2Os2O7. Through a comparison between the two-magnon scattering and spin-wave theory, we confirm the large single ion anisotropy in this material and show that the Dzyaloshinskii-Moriya and exchange interactions play a significant role in the spin-wave dispersions. The Raman data also reveal complex spin-charge-lattice coupling and indicate that the metal-insulator transition in Cd2Os2O7 is Lifshitz-type. Our work establishes Raman scattering as a simple and powerful method for exploring the spin dynamics in 5d pyrochlore magnets.Pyrochlore 5d transition metal oxides are expected to have interesting forms of magnetic order but are hard to study with conventional probes. Here the authors show that Raman scattering can be used to measure magnetic excitations in Cd2Os2O7 and that it exhibits complex spin-charge-lattice coupling.

Epitaxial thin films of pyrochlore iridate Bi2+xIr2-yO7-δ: structure, defects and transport properties

While pyrochlore iridate thin films are theoretically predicted to possess a variety of emergent topological properties, experimental verification of these predictions can be obstructed by the challenge in thin film growth. Here we report on the pulsed laser deposition and characterization of thin films of a representative pyrochlore compound Bi₂Ir₂O₇. The films were epitaxially grown on yttria-stabilized zirconia substrates and have lattice constants that are a few percent larger than that of the bulk single crystals. The film composition shows a strong dependence on the oxygen partial pressure. Density-functional-theory calculations indicate the existence of Bi_Ir antisite defects, qualitatively consistent with the high Bi: Ir ratio found in the films. Both Ir and Bi have oxidation states that are lower than their nominal values, suggesting the existence of oxygen deficiency. The iridate thin films show a variety of intriguing transport characteristics, including multiple charge carriers, logarithmic dependence of resistance on temperature, antilocalization corrections to conductance due to spin-orbit interactions, and linear positive magnetoresistance.

Multipole Superconductivity in Nonsymmorphic Sr_{2}IrO_{4}

Discoveries of marked similarities to high-T_{c} cuprate superconductors point to the realization of superconductivity in the doped J_{eff}=1/2 Mott insulator Sr_{2}IrO_{4}. Contrary to the mother compound of cuprate superconductors, several stacking patterns of in-plane canted antiferromagnetic moments have been reported, which are distinguished by the ferromagnetic components as -++-, ++++, and -+-+. In this paper, we clarify unconventional features of the superconductivity coexisting with -++- and -+-+ structures. Combining the group theoretical analysis and numerical calculations for an effective J_{eff}=1/2 model, we show unusual superconducting gap structures in the -++- state protected by nonsymmorphic magnetic space group symmetry. Furthermore, our calculation shows that the Fulde-Ferrell-Larkin-Ovchinnikov superconductivity is inevitably stabilized in the -+-+ state since the odd-parity magnetic -+-+ order makes the band structure asymmetric by cooperating with spin-orbit coupling. These unusual superconducting properties are signatures of magnetic multipole order in nonsymmorphic crystal.

Two-Dimensional J_{eff}=1/2 Antiferromagnetic Insulator Unraveled from Interlayer Exchange Coupling in Artificial Perovskite Iridate Superlattices

We report an experimental investigation of the two-dimensional J_{eff}=1/2 antiferromagnetic Mott insulator by varying the interlayer exchange coupling in [(SrIrO_{3})_{1}, (SrTiO_{3})_{m}] (m=1, 2 and 3) superlattices. Although all samples exhibited an insulating ground state with long-range magnetic order, temperature-dependent resistivity measurements showed a stronger insulating behavior in the m=2 and m=3 samples than the m=1 sample which displayed a clear kink at the magnetic transition. This difference indicates that the blocking effect of the excessive SrTiO_{3} layer enhances the effective electron-electron correlation and strengthens the Mott phase. The significant reduction of the Néel temperature from 150 K for m=1 to 40 K for m=2 demonstrates that the long-range order stability in the former is boosted by a substantial interlayer exchange coupling. Resonant x-ray magnetic scattering revealed that the interlayer exchange coupling has a switchable sign, depending on the SrTiO_{3} layer number m, for maintaining canting-induced weak ferromagnetism. The nearly unaltered transition temperature between the m=2 and the m=3 demonstrated that we have realized a two-dimensional antiferromagnet at finite temperatures with diminishing interlayer exchange coupling.

Coulomb correlations in 4d and 5d oxides from first principles-or how spin-orbit materials choose their effective orbital degeneracies

The interplay of spin-orbit coupling and Coulomb correlations has become a hot topic in condensed matter theory and is especially important in 4d and 5d transition metal oxides, like iridates or rhodates. Here, we review recent advances in dynamical mean-field theory (DMFT)-based electronic structure calculations for treating such compounds, introducing all necessary implementation details. We also discuss the evaluation of Hubbard interactions in spin-orbit materials. As an example, we perform DMFT calculations on insulating strontium iridate (Sr₂IrO₄) and its 4d metallic counterpart, strontium rhodate (Sr₂RhO₄). While a Mott-insulating state is obtained for Sr₂IrO₄ in its paramagnetic phase, the spectral properties and Fermi surfaces obtained for Sr₂RhO₄ show excellent agreement with available experimental data. Finally, we discuss the electronic structure of these two compounds by introducing the notion of effective spin-orbital degeneracy as the key quantity that determines the correlation strength. We stress that effective spin-orbital degeneracy introduces an additional axis into the conventional picture of a phase diagram based on filling and on the ratio of interactions to bandwidth, analogous to the degeneracy-controlled Mott transition in d¹ perovskites.

Relation between the Co-O bond lengths and the spin state of Co in layered Cobaltates: a high-pressure study

The pressure-response of the Co-O bond lengths and the spin state of Co ions in a hybrid 3d-5d solid-state oxide Sr₂Co_0.5Ir_0.5O₄ with a layered K₂NiF₄-type structure was studied by using hard X-ray absorption and emission spectroscopies. The Co-K and the Ir-L₃ X-ray absorption spectra demonstrate that the Ir⁵⁺ and the Co³⁺ valence states at ambient conditions are not affected by pressure. The Co Kβ emission spectra, on the other hand, revealed a gradual spin state transition of Co³⁺ ions from a high-spin (S = 2) state at ambient pressure to a complete low-spin state (S = 0) at 40 GPa without crossing the intermediate spin state (S = 1). This can be well understood from our calculated phase diagram in which we consider the energies of the low spin, intermediate spin and high spin states of Co³⁺ ions as a function of the anisotropic distortion of the octahedral local coordination in the layered oxide. We infer that a short in-plane Co-O bond length (<1.90 Å) as well as a very large ratio of Co-O_apex/Co-O_in-plane is needed to stabilize the IS Co³⁺, a situation which is rarely met in reality.

Neutron scattering by Dirac multipoles

Scattering by magnetic charge formed by Dirac multipoles that are magnetic and polar is examined in the context of materials with properties that challenge conventional concepts. An order parameter composed of Dirac quadrupoles has been revealed in the pseudo-gap phase of ceramic, high-T _c superconductors on the basis of Kerr effect and magnetic neutron Bragg diffraction measurements. Construction of Dirac quadrupoles that emerge from centrosymmetric sites used by Cu ions in the ceramic superconductor Hg1201 is illustrated, together with selection rules for excitations that will feature in neutron inelastic scattering, and RIXS experiments. We report magnetic scattering amplitudes for diffraction by polar multipoles that have universal value, because they are not specific to ceramic superconductors. To illustrate this attribute, we consider neutron Bragg diffraction from a magnetically ordered iridate (Sr₂IrO₄) and discuss shortcomings in published interpretations of diffraction data.

Topological Magnon Bands and Unconventional Superconductivity in Pyrochlore Iridate Thin Films

We theoretically study the magnetic properties of pyrochlore iridate bilayer and trilayer thin films grown along the [111] direction using a strong coupling approach. We find the ground state magnetic configurations on a mean field level and carry out a spin-wave analysis about them. In the trilayer case the ground state is found to be the all-in-all-out (AIAO) state, whereas the bilayer has a deformed AIAO state. For all parameters of the spin-orbit coupled Hamiltonian we study, the lowest magnon band in the trilayer case has a nonzero Chern number. In the bilayer case we also find a parameter range with nonzero Chern numbers. We calculate the magnon Hall response for both geometries, finding a striking sign change as a function of temperature. Using a slave-boson mean-field theory we study the doping of the trilayer system and discover an unconventional time-reversal symmetry broken d+id superconducting state. Our study complements prior work in the weak coupling limit and suggests that the [111] grown thin film pyrochlore iridates are a promising candidate for topological properties and unconventional orders.