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

Towards electrical-current control of quantum states in spin-orbit-coupled matter

Novel materials, which often exhibit surprising or even revolutionary physical properties, are necessary for critical advances in technologies. Simultaneous control of structural and physical properties via a small electrical current is of great significance both fundamentally and technologically. Recent studies demonstrate that a combination of strong spin-orbit interactions and a distorted crystal structure in magnetic Mott insulators is sufficient to attain this long-desired goal. In thistopical review, we highlight underlying properties of this class of materials and present two representative antiferromagnetic Mott insulators, namely, 4d-electron based Ca2RuO4and 5d-electron based Sr2IrO4, as model systems. In essence, a small, applied electrical current engages with the lattice, critically reducing structural distortions, which in turn readily suppresses the antiferromagnetic and insulating state and subsequently results in emergent new states. While details may vary in different materials, at the heart of these phenomena are current-reduced lattice distortions, which, via spin-orbit interactions, dictate physical properties. Electrical current, which joins magnetic field, electric field, pressure, light, etc as a new external stimulus, provides a new, key dimension for materials research, and also pose a series of intriguing questions that may provide the impetus for advancing our understanding of spin-orbit-coupled matter. ThisTopical Reviewprovides a brief introduction, a few hopefully informative examples and some general remarks. It is by no means an exhaustive report of the current state of studies on this topic.

Anisotropic Triangular Lattice Realized in Rhenium Oxychlorides A3ReO5Cl2 (A = Ba, Sr)

We report the synthesis, crystal structure, and magnetic properties of the two new quantum antiferromagnets A₃ReO₅Cl₂ (A = Sr, Ba). The crystal structure is isostructural with the mineral pinalite Pb₃WO₅Cl₂, in which the Re⁶⁺ ion is square pyramidally coordinated by five oxide atoms and forms an anisotropic triangular lattice (ATL) made of S = 1/2 spins. The magnetic interactions J and J' in the ATL are estimated from magnetic susceptibilities to be 19.5 (44.9) and 9.2 (19.3) K, respectively, with J'/J = 0.47 (0.43) for A = Ba (Sr). For each compound, the heat capacity at low temperatures shows a large T-linear component with no signature of long-range magnetic order above 2 K, which suggests a gapless spin liquid state of one-dimensional character of the J chains in spite of the significantly large J' couplings. This is a consequence of one-dimensionalization by geometrical frustration in the ATL magnet; a similar phenomenon has been observed in two compounds with slightly smaller J'/J values: Cs₂CuCl₄ (J'/J = 0.3) and the related compound Ca₃ReO₅Cl₂ (0.32). Our findings demonstrate that 5d mixed-anion compounds provide a unique opportunity to explore novel quantum magnetism.

Observations of ferromagnetic cluster glass and exchange bias behavior in the double perovskite compound La2Cu0.9Cr0.1IrO6

La₂CuIrO₆ is a spin-orbit coupled Mott insulator, and shows a transition to noncollinear antiferromagnetic state from paramagnetic state below 74 K, and further into a weak ferromagnetic state below 54 K. Despite having two different magnetic phases, the La₂CuIrO₆ compound does not exhibit exchange bias phenomenon. In this present work, we report an experimental investigation on the structural and magnetic properties of the double perovskite compound La₂Cu_0.9Cr_0.1IrO₆ through high-resolution synchrotron x-ray diffraction, x-ray absorption near edge structure (XANES), and temperature and field-dependent magnetization measurements. Powder x-ray diffraction analysis reveals that the sample crystallizes in triclinic structure (space group P [Formula: see text]) alike parent La₂CuIrO₆ compound, while XANES measurements rule out the possibility of valence state alteration between constituting elements in this sample. Interestingly, La₂Cu_0.9Cr_0.1IrO₆ compound is found to exhibit ferromagnetic cluster glass behavior, where field-cooled magnetization undergoes two ferromagnetic transitions. A significant enhancement of ferromagnetic component is also evident from hysteresis loop study, which is likely associated with the electron hopping between J _eff = 1/2 pseudospin state of Ir⁴⁺ ions and empty e_g-orbital of Cr³⁺ ions. Exclusively, this Cr-doped compound exhibits exchange bias effect, which is related to the complex interfacial exchange coupling between the ferromagnetic clusters and the host antiferromagnetic matrix.

First principles calculations of the electric field gradient tensors of Ba2NaOsO6, a Mott insulator with strong spin orbit coupling

We present first principles calculations of the electrostatic properties of Ba2NaOsO6(BNOO), a 5d1Mott insulator with strong spin orbit coupling (SOC) in its low temperature quantum phases. In light of recent NMR experiments showing that BNOO develops a local octahedral distortion that is accompanied by the emergence of an electric field gradient (EFG) and precedes the formation of long range magnetic order (Luet al2017Nat. Commun.814407, Liuet al2018Phys. Rev. B97224103; Liuet al2018Physica B536863), we calculated BNOO's EFG tensor for several different model distortions. The local orthorhombic distortion that we identified as most strongly agreeing with experiment corresponds to a Q2 distortion mode of the Na-O octahedra, in agreement with conclusions given in (Liuet al2018Phys. Rev. B97224103). Furthermore, we found that the EFG is insensitive to the type of underlying magnetic order. By combining NMR results with first principles modeling, we have thus forged a more complete understanding of BNOO's structural and magnetic properties, which could not be achieved based upon experiment or theory alone.

The Jeff = 1/2 Antiferromagnet Sr2 IrO4 : A Golden Avenue toward New Physics and Functions

Iridates have been providing a fertile ground for studying emergent phases of matter that arise from the delicate interplay of various fundamental interactions with approximate energy scale. Among these highly focused quantum materials, the perovskite Sr₂ IrO₄ , which belongs to the Ruddlesden-Popper series, stands out and has been intensively addressed in the last decade, since it hosts a novel J_eff = 1/2 state that is a profound manifestation of strong spin-orbit coupling. Moreover, the J_eff = 1/2 state represents a rare example of iridates that is better understood both theoretically and experimentally. Here, Sr₂ IrO₄ is taken as an example to review the recent advances of the J_eff = 1/2 state in two aspects: materials fundamentals and functionality potentials. In the fundamentals part, the basic issues for the layered canted antiferromagnetic order of the J_eff = 1/2 magnetic moments in Sr₂ IrO₄ are illustrated, and then the progress of the antiferromagnetic order modulation through diverse routes is highlighted. Subsequently, for the functionality potentials, fascinating properties such as atomic-scale giant magnetoresistance, anisotropic magnetoresistance, and nonvolatile memory, are addressed. To conclude, prospective remarks and an outlook are given.

Nonmagnetic Ground States and a Possible Quadrupolar Phase in 4d and 5d Lacunar Spinel Selenides GaM_{4}Se_{8} (M=Nb, Ta)

Structural and magnetic properties of cubic spinel selenides GaM_{4}Se_{8} (M=Nb, Ta), which are candidates for the molecular J_{eff}=3/2 Mott insulators, are investigated. The effective magnetic moments are reduced compared to the spin only value, indicating the presence of sizable spin-orbit coupling. GaNb_{4}Se_{8} and GaTa_{4}Se_{8} exhibit phase transitions into the nonmagnetic ground states with orthorhombic and tetragonal structures, respectively, which are robust against magnetic field up to at least 60 T. A cubic-cubic phase transition is observed in GaNb_{4}Se_{8} preceding the magnetic transition, suggesting the existence of a quadrupolar-ordered phase theoretically predicted in the J_{eff}=3/2 Mott insulator.

First-principles-based calculation of branching ratio for 5d, 4d, and 3dtransition metal systems

A new first-principles computation scheme to calculate 'branching ratio' has been applied to various 5d, 4d, and 3d transition metal elements and compounds. This recently suggested method is based on a theory which assumes the atomic core hole interacts barely with valence electrons. While it provides an efficient way to calculate the experimentally measurable quantity without generating spectrum itself, its reliability and applicability should be carefully examined especially for the light transition metal systems. Here we select 36 different materials and compare the calculation results with experimental data. It is found that our scheme well describes 5d and 4d transition metal systems whereas, for 3d materials, the difference between the calculation and experiment is quite significant. It is attributed to the neglect of core-valence interaction whose energy scale is comparable with the spin-orbit coupling of core p orbitals.

Mott gap collapse in lightly hole-doped Sr2-xKxIrO4

The evolution of Sr₂IrO₄ upon carrier doping has been a subject of intense interest, due to its similarities to the parent cuprates, yet the intrinsic behaviour of Sr₂IrO₄ upon hole doping remains enigmatic. Here, we synthesize and investigate hole-doped Sr_2-xK_xIrO₄ utilizing a combination of reactive oxide molecular-beam epitaxy, substitutional diffusion and in-situ angle-resolved photoemission spectroscopy. Upon hole doping, we observe the formation of a coherent, two-band Fermi surface, consisting of both hole pockets centred at (π, 0) and electron pockets centred at (π/2, π/2). In particular, the strong similarities between the Fermi surface topology and quasiparticle band structure of hole- and electron-doped Sr₂IrO₄ are striking given the different internal structure of doped electrons versus holes.

Strain-Modulated Slater-Mott Crossover of Pseudospin-Half Square-Lattice in (SrIrO_{3})_{1}/(SrTiO_{3})_{1} Superlattices

We report on the epitaxial strain-driven electronic and antiferromagnetic modulations of a pseudospin-half square-lattice realized in superlattices of (SrIrO_{3})_{1}/(SrTiO_{3})_{1}. With increasing compressive strain, we find the low-temperature insulating behavior to be strongly suppressed with a corresponding systematic reduction of both the Néel temperature and the staggered moment. However, despite such a suppression, the system remains weakly insulating above the Néel transition. The emergence of metallicity is observed under large compressive strain but only at temperatures far above the Néel transition. These behaviors are characteristics of the Slater-Mott crossover regime, providing a unique experimental model system of the spin-half Hubbard Hamiltonian with a tunable intermediate coupling strength.

Superconductivity in 5d transition metal Laves phase SrIr2

We report here the superconducting properties of a Laves phase superconductor SrIr₂, which has a cubic MgCu₂ structure. SrIr₂ is a type-II superconductor, with a T _c of 5.9 K. The estimated superconducting parameters of lower critical field µ ₀ H _c1 and upper critical field µ ₀ H _c2, coherence length ξ(0), penetration depth λ(0) and Ginzburg-Landau (GL) parameter κ(0) are approximately µ ₀ H _c1  =  101 Oe, µ ₀ H _c2(0)  =  5.9 T, ξ(0)  =  7.47 nm, λ(0)  =  237 nm, and κ(0)  =  31.7, respectively. The specific-heat data indicate that SrIr₂ is a strong-coupling superconductor because the value of ΔC/γT _c is approximately 1.71, which is larger than the value of 1.43 that is expected from the BCS theory. The physical properties obtained in this study are explained well by theoretical calculations including spin-orbit coupling (SOC). This result indicates that the physical properties of SrIr₂ are strongly affected by the presence of SOC.

Controllable Thickness Inhomogeneity and Berry Curvature Engineering of Anomalous Hall Effect in SrRuO3 Ultrathin Films

In quantum matters hosting electron-electron correlation and spin-orbit coupling, spatial inhomogeneities, arising from competing ground states, can be essential for understanding exotic topological properties. A prominent example is Hall anomalies observed in SrRuO₃ films, which were interpreted in terms of either magnetic skyrmion-induced topological Hall effect or inhomogeneous anomalous Hall effect (AHE). To clarify this ambiguity, we systematically investigated the evolution of AHE with controllable inhomogeneities in SrRuO₃ film thickness (t_SRO). By exploiting the step-flow growth of SrRuO₃ films, we induced a microscopically ordered stripe pattern with one-unit-cell differences in t_SRO. The associated spatial distribution of momentum-space Berry curvatures enables a two-channel AHE with hump-like Hall anomalies, which can be continuously engineered according to non-integer t_SRO. We further microscopically characterized the stripe-like ferromagnetic domains and two-step magnetic switching behavior in the inhomogeneous SrRuO₃ film. These unique features can be utilized to identify the two-channel AHE model and understand its microscopic origin.

Magnetic Anisotropy of a Quasi Two-Dimensional Canted Antiferromagnet

We report the control of the interplane magnetic exchange coupling in CaIrO₃ perovskite thin films and superlattices with SrTiO₃. By analyzing the anisotropic magneto-transport data, we demonstrate that a semimetallic paramagnetic CaIrO₃ turns into a canted antiferromagnetic Mott insulator at reduced dimensions. The emergence of a biaxial magneto-crystalline anisotropy indicates the canted moment responding to the cubic symmetry. Extending to superlattices and probing oxygen octahedral rotation by half-integer X-ray Braggs diffraction, a more complete picture about the canted moment evolution with interplane coupling can be understood. Remarkably, a rotation of the canted moments' easy axes by 45° is also observed by a sign reversal of the in-plane strain. These results demonstrate the robustness of anisotropic magnetoresistance in revealing quasi two-dimensional canted antiferromagnets, as well as valuable insights about quadrupolar magnetoelastic coupling, relevant for designing future antiferromagnetic spintronic devices.

The effect of carrier doping on magnetism and electronic behavior in double perovskite La2ZnIrO6

Tuning of spin-orbit coupling and electron correlation effects in iridates by introducing electron or hole carriers can produce interesting physical phenomena. In this work, we experimentally investigate the electron/hole doping effect on magnetism and electrical transport in the canted antiferromagnetic (AFM) double perovskite La₂ZnIrO₆, where hole/electron doping are realized in two serial La₂Zn_1-x Li _x IrO₆ (0  ⩽  x  ⩽  0.35) and La₂Zn_1-yGa _yIrO₆ (0  ⩽  y   ⩽  0.3) compounds, respectively. The x-ray photoelectron spectroscopy (XPS) reveals the existence of Ir⁵⁺ and Ir³⁺ oxide states in the Li⁺ and Ga³⁺ doped La₂ZnIrO₆. The magnetic susceptibilities and electron spin resonance (ESR) results reveal different responses between the Ir⁵⁺(5d⁴) and Ir³⁺ (5d⁶) ions in doped La₂ZnIrO₆, the Ir⁵⁺ ions have Van-Vleck paramagnetic contribution contrast to the completely nonmagnetic Ir³⁺ ions. Moreover, the Li⁺ doping cause more dramatic suppression of transition temperature (T _N) and net ferromagnetic (FM) moments. All the Li⁺/Ga³⁺ doped samples remain Mott insulating state well fitted by the variable-range-hopping (VRH) transport mechanism. As a comparison, hole-doping is more effective to enhance the electrical conductivity than the case of electron, suggesting possible asymmetry of density of states nearby the Fermi level.

Possible Quantum Paramagnetism in Compressed Sr_{2}IrO_{4}

The effect of compression on the magnetic ground state of Sr_{2}IrO_{4} is studied with x-ray resonant techniques in the diamond anvil cell. The weak interlayer exchange coupling between square-planar 2D IrO_{2} layers is readily modified upon compression, with a crossover between magnetic structures around 7 GPa mimicking the effect of an applied magnetic field at ambient pressure. Higher pressures drive an order-disorder magnetic phase transition with no magnetic order detected above 17-20 GPa. The persistence of strong exchange interactions between J_{eff}=1/2 magnetic moments within the insulating IrO_{2} layers up to at least 35 GPa points to a highly frustrated magnetic state in compressed Sr_{2}IrO_{4}, opening the door for realization of novel quantum paramagnetic phases driven by extended 5d orbitals with entangled spin and orbital degrees of freedom.

Ir 5d-band derived superconductivity in LaIr3

The superconducting properties of rhombohedral LaIr₃ were examined using susceptibility, resistivity, heat capacity, and zero-field (ZF) and transverse-field (TF) muon spin relaxation and rotation ([Formula: see text]SR) measurements. The susceptibility and resistivity measurements confirm a superconducting transition below [Formula: see text] K. Two successive transitions are observed in the heat capacity data, one at [Formula: see text] K and a second at 1.2 K below [Formula: see text]. The heat capacity jump is [Formula: see text], which is lower than 1.43 expected for Bardeen-Cooper-Schrieffer (BCS) weak-coupling limit. TF-[Formula: see text]SR measurements reveal a fully gapped s-wave superconductivity with [Formula: see text], which is small compared to the BCS value of 3.56, suggesting weak-coupling superconductivity. The magnetic penetration depth, [Formula: see text], estimated from TF-[Formula: see text]SR gives [Formula: see text] nm, a superconducting carrier density [Formula: see text] carriers m^-3 and a carrier effective-mass enhancement factor [Formula: see text]. ZF-[Formula: see text]SR data show no evidence for any spontaneous magnetic fields below [Formula: see text], which demonstrates that time-reversal symmetry is preserved in the superconducting state of LaIr₃.

Atomic-Scale Metal-Insulator Transition in SrRuO3 Ultrathin Films Triggered by Surface Termination Conversion

The metal-insulator transition (MIT) in transition-metal-oxide is fertile ground for exploring intriguing physics and potential device applications. Here, an atomic-scale MIT triggered by surface termination conversion in SrRuO₃ ultrathin films is reported. Uniform and effective termination engineering at the SrRuO₃ (001) surface can be realized via a self-limiting water-leaching process. As the surface termination converts from SrO to RuO₂ , a highly insulating and nonferromagnetic phase emerges within the topmost SrRuO₃ monolayer. Such a spatially confined MIT is corroborated by systematic characterizations on electrical transport, magnetism, and scanning tunneling spectroscopy. Density functional theory calculations and X-ray linear dichroism further suggest that the surface termination conversion breaks the local octahedral symmetry of the crystal field. The resultant modulation in 4d orbital occupancy stabilizes a nonferromagnetic insulating surface state. This work introduces a new paradigm to stimulate and tune exotic functionalities of oxide heterostructures with atomic precision.

Optical Signature of a Crossover from Mott- to Slater-Type Gap in Sr_{2}Ir_{1-x}Rh_{x}O_{4}

With optical spectroscopy we provide evidence that the insulator-metal transition in Sr_{2}Ir_{1-x}Rh_{x}O_{4} occurs close to a crossover from the Mott- to the Slater-type. The Mott gap at x=0 persists to high temperature and evolves without an anomaly across the Néel temperature, T_{N}. Upon Rh doping, it collapses rather rapidly and vanishes around x=0.055. Notably, just as the Mott gap vanishes yet another gap appears that is of the Slater-type and develops right below T_{N}. This Slater gap is only partial and is accompanied by a reduced scattering rate of the remaining free carriers, similar as in the parent compounds of the iron arsenide superconductors.

Superconducting behavior of a new metal iridate compound, SrIr2, under pressure

Herein, we investigated the pressure dependence of electric transport in a new type of superconducting metal iridate compound, SrIr₂, that exhibits a superconducting transition temperature, T _c, as high as 6.6 K at ambient pressure, in order to complete the T _c-pressure (p ) phase diagram. Very recently, this sample's superconductivity was discovered by our group, but the superconducting behavior has not yet been clarified under pressure. In this study, we fully investigated this sample's superconductivity in a wide pressure range. The T _c value decreased with an increase in pressure, but the onset superconducting transition temperature, [Formula: see text], increased above a pressure of 8 GPa, indicating an unconventional superconductivity different from a BCS-type superconductor. The magnetic field dependence of electric resistance (R) against temperature (R  -  T plot) recorded at 7.94 and 11.3 GPa suggested an unconventional superconductivity, followed by a p -wave polar model, supporting the deviation from a simple s-wave pairing. Moreover, we fully investigated the pressure dependence of crystal structure in SrIr₂ and discussed the correlation between superconductivity and crystal structure. This is the first systematic study on superconducting behavior of a new type of metal iridate compound, MIr₂ (M: alkali-earth metal atom), under pressure.

Correlated paramagnetism and interplay of magnetic and phononic degrees of freedom in 3d-5d coupled La2CuIrO6

Conventional paramagnetism-a state with finite magnetic moment per ion sans long range magnetic ordering, but with lowering temperature the moment each ion picks up a particular direction, breaking spin rotational symmetry, and results into long-range magnetic ordering. However, in systems with competing multiple degrees of freedom this conventional notion may easily break and results into short range correlation much above the global magnetic transition temperature. La₂CuIrO₆ with complex interplay of spins (s  =  1/2) on Cu site and pseudo-spin (j   =  1/2) on Ir site owing to strong spin-orbit coupling provides fertile ground to observe such correlated phenomena. By a comprehensive temperature dependent Raman study, we have shown the presence of such a correlated paramagnetic state in La₂CuIrO₆ much above the long-range magnetic ordering temperature (T _N ). Our observation of strong interactions of phonons, associated with Cu/Ir octahedra, with underlying magnetic degrees of freedom mirrored in the observed Fano asymmetry, which remarkably persists as high as ~3.5T _N clearly signals the existence of correlated paramagnetism hence broken spin rotational symmetry. Our detailed analysis also reveals anomalous changes in the self-energy parameters of the phonon modes, i.e. mode frequencies and linewidth, below T _N , providing a useful gauge for monitoring the strong coupling between phonons and magnetic degrees of freedom.

Anomalous magnetoresistance due to longitudinal spin fluctuations in a Jeff = 1/2 Mott semiconductor

As a hallmark of electronic correlation, spin-charge interplay underlies many emergent phenomena in doped Mott insulators, such as high-temperature superconductivity, whereas the half-filled parent state is usually electronically frozen with an antiferromagnetic order that resists external control. We report on the observation of a positive magnetoresistance that probes the staggered susceptibility of a pseudospin-half square-lattice Mott insulator built as an artificial SrIrO₃/SrTiO₃ superlattice. Its size is particularly large in the high-temperature insulating paramagnetic phase near the Néel transition. This magnetoresistance originates from a collective charge response to the large longitudinal spin fluctuations under a linear coupling between the external magnetic field and the staggered magnetization enabled by strong spin-orbit interaction. Our results demonstrate a magnetic control of the binding energy of the fluctuating particle-hole pairs in the Slater-Mott crossover regime analogous to the Bardeen-Cooper-Schrieffer-to-Bose-Einstein condensation crossover of ultracold-superfluids.

Spin-charge interactions are at the core of electronic correlation phenomena in Mott insulators. Here, the authors observe a positive anomalous magnetoresistance in a SrIrO₃/SrTiO₃ superlattice, indicative of strong spin-charge fluctuations in this pseudospin-half square-lattice Mott insulator.

Spectroscopic Evidence for Electron-Boson Coupling in Electron-Doped Sr_{2}IrO_{4}

The pseudogap, d-wave superconductivity and electron-boson coupling are three intertwined key ingredients in the phase diagram of the cuprates. Sr_{2}IrO_{4} is a 5d-electron counterpart of the cuprates in which both the pseudogap and a d-wave instability have been observed. Here, we report spectroscopic evidence for the presence of the third key player in electron-doped Sr_{2}IrO_{4}: electron-boson coupling. A kink in nodal dispersion is observed with an energy scale of ∼50  meV. The strength of the kink changes with doping, but the energy scale remains the same. These results provide the first noncuprate platform for exploring the relationship between the pseudogap, d-wave instability, and electron-boson coupling in doped Mott insulators.

Weak ferromagnetic insulator with huge coercivity in monoclinic double perovskite La2CuIrO6

Insulating ferromagnets with high T _C are required for many new magnetic devices. More complexity arises when strongly correlated 3d ions coexist with strongly spin-orbit coupled 5d ones in a double perovskite. Here, we perform the structural, magnetic, and density functional theory (DFT) study of such double perovskite La₂CuIrO₆. A new P2₁/n polymorph is found according to the comprehensive analysis of x-ray, Raman scattering and phonon spectrum. The magnetization reveals a weak ferromagnetic (FM) transition at T _C  =  62 K and short range FM order in higher temperature range. A huge coercivity is found as high as H _C ~ 11.96 kOe at 10 K, which, in combination with the negative trapped field, results in the magnetization reversal in the zero field cooling measurement. The first principle calculations confirm the observed FM state and suggest La₂CuIrO₆ of this polymorph is a Mott insulating ferromagnet assisted by the spin-orbit coupling.

Two dimensional electron gas in the [Formula: see text]-doped iridates with strong spin-orbit coupling: La[Formula: see text]Sr2IrO4

Iridates are of considerable current interest because of the strong spin-orbit coupling that leads to a variety of new phenomena. Using density-functional studies, we predict the formation of a spin-orbital entangled two dimensional electron gas (2DEG) in the [Formula: see text]-doped iridate La[Formula: see text]Sr₂IrO₄, where a single SrO layer is replaced by a LaO layer. The extra La electron resides close to the [Formula: see text]-doped layer, partially occupying the [Formula: see text] upper Hubbard band and thereby making the interface metallic. The magnetic structure of the bulk is destroyed near the interface, with the Ir₀ layer closest to the interface becoming non-magnetic, while the next layer (Ir₁) continues to maintain the AFM structure of the bulk, but with a reduced magnetic moment. The Fermi surface consists of a hole pocket and an electron pocket, located in two different Ir layers (Ir₀ and Ir₁), with both carriers derived from the [Formula: see text] upper Hubbard band. The presence of both electrons and holes at the [Formula: see text]-doped interface suggests unusual transport properties, leading to possible device applications.

Evidence of Slater-type mechanism as origin of insulating state in Sr2IrO4

For iridates with large spatially extended 5d orbitals, it may be anticipated that distant neighbor interactions would play a crucial role in their ground state properties. From this perspective, we investigate the magnetic structure of Sr₂IrO₄ by including interactions beyond first and second neighbors, via supercell modeling. Adopting to first-principles scalar relativistic methods, it is found that the minimum in total energy among various magnetic structures correspond to a [Formula: see text] type antiferromagnetic ordering of the Ir ions for which the magnitude of the electronic gap, that of the Ir local moments and, the facsimile of the two-peaked structure in the optical conductivity spectra of Sr₂IrO₄ were found to be in good agreement with the experiments. The results unequivocally show that the origin of the electronic gap in Sr₂IrO₄ is due to an unconventional antiferromagnetic ordering of Ir ions, thereby classifying the system as a Slater magnet, rather than the spin-orbit coupling driven [Formula: see text] Mott insulator.

Interfacial charge-transfer Mott state in iridate-nickelate superlattices

We investigate [Formula: see text]/[Formula: see text] superlattices in which we observe a full electron transfer at the interface from Ir to Ni, triggering a massive structural and electronic reconstruction. Through experimental characterization and first-principles calculations, we determine that a large crystal field splitting from the distorted interfacial [Formula: see text] octahedra surprisingly dominates over the spin-orbit coupling and together with the Hund's coupling results in the high-spin (S = 1) configurations on both the Ir and Ni sites. This demonstrates the power of interfacial charge transfer in coupling lattice, charge, orbital, and spin degrees of freedom, opening fresh avenues of investigation of quantum states in oxide superlattices.

Lifshitz-Transition-Driven Metal-Insulator Transition in Moderately Spin-Orbit-Coupled Sr_{2-x}La_{x}RhO_{4}

Motivated by the novel insulating state of Sr_{2}IrO_{4} from strong spin-orbit coupling (SOC), we investigate, by means of angle resolved photoemission, the metal-insulator transition (MIT) mechanism in Sr_{2-x}La_{x}RhO_{4} whose mother compound is isovalent and isostructural but has smaller SOC strength compared to Sr_{2}IrO_{4}. Transport and angle resolved photoemission results from single crystalline Sr_{2-x}La_{x}RhO_{4} revealed that the MIT occurs coincidentally with a multi- to single-band transition (Lifshitz transition) at x=0.4. Starting from x=0.4, there is a gradual but anomalous enhancement in the band gap size with additional electron doping, suggesting that the insulating phase in Sr_{2-x}La_{x}RhO_{4} is a new type which has been rarely investigated. These results suggest that the insulating phase in Sr_{2-x}La_{x}RhO_{4} is likely induced by the moderate SOC strength and electron doping effect from the La. Our findings not only elucidate the MIT mechanism in Sr_{2-x}La_{x}RhO_{4}, but may also open new avenues for novel MIT research in moderate SOC regimes.

Resonant inelastic X-ray scattering of magnetic excitations under pressure

Resonant inelastic X-ray scattering (RIXS) is an extremely valuable tool for the study of elementary, including magnetic, excitations in matter. The latest developments of this technique have mostly been aimed at improving the energy resolution and performing polarization analysis of the scattered radiation, with a great impact on the interpretation and applicability of RIXS. Instead, this article focuses on the sample environment and presents a setup for high-pressure low-temperature RIXS measurements of low-energy excitations. The feasibility of these experiments is proved by probing the magnetic excitations of the bilayer iridate Sr₃Ir₂O₇ at pressures up to 12 GPa.

First-principles studies of spin-orbital physics in pyrochlore oxides

The pyrochlore oxides [Formula: see text]O₇ exhibit a complex interplay between geometrical frustration, electronic correlations, and spin-orbit coupling (SOC), due to the lattice structure and active charge, spin, and orbital degrees of freedom. Understanding the properties of these materials is a theoretical challenge, because their intricate nature depends on material-specific details and quantum many-body effects. Here we review our recent studies based on first-principles calculations and quantum many-body theories for 4d and 5d pyrochlore oxides with B  =  Mo, Os, and Ir. In these studies, the SOC and local electron correlations are treated within the local density approximation (LDA)  +  U and LDA  +  dynamical mean-field theory formalisms. We also discuss the technical aspects of these calculations.

Spectral functions of Sr2IrO4: theory versus experiment

The spin-orbit Mott insulator Sr₂IrO₄ has attracted a lot of interest in recent years from theory and experiment due to its close connection to isostructural high-temperature copper oxide superconductors. Despite not being superconductive, its spectral features closely resemble those of the cuprates, including Fermi surface and pseudogap properties. In this article, we review and extend recent work in the theoretical description of the spectral function of pure and electron-doped Sr₂IrO₄ based on a cluster extension of dynamical mean-field theory ('oriented-cluster DMFT') and compare it to available angle-resolved photoemission data. Current theories provide surprisingly good agreement for pure and electron-doped Sr₂IrO₄, both in the paramagnetic and antiferromagnetic phases. Most notably, one obtains simple explanations for the experimentally observed steep feature around the M point and the pseudo-gap-like spectral feature in electron-doped Sr₂IrO₄.

Hopping-Induced Ground-State Magnetism in 6H Perovskite Iridates

Investigation of elementary excitations has advanced our understanding of many-body physics governing most physical properties of matter. Recently spin-orbit excitons have drawn much attention, whose condensates near phase transitions exhibit Higgs mode oscillations, a long-sought-after physical phenomenon [A. Jain, et al., Nat. Phys. 13, 633 (2017)NPAHAX1745-247310.1038/nphys4077]. These critical transition points, resulting from competing spin-orbit coupling (SOC), local crystalline symmetry, and exchange interactions, are not obvious in iridium-based materials, where SOC prevails in general. Here, we present results of resonant inelastic x-ray scattering on a spin-orbital liquid Ba_{3}ZnIr_{2}O_{9} and three other 6H-hexagonal perovskite iridates that show magnetism, contrary to the nonmagnetic singlet ground state expected due to strong SOC. Our results show that substantial hopping between closely placed Ir^{5+} ions within Ir_{2}O_{9} dimers in these 6H iridates modifies spin-orbit coupled states and reduces spin-orbit excitation energies. Here, we are forced to use at least a two-site model to match the excitation spectrum going in-line with the strong intradimer hopping. Apart from SOC, low-energy physics of iridates is thus critically dependent on hopping and may not be ignored even for systems having moderate hopping, where the excitation spectra can be explained using an atomic model. SOC, which is generally found to be 0.4-0.5 eV in iridates, is scaled in effect down to ∼0.26  eV for the 6H systems, sustaining the hope of achieving quantum criticality by tuning Ir-Ir separation.

Recovery of photoexcited magnetic ordering in Sr2IrO4

The recovery of antiferromagnetic and lattice order of Sr₂IrO₄ upon laser excitation was measured by time-resolved x-ray diffraction on nanosecond time scales. The in situ measurements of both magnetic and lattice order parameters allow direct comparison of their time evolutions without ambiguity. We found that the magnetic order recovers with two time constants. The fast sub-nanosecond recovery is associated with the re-establishment of three dimensional antiferromagnetic order while the slow sub-nanosecond recovery agrees with the lattice cooling on tens of nanoseconds. The strong oscillating behavior of magnetic order during the long time recovery may be related to complicated dynamics of defect-pinned magnetic domains.

Doping-induced insulator-metal transition in the Lifshitz magnetic insulator NaOsO3

By means of first principles schemes based on magnetically constrained density functional theory and on the band unfolding technique we study the effect of doping on the conducting behaviour of the Lifshitz magnetic insulator NaOsO₃. Electron doping is treated within a supercell approach by replacing sodium with magnesium at different concentrations ([Formula: see text], [Formula: see text]). Undoped NaOsO₃ is subjected to a temperature-driven Lifshitz transition involving a continuous closing of the gap due to longitudinal and rotational spin fluctuations (Kim et al 2016 Phys. Rev. B 94 241113). Here we find that Mg doping suppresses the insulating state, gradually drives the system to a metallic state (via an intermediate bad metal phase) and the transition is accompanied by a progressive lowering of the Os magnetic moment. We inspected the role of longitudinal spin fluctuations by constraining the amplitude of the local Os moments and found that a robust metal state can be achieved below a critical moment. In analogy with the undoped case we conjecture that the decrease of the local moment can be controlled by temperature effects, in accordance with the theory of itinerant electron magnetism.

Ultrafast dynamics of spin and orbital correlations in quantum materials: an energy- and momentum-resolved perspective

Many remarkable properties of quantum materials emerge from states with intricate coupling between the charge, spin and orbital degrees of freedom. Ultrafast photo-excitation of these materials holds great promise for understanding and controlling the properties of these states. Here, we introduce time-resolved resonant inelastic X-ray scattering (tr-RIXS) as a means of measuring the charge, spin and orbital excitations out of equilibrium. These excitations encode the correlations and interactions that determine the detailed properties of the states generated. After outlining the basic principles and instrumentations of tr-RIXS, we review our first observations of transient antiferromagnetic correlations in quasi two dimensions in a photo-excited Mott insulator and present possible future routes of this fast-developing technique. The increasing number of X-ray free electron laser facilities not only enables tackling long-standing fundamental scientific problems, but also promises to unleash novel inelastic X-ray scattering spectroscopies. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Spin-orbit coupling driven novel magnetism in d 5 6H-perovskite iridates Ba3IrTi2O9 and Ba3TiIr2O9

In the present paper, we have carried out a comparative first principles as well as model Hamiltonian study to understand the novel magnetism in 6H perovskite iridates Ba₃IrTi₂O₉ and Ba₃TiIr₂O₉ resulting from an unusual combination of geometrical as well as exchange frustration owing to their unique crystal geometry. Our model calculations corroborated with multipolar analysis provides a comprehensive understanding of the spin-orbit entangled [Formula: see text] pseudo-spin states in both materials. While, the [Formula: see text] character is quite robust in the former compound, it is found to be directly related to the nature of magnetism in the latter iridate. The identification of the relevant spin model for the ideal structure of Ba₃IrTi₂O₉ suggests that the Heisenberg exchange interaction dominates the Kitaev term favoring long range magnetic order in the system in line with the ab initio study while the other iridate Ba₃TiIr₂O₉ has the posibility to host novel spin-orbital singlet state with no resultant moment.

Orbital Symmetry and Orbital Excitations in High-Tc Superconductors

We discuss a few possibilities of high- T c superconductivity with more than one orbital symmetry contributing to the pairing. First, we show that the high energies of orbital excitations in various cuprates suggest a simplified model with a single orbital of x 2 − y 2 symmetry doped by holes. Next, several routes towards involving both e g orbital symmetries for doped holes are discussed: (i) some give superconductivity in a CuO 2 monolayer on Bi2212 superconductors, Sr 2 CuO 4 − δ , Ba 2 CuO 4 − δ , while (ii) others as nickelate heterostructures or Eu 2 − x Sr x NiO 4 , could in principle realize it as well. At low electron filling of Ru ions, spin-orbital entangled states of t 2 g symmetry contribute in Sr 2 RuO 4 . Finally, electrons with both t 2 g and e g orbital symmetries contribute to the superconducting properties and nematicity of Fe-based superconductors, pnictides or FeSe. Some of them provide examples of orbital-selective Cooper pairing.

Particle–hole fluctuations and possible superconductivity in doped α-RuCl3*

We study various particle–hole excitations and possible superconducting pairings mediated by these fluctuations in doped α-RuCl3 by using multi-band Hubbard model with all t2g orbitals. By performing a random-phase-approximation (RPA) analysis, we find that among all particle–hole excitations, the j eff = 1/2 pseudospin fluctuations are dominant, suggesting the robustness of j eff = 1/2 picture even in the doped systems. We also find that the most favorable superconducting state has a d-wave pairing symmetry.

Overdamped Antiferromagnetic Strange Metal State in Sr_{3}IrRuO_{7}

The unconventional electronic ground state of Sr_{3}IrRuO_{7} is explored via resonant x-ray scattering techniques and angle-resolved photoemission measurements. As the Ru content approaches x=0.5 in Sr_{3}(Ir_{1-x}Ru_{x})_{2}O_{7}, intermediate to the J_{eff}=1/2 Mott state in Sr_{3}Ir_{2}O_{7} and the quantum critical metal in Sr_{3}Ru_{2}O_{7}, a thermodynamically distinct metallic state emerges. The electronic structure of this intermediate phase lacks coherent quasiparticles, and charge transport exhibits a linear temperature dependence over a wide range of temperatures. Spin dynamics associated with the long-range antiferromagnetism of this phase show nearly local, overdamped magnetic excitations and an anomalously large energy scale of 200 meV-an energy far in excess of exchange energies present within either the Sr_{3}Ir_{2}O_{7} or Sr_{3}Ru_{2}O_{7} solid-solution end points. Overdamped quasiparticle dynamics driven by strong spin-charge coupling are proposed to explain the incoherent spectral features of the strange metal state in Sr_{3}IrRuO_{7}.

Unusual exchange bias in Sr2FeIrO6/La0.67Sr0.33MnO3 multilayer

Here, we study interface induced magnetic properties in a 3d-5d based multilayer made of La_0.67Sr_0.33MnO₃ and double perovskite Sr₂FeIrO₆, respectively. Bulk La_0.67Sr_0.33MnO₃ is metallic and shows ferromagnetic (FM) ordering above room temperature. In contrast, bulk Sr₂FeIrO₆, is an antiferromagnet (AFM) with a Néel temperature around 45 K ([Formula: see text]) and exhibits an insulating behavior. Two set of multilayers have been grown on SrTiO₃ (1 0 0) crystal with varying thickness of FM layer. A multilayer with equal thickness of La_0.67Sr_0.33MnO₃ and Sr₂FeIrO₆ (∼10 nm) shows exchange bias (EB) effect both in conventionally field cooled (FC) as well as in zero field cooled (ZFC) magnetic hysteresis measurements which is rather unusual. The ZFC EB effect is weakened both with increasing maximum field during initial magnetization process at low temperature and with increasing temperature. Interestingly, a multilayer with reduced thickness of La_0.67Sr_0.33MnO₃ (∼5 nm) does not exhibit ZFC EB phenomenon, however, the FC EB effect is strengthened showing much higher value. We believe that an AFM type exchange coupling at the interface and its evolution during initial application of magnetic field causes this unusual EB in present multilayers.

Nuclear resonant scattering from 193Ir as a probe of the electronic and magnetic properties of iridates

The high brilliance of modern synchrotron radiation sources facilitates experiments with high-energy x-rays across a range of disciplines, including the study of the electronic and magnetic correlations using elastic and inelastic scattering techniques. Here we report on Nuclear Resonance Scattering at the 73 keV nuclear level in ¹⁹³Ir. The transitions between the hyperfine split levels show an untypically high E2/M1 multi-polarity mixing ratio combined with an increased sensitivity to certain changes in the hyperfine field direction compared to non-mixing transitions. The method opens a new way for probing local magnetic and electronic properties of correlated materials containing iridium and provides novel insights into anisotropic magnetism in iridates. In particular, unexpected out-of-plane components of magnetic hyperfine fields and non-zero electric field gradients in Sr₂IrO₄ have been detected and attributed to the strong spin-orbit interaction in this iridate. Due to the high, 62% natural abundance of the ¹⁹³Ir isotope, no isotopic enrichment of the samples is required, qualifying the method for a broad range of applications.

Direct Detection of Dimer Orbitals in Ba_{5}AlIr_{2}O_{11}

The electronic states of many Mott insulators, including iridates, are often conceptualized in terms of localized atomic states such as the famous "J_{eff}=1/2 state." Although orbital hybridization can strongly modify such states and dramatically change the electronic properties of materials, probing this process is highly challenging. In this Letter, we directly detect and quantify the formation of dimer orbitals in an iridate material Ba_{5}AlIr_{2}O_{11} using resonant inelastic x-ray scattering. Sharp peaks corresponding to the excitations of dimer orbitals are observed and analyzed by a combination of density functional theory calculations and theoretical simulations based on an Ir-Ir cluster model. Such partially delocalized dimer states lead to a redefinition of the angular momentum of the electrons and changes in the magnetic and electronic behaviors of the material. We use this to explain the reduction of the observed magnetic moment with respect to predictions based on atomic states. This study opens new directions to study dimerization in a large family of materials, including solids, heterostructures, molecules, and transient states.

Magnetism in iridate heterostructures leveraged by structural distortions

Fundamental control of magnetic coupling through heterostructure morphology is a prerequisite for rational engineering of magnetic ground states. We report the tuning of magnetic interactions in superlattices composed of single and bilayers of SrIrO₃ inter-spaced with SrTiO₃ in analogy to the Ruddlesden-Popper series iridates. Magnetic scattering shows predominately c-axis antiferromagnetic orientation of the magnetic moments for the bilayer, as in Sr₃Ir₂O₇. However, the magnetic excitation gap, measured by resonant inelastic x-ray scattering, is quite different between the two structures, evidencing a significant change in the stability of the competing magnetic phases. In contrast, the single layer iridate hosts a more bulk-like gap. We find these changes are driven by bending of the c-axis Ir-O-Ir bond, which is much weaker in the single layer, and subsequent local environment changes, evidenced through x-ray diffraction and magnetic excitation modeling. Our findings demonstrate how large changes in the magnetic interactions can be tailored and probed in spin-orbit coupled heterostructures by engineering subtle structural modulations.

Orbiton-phonon coupling in Ir5+(5d 4) double perovskite Ba2YIrO6

Ba₂YIrO₆, a Mott insulator, with four valence electrons in Ir⁵⁺ d-shell (5d ⁴) is supposed to be non-magnetic, with J _eff  =  0, within the atomic physics picture. However, recent suggestions of non-zero magnetism have raised some fundamental questions about its origin. We focus on the phonon dynamics, probed via Raman scattering, as a function of temperature and different incident photon energies, as an external perturbation. Our studies reveal strong renormalization of the phonon self-energy parameters and integrated intensity for first-order modes, especially redshift of the few first-order modes with decreasing temperature and anomalous softening of modes associated with IrO₆ octahedra, as well as high energy Raman bands attributed to the strong anharmonic phonons and coupling with orbital excitations. The distinct renormalization of second-order Raman bands with respect to their first-order counterpart suggest that higher energy Raman bands have significant contribution from orbital excitations. Our observation indicates that strong anharmonic phonons coupled with electronic/orbital degrees of freedom provides a knob for tuning the conventional electronic levels for 5d-orbitals, and this may give rise to non-zero magnetism as postulated in recent theoretical calculations with rich magnetic phases.

Pseudo-Jahn-Teller Effect and Magnetoelastic Coupling in Spin-Orbit Mott Insulators

The consequences of the Jahn-Teller (JT) orbital-lattice coupling for magnetism of pseudospin J_{eff}=1/2 and J_{eff}=0 compounds are addressed. In the former case, represented by Sr_{2}IrO_{4}, this coupling generates, through the so-called pseudo-JT effect, orthorhombic deformations of a crystal concomitant with magnetic ordering. The orthorhombicity axis is tied to the magnetization and rotates with it under magnetic field. The theory resolves a number of puzzles in Sr_{2}IrO_{4} such as the origin of in-plane magnetic anisotropy and magnon gaps, metamagnetic transition, etc. In J_{eff}=0 systems, the pseudo-JT effect leads to spin-nematic transition well above magnetic ordering, which may explain the origin of "orbital order" in Ca_{2}RuO_{4}.

Electron Correlations Engineer Catalytic Activity of Pyrochlore Iridates for Acidic Water Oxidation

The development of highly efficient oxygen-evolving catalysts compatible with powerful proton-exchange-membrane-based electrolyzers in acid environments is of prime importance for sustainable hydrogen production. In this field, understanding the role of electronic structure of catalysts on catalytic activity is essential but still lacking. Herein, a family of pyrochlore oxides R₂ Ir₂ O₇ (R = rare earth ions) is reported as acidic oxygen-evolving catalysts with superior-specific activities. More importantly, it is found that the intrinsic activity of this material significantly increases with the R ionic radius. Electronic structure studies reveal that the increased R ionic radius weakens electron correlations in these iridate oxides. This weakening induces an insulator-metal transition and an enhancement of IrO bond covalency, both of which promote oxygen evolution kinetics. This work demonstrates the importance of engineering the electron correlations to rationalize the catalytic activity toward water oxidation in strongly correlated transition-metal oxides.

Silver route to cuprate analogs

The parent compound of high-[Formula: see text] superconducting cuprates is a unique Mott insulator consisting of layers of spin-[Formula: see text] ions forming a square lattice and with a record high in-plane antiferromagnetic coupling. Compounds with similar characteristics have long been searched for without success. Here, we use a combination of experimental and theoretical tools to show that commercial [Formula: see text] is an excellent cuprate analog with remarkably similar electronic parameters to [Formula: see text] but larger buckling of planes. Two-magnon Raman scattering and inelastic neutron scattering reveal a superexchange constant reaching 70% of that of a typical cuprate. We argue that structures that reduce or eliminate the buckling of the [Formula: see text] planes could have an antiferromagnetic coupling that matches or surpasses the cuprates.

Sr2Fe1+xRe1−xO6 double perovskites: magnetoresistance and (magneto)thermopower

Polycrystalline Sr₂Fe_1+xRe_1−xO₆ samples have been synthesized, structurally characterized by X-ray powder diffraction, transmission electron microscopy, X-ray absorption spectroscopy, and measurements of their magnetotransport properties were performed.

Resonant inelastic x-ray incarnation of Young's double-slit experiment

Young's archetypal double-slit experiment forms the basis for modern diffraction techniques: The elastic scattering of waves yields an interference pattern that captures the real-space structure. Here, we report on an inelastic incarnation of Young's experiment and demonstrate that resonant inelastic x-ray scattering (RIXS) measures interference patterns, which reveal the symmetry and character of electronic excited states in the same way as elastic scattering does for the ground state. A prototypical example is provided by the quasi-molecular electronic structure of insulating Ba₃CeIr₂O₉ with structural Ir dimers and strong spin-orbit coupling. The double "slits" in this resonant experiment are the highly localized core levels of the two Ir atoms within a dimer. The clear double-slit-type sinusoidal interference patterns that we observe allow us to characterize the electronic excitations, demonstrating the power of RIXS interferometry to unravel the electronic structure of solids containing, e.g., dimers, trimers, ladders, or other superstructures.