Hallmarks of the Mott-metal crossover in the hole-doped pseudospin-1/2 Mott insulator Sr2IrO4

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

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

Non-Centrosymmetric Sr2IrO4 Obtained Under High Pressure

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

Electronic structure and correlations in planar trilayer nickelate Pr4Ni3O8

The discovery of superconductivity in planar nickelates raises the question of how the electronic structure and correlations of Ni¹⁺ compounds compare to those of the Cu²⁺ cuprate superconductors. Here, we present an angle-resolved photoemission spectroscopy (ARPES) study of the trilayer nickelate Pr₄Ni₃O₈, revealing a Fermi surface resembling that of the hole-doped cuprates but with critical differences. Specifically, the main portions of the Fermi surface are extremely similar to that of the bilayer cuprates, with an additional piece that can accommodate additional hole doping. We find that the electronic correlations are about twice as strong in the nickelates and are almost k-independent, indicating that they originate from a local effect, likely the Mott interaction, whereas cuprate interactions are somewhat less local. Nevertheless, the nickelates still demonstrate the strange-metal behavior in the electron scattering rates. Understanding the similarities and differences between these two families of strongly correlated superconductors is an important challenge.

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

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

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

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

Interfacial charge transfer and persistent metallicity of ultrathin SrIrO3/SrRuO3 heterostructures

Interface quantum materials have yielded a plethora of previously unknown phenomena, including unconventional superconductivity, topological phases, and possible Majorana fermions. Typically, such states are detected at the interface between two insulating constituents by electrical transport, but whether either material is conducting, transport techniques become insensitive to interfacial properties. To overcome these limitations, we use angle-resolved photoemission spectroscopy and molecular beam epitaxy to reveal the electronic structure, charge transfer, doping profile, and carrier effective masses in a layer-by-layer fashion for the interface between the Dirac nodal-line semimetal SrIrO₃ and the correlated metallic Weyl ferromagnet SrRuO₃. We find that electrons are transferred from the SrIrO₃ to SrRuO₃, with an estimated screening length of λ = 3.2 ± 0.1 Å. In addition, we find that metallicity is preserved even down to a single SrIrO₃ layer, where the dimensionality-driven metal-insulator transition typically observed in SrIrO₃ is avoided because of strong hybridization of the Ir and Ru t_2g states.

Electronic band structure of iridates

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

The 'dark phase' in Sr2Ir1-xRhxO4revealed by Seebeck and Hall measurements

It was found that, although isovalent, Rh substituted for Ir in Sr₂IrO₄may trap one electron inducing effective hole doping of Ir sites. Transport and thermoelectric measurements on Sr₂Ir_1-xRh_xO₄single crystals presented here reveal the existence of an electron-like contribution to transport, in addition to the hole-doped one. As no electron band shows up in ARPES measurements, this points to the possibility that this hidden electron may delocalize in disordered clusters.

Advanced First-Principle Modeling of Relativistic Ruddlesden—Popper Strontium Iridates

In this review, we provide a survey of the application of advanced first-principle methods on the theoretical modeling and understanding of novel electronic, optical, and magnetic properties of the spin-orbit coupled Ruddlesden–Popper series of iridates Srn+1IrnO3n+1 (n = 1, 2, and ∞). After a brief description of the basic aspects of the adopted methods (noncollinear local spin density approximation plus an on-site Coulomb interaction (LSDA+U), constrained random phase approximation (cRPA), GW, and Bethe–Salpeter equation (BSE)), we present and discuss select results. We show that a detailed phase diagrams of the metal–insulator transition and magnetic phase transition can be constructed by inspecting the evolution of electronic and magnetic properties as a function of Hubbard U, spin–orbit coupling (SOC) strength, and dimensionality n, which provide clear evidence for the crucial role played by SOC and U in establishing a relativistic (Dirac) Mott–Hubbard insulating state in Sr2IrO4 and Sr3Ir2O7. To characterize the ground-state phases, we quantify the most relevant energy scales fully ab initio—crystal field energy, Hubbard U, and SOC constant of three compounds—and discuss the quasiparticle band structures in detail by comparing GW and LSDA+U data. We examine the different magnetic ground states of structurally similar n = 1 and n = 2 compounds and clarify that the origin of the in-plane canted antiferromagnetic (AFM) state of Sr2IrO4 arises from competition between isotropic exchange and Dzyaloshinskii–Moriya (DM) interactions whereas the collinear AFM state of Sr3Ir2O7 is due to strong interlayer magnetic coupling. Finally, we report the dimensionality controlled metal–insulator transition across the series by computing their optical transitions and conductivity spectra at the GW+BSE level from the the quasi two-dimensional insulating n = 1 and 2 phases to the three-dimensional metallic n=∞ phase.

Doping and temperature evolutions of optical response of Sr3(Ir1-xRux)2O7

We report on optical spectroscopic study of the Sr₃(Ir_1-xRu_x)₂O₇ system over a wide doping regime. We find that the changes in the electronic structure occur in the limited range of the concentration of Ru ions where the insulator-metal transition occurs. In the insulating regime, the electronic structure associated with the effective total angular momentum J_eff = 1/2 Mott state remains robust against Ru doping, indicating the localization of the doped holes. Upon entering the metallic regime, the Mott gap collapses and the Drude-like peak with strange metallic character appears. The evolution of the electronic structure registered in the optical data can be explained in terms of a percolative insulator-metal transition. The phonon spectra display anomalous doping evolution of the lineshapes. While the phonon modes of the compounds deep in the insulating and metallic regimes are almost symmetric, those of the semiconducting compound with x = 0.34 in close proximity to the doping-driven insulator-metal transition show a pronounced asymmetry. The temperature evolution of the phonon modes of the x = 0.34 compound reveals the asymmetry is enhanced in the antiferromagnetic state. We discuss roles of the S = 1 spins of the Ru ions and charge excitations for the conspicuous lineshape asymmetry of the x = 0.34 compound.

Symmetry-Resolved Two-Magnon Excitations in a Strong Spin-Orbit-Coupled Bilayer Antiferromagnet

We used a combination of polarized Raman spectroscopy and spin wave calculations to study magnetic excitations in the strong spin-orbit-coupled bilayer perovskite antiferromagnet Sr_{3}Ir_{2}O_{7}. We observed two broad Raman features at ∼800 and ∼1400  cm^{-1} arising from magnetic excitations. Unconventionally, the ∼800  cm^{-1} feature is fully symmetric (A_{1g}) with respect to the underlying tetragonal (D_{4h}) crystal lattice which, together with its broad line shape, definitively rules out the possibility of a single magnon excitation as its origin. In contrast, the ∼1400  cm^{-1} feature shows up in both the A_{1g} and B_{2g} channels. From spin wave and two-magnon scattering cross-section calculations of a tetragonal bilayer antiferromagnet, we identified the ∼800  cm^{-1} (1400  cm^{-1}) feature as two-magnon excitations with pairs of magnons from the zone-center Γ point (zone-boundary van Hove singularity X point). We further found that this zone-center two-magnon scattering is unique to bilayer perovskite magnets which host an optical branch in addition to the acoustic branch, as compared to their single layer counterparts. This zone-center two-magnon mode is distinct in symmetry from the time-reversal symmetry broken "spin wave gap" and "phase mode" proposed to explain the ∼92  meV (742  cm^{-1}) gap in resonant inelastic x-ray spectroscopy magnetic excitation spectra of Sr_{3}Ir_{2}O_{7}.

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.

Magnetic fluctuations and the spin-orbit interaction in Mott insulating CoO

Motivated by the presence of an unquenched orbital angular momentum in CoO, a team at Chalk River, including a recently hired research officer Roger Cowley, performed the first inelastic neutron scattering experiments on the classic Mott insulator [Sakuraiet al1968Phys. Rev.167510]. Despite identifying two magnon modes at the zone boundary, the team was unable to parameterise the low energy magnetic excitation spectrum belowTNusing conventional pseudo-bosonic approaches, instead achieving only qualitative agreement. It would not be for another 40 years that Roger, now at Oxford and motivated by the discovery of the high-Tccuprate superconductors [Bednorz and Muller 1986Z. Phys. B64189], would make another attempt at the parameterisation of the magnetic excitation spectrum that had previously alluded him at the start of his career. Upon his return to CoO, Roger found a system embroiled in controversy, with some of its most fundamental parameters still remaining undetermined. Faced with such a formidable task, Roger performed a series of inelastic neutron scattering experiments in the early 2010s on both CoO and a magnetically dilute structural analogue Mg0.97Co0.03O. These experiments would prove instrumental in the determination of both single-ion [Cowleyet al2013Phys. Rev. B88205117] and cooperative magnetic parameters [Sarteet al2018Phys. Rev. B98024415] for CoO. Both these sets of parameters would eventually be used in a spin-orbit exciton model [Sarteet al2019Phys. Rev. B100075143], developed by his longtime friend and collaborator Bill Buyers, to successfully parameterise the complex spectrum that both measured at Chalk River almost 50 years prior. The story of CoO is of one that has come full circle, one filled with both spectacular failures and intermittent, yet profound, little victories.

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.

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.

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.

Preferential quenching of 5d antiferromagnetic order in Sr3(Ir1-x Mn x )2O7

The breakdown of [Formula: see text] antiferromagnetism in the limit of strong disorder is studied in Sr₃(Ir_1-x Mn _x )₂O₇. Upon Mn-substitution, antiferromagnetic ordering of the Ir cations becomes increasingly two-dimensional, resulting in the complete suppression of long-range Ir magnetic order above [Formula: see text]. Long-range antiferromagnetism however persists on the Mn sites to higher Mn concentrations (x  >  0.25) and is necessarily mediated via a random network of majority Ir sites. Our data suggest a shift in the Mn valence from Mn⁴⁺ to Mn³⁺ at intermediate doping levels, which in turn generates nonmagnetic Ir⁵⁺ sites and suppresses long-range order within the Ir network. The collapse of long-range [Formula: see text] antiferromagnetism and the survival of percolating antiferromagnetic order on Mn-sites demonstrates a complex 3d-5d exchange process that surprisingly enables minority Mn spins to order far below the conventional percolation threshold for a bilayer square lattice.

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.

Conductivity Spectrum of Ultracold Atoms in an Optical Lattice

We measure the conductivity of neutral fermions in a cubic optical lattice. Using in situ fluorescence microscopy, we observe the alternating current resultant from a single-frequency uniform force applied by displacement of a weak harmonic trapping potential. In the linear response regime, a neutral-particle analog of Ohm's law gives the conductivity as the ratio of total current to force. For various lattice depths, temperatures, interaction strengths, and fillings, we measure both real and imaginary conductivity, up to a frequency sufficient to capture the transport dynamics within the lowest band. The spectral width of the real conductivity reveals the current dissipation rate in the lattice, and the integrated spectral weight is related to thermodynamic properties of the system through a sum rule. The global conductivity decreases with increased band-averaged effective mass, which at high temperatures approaches a T-linear regime. Relaxation of current is observed to require a finite lattice depth, which breaks Galilean invariance and enables damping through collisions between fermions.

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.

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.

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.

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.

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.

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.

Ultrafast magnetodynamics with free-electron lasers

The study of ultrafast magnetodynamics has entered a new era thanks to the groundbreaking technological advances in free-electron laser (FEL) light sources. The advent of these light sources has made possible unprecedented experimental schemes for time-resolved x-ray magneto-optic spectroscopies, which are now paving the road for exploring the ultimate limits of out-of-equilibrium magnetic phenomena. In particular, these studies will provide insights into elementary mechanisms governing spin and orbital dynamics, therefore contributing to the development of ultrafast devices for relevant magnetic technologies. This topical review focuses on recent advancement in the study of non-equilibrium magnetic phenomena from the perspective of time-resolved extreme ultra violet (EUV) and soft x-ray spectroscopies at FELs with highlights of some important experimental results.

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.

Fermiology and electron dynamics of trilayer nickelate La4Ni3O10

Layered nickelates have the potential for exotic physics similar to high T_C superconducting cuprates as they have similar crystal structures and these transition metals are neighbors in the periodic table. Here we present an angle-resolved photoemission spectroscopy (ARPES) study of the trilayer nickelate La₄Ni₃O₁₀ revealing its electronic structure and correlations, finding strong resemblances to the cuprates as well as a few key differences. We find a large hole Fermi surface that closely resembles the Fermi surface of optimally hole-doped cuprates, including its \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{x^2-y^2}$$\end{document}dx2-y2 orbital character, hole filling level, and strength of electronic correlations. However, in contrast to cuprates, La₄Ni₃O₁₀ has no pseudogap in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{x^2-y^2}$$\end{document}dx2-y2 band, while it has an extra band of principally \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{3z^2-r^2}$$\end{document}d3z2-r2 orbital character, which presents a low temperature energy gap. These aspects drive the nickelate physics, with the differences from the cuprate electronic structure potentially shedding light on the origin of superconductivity in the cuprates.

Exploration of the electronic structure of nickelates with similar crystal structure to cuprates may shed a light on the origin of high T_c superconductivity. Here, Li et al. report strong resemblances and key differences of the electronic structure of trilayer nickelate La₄Ni₃O₁₀ compared to the cuprate superconductors.

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.

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.

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

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

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

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

Ultrafast energy- and momentum-resolved dynamics of magnetic correlations in the photo-doped Mott insulator Sr2IrO4

Measuring how the magnetic correlations evolve in doped Mott insulators has greatly improved our understanding of the pseudogap, non-Fermi liquids and high-temperature superconductivity. Recently, photo-excitation has been used to induce similarly exotic states transiently. However, the lack of available probes of magnetic correlations in the time domain hinders our understanding of these photo-induced states and how they could be controlled. Here, we implement magnetic resonant inelastic X-ray scattering at a free-electron laser to directly determine the magnetic dynamics after photo-doping the Mott insulator Sr2IrO4. We find that the non-equilibrium state, 2 ps after the excitation, exhibits strongly suppressed long-range magnetic order, but hosts photo-carriers that induce strong, non-thermal magnetic correlations. These two-dimensional (2D) in-plane Néel correlations recover within a few picoseconds, whereas the three-dimensional (3D) long-range magnetic order restores on a fluence-dependent timescale of a few hundred picoseconds. The marked difference in these two timescales implies that the dimensionality of magnetic correlations is vital for our understanding of ultrafast magnetic dynamics.