Locking of iridium magnetic moments to the correlated rotation of oxygen octahedra in Sr₂IrO₄ revealed by x-ray resonant scattering

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

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

Frustration, strain and phase co-existence in the mixed valent hexagonal iridate Ba3NaIr2O9

Using detailed synchrotron diffraction, magnetization, thermodynamic and transport measurements, we investigate the relationship between the mixed valence of Ir, lattice strain and the resultant structural and magnetic ground states in the geometrically frustrated triple perovskite iridate Ba₃NaIr₂O₉. We observe a complex interplay between lattice strain and structural phase co-existence, which is typically not observed in this family of compounds. The low temperature magnetic ground state is characterized by the absence of long-range magnetic order, and points towards the condensation of a cluster glass state from an extended regime of short range magnetic correlations.

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.

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.

Strain engineering of the charge and spin-orbital interactions in Sr2IrO4

Understanding the relationship between entangled degrees of freedom (DOF) is a central problem in correlated materials and the possibility to influence their balance is promising toward realizing novel functionalities. In Sr₂IrO₄, the interaction between spin–orbit coupling and electron correlations induces an exotic ground state with magnetotransport properties promising for antiferromagnetic spintronics applications. Moreover, the coupling between orbital and spin DOF renders the magnetic structure sensitive to the Ir–O bond environment. To date, a detailed understanding of the microscopic spin-lattice and electron–phonon interactions is still lacking. Here, we use strain engineering to perturb the local lattice environment and, by tracking the response of the low-energy elementary excitations, we unveil the response of the microscopic spin and charge interactions.

In the high spin–orbit-coupled Sr₂IrO₄, the high sensitivity of the ground state to the details of the local lattice structure shows a large potential for the manipulation of the functional properties by inducing local lattice distortions. We use epitaxial strain to modify the Ir–O bond geometry in Sr₂IrO₄ and perform momentum-dependent resonant inelastic X-ray scattering (RIXS) at the metal and at the ligand sites to unveil the response of the low-energy elementary excitations. We observe that the pseudospin-wave dispersion for tensile-strained Sr₂IrO₄ films displays large softening along the [h,0] direction, while along the [h,h] direction it shows hardening. This evolution reveals a renormalization of the magnetic interactions caused by a strain-driven cross-over from anisotropic to isotropic interactions between the magnetic moments. Moreover, we detect dispersive electron–hole pair excitations which shift to lower (higher) energies upon compressive (tensile) strain, manifesting a reduction (increase) in the size of the charge gap. This behavior shows an intimate coupling between charge excitations and lattice distortions in Sr₂IrO₄, originating from the modified hopping elements between the t_2g orbitals. Our work highlights the central role played by the lattice degrees of freedom in determining both the pseudospin and charge excitations of Sr₂IrO₄ and provides valuable information toward the control of the ground state of complex oxides in the presence of high spin–orbit coupling.

Anisotropic magnetoresistance in spin-orbit semimetal SrIrO 3

SrIrO 3 , the three-dimensional member of the Ruddlesden-Popper iridates, is a paramagnetic semimetal characterised by a the delicate interplay between spin-orbit coupling and Coulomb repulsion. In this work, we study the anisotropic magnetoresistance (AMR) of SrIrO 3 thin films, which is closely linked to spin-orbit coupling and probes correlations between electronic transport, magnetic order and orbital states. We show that the low-temperature negative magnetoresistance is anisotropic with respect to the magnetic field orientation, and its angular dependence reveals the appearance of a fourfold symmetric component above a critical magnetic field. We show that this AMR component is of magnetocrystalline origin, and attribute the observed transition to a field-induced magnetic state in SrIrO 3 .

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.

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.

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}.

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

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

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.

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.

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

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

Electronic and magnetic properties of multiferroic ScFeO3 available from diffraction experiments

Electronic and magnetic properties of ferric ions (3d ⁵) in multiferroic ScFeO₃ are puzzling, in part because they are different from the only other multiferroic known to possess the same polar chemical structure, BiFeO₃. Open questions about ScFeO₃ can be addressed by confronting observations with results for G-type antiferromagnetism allowed by the lithium niobate (LiNbO₃)-like parent R3c structure. Calculated structure factors for resonant x-ray diffraction include all charge-like quadrupoles allowed by symmetry, and if experimental results for ScFeO₃ subsequently imply they are different from zero then ferric ions cannot be in the high-spin ⁶S state. The same type of experiment can reveal the moment direction in the G-type antiferromagnetism, according to our calculations, and thereby contribute to understanding magnetic anisotropy. Furthermore, structure factors for magnetic neutron diffraction by ScFeO₃ include Dirac multipoles that are time-odd and parity-odd, e.g. dipoles that are often called anapoles or toroidal moments. Apart from Dirac multipoles, the conventional approach to the interpretation of neutron Bragg diffraction data will be inadequate if ferric ions (Fe³⁺) are not in the high-spin ⁶S state, because the scattering amplitude includes more than simple dipole moments in the general case.

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

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

Orbital reconstruction in nonpolar tetravalent transition-metal oxide layers

A promising route to tailoring the electronic properties of quantum materials and devices rests on the idea of orbital engineering in multilayered oxide heterostructures. Here we show that the interplay of interlayer charge imbalance and ligand distortions provides a knob for tuning the sequence of electronic levels even in intrinsically stacked oxides. We resolve in this regard the d-level structure of layered Sr₂IrO₄ by electron spin resonance. While canonical ligand-field theory predicts g_||-factors less than 2 for positive tetragonal distortions as present in Sr₂IrO₄, the experiment indicates g_|| is greater than 2. This implies that the iridium d levels are inverted with respect to their normal ordering. State-of-the-art electronic-structure calculations confirm the level switching in Sr₂IrO₄, whereas we find them in Ba₂IrO₄ to be instead normally ordered. Given the nonpolar character of the metal-oxygen layers, our findings highlight the tetravalent transition-metal 214 oxides as ideal platforms to explore d-orbital reconstruction in the context of oxide electronics.

The iridate compounds display interesting physical properties, including quasi-two-dimensional behaviour similar to cuprates. Bogdanov et al. explore the d-level structure of Sr₂IrO₄ using electron spin resonance measurements and detailed calculations and find it is inverted compared to its normal ordering

Structural distortion-induced magnetoelastic locking in Sr(2)IrO(4) revealed through nonlinear optical harmonic generation

We report a global structural distortion in Sr_{2}IrO_{4} using spatially resolved optical second and third harmonic generation rotational anisotropy measurements. A symmetry lowering from an I4_{1}/acd to I4_{1}/a space group is observed both above and below the Néel temperature that arises from a staggered tetragonal distortion of the oxygen octahedra. By studying an effective superexchange Hamiltonian that accounts for this lowered symmetry, we find that perfect locking between the octahedral rotation and magnetic moment canting angles can persist even in the presence of large noncubic local distortions. Our results explain the origin of the forbidden Bragg peaks recently observed in neutron diffraction experiments and reconcile the observations of strong tetragonal distortion and perfect magnetoelastic locking in Sr_{2}IrO_{4}.

Mott insulator-to-metal transition in yttrium-doped CaIrO₃

We report on the study of insulator-to-metal transition in post-perovskite compound CaIrO3. It is discovered that a gradual chemical substitution of calcium by yttrium leads to the onset of strong metallic behavior in this compound. This observation is in stark contrast to BaIrO3, which preserves its Mott insulating behavior despite excess of the charge carriers due to yttrium doping. Magnetic measurements reveal that both compounds tend to exhibit magnetic character irrespective of the chemical substitution of Ca or Ba. We analyze these unusual observations in light of recent researches that suggest that CaIrO3 does not necessarily possess j = 1/2 ground state due to structural distortion. The insulator-to-metal transition in CaIrO3 will spur new researches to explore more exotic ground state, including superconductivity, in post-perovskite Mott insulators.

CaIrO3: a spin-orbit Mott insulator beyond the j(eff) ground state

In CaIrO3, electronic correlation, spin-orbit coupling, and tetragonal crystal field splitting are predicted to be of comparable strength. However, the nature of its ground state is still an object of debate, with contradictory experimental and theoretical results. We probe the ground state of CaIrO3 and assess the effective tetragonal crystal field splitting and spin-orbit coupling at play in this system by means of resonant inelastic x-ray scattering. We conclude that insulating CaIrO3 is not a j(eff) = 1/2 iridate and discuss the consequences of our finding to the interpretation of previous experiments. In particular, we clarify how the Mott insulating state in iridates can be readily extended beyond the j(eff) = 1/2 ground state.