Recent progress on correlated electron systems with strong spin-orbit coupling

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

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

Ba9RE2(SiO4)6 (RE = Ho-Yb): A Family of Rare-Earth-Based Honeycomb-Lattice Magnets

Rare-earth (RE)-based honeycomb-lattice materials with strong spin-orbit coupled Jeff = 1/2 moments have attracted great interest as a platform to realize the Kitaev quantum spin liquid (QSL) state. Herein, we report the discovery of a family of RE-based honeycomb-lattice magnets Ba9RE2(SiO4)6 (RE = Ho-Yb), which crystallize into the rhombohedral structure with the space group R3̅. In these serial compounds, magnetic RE3+ ions are arranged on a perfect honeycomb lattice within the ab-plane and stacked in the "ABCABC"-type fashion along the c-axis. All synthesized Ba9RE2(SiO4)6 (RE = Ho-Yb) polycrystals exhibit the dominant antiferromagnetic interaction and absence of magnetic order down to 2 K. In combination with the magnetization and electron spin resonance results, magnetic behaviors are discussed for the compounds with different RE ions. Moreover, the as-grown Ba9Yb2(SiO4)6 single crystals show large magnetic frustration with frustration index f = θCW/TN > 8 and no long-range magnetic ordering down to 0.15 K, being a possible QSL candidate material. These series of compounds are attractive for exploring the exotic magnetic phases of Kitaev materials with 4f electrons.

Emergent quantum phenomena in atomically engineered iridate heterostructures

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

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

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

Low-field magnetic anisotropy of Sr2IrO4

Magnetic anisotropy in strontium iridate (Sr₂IrO₄) is essential because of its strong spin-orbit coupling and crystal field effect. In this paper, we present a detailed mapping of the out-of-plane (OOP) magnetic anisotropy in Sr₂IrO₄for different sample orientations using torque magnetometry measurements in the low-magnetic-field region before the isospins are completely ordered. Dominant in-plane anisotropy was identified at low fields, confirming thebaxis as an easy magnetization axis. Based on the fitting analysis of the strong uniaxial magnetic anisotropy, we observed that the main anisotropic effect arises from a spin-orbit-coupled magnetic exchange interaction affecting the OOP interaction. The effect of interlayer exchange interaction results in additional anisotropic terms owing to the tilting of the isospins. The results are relevant for understanding OOP magnetic anisotropy and provide a new way to analyze the effects of spin-orbit-coupling and interlayer magnetic exchange interactions. This study provides insight into the understanding of bulk magnetic, magnetotransport, and spintronic behavior on Sr₂IrO₄for future studies.

Spin-orbit effects in pentavalent iridates: models and materials

Spin-orbit effects in heavy 5dtransition metal oxides, in particular, iridates, have received enormous current interest due to the prediction as well as the realization of a plethora of exotic and unconventional magnetic properties. While a bulk of these works are based on tetravalent iridates (d⁵), where the counter-intuitive insulating state of the rather extended 5dorbitals are explained by invoking strong spin-orbit coupling, the recent quest in iridate research has shifted to the other valencies of Ir, of which pentavalent iridates constitute a notable representative. In contrast to the tetravalent iridates, spin-orbit entangled electrons ind⁴systems are expected to be confined to theJ= 0 singlet state without any resultant moment or magnetic response. However, it has been recently predicted that, magnetism ind⁴systems may occur via magnetic condensation of excitations across spin-orbit-coupled states. In reality, the magnetism in Ir⁵⁺systems are often quite debatable both from theoretical as well as experimental point of view. Here we provide a comprehensive overview of the spin-orbit coupledd⁴model systems and its implications in the studied pentavalent iridates. In particular, we review here the current experimental and theoretical understanding of the double perovskite (A₂BYIrO₆,A= Sr, Ba,B= Y, Sc, Gd), 6H-perovskite (Ba₃MIr₂O₉,M= Zn, Mg, Sr, Ca), post-perovskite (NaIrO₃), and hexagonal (Sr₃MIrO₆) iridates, along with a number of open questions that require future investigation.

Comprehensive Electrical Control of Metamagnetic Transition of a Quasi-2D Antiferromagnet by In Situ Anisotropic Strain

Effective nonmagnetic control of the spin structure is at the forefront of the study for functional quantum materials. This study demonstrates that, by applying an anisotropic strain up to only 0.05%, the metamagnetic transition field of spin-orbit-coupled Mott insulator Sr₂ IrO₄ can be in situ modulated by almost 300%. Simultaneous measurements of resonant X-ray scattering and transport reveal that this drastic response originates from the complete strain-tuning of the transition between the spin-flop and spin-flip limits, and is always accompanied by large elastoconductance and magnetoconductance. This enables electrically controllable and electronically detectable metamagnetic switching, despite the antiferromagnetic insulating state. The obtained strain-magnetic field phase diagram reveals that C₄ -symmetry-breaking anisotropy is introduced by strain via pseudospin-lattice coupling, directly demonstrating the pseudo-Jahn-Teller effect of spin-orbit-coupled complex oxides. The extracted coupling strength is much weaker than the superexchange interactions, yet crucial for the spontaneous symmetry-breaking, affording the remarkably efficient strain-control.

Topological Magnons with Nodal-Line and Triple-Point Degeneracies: Implications for Thermal Hall Effect in Pyrochlore Iridates

We analyze the magnon excitations in pyrochlore iridates with all-in-all-out (AIAO) antiferromagnetic order, focusing on their topological features. We identify the magnetic point group symmetries that protect the nodal-line band crossings and triple-point degeneracies that dominate the Berry curvature. We find three distinct regimes of magnon band topology, as a function of the ratio of Dzyaloshinskii-Moriya interaction to the antiferromagnetic exchange. We show how the thermal Hall response provides a unique probe of the topological magnon band structure in AIAO systems.

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.

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.

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.

Nonsymmorphic-Symmetry-Protected Topological Magnons in Three-Dimensional Kitaev Materials

Topological phases in magnetic materials offer novel tunability of topological properties via varying the underlying magnetism. We show that three-dimensional Kitaev materials with nonsymmorphic symmetries can provide a great opportunity for controlling symmetry-protected topological nodal magnons. These materials are originally considered as strong candidates for the Kitaev quantum spin liquid due to the bond-dependent frustrating spin-exchange interactions. As a concrete example, we consider the symmetry and topology of the magnons in the canted zigzag ordered state in the hyperhoneycomb β-Li_{2}IrO_{3}, which can be obtained by applying a magnetic field in the counter-rotating spiral state at zero field. It is shown that the magnetic glide symmetries and the non-Hermitian nature of the bosonic magnons lead to unique topological protection that is different from the case of their fermionic counterparts. We investigate how such topological magnons can be controlled by changing the symmetry of the underlying spin-exchange interactions.

Large Variation of Dirac Semimetal State in Perovskite CaIrO_{3} with Pressure-Tuning of Electron Correlation

The impact of electron correlation on the Dirac semimetal state is investigated for perovskite CaIrO_{3} in terms of the magnetotransport properties under varying pressures. The reduction of electron correlation with a pressure of 1 GPa enhances the Fermi velocity as much as 40%, but it reduces the mobility by an order of magnitude by detuning the Dirac node from the Fermi energy. Moreover, the giant magnetoresistance at the quantum limit due to the one-dimensional confinement of Dirac electrons is critically suppressed under pressure. These results indicate that the electron correlation is a crucial knob for controlling the transport of a correlated Dirac semimetal.

Electronic Structure of a Graphene-like Artificial Crystal of NdNiO3

Artificial complex-oxide heterostructures containing ultrathin buried layers grown along the pseudocubic [111] direction have been predicted to host a plethora of exotic quantum states arising from the graphene-like lattice geometry and the interplay between strong electronic correlations and band topology. To date, however, electronic-structural investigations of such atomic layers remain an immense challenge due to the shortcomings of conventional surface-sensitive probes with typical information depths of a few angstroms. Here, we use a combination of bulk-sensitive soft X-ray angle-resolved photoelectron spectroscopy (SX-ARPES), hard X-ray photoelectron spectroscopy (HAXPES), and state-of-the-art first-principles calculations to demonstrate a direct and robust method for extracting momentum-resolved and angle-integrated valence-band electronic structure of an ultrathin buckled graphene-like layer of NdNiO₃ confined between two 4-unit cell-thick layers of insulating LaAlO₃. The momentum-resolved dispersion of the buried Ni d states near the Fermi level obtained via SX-ARPES is in excellent agreement with the first-principles calculations and establishes the realization of an antiferro-orbital order in this artificial lattice. The HAXPES measurements reveal the presence of a valence-band bandgap of 265 meV. Our findings open a promising avenue for designing and investigating quantum states of matter with exotic order and topology in a few buried layers.

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.

Selective probing of magnetic order on Tb and Ir sites in stuffed Tb2Ir2O7 using resonant x-ray scattering

We study the magnetic structure of the 'stuffed' (Tb-rich) pyrochlore iridate Tb_2+x Ir_2-x O_7-y (x ∼ 0.18), using resonant elastic x-ray scattering (REXS). In order to disentangle contributions from Tb and Ir magnetic sublattices, experiments were performed at the Ir L ₃ and Tb M ₅ edges, which provide selective sensitivity to Ir 5d and Tb 4f  magnetic moments, respectively. At the Ir L ₃ edge, we found the onset of long-range [Formula: see text] magnetic order below [Formula: see text] K, consistent with the expected signal of all-in all-out (AIAO) magnetic order. Using a single-ion model to calculate REXS cross-sections, we estimate an ordered magnetic moment of [Formula: see text] at 5 K. At the Tb M ₅ edge, long-range [Formula: see text] magnetic order appeared below  ∼[Formula: see text] K, also consistent with an AIAO magnetic structure on the Tb site. Additional insight into the magnetism of the Tb sublattice is gleaned from measurements at the M ₅ edge in applied magnetic fields up to 6 T, which is found to completely suppress the Tb AIAO magnetic order. In zero applied field, the observed gradual onset of the Tb sublattice magnetisation with temperature suggests that it is induced by the magnetic order on the Ir site. The persistence of AIAO magnetic order, despite the greatly reduced ordering temperature and moment size compared to stoichiometric Tb₂Ir₂O₇, for which [Formula: see text] K and [Formula: see text], indicates that stuffing could be a viable means of tuning the strength of electronic correlations, thereby potentially offering a new strategy to achieve topologically non-trivial band crossings in pyrochlore iridates.

Sawtooth Torque in Anisotropic j_{eff}=1/2 Magnets: Application to α-RuCl_{3}

The so-called "Kitaev candidate" materials based on 4d^{5} and 5d^{5} metals have recently emerged as magnetic systems displaying strongly anisotropic exchange interactions reminiscent of the Kitaev's honeycomb model. Recently, these materials have been shown to commonly display a distinct sawtooth angular dependence of the magnetic torque over a wide range of magnetic fields. While higher order chiral spin interactions have been considered as a source of this observation, we show here that bilinear anisotropic interactions and/or g anisotropy are each sufficient to explain the observed torque response, which may be distinguished on the basis of high-field measurements. These findings unify the understanding of magnetic torque experiments in a variety of Kitaev candidate materials.

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.

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

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

Kondo Insulator to Semimetal Transformation Tuned by Spin-Orbit Coupling

Recent theoretical studies of topologically nontrivial electronic states in Kondo insulators have pointed to the importance of spin-orbit coupling (SOC) for stabilizing these states. However, systematic experimental studies that tune the SOC parameter λ_{SOC} in Kondo insulators remain elusive. The main reason is that variations of (chemical) pressure or doping strongly influence the Kondo coupling J_{K} and the chemical potential μ-both essential parameters determining the ground state of the material-and thus possible λ_{SOC} tuning effects have remained unnoticed. Here, we present the successful growth of the substitution series Ce_{3}Bi_{4}(Pt_{1-x}Pd_{x})_{3} (0≤x≤1) of the archetypal (noncentrosymmetric) Kondo insulator Ce_{3}Bi_{4}Pt_{3}. The Pt-Pd substitution is isostructural, isoelectronic, and isosize, and it therefore is likely to leave J_{K} and μ essentially unchanged. By contrast, the large mass difference between the 5d element Pt and the 4d element Pd leads to a large difference in λ_{SOC}, which thus is the dominating tuning parameter in the series. Surprisingly, with increasing x (decreasing λ_{SOC}), we observe a Kondo insulator to semimetal transition, demonstrating an unprecedented drastic influence of the SOC. The fully substituted end compound Ce_{3}Bi_{4}Pd_{3} shows thermodynamic signatures of a recently predicted Weyl-Kondo semimetal.

Topological Magnon Bands and Unconventional Superconductivity in Pyrochlore Iridate Thin Films

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