We report equilibrium and nonequilibrium optical measurements on the recently synthesized "harmonic" honeycomb iridate γ-Li$_2$IrO$_3$ (LIO), as well as the layered honeycomb iridate Na$_2$IrO$_3$ (NIO). Using Fourier transform infrared microscopy we performed reflectance measurements on LIO, from which we obtained the optical conductivity below 2 eV. In addition we measured the photoinduced changed in reflectance, ΔR, as a function of time, t, temperature, T, and probe field polarization in both LIO and NIO. In LIO, ΔR(t,T) is anisotropic and comprised of three T dependent components. Two of these components are related to the onset of magnetic order and the third is related to a photoinduced population of metastable electronic excited states. In NIO, ΔR(t,T) has a single T dependent component that is strikingly similar to the electronic excitation component of ΔR in LIO. Through analysis and comparison of ΔR(t,T) for two compounds, we extract information on the onset of magnetic correlations at and above the transition temperature in LIO, the bare spin-flip scattering rate in equilibrium, the lifetime of low-lying quasiparticle excitations, and the polarization dependence of optical transitions that are sensitive to magnetic order.
We report the successful synthesis of single-crystals of the layered iridate, (Na$_{1-x}$Li$_{x}$)$_2$IrO$_3$, $0\leq x \leq 0.9$, and a thorough study of its structural, magnetic, thermal and transport properties. The new compound allows a controlled interpolation between Na$_2$IrO$_3$ and Li$_2$IrO$_3$, while maintaing the novel quantum magnetism of the honeycomb Ir$^{4+}$ planes. The measured phase diagram demonstrates a dramatic suppression of the Néel temperature, $T_N$, at intermediate $x$ suggesting that the magnetic order in Na$_2$IrO$_3$ and Li$_2$IrO$_3$ are distinct, and that at $x\…
To determine the strength of essential electronic and magnetic interactions in the iridates Sr$_2$IrO$_4$ and Ba$_2$IrO$_4$ - potential platforms for high-temperature superconductivity - we use many-body techniques from wavefunction-based electronic-structure theory. Multiplet physics, spin-orbit interactions, and Ir-O hybridization are all treated on equal footing, fully {\it ab initio}. Our calculations put the lowest d-d excitations of Sr$_2$IrO$_4$/Ba$_2$IrO$_4$ at 0.69/0.64 eV, substantially lower than in isostructural cuprates. Charge-transfer excitations start at 3.0/1.9 eV and the magn…
The fractionalization of elementary excitations in quantum spin systems is a central theme in current condensed matter physics. The Kitaev honeycomb spin model provides a prominent example of exotic fractionalized quasiparticles, composed of itinerant Majorana fermions and gapped gauge fluxes. However, identification of the Majorana fermions in a three-dimensional honeycomb lattice remains elusive. Here we report spectroscopic signatures of fractional excitations in the harmonic-honeycomb iridates $β$- and $γ$-Li$_2$IrO$_3$. Using polarization resolved Raman spectroscopy, we find that the dyna…
Direct experimental investigations of the low-energy electronic structure of the Na$_2$IrO$_3$ iridate insulator are sparse and draw two conflicting pictures. One relies on flat bands and a clear gap, the other involves dispersive states approaching the Fermi level, pointing to surface metallicity. Here, by a combination of angle-resolved photoemission, photoemission electron microscopy, and x-ray absorption, we show that the correct picture is more complex and involves an anomalous band, arising from charge transfer from Na atoms to Ir-derived states. Bulk quasiparticles do exist, but in one …
We propose an insulating 2D phase of IrO$_{2}$, predicted by $\textit{ab initio}$ evolutionary algorithms. The predicted phase is a van der Waals crystal, in which Ir forms a triangular lattice, and is energetically competitive with the metastable spinel phase, observed experimentally. Electronic structure calculations show that the magnetic properties of this phase are highly nontrivial, with an almost perfect degeneracy of 120$^{\circ}$ $\textit{Neel}$ and $Y$-stripe orders, and unusually soft magnetic moments. The resulting behavior, which we term $\textit{easy plane anisotropy}$, is entire…
Here, we report an investigation of structural, magnetic and electronic properties in Y-doped layered iridate (Sr$_{1-x}$Y$_x$)$_2$IrO$_4$ ($x$ $\leq$ 0.1). The parent Sr$_2$IrO$_4$ is a well-studied spin-orbit coupling (SOC) induced insulator with an antiferromagnetic ground state. The Y-doping here equivalently acts for electron doping without altering the vital parameters such as, SOC and electron correlation. Experimental results show a minute change in structural parameters and an equivalent charge conversion from Ir$^{4+}$ to Ir$^{3+}$. Unlike similarly other electron-doped system, the l…
We report a resonant inelastic x-ray scattering (RIXS) investigation of ultra-thin epitaxial films of Ba$_2$IrO$_4$, and compare their low energy magnetic and spin-orbit excitations to those of their sister compound Sr$_2$IrO$_4$. Due to the 180$^\circ$ Ir-O-Ir bond, the bandwidth of the magnon and spin-orbiton is significantly larger in Ba$_2$IrO$_4$, making it difficult to describe these two types of excitations as separate well-defined quasiparticles. Both types of excitations are found to be quite sensitive to the effect of epitaxial strain. In addition, we find that the d-level inversion …
We present a thorough experimental study of the three-dimensional hyperhoneycomb Kitaev magnet $β$-Li$_2$IrO$_3$, using a combination of inelastic neutron scattering (INS), time-domain THz spectroscopy, and heat capacity measurements. The main results include a massive low-temperature reorganization of the INS spectral weight that evolves into a broad peak centered around 12 meV, and a distinctive peak in the THz data at 2.8(1) meV. A detailed comparison to powder-averaged spin-wave theory calculations reveals that the positions of these two features are controlled by the anisotropic $Γ$ coupl…
We have used resonant inelastic x-ray scattering to reveal optical magnons in a honeycomb lattice iridate $α$-Li$_{2}$IrO$_{3}$. The spectrum in the energy region 20-25 meV exhibits momentum dependence, of which energy is highest at the location of the magnetic Bragg peak, ($\textit{h}, \textit{k}$) = ($\pm$0.32, 0), and lowered toward (0, 0) and ($\pm$1, 0). We compare our data with a linear spin-wave theory based on a generic nearest-neighbor spin model. We find that a dominant bond-directional Kitaev interaction of order 20 meV is required to explain the energy scale observed in our study. …
We have synthesized single crystals of Na$_2$(Ir$_{1-x}$Ti$_x$)O$_3$ and polycrystals of Li$_2$(Ir$_{1-x}$Ti$_x$)O$_3$ and studied the effect of magnetic depletion on the magnetic properties by measurements of the magnetic susceptibility, specific heat and magnetocaloric effect at temperatures down to 0.1~K. In both systems, the non-magnetic substitution rapidly changes the magnetically ordered ground state into a spin glass, indicating strong frustration. While for the Li system the Weiss temperature $Θ_{\rm W}$ remains unchanged up to $x=0.55$, a strong decrease $|Θ_{\rm W}|$ is found for th…
Hyperhoneycomb iridate $β$-Li$_2$IrO$_3$ is a three-dimensional analogue of two-dimensional honeycomb iridates, such as $α$-Li$_2$IrO$_3$, which recently appeared as another playground for the physics of Kitaev-type spin liquid. $β$-Li$_2$IrO$_3$ shows a non-collinear spiral ordering of spin-orbital-entangled $J_{\rm eff}$ = 1/2 moments at low temperature, which is known to be suppressed under a pressure of $\sim$2 GPa. With further increase of pressure, a structural transition is observed at $P_{\rm S}$ $\sim$ 4 GPa at room temperature. Using the neutron powder diffraction technique, the crys…
We report a polarized Raman scattering study of the lattice dynamics of $β$-Li$_2$IrO$_3$ under hydrostatic pressures up to 7.62 GPa. At ambient pressure, $β$-Li$_2$IrO$_3$ exhibits the hyperhoneycomb crystal structure and a magnetically ordered state of spin-orbit entangled Jeff = 1/2 moments that is strongly influenced by bond-directional (Kitaev) exchange interactions. At a critical pressure of ~ 4.1 GPa, the phonon spectrum changes abruptly consistent with the reported structural transition into a monoclinic, dimerized phase. A comparison to the phonon spectra obtained from density functio…
We study the effect of isoelectronic doping and external pressure in tuning the ground state of the honeycomb iridate Na$_2$IrO$_3$ by combining optical spectroscopy with synchrotron x-ray diffraction measurements on single crystals. The obtained optical conductivity of Na$_2$IrO$_3$ is discussed in terms of a Mott insulating picture versus the formation of quasimolecular orbitals and in terms of Kitaev-interactions. With increasing Li content $x$, (Na$_{1-x}$Li$_x$)$_2$IrO$_3$ moves deeper into the Mott insulating regime and there are indications that up to a doping level of 24\% the compound…
Single-crystal x-ray diffraction studies with synchrotron radiation on the honeycomb iridate $α$-Li$_{2}$IrO$_{3}$ reveal a pressure-induced structural phase transition with symmetry lowering from monoclinic to triclinic at a critical pressure of $P_{c}$ = 3.8 GPa. According to the evolution of the lattice parameters with pressure, the transition mainly affects the $ab$ plane and thereby the Ir hexagon network, leading to the formation of Ir--Ir dimers. These observations are independently predicted and corroborated by our \textit{ab initio} density functional theory calculations where we find…
Motivated by an experimental report of iridate superlattices, we performed first-principle electronic structure calculations for SrIrO$_3$/SrTiO$_3$. Heterostructuring causes SrIrO$_3$ to become Sr$_2$IrO$_4$-like, and the system has the well-defined $j_{\rm eff}$=1/2 states near the Fermi level as well as canted antiferromagnetic order within the quasi-two-dimensional IrO$_2$ plane. In response to a larger tensile strain, the band gap is increased due to the resulting increase in bond length and the bandwidth reduction. The ground state magnetic properties are discussed in comparison to the m…
A family of insulating iridates with chemical formula Li$_2$IrO$_3$ has recently been discovered, featuring three distinct crystal structures $α,β,γ$ (honeycomb, hyperhoneycomb, stripyhoneycomb). Measurements on the three-dimensional polytypes, $β$- and $γ$-Li$_2$IrO$_3$, found that they magnetically order into remarkably similar spiral phases, exhibiting a non-coplanar counter-rotating spiral magnetic order with equivalent q=0.57 wavevectors. We examine magnetic Hamiltonians for this family and show that the same triplet of nearest-neighbor Kitaev-Heisenberg-Ising (KJI) interactions reproduce…
The magnetic field response of the Mott-insulating honeycomb iridate Na$_{2}$IrO$_{3}$ is investigated using torque magnetometry measurements in magnetic fields up to 60 tesla. A peak-dip structure is observed in the torque response at magnetic fields corresponding to an energy scale close to the zigzag ordering ($\approx 15~K$) temperature. Using exact diagonalization calculations, we show that such a distinctive signature in the torque response constrains the effective spin models for these classes of Kitaev materials to ones with dominant ferromagnetic Kitaev interactions, while alternative…
We study theoretically the Raman scattering response $I(ω)$ in the gapless quantum spin liquid phase of the Kitaev-Heisenberg model. The dominant polarization-independent contribution $I_K (ω)$ reflects the density of states of the emergent Majorana fermions in the ground-state flux-sector. The integrability-breaking Heisenberg exchange generates a second contribution, whose dominant part $I_H (ω)$ has the form of a quantum quench corresponding to an abrupt insertion of four $Z_2$ gauge fluxes. This results in a weakly polarization dependent response with a sharp peak at the energy of the flux…
We report angle-resolved photoemission (ARPES) measurements, density functional and model tight-binding calculations on Ba$_2$IrO$_4$ (Ba-214), an antiferromagnetic ($T_N=230$ K) insulator. Ba-214 does not exhibit the rotational distortion of the IrO$_6$ octahedra that is present in its sister compound Sr$_2$IrO$_4$ (Sr-214), and is therefore an attractive reference material to study the electronic structure of layered iridates. We find that the band structures of Ba-214 and Sr-214 are qualitatively similar, hinting at the predominant role of the spin-orbit interaction in these materials. Temp…
We determine the motion of a charge (hole or electron) added to the Mott insulating, antiferromagnetic (AF) ground-state of quasi-2D iridates such as Ba 2 IrO 4 or Sr 2 IrO 4 . We show that correlation effects, calculated within the self-consistent Born approximation, render the hole and electron case very different. An added electron forms a spin-polaron, which closely resembles the well-known cuprates, but the situation of a removed electron is far more complex. Many-body 5d 4 configurations form which can be singlet and triplets of total angular momentum J and strongly affect the hole motio…
Over the last few years, Sr$_2$IrO$_4$, a single-layer member of the Ruddlesden-Popper series iridates, has received much attention as a close analog of cuprate high-temperature superconductors. Although there is not yet firm evidence for superconductivity, a remarkable range of cuprate phenomenology has been reproduced in electron- and hole-doped iridates including pseudogaps, Fermi arcs, and $d$-wave gaps. Further, a number of symmetry breaking orders reminiscent of those decorating the cuprate phase diagram have been reported using various experimental probes. We discuss how the electronic …
Analogs of the high-T$_c$ cuprates have been long sought after in transition metal oxides. Due to the strong spin-orbit coupling (SOC), the $5d$ perovskite iridates Sr$_2$IrO$_4$ exhibit a low-energy electronic structure remarkably similar to the cuprates. Whether a superconducting state exists as in the cuprates requires understanding the correlated spin-orbit entangled electronic states. Recent experiments discovered hidden order in the parent and electron doped iridates, some with striking analogies to the cuprates, including Fermi surface pockets, Fermi arcs, and pseudogap. Here, we study …
Kitaev's honeycomb spin-liquid model and its proposed realization in materials such as $α$-RuCl$_3$, Li$_2$IrO$_3$ and Na$_2$IrO$_3$ continue to present open questions about how the dynamics of a spin-liquid are modified in the presence of non-Kitaev interactions as well as the presence of inhomogeneities. Here we use $^{23}$Na nuclear magnetic resonance to probe both static and dynamical magnetic properties in single crystal Na$_2$IrO$_3$. We find that the NMR shift follows the bulk susceptibility above 30 K but deviates from it below; moreover below $T_N$ the spectra show a broad distributio…
In this work, we investigate the microscopic nature of the magnetism in honeycomb iridium-based systems by performing a systematic study of how the effective magnetic interactions in these compounds depend on various electronic microscopic parameters. We show that the minimal model describing the magnetism in A$_2$IrO$_3$ includes both isotropic and anisotropic Kitaev-type spin-exchange interactions between nearest and next-nearest neighbor Ir ions, and that the magnitude of the Kitaev interaction between next-nearest neighbor Ir magnetic moments is comparable with nearest neighbor interaction…
Two recent theoretical works studied the role of Kitaev interactions in the newly observed incommensurate magnetic order in the hyper-honeycomb ($β$-Li$_2$IrO$_3$) and stripy-honeycomb ($γ$-Li$_2$IrO$_3$) iridates. Each of these works analyzed a different model ($JKΓ$ versus coupled zigzag chain model) using a contrasting method (classical versus soft-spin analysis). The lack of commonality between these works precludes meaningful comparisons and a proper understanding of these unusual orderings. In this study, we complete the unfinished picture initiated by these two works by solving both mod…
We report the structure, magnetic, and thermal property measurements on single crystalline and polycrystalline samples of Ru substituted honeycomb lattice iridate Na$_2$Ir$_x$Ru$_{1-x}$O$_3$ (x = 0, 0.05, 0.1, 0.15, 0.2, 0.3, 0.5). The evolution of magnetism in Na$_2$Ir$_x$Ru$_{1-x}$O$_3$ has been studied using dc and ac magnetic susceptibility, and heat capacity measurements. The parent compound Na$_2$IrO$_3$ is a spin-orbit driven Mott insulator with magnetic order of reduced moments below $T_N = 15$~K\@. In the Ru substituted samples the antiferromagnetic long range state is replaced by a s…
A pressure-induced collapse of magnetic ordering in $β$-Li$_2$IrO$_3$ at $P_m\sim1.5- 2$ GPa has previously been interpreted as evidence for possible emergence of spin liquid states in this hyperhoneycomb iridate, raising prospects for experimental realizations of the Kitaev model. Based on structural data obtained at \emph{room temperature}, this magnetic transition is believed to originate in small lattice perturbations that preserve crystal symmetry, and related changes in bond-directional anisotropic exchange interactions. Here we report on the evolution of the crystal structure of $β$-Li$…
We studied the electronic structure of $β$-Li$_2$IrO$_3$ insulator within the density-functional theory using the generalized gradient approximation with taking into account strong Coulomb correlations in the framework of the fully relativistic spin-polarized Dirac linear muffin-tin orbital band-structure method. The $β$-Li$_2$IrO$_3$ undergoes a pressure-induced structural and magnetic phase transitions at $P_c$ $\sim$4 GPa with symmetry lowering to the monoclinic $C2/c$. The structural phase transition is accompanied by the formation of Ir$_2$ dimers on the zigzag chains, with an Ir-Ir dista…
We have investigated experimentally and theoretically the series (Na$_{1-x}$Li$_{x}$)$_{2}$IrO$_{3}$. Contrary to what has been believed so far, only for $x\leq0.25$ the system forms uniform solid solutions. For larger Li content, as evidenced by powder X-ray diffraction, scanning electron microscopy and density functional theory calculations, the system shows a miscibility gap and a phase separation into an ordered Na$_{3}$LiIr$_2$O$_{6}$ phase with alternating Na$_3$ and LiIr$_2$O$_6$ planes, and a Li-rich phase close to pure Li$_{2}$IrO$_{3}$. For $x\leq 0.25$ we observe (1) an increase of …
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 $δ$-doped iridate La$_δ$Sr$_2$IrO$_4$, where a single SrO layer is replaced by a LaO layer. The extra La electron resides close to the $δ$-doped layer, partially occupying the $J_{\rm eff}= 1/2 $ upper Hubbard band and thereby making the interface metallic. The magnetic structure of the bulk is destroyed near the interface, with the Ir$_0…
By performing resonant inelastic x-ray scattering (RIXS) measurements at the Ir $\mathit{L_{\mathrm{3}}}$ edge, we have investigated the low-energy elementary excitations in a series of double perovskite iridate single crystals, La$_{2}$$\mathit{M}$IrO$_{6}$ ($\mathit{M}$ = Co, Ni, and Zn). Almost dispersionless magnetic excitations at $\sim$ 42(6) meV and $\sim$ 35(5) meV have been observed in crystals containing magnetic 3$\mathit{d}$ ions, La$_{2}$CoIrO$_{6}$ and La$_{2}$NiIrO$_{6}$, respectively. In contrast, this low-energy magnetic excitation is absent in La$_{2}$ZnIrO$_{6}$ in which the…
Temperature-pressure phase diagram of the Kitaev hyperhoneycomb iridate $β$-Li$_2$IrO$_3$ is explored using magnetization, thermal expansion, magnetostriction, and muon spin rotation ($μ$SR) measurements, as well as single-crystal x-ray diffraction under pressure and ab initio calculations. The Neel temperature of $β$-Li$_2$IrO$_3$ increases with the slope of 0.9 K/GPa upon initial compression, but the reduction in the polarization field $H_c$ reflects a growing instability of the incommensurate order. At 1.4 GPa, the ordered state breaks down upon a first-order transition giving way to a new …
Iridates such as Sr$_2$IrO$_4$ are of considerable interest owing to the formation of the Mott insulating state driven by a large spin-orbit coupling. However, in contrast to the expectation from the Nagaoka Theorem that a single doped hole or electron destroys the anti-ferromagnetic (AFM) state of the half-filled Hubbard model in the large U limit, the anti-ferromagnetism persists in the doped Iridates for a large dopant concentration beyond half-filling. With a tight-binding description of the relevant J$_{\rm eff}$ = 1/2 states by the third-neighbor ($t_1$, $t_2$, $t_3$, $U$) Hubbard model …
Spin-orbit coupling in heavy 5$d$ metal oxides, in particular, iridates have received tremendous interest in recent years due to the realization of exotic electronic and magnetic phases. Here, we report the synthesis, structural, magnetic, thermodynamic, and optical properties of the ternary iridate Pr$_3$IrO$_7$. Single crystals of Pr$_3$IrO$_7$ have been grown by the KF flux method. Structural analysis shows that Pr$_3$IrO$_7$ crystallizes in an orthorhombic phase with $Cmcm$ symmetry. The electron energy loss spectroscopy study indicates that Pr is in a 3+ valence state, which implies a 5+ …
The recently discovered three-dimensional hyperhoneycomb iridate, $β$-Li$_2$IrO$_3$, has raised hopes for the realization of dominant Kitaev interaction between spin-orbit entangled local moments due to its near-ideal lattice structure. If true, this material may lie close to the sought-after quantum spin liquid phase in three dimensions. Utilizing ab-initio electronic structure calculations, we first show that the spin-orbit entangled basis, $j_{\rm eff}$=1/2, correctly captures the low energy electronic structure. The effective spin model derived in the strong coupling limit supplemented by …
Using resonant x-ray diffraction, we observe an easy c-axis collinear antiferromagnetic structure for the bilayer Sr$_3$Ir$_2$O$_7$, a significant contrast to the single layer Sr$_2$IrO$_4$ with in-plane canted moments. Based on a microscopic model Hamiltonian, we show that the observed spin-flop transition as a function of number of IrO$_2$ layers is due to strong competition among intra- and inter-layer bond-directional pseudo-dipolar interactions of the spin-orbit entangled $J_{eff}$=1/2 moments. With this we unravel the origin of anisotropic exchange interactions in a Mott insulator in the…
By ab initio many-body quantum chemistry calculations, we determine the strength of the symmetric anisotropy in the 5$d^5$ j $\approx$ 1/2 layered material Ba$_2$IrO$_4$. While the calculated anisotropic couplings come out in the range of a few meV, orders of magnitude stronger than in analogous 3d transition-metal compounds, the Heisenberg superexchange still defines the largest energy scale. The ab initio results reveal that individual layers of Ba$_2$IrO$_4$ provide a close realization of the quantum spin-1/2 Heisenberg-compass model on the square lattice. We show that the experimentally ob…
The spin-orbit coupling (SOC) interactions, electron correlation effects and Hund coupling cooperate and compete with each other, leading to novel properties, quantum phase and non-trivial topological electronic behavior in iridium oxides. Because of the well separated IrO6 octahedra approaching cubic crystal-field limit, the hexagonal iridates Sr3MIrO6 (M = Sr, Na and Li) serves as a canonical model system to investigate the underlying physical properties that arises from the novel Jeff state. Based on density functional theory calculations complemented by Green's function methods, we systema…
Contrary to the original expectation, Na$_2$IrO$_3$ is not a Kitaev's quantum spin liquid (QSL) but shows a zig-zag-type antiferromagnetic order in experiments. Here we propose experimental clues and criteria to measure how a material in hand is close to the Kitaev's QSL state. For this purpose, we systematically study thermal and spin excitations of a generalized Kitaev-Heisenberg model studied by Chaloupka $et$ $al$. in Phys. Rev. Lett. 110, 097204 (2013) and an effective ab initio Hamiltonian for Na$_2$IrO$_3$ proposed by Yamaji $et$ $al$. in Phys. Rev. Lett. 113, 107201 (2014), by employin…
We studied the effect of external pressure on the electrodynamic properties of $α$-Li$_2$IrO$_3$ single crystals in the frequency range of the phonon modes and the Ir $d$-$d$ transitions. The abrupt hardening of several phonon modes under pressure supports the onset of the dimerized phase at the critical pressure $P_c$=3.8 GPa. With increasing pressure an overall decrease in spectral weight of the Ir $d$-$d$ transitions is found up to $P_c$. Above $P_c$, the local (on-site) $d$-$d$ excitations gain spectral weight with increasing pressure, which hints at a pressure-induced increase in the octa…
Oxides containing iridium ions display a range of magnetic and conducting properties that depend on the delicate balance between interactions and are controlled, at least in part, by the details of the crystal architecture. We have used muon-spin rotation ($μ$SR) to study the local field in four iridium oxides, Ca$_4$IrO$_6$, Ca$_5$Ir$_3$O$_{12}$, Sr$_3$Ir$_2$O$_7$ and Sr$_2$IrO$_4$, which show contrasting behavior. Our $μ$SR data on Ca$_4$IrO$_6$ and Ca$_5$Ir$_3$O$_{12}$ are consistent with conventional antiferromagnetism where quasistatic magnetic order develops below $T_{\rm N}=13.85(6)$ K …
We report on the selective fabrication of high-quality Sr$_2$IrO$_4$ and SrIrO$_3$ epitaxial thin films from a single polycrystalline Sr$_2$IrO$_4$ target by pulsed laser deposition. Using a combination of X-ray diffraction and photoemission spectroscopy characterizations, we discover that within a relatively narrow range of substrate temperature, the oxygen partial pressure plays a critical role in the cation stoichiometric ratio of the films, and triggers the stabilization of different Ruddlesden-Popper (RP) phases. Resonant X-ray absorption spectroscopy measurements taken at the Ir $L$-edge…
We study the nearest neighboring spin-1/2 Kitaev-Heisenberg-Gamma ($KJΓ$) model on the honeycomb lattice in the parameter region of ferromagnetic (FM) Kitaev and antiferromagnetic (AFM) Heisenberg couplings relevant for honeycomb iridates, using a coupled-chain analysis. Starting from the gapless Luttinger liquid phase of a decoupled $KJΓ$ chain, the inter-chain interactions in the two-dimensional model is treated within a self-consistent mean field approach based on the Luttinger liquid theory. In the FM Gamma region, our analysis recovers the reported 120$^\circ$ magnetic order, previously o…
The rich phase diagram of the prototypical iridate Ba$_2$IrO$_4$: Effective low-energy models and metal-insulator transition
Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université（矿物学、材料物理与宇宙化学研究所，索邦大学）；Laboratoire de Chimie et Physique Quantiques, Université Toulouse III - Paul Sabatier（量子化学与物理学实验室，图卢兹第三大学-保罗·萨巴蒂尔大学）
Iridate oxides on a honeycomb lattice are considered promising candidates for realization of quantum spin liquid states. We investigate the magnetic couplings in a structural model for a honeycomb iridate K$_2$IrO$_3$, with $C_3$ point group symmetry at the Ir sites, which is an end member of the recently synthesized iridate family K$_x$Ir$_y$O$_2$. Using \textit{ab-initio} quantum chemical methods, we elucidate the subtle relationship between the real space symmetry and magnetic anisotropy and show that the higher point group symmetry leads to high frustration with strong magnetic anisotropy …
Motivated by the recent synthesis of two insulating Li$_2$IrO$_3$ polymorphs, where Ir$^{4+}$ $S_{eff}$=1/2 moments form 3D ("harmonic") honeycomb structures with threefold coordination, we study magnetic Hamiltonians on the resulting $β$-Li$_2$IrO$_3$ hyperhoneycomb lattice and $γ$-Li$_2$IrO$_3$ stripyhoneycomb lattice. Experimentally measured magnetic susceptibilities suggest that Kitaev interactions, predicted for the ideal 90$^\circ$ Ir-O-Ir bonds, are sizable in these materials. We first consider pure Kitaev interactions, which lead to an exactly soluble 3D quantum spin liquid (QSL) with …
A rare combination of strong spin-orbit coupling and electron-electron correlations makes the iridate Mott insulator Sr$_2$IrO$_4$ a promising host for novel electronic phases of matter. The resemblance of its crystallographic, magnetic and electronic structures to La$_2$CuO$_4$, as well as the emergence upon doping of a pseudogap region and a low temperature $d$-wave gap, has particularly strengthened analogies to cuprate high-$T_c$ superconductors. However, unlike the cuprate phase diagram that features a plethora of broken symmetry phases in a pseudogap region that include charge density wa…
Motivated by recent experiments exploring the spin-orbit-coupled magnetism in $4d$- and $5d$-band transition metal oxides, we study magnetic interactions in Ir- and Rh-based compounds. In these systems, the comparable strength of spin-orbit coupling (SOC), crystal field splitting (CF) and Coulomb and Hund's coupling leads to a rich variety of magnetic exchange interactions, leading to new types of ground states. Using a strong coupling approach, we derive effective low-energy super-exchange Hamiltonians from the multi-orbital Hubbard model by taking full account of the Coulomb and Hund's inter…
Iridates supply fertile grounds for unconventional phenomena and exotic electronic phases. With respect to well-studied octahedrally-coordinated iridates, we pay our attention to a rather unexplored iridate, Na4IrO4, showing an unusual square-planar coordination. The latter is key to rationalize the electronic structure and magnetic property of Na4IrO4, which is here explored by first-principles density functional theory and Monte Carlo simulations. Due to the uncommon square-planar crystal field, Ir 5d states adopt intermediate-spin state with double occupation of dz2 orbital, leading to a si…
$\mathrm{Cu_2IrO_3}$ is among the newest layered honeycomb iridates and a promising candidate to harbor a Kitaev quantum spin liquid state. Here, we investigate the pressure and temperature dependence of its structure through a combination of powder x-ray diffraction and x-ray absorption fine structure measurements, as well as $ab$-$initio$ evolutionary structure search. At ambient pressure, we revise the previously proposed $C2/c$ solution with a related but notably more stable $P2_1/c$ structure. Pressures below 8 GPa drive the formation of Ir-Ir dimers at both ambient and low temperatures, …
We investigate the electronic structure and magnetic properties of a $J_\text{eff} = 1/2$ iridate Ca$_4$IrO$_6$ and the implications of doping electrons and holes using ab initio density functional theory. Our calculations considering spin-orbit interaction reveal that although the Mott-insulating parent compound transforms into a conductor upon doping, antiferromagnetism sustains in the doped system, albeit with a grossly noncollinear arrangement of the spins. We find a strong spin-orbit interaction and magneto-crystalline anisotropy, causing frustration in the system, possibly leading to the…
Motivated by experiments on the carrier-doped bilayer iridate $(\text{Sr}_{1-x}\text{La}_x)_3\text{Ir}_2\text{O}_7$, we study the dynamics of a single doped electron in a bilayer magnet in the presence of spin-orbit coupling, taking into account the spatially staggered rotation of IrO$_6$ octahedra. We employ an effective single-orbital bilayer $t$-$J$ model, concentrating on the quantum paramagnetic phase near the magnetic quantum critical point. We determine the carrier dispersion using a combination of self-consistent Born and bond-operator techniques. Extrapolating to finite small carrier …
The mixing of orbital and spin character in the wave functions of the $5d$ iridates has led to predictions of strong couplings among their lattice, electronic and magnetic degrees of freedom. As well as realizing a novel spin-orbit assisted Mott-insulating ground state, the perovskite iridate Sr$_{2}$IrO$_{4}$ has strong similarities with the cuprate La$_{2}$CuO$_{4}$, which on doping hosts a charge-density wave that appears intimately connected to high-temperature superconductivity. These phenomena can be sensitively probed through momentum-resolved measurements of the lattice dynamics, made …
We investigated the magnetic properties of the ilmenite-type iridate CdIrO$_3$ with a honeycomb lattice formed by Ir$^{4+}$ ions prepared via a solid-state metathesis. The magnetization measurements with using the powder sample reveal a large effective magnetic moment and a fairly strong antiferromagnetic interaction, indicating a deviation from the Kitaev model. Considering the relationship between magnetism and crystal structure in CdIrO$_3$ with comparing with the other ilmenite-type iridates ZnIrO$_3$ and MgIrO$_3$, we conclude that insulating CdIrO$_3$ cannot be describe as a $J_{\rm eff}…
$\rm Sr_2IrO_4$ is an archetypal spin-orbit-coupled Mott insulator and has been extensively studied in part because of a wide range of predicted novel states. Limited experimental characterization of these states thus far brings to light the extraordinary susceptibility of the physical properties to the lattice, particularly, the Ir-O-Ir bond angle. Here, we report a newly observed microscopic rotation of the IrO$_6$ octahedra below 50~K measured by single crystal neutron diffraction. This sharp lattice anomaly provides keys to understanding the anomalous low-temperature physics and a direct c…
The unconventional magnetic orderings found in Kitaev spin liquid candidates suggest frustration of spin interactions, and raise a possibility of nearby spin liquid phases. In particular, counter-rotating spiral ordering in three-dimensional (3D) iridates is striking, and understanding the microscopic mechanism of such ordering may provide routes to 3D Kitaev spin liquids. We study a minimal 3D model including Kitaev $K$ and a symmetric off-diagonal bond-dependent $Γ$ interaction on the hyperhoneycomb lattice using exact diagonalization. We first show that a 12-site unitary transformation unve…
We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir$^{4+}$ ions in a family of layered iridates $A_2$IrO$_3$ ($A$=Li,Na). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Néel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is t…
