Honeycomb Lattice Iridates Research Articles

Pressure tuning of structure, magnetic frustration, and carrier conduction in the Kitaev spin liquid candidate Cu2IrO3

The layered honeycomb lattice iridate Cu$_2$IrO$_3$ is the closest realization of the Kitaev quantum spin liquid, primarily due to the enhanced interlayer separation and nearly ideal honeycomb lattice. We report pressure-induced structural evolution of Cu$_2$IrO$_3$ by powder x-ray diffraction (PXRD) up to $\sim$17 GPa and Raman scattering measurements up to $\sim$25 GPa. A structural phase transition (monoclinic $C2/c \: \rightarrow$ triclinic $P\bar{1}$) is observed with a broad mixed phase pressure range ($\sim$4 to 15 GPa). The triclinic phase consists of heavily distorted honeycomb lattice with Ir-Ir dimer formation and a collapsed interlayer separation. In the stability range of the low-pressure monoclinic phase, structural evolution maintains the Kitaev configuration up to 4 GPa. This is supported by the observed enhanced magnetic frustration in dc susceptibility without emergence of any magnetic ordering and an enhanced dynamic Raman susceptibility. High-pressure resistance measurements up to 25 GPa in the temperature range 1.4--300 K show resilient non-metallic $R$($T$) behaviour with significantly reduced resistivity in the high-pressure phase. The Mott 3D variable-range-hopping conduction with much reduced characteristic energy scale $T_0$ suggests that the high-pressure phase is at the boundary of localized-itinerant crossover. Using first-principles density functional theoretical (DFT) calculations, we find that at ambient pressure $\rm Cu_2IrO_3$ exists in monoclinic $P2_1/c$ phase which is energetically lower than $C2/c$ phase (both the structures are consistent with experimental XRD pattern). DFT reveals structural transition from $P2_1/c$ to $P\bar{1}$ structure at 7 GPa (involving dimerization of Ir-Ir bonds) in agreement with experimentally observed transition pressure.

Honeycomb lattice iridate on the verge of Mott-collapse

A new honeycomb lattice iridate (La,Na)IrO3 (≈LaNaIr2O6) is successfully synthesized from the spin–orbit coupled Mott insulator Na2IrO3 by replacing the interlayer Na+ ions with La3+ ions. (La,Na)IrO3 shows a finite Sommerfeld term in heat capacity and a −lnT dependence of resistivity, indicating a realization of a metallic state driven by a Mott collapse. Furthermore, crystal structure analysis reveals the formation of Ir zig-zag chains with metal–metal bonding, increasing kinetic energy resulting in the Mott collapse. This observation would be due to a Mott collapse induced in a J eff = 1/2 spin–orbit coupling Mott insulator with an Ir honeycomb lattice by topochemical control of the ionic configuration.

Electronic and Magnetic Properties of Spin-Orbit-Entangled Honeycomb Lattice Iridates MIrO3 (M = Cd, Zn, and Mg).

By means of density functional theory calculations with the inclusion of spin-orbit coupling, we present a comprehensive investigation of the structural, electronic, and magnetic properties of the novel series of ilmenite-type honeycomb lattice iridates MIrO3 (M = Cd, Zn, and Mg), the potential candidates for realizing the quantum spin liquid. Our findings are as follows: (i) the structural relaxations could not properly capture the abnormal thin two-dimensional honeycomb IrO6 layers in CdIrO3, making the experimentally proposed crystal structure questionable. Furthermore, the calculations within the experimental structure could not correctly determine the magnetic ground state; however, the results within the optimized one rectify this scenario and provide a precise and reasonable description of its electronic and magnetic properties, which is in good agreement with the experimental observations and that of Zn and Mg analogues. In this regard, we hope that our report will inspire additional studies on this issue and eventually resolve the crystal structure of CdIrO3. (ii) We identified that the magnetic ground state of this series of iridates MIrO3 is the zigzag antiferromagnetic ordering, where ferromagnetic zigzag chains are coupling antiferromagnetically across the bridging bonds within a hexagon. (iii) Though it is widely assumed that all the iridates can be well described based on the spin-orbit-assisted Jeff = 1/2 Mott insulating state model, detailed analysis of electronic band structures indicates that the formation of quasimolecular orbitals (QMOs) within a hexagon plays a non-negligible role in appropriately depicting the electronic and magnetic properties. Finally, (iv) we found that all the antiferromagnetic patterns are insulating with finite band gaps. Clarifying the effect of magnetic ordering on the electronic structures is important because it reminds us of potential erroneous identification/prediction of the ground state. The results suggest that precisely determining the magnetic ground state and adopting it in the simulations are imperative for faithfully rendering the electronic properties of a compound. Our results underline the importance of structural factor, spin-orbit coupling, correlation correction, the formation of the QMOs within the hexagon, as well as magnetic ordering in elucidating the electronic structure of a series of ilmenite-type honeycomb lattice iridates MIrO3.

Optical magnons with dominant bond-directional exchange interactions in the honeycomb lattice iridate α−Li2IrO3

We have used resonant inelastic x-ray scattering to reveal optical magnons in a honeycomb lattice iridate $\alpha$-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. The observed excitations are understood as stemming from optical magnon modes whose intensity is modulated by a structure factor, resulting in the apparent momentum dependence. We also observed diffuse magnetic scattering arising from the short-range magnetic correlation well above $\textit{T}_{N}$. In contrast to Na$_{2}$IrO$_{3}$, this diffuse scattering lacks the $C_3$ rotational symmetry of the honeycomb lattice, suggesting that the bond anisotropy is far from negligible in $\alpha$-Li$_{2}$IrO$_{3}$.

Electronic and structural properties of the honeycomb iridates A2IrO3 ( A=Na , Li) at elevated pressures

The honeycomb lattice iridates ${A}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$ ($A=\mathrm{Na}$, Li) are spin-orbit assisted Mott insulators proximate to Kitaev's quantum spin liquid. The insulating state as well as the magnetic properties are believed to arise due to a delicate balance of several energy scales. We report on high-pressure electrical transport and x-ray-diffraction measurements on ${A}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$ ($A=\mathrm{Na}$, Li) in an attempt to study their structural and electronic evolution with pressure. We found that while $\mathrm{L}{\mathrm{i}}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$ undergoes a structural phase transition into the dimerized state at a pressure of $P$ \ensuremath{\sim} 4 GPa, in $\mathrm{N}{\mathrm{a}}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$ the conservation of the original $C2/m$ structure up to at least 58 GPa is observed. In addition, $\mathrm{L}{\mathrm{i}}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$ undergoes a sluggish structural rearrangement at the pressure range 20--40 GPa coinciding with a significant decrease in resistance. Despite dissimilar structural evolution and different mechanisms of the electrical conductivity, Arrhenius conductivity for $\mathrm{N}{\mathrm{a}}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$ and Mott variable-range hopping in $\mathrm{L}{\mathrm{i}}_{2}\mathrm{Ir}{\mathrm{O}}_{3}$, both systems show a very similar $R$($P$) behavior. Namely, after a nonmonotonic decrease of the resistance $R$ and the charge gap \ensuremath{\Delta}, the \ensuremath{\Delta} stabilizes at about 45 GPa and even increases slightly with pressure; the $R$($T$) shows insulating behavior up to the highest pressure measured, 80 and 55 GPa, respectively. This resilient nonmetallic behavior of the studied iridates suggests a formation close to a localized-itinerant crossover of unusual electronic states, whose possible features are discussed. Unforeseeably, the $R$($P$) behavior is not dependent on the buffer element $A$, which seems essential for understanding the nature of the electrical conductivity in iridates.

Impact of disorder on dynamics and ordering in the honeycomb-lattice iridate Na2IrO3

Kitaev's honeycomb spin-liquid model and its proposed realization in materials such as $\alpha$-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 distribution of internal magnetic fields. Both of these results provide evidence for inequivalent magnetic sites at low temperature, suggesting inhomogeneities are important for the magnetism. The spin-lattice relaxation rate is isotropic and diverges at $T_N$, suggesting that the Kitaev cubic axes may control the critical quantum spin fluctuations. In the ordered state, we observe gapless excitations, which may arise from site substitution, emergent defects from milder disorder, or possibly be associated with nearby quantum paramagnetic states distinct from the Kitaev spin liquid.

Dynamic surface modification due to effusion of Na in Na2IrO3

The honeycomb lattice iridate Na2IrO3 shows frustrated magnetism and can potentially display Kitaev-like exchange interactions. Recently, it was shown that the electronic properties of the surface of crystalline Na2IrO3 can be tuned by Ar plasma treatment in a controlled manner, leading to various phases of matter ranging from a fully gapped to a metallic surface, where the possibility of a charge-density wave like transition has been suggested. Here, through direct imaging with an atomic force microscope (AFM) in air, we show that the surface of crystalline Na2IrO3 evolves rapidly as elemental Na effuses out of the interleave planes to the surface and undergoes sublimation, thereby disappearing from the surface gradually over time. Using conductive AFM, we recorded a series of topographs and surface current maps simultaneously and found that the modification of the surface leads to change in the electronic properties in a dynamic fashion until the whole system reaches a dynamic equilibrium. These observations are important in the context of the exotic electronic and magnetic properties that the surface of Na2IrO3 displays.

Magnetic impurity doping induced spin-glass state and short-range zigzag order in the honeycomb iridate Na2IrO3

Based on the modified Heisenberg–Kitaev model, the effects of magnetic substitution on the magnetic properties of the honeycomb-lattice iridate are studied using Monte Carlo simulations. It is observed that the long-range zigzag state of the original system is rather fragile and can be replaced by a spin-glass state even for small substitution, well consistent with the experimental observation in Ru-substituted samples (Mehlawat et al 2015 Phys. Rev. B 92 134412). Both the disordered Heisenberg and Kitaev interactions caused by the magnetic ion-doping are suggested to be responsible for the magnetic phase transitions in the system. More interestingly, a short-range zigzag order is suggested to survive above the freezing temperature even at high magnetic impurity doping levels.

First-order density-wave-like transitions in surface-dopedNa2IrO3

We demonstrate that the surface of the honeycomb lattice iridate Na$_2$IrO$_3$ is extremely tunable by plasma etching. We have succeeded in turning the surface of Na$_2$IrO$_3$ metallic by Ar plasma etching which leads to the removal of Na from the surface. The surface structure does not change in this process as revealed by grazing incidence small angle x-ray scattering (GISAXS). The sheet resistance $R_s$ can be reduced by several orders of magnitude by varying the etching duration. Temperature dependent $R_s(T)$ for the metallic samples show signatures of spin or charge density wave transitions with abrupt changes in $R_s$. Thermal hysteresis between cooling and warming measurements across the transition indicates a first order transition. For the most metallic sample $R_s(T)$ data at low temperatures follow a $T^2$ behaviour suggesting normal Fermi liquid behaviour.

Fragile magnetic order in the honeycomb lattice IridateNa2IrO3revealed by magnetic impurity doping

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 spin glass like state even for the smallest substitution suggesting that the magnetic order in Na$_2$IrO$_3$ is extremely fragile. We argue that these behaviors indicate the importance of nearest-neighbor magnetic exchange in the parent Na$_2$IrO$_3$. Additionally, all samples show insulating electrical transport.

Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for the honeycomb-lattice iridatesA2IrO3

We have explored the hidden symmetries of a generic four-parameter nearest-neighbor spin model, allowed in honeycomb lattice compounds under trigonal compression. Our method utilizes a systematic algorithm to identify all dual transformations of the model that map the Hamiltonian on itself, changing the parameters and providing exact links between different points in its parameter space. We have found the complete set of points of hidden SU(2) symmetry at which seemingly highly anisotropic model can be mapped back on the Heisenberg model and inherits therefore its properties such as the presence of gapless Goldstone modes. The procedure used to search for the hidden symmetries is quite general and may be extended to other bond-anisotropic spin models and other lattices, such as the triangular, kagome, hyper-honeycomb, or harmonic-honeycomb lattices. We apply our findings to the honeycomb lattice iridates Na2IrO3 and Li2IrO3, and illustrate how they help to identify plausible values of the model parameters that are compatible with the available experimental data.

Direct evidence for dominant bond-directional interactions in a honeycomb lattice iridate Na2IrO3

Heisenberg interactions are ubiquitous in magnetic materials and play a central role in modelling and designing quantum magnets. Bond-directional interactions1,2,3 offer a novel alternative to Heisenberg exchange and provide the building blocks of the Kitaev model4, which has a quantum spin liquid as its exact ground state. Honeycomb iridates, A2IrO3 (A = Na, Li), offer potential realizations of the Kitaev magnetic exchange coupling, and their reported magnetic behaviour may be interpreted within the Kitaev framework. However, the extent of their relevance to the Kitaev model remains unclear, as evidence for bond-directional interactions has so far been indirect. Here we present direct evidence for dominant bond-directional interactions in antiferromagnetic Na2IrO3 and show that they lead to strong magnetic frustration. Diffuse magnetic X-ray scattering reveals broken spin-rotational symmetry even above the Néel temperature, with the three spin components exhibiting short-range correlations along distinct crystallographic directions. This spin- and real-space entanglement directly uncovers the bond-directional nature of these interactions, thus providing a direct connection between honeycomb iridates and Kitaev physics.

Magnetism in spin models for depleted honeycomb-lattice iridates: Spin-glass order towards percolation

Iridates are characterized by a fascinating interplay of spin-orbit and electron-electron interactions. The honeycomb-lattice materials ${A}_{2}{\mathrm{IrO}}_{3}$ $(A=\text{Na},\text{Li})$ have been proposed to realize pseudospin-1/2 Mott insulating states with strongly anisotropic exchange interactions, described by the Heisenberg-Kitaev model, but other scenarios involving longer-range exchange interactions or more delocalized electrons have been put forward as well. Here we study the influence of nonmagnetic doping, i.e., depleted moments, on the magnetic properties of experimentally relevant variants of the Heisenberg-Kitaev and Heisenberg ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ models. We generically find that the zigzag order of the clean system is replaced, upon doping, by a spin-glass state with short-ranged zigzag correlations. We determine the spin-glass temperature as a function of the doping level and show that this quantity allows one to assess the importance of longer-range exchange interactions when the doping is driven across the site-percolation threshold of the honeycomb lattice.

Correlated Quantum Phenomena in the Strong Spin-Orbit Regime

We discuss phenomena arising from the combined influence of electron correlation and spin-orbit coupling (SOC), with an emphasis on emergent quantum phases and transitions in heavy transition metal compounds with 4d and 5d elements. A common theme is the influence of spin-orbital entanglement produced by SOC, which influences the electronic and magnetic structure. In the weak-to-intermediate correlation regime, we show how nontrivial band-like topology leads to a plethora of phases related to topological insulators (TIs). We expound these ideas using the example of pyrochlore iridates, showing how many novel phases, such as the Weyl semimetal, axion insulator, topological Mott insulator, and TIs, may arise in this context. In the strong correlation regime, we argue that spin-orbital entanglement fully or partially removes orbital degeneracy, reducing or avoiding the normally ubiquitous Jahn-Teller effect. As we illustrate for the honeycomb-lattice iridates and double perovskites, this leads to enhanced quantum fluctuations of the spin-orbital entangled states and the chance to promote exotic spin liquid and multipolar ordered ground states. Connections to experiments, materials, and future directions are discussed.

Crystal-field splitting and correlation effect on the electronic structure of A2IrO3.

The electronic structure of the honeycomb lattice iridates Na(2)IrO(3) and Li(2)IrO(3) has been investigated using resonant inelastic x-ray scattering (RIXS). Crystal-field-split d-d excitations are resolved in the high-resolution RIXS spectra. In particular, the splitting due to noncubic crystal fields, derived from the splitting of j(eff)=3/2 states, is much smaller than the typical spin-orbit energy scale in iridates, validating the applicability of j(eff) physics in A(2)IrO(3). We also find excitonic enhancement of the particle-hole excitation gap around 0.4 eV, indicating that the nearest-neighbor Coulomb interaction could be large. These findings suggest that both Na(2)IrO(3) and Li(2)IrO(3) can be described as spin-orbit Mott insulators, similar to the square lattice iridate Sr(2)IrO(4).