From a Quasimolecular Band Insulator to a Relativistic Mott Insulator in t_{2g}^{5} Systems with a Honeycomb Lattice Structure

Exploring a New Regime of Molecular Orbital Physics in 4d Cluster Magnets with Resonant Inelastic X-Ray Scattering

Molecular orbital systems with clusters of heavy transition metal (TM) ions are one of the most important classes of model materials for studying the interplay between local physics and effects of itinerancy. Despite a large number of candidates identified in the family of 4d TM materials, an understanding of their physics from competing microscopic energy scales is still missing. We bridge this gap by reporting the first resonant inelastic x-ray scattering (RIXS) measurement on a well-known series of Ru cluster magnets with a 6H-perovskite structure Ba_{3}MRu_{2}O_{9} (M^{3+}=In^{3+}, Y^{3+}, La^{3+}) comprised of Ru dimers. In addition to providing a microscopic explanation for their anomalous magnetic properties, our RIXS measurements combined with theoretical modeling uncover a new regime of molecular orbital physics where the combined effect of large hopping and small spin-orbit coupling results in highly fragile electronic states in the Ru-dimer compounds directly manifested as an abrupt change in the RIXS spectrum accompanying a tiny change in the local structure tuned by the M-site ion. This unique combination of energy scales found only in the 4d but not the 5d cluster magnets highlights the value of these materials as a new platform for studying quantum phase transition involving molecular orbitals.

Fluorite-related iridate Pr3IrO7: crystal growth, structure, magnetism, thermodynamic, and optical properties

Spin-orbit coupling in heavy 5dmetal 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 Pr₃IrO₇. Single crystals of Pr₃IrO₇have been grown by the KF flux method. Structural analysis shows that Pr₃IrO₇crystallizes in an orthorhombic phase withCmcmsymmetry. The electron energy loss spectroscopy study indicates that Pr is in a 3+ valence state, which implies a 5+ oxidation state of Ir. Magnetization data measured at high and low magnetic fields do not exhibit any bifurcation betweenM_ZFCandM_FC, however, a weak hump inM(T) is observed atT∗∼10.4 K. The specific heat data reveal two maxima at ∼253 and ∼4.8 K. The optical conductivityσ1(ω)spectrum shows 24 infrared-active phonon modes and reveals an insulating behavior with an optical gapΔOPof size ∼500 meV. During cooling down, the temperature-dependent reflectivity spectrum reveals eight extra phonon modes below the structural phase transition (∼253 K). An anomaly is observed at aroundT∗in the temperature evolution of infrared-active mode frequencies suggesting the presence of significant spin-phonon coupling in the system.

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.

Pressure-Tuned Interactions in Frustrated Magnets: Pathway to Quantum Spin Liquids?

Quantum spin liquids are prime examples of strongly entangled phases of matter with unconventional exotic excitations. Here, strong quantum fluctuations prohibit the freezing of the spin system. On the other hand, frustrated magnets, the proper platforms to search for the quantum spin liquid candidates, still show a magnetic ground state in most of the cases. Pressure is an effective tuning parameter of structural properties and electronic correlations. Nevertheless, the ability to influence the magnetic phases should not be forgotten. We review experimental progress in the field of pressure-tuned magnetic interactions in candidate systems. Elaborating on the possibility of tuned quantum phase transitions, we further show that chemical or external pressure is a suitable parameter in these exotic states of matter.

Vison Crystals in an Extended Kitaev Model on the Honeycomb Lattice

We introduce an extension of the Kitaev honeycomb model by including four-spin interactions that preserve the local gauge structure and, hence, the integrability of the original model. The extended model has a rich phase diagram containing five distinct vison crystals, as well as a symmetric π-flux spin liquid with a Fermi surface of Majorana fermions and a sequence of Lifshitz transitions. We discuss possible experimental signatures and, in particular, present finite-temperature Monte Carlo calculations of the specific heat and the static vison structure factor. We argue that our extended model emerges naturally from generic perturbations to the Kitaev honeycomb model.

Hopping-Induced Ground-State Magnetism in 6H Perovskite Iridates

Investigation of elementary excitations has advanced our understanding of many-body physics governing most physical properties of matter. Recently spin-orbit excitons have drawn much attention, whose condensates near phase transitions exhibit Higgs mode oscillations, a long-sought-after physical phenomenon [A. Jain, et al., Nat. Phys. 13, 633 (2017)NPAHAX1745-247310.1038/nphys4077]. These critical transition points, resulting from competing spin-orbit coupling (SOC), local crystalline symmetry, and exchange interactions, are not obvious in iridium-based materials, where SOC prevails in general. Here, we present results of resonant inelastic x-ray scattering on a spin-orbital liquid Ba_{3}ZnIr_{2}O_{9} and three other 6H-hexagonal perovskite iridates that show magnetism, contrary to the nonmagnetic singlet ground state expected due to strong SOC. Our results show that substantial hopping between closely placed Ir^{5+} ions within Ir_{2}O_{9} dimers in these 6H iridates modifies spin-orbit coupled states and reduces spin-orbit excitation energies. Here, we are forced to use at least a two-site model to match the excitation spectrum going in-line with the strong intradimer hopping. Apart from SOC, low-energy physics of iridates is thus critically dependent on hopping and may not be ignored even for systems having moderate hopping, where the excitation spectra can be explained using an atomic model. SOC, which is generally found to be 0.4-0.5 eV in iridates, is scaled in effect down to ∼0.26  eV for the 6H systems, sustaining the hope of achieving quantum criticality by tuning Ir-Ir separation.

Models and materials for generalized Kitaev magnetism

The exactly solvable Kitaev model on the honeycomb lattice has recently received enormous attention linked to the hope of achieving novel spin-liquid states with fractionalized Majorana-like excitations. In this review, we analyze the mechanism proposed by Jackeli and Khaliullin to identify Kitaev materials based on spin-orbital dependent bond interactions and provide a comprehensive overview of its implications in real materials. We set the focus on experimental results and current theoretical understanding of planar honeycomb systems (Na₂IrO₃, α-Li₂IrO₃, and α-RuCl₃), three-dimensional Kitaev materials (β- and γ-Li₂IrO₃), and other potential candidates, completing the review with the list of open questions awaiting new insights.

Direct experimental observation of the molecular J eff = 3/2 ground state in the lacunar spinel GaTa4Se8

Strong spin–orbit coupling lifts the degeneracy of t_2g orbitals in 5d transition-metal systems, leaving a Kramers doublet and quartet with effective angular momentum of J_eff = 1/2 and 3/2, respectively. These spin–orbit entangled states can host exotic quantum phases such as topological Mott state, unconventional superconductivity, and quantum spin liquid. The lacunar spinel GaTa₄Se₈ was theoretically predicted to form the molecular J_eff = 3/2 ground state. Experimental verification of its existence is an important first step to exploring the consequences of the J_eff = 3/2 state. Here, we report direct experimental evidence of the J_eff = 3/2 state in GaTa₄Se₈ by means of excitation spectra of resonant inelastic X-ray scattering at the Ta L₃ and L₂ edges. We find that the excitations involving the J_eff = 1/2 molecular orbital are absent only at the Ta L₂ edge, manifesting the realization of the molecular J_eff = 3/2 ground state in GaTa₄Se₈.

The strong interaction between electron spin and orbital degrees of freedom in 5d oxides can lead to exotic electronic ground states. Here the authors use resonant inelastic X-ray scattering to demonstrate that the theoretically proposed J_eff = 3/2 state is realised in GaTa₄Se₈.

Correlation induced electron-hole asymmetry in quasi- two-dimensional iridates

The resemblance of crystallographic and magnetic structures of the quasi-two-dimensional iridates Ba₂IrO₄ and Sr₂IrO₄ to La₂CuO₄ points at an analogy to cuprate high-Tc superconductors, even if spin-orbit coupling is very strong in iridates. Here we examine this analogy for the motion of a charge (hole or electron) added to the antiferromagnetic ground state. We show that correlation effects render the hole and electron case in iridates very different. An added electron forms a spin polaron, similar to the cuprates, but the situation of a removed electron is far more complex. Many-body 5d ⁴ configurations form which can be singlet and triplet states of total angular momentum that strongly affect the hole motion. This not only has ramifications for the interpretation of (inverse-)photoemission experiments but also demonstrates that correlation physics renders electron- and hole-doped iridates fundamentally different.Some iridate compounds such as Sr₂IrO₄ have electronic and atomic structures similar to quasi-2D copper oxides, raising the prospect of high temperature superconductivity. Here, the authors show that there is significant electron-hole asymmetry in iridates, contrary to expectations from the cuprates.

Electronic Structure of the Kitaev Material α-RuCl3 Probed by Photoemission and Inverse Photoemission Spectroscopies

Recently, α-RuCl₃ has attracted much attention as a possible material to realize the honeycomb Kitaev model of a quantum-spin-liquid state. Although the magnetic properties of α-RuCl₃ have been extensively studied, its electronic structure, which is strongly related to its Kitaev physics, is poorly understood. Here, the electronic structure of α-RuCl₃ was investigated by photoemission (PE) and inverse-photoemission (IPE) spectroscopies. The band gap was directly measured from the PE and IPE spectra and was found to be 1.9 eV, much larger than previously estimated values. Local density approximation (LDA) calculations showed that the on-site Coulomb interaction U could open the band gap without spin-orbit coupling (SOC). However, the SOC should also be incorporated to reproduce the proper gap size, indicating that the interplay between U and SOC plays an essential role. Several features of the PE and IPE spectra could not be explained by the results of LDA calculations. To explain such discrepancies, we performed configuration-interaction calculations for a RuCl₆^3- cluster. The experimental data and calculations demonstrated that the 4d compound α-RuCl₃ is a J_eff = 1/2 Mott insulator rather than a quasimolecular-orbital insulator. Our study also provides important physical parameters required for verifying the proposed Kitaev physics in α-RuCl₃.