Role of Hydrogen in the Spin-Orbital-Entangled Quantum Liquid Candidate H_{3}LiIr_{2}O_{6}

Momentum-independent magnetic excitation continuum in the honeycomb iridate H3LiIr2O6

Understanding the interplay between the inherent disorder and the correlated fluctuating-spin ground state is a key element in the search for quantum spin liquids. H3LiIr2O6 is considered to be a spin liquid that is proximate to the Kitaev-limit quantum spin liquid. Its ground state shows no magnetic order or spin freezing as expected for the spin liquid state. However, hydrogen zero-point motion and stacking faults are known to be present. The resulting bond disorder has been invoked to explain the existence of unexpected low-energy spin excitations, although data interpretation remains challenging. Here, we use resonant X-ray spectroscopies to map the collective excitations in H3LiIr2O6 and characterize its magnetic state. In the low-temperature correlated state, we reveal a broad bandwidth of magnetic excitations. The central energy and the high-energy tail of the continuum are consistent with expectations for dominant ferromagnetic Kitaev interactions between dynamically fluctuating spins. Furthermore, the absence of a momentum dependence to these excitations are consistent with disorder-induced broken translational invariance. Our low-energy data and the energy and width of the crystal field excitations support an interpretation of H3LiIr2O6 as a disordered topological spin liquid in close proximity to bond-disordered versions of the Kitaev quantum spin liquid.

Orbital Effects in Solids: Basics, Recent Progress, and Opportunities

The properties of transition metal compounds are largely determined by nontrivial interplay of different degrees of freedom: charge, spin, lattice, and also orbital ones. Especially rich and interesting effects occur in systems with orbital degeneracy. For example, they result in the famous Jahn-Teller effect, leading to a plethora of consequences for static and dynamic properties, including nontrivial quantum effects. In the present review, we discuss the main phenomena in the physics of such systems, paying central attention to the novel manifestations of those. After shortly summarizing the basic phenomena and their descriptions, we concentrate on several specific directions in this field. One of them is the reduction of effective dimensionality in many systems with orbital degrees of freedom due to the directional character of orbitals, with the concomitant appearance of some instabilities that lead in particular to the formation of dimers, trimers, and similar clusters in a material. The properties of such cluster systems, which are largely determined by their orbital structure, are discussed in detail, and many specific examples of those in different materials are presented. Another big field that has acquired special significance relatively recently is the role of the relativistic spin-orbit interaction. The mutual influence of this interaction and the more traditional Jahn-Teller physics is treated in detail in the second part of the review. In discussing all of these questions, special attention is paid to novel quantum effects.

Novel Chiral Quantum Spin Liquids in Kitaev Magnets

Quantum magnets with pure Kitaev spin exchange interactions can host a gapped quantum spin liquid with a single Majorana edge mode propagating in the counterclockwise direction when a small positive magnetic field is applied. Here, we show how under a sufficiently strong positive magnetic field a topological transition into a gapped quantum spin liquid with two Majorana edge modes propagating in the clockwise direction occurs. The Dzyaloshinskii-Moriya interaction is found to turn the nonchiral Kitaev's gapless quantum spin liquid into a chiral one with equal Berry phases at the two Dirac points. Thermal Hall conductance experiments can provide evidence of the novel topologically gapped quantum spin liquid states predicted.

Heisenberg-Kitaev physics in magnetic fields

Magnetic insulators in the regime of strong spin-orbit coupling exhibit intriguing behaviors in external magnetic fields, reflecting the frustrated nature of their effective interactions. We review the recent advances in understanding the field responses of materials that are described by models with strongly bond-dependent spin exchange interactions, such as Kitaev's celebrated honeycomb model and its extensions. We discuss the field-induced phases and the complex magnetization processes found in these theories and compare with experimental results in the layered Mott insulators [Formula: see text]-RuCl₃ and Na₂IrO₃, which are believed to realize this fascinating physics.

Bond-Disordered Spin Liquid and the Honeycomb Iridate H_{3}LiIr_{2}O_{6}: Abundant Low-Energy Density of States from Random Majorana Hopping

The 5d-electron honeycomb compound H_{3}LiIr_{2}O_{6} [K. Kitagawa et al., Nature (London) 554, 341 (2018)NATUAS0028-083610.1038/nature25482] exhibits an apparent quantum spin liquid state. In this intercalated spin-orbital compound, a remarkable pileup of low-energy states was experimentally observed in specific heat and spin relaxation. We show that a bond-disordered Kitaev model can naturally account for this phenomenon, suggesting that disorder plays an essential role in its theoretical description. In the exactly soluble Kitaev model, we obtain, via spin fractionalization, a random bipartite hopping problem of Majorana fermions in a random flux background. This has a divergent low-energy density of states of the required power-law form N(E)∝E^{-ν} with a drifting exponent which takes on the value ν≈1/2 for relatively strong bond disorder. Breaking time-reversal symmetry removes the divergence of the density of states, as does applying a magnetic field in experiment. We discuss the implication of our scenario, both for future experiments and from a broader perspective.