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arXiv:1710.01307 · Physical review. B./Physical review. B

Theory of a quantum spin liquid in the hydrogen-intercalated honeycomb iridate H3LiIr2O6

Kevin Slagle, Wonjune Choi, Li Ern Chern, Yong Baek Kim

Published Mar 28, 2018• 33 citations
arXivHTMLPDF

Abstract

We propose a theoretical model for a gapless spin liquid phase that may have been observed in a recent experiment on ${\mathrm{H}}_{3}{\mathrm{LiIr}}_{2}{\mathrm{O}}_{6}$. Despite the insulating and nonmagnetic nature of the material, the specific heat coefficient $C/T\ensuremath{\sim}1/\sqrt{T}$ in zero magnetic field and $C/T\ensuremath{\sim}T/{B}^{3/2}$ with finite magnetic field $B$ have been observed. In addition, the NMR relaxation rate shows $1/({T}_{1}T)\ensuremath{\sim}{(C/T)}^{2}$. Motivated by the fact that the interlayer/in-plane lattice parameters are reduced/elongated by the hydrogen intercalation of the parent compound ${\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$, we consider four layers of the Kitaev honeycomb lattice model with additional interlayer exchange interactions. It is shown that the resulting spin liquid excitations reside mostly in the top and bottom layers of such a layered structure and possess a quartic dispersion. In an applied magnetic field, each quartic mode is split into four Majorana cones with the velocity $v\ensuremath{\sim}{B}^{3/4}$. We suggest that the spin liquid phase in these ``defect'' layers, placed between different stacking patterns of the honeycomb layers, can explain the major phenomenology of the experiment, which can be taken as evidence that the Kitaev interaction plays the primary role in the formation of a quantum spin liquid in this material.

DOI
10.1103/physrevb.97.115159

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We propose a theoretical model for a gapless spin liquid phase that may have been observed in a recent experiment on H3LiIr2O6{\mathrm{H}}_{3}{\mathrm{LiIr}}_{2}{\mathrm{O}}_{6}H3​LiIr2​O6​. Despite the insulating and nonmagnetic nature of the material, the specific heat coefficient C/T\ensuremath∼1/TC/T\ensuremath{\sim}1/\sqrt{T}C/T\ensuremath∼1/T​ in zero magnetic field and C/T\ensuremath∼T/B3/2C/T\ensuremath{\sim}T/{B}^{3/2}C/T\ensuremath∼T/B3/2 with finite magnetic field BBB have been observed. In addition, the NMR relaxation rate shows 1/(T1T)\ensuremath∼(C/T)21/({T}_{1}T)\ensuremath{\sim}{(C/T)}^{2}1/(T1​T)\ensuremath∼(C/T)2. Motivated by the fact that the interlayer/in-plane lattice parameters are reduced/elongated by the hydrogen intercalation of the parent compound Li2IrO3{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}Li2​IrO3​, we consider four layers of the Kitaev honeycomb lattice model with additional interlayer exchange interactions. It is shown that the resulting spin liquid excitations reside mostly in the top and bottom layers of such a layered structure and possess a quartic dispersion. In an applied magnetic field, each quartic mode is split into four Majorana cones with the velocity v\ensuremath∼B3/4v\ensuremath{\sim}{B}^{3/4}v\ensuremath∼B3/4. We suggest that the spin liquid phase in these ``defect'' layers, placed between different stacking patterns of the honeycomb layers, can explain the major phenomenology of the experiment, which can be taken as evidence that the Kitaev interaction plays the primary role in the formation of a quantum spin liquid in this material.
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.
A quantum spin liquid is a magnetic phase of matter that is remarkable for its ground state long-range entanglement and fractional excitations. A quantum spin liquid appears in the well-known Kitaev honeycomb spin-half model. In a magnetic field, there is a phase transition to a topological phase with an energy gap in the bulk and chiral Majorana fermions at the edge. However, recent nuclear magnetic resonance experiments suggest excitations without a gap in this phase, signalled by the cubic temperature dependence of the spin-lattice relaxation rate at low temperatures. In this work, I propose a mechanism to account for this experimental result. I use the localization of chiral Majorana modes in defects to explain the presence of gapless modes in the bulk. Treating the weak interaction between the chiral modes in the defects within a mean-field approximation, I find that these modes remain gapless when the interaction is below a critical value that depends on the magnetic field strength. I used the effective low-energy theory to calculate the spin-lattice relaxation rate and found a behavior that agrees with the experimental result.
Strong spin-orbital-coupling magnetic systems with the honeycomb structure can provide bond-directional interactions which may result in Kitaev quantum spin liquids and exotic anyonic excitations. However, one of the key ingredients in real materials---disorders---has been much less studied in Kitaev systems. Here we synthesized a trigonal ${\mathrm{SrIr}}_{2}{\mathrm{O}}_{6\ensuremath{-}\ensuremath{\delta}}$ with $\ensuremath{\delta}\ensuremath{\approx}0.25$, which consists of two-dimensional honeycomb Ir planes with edge-sharing IrO6{\mathrm{IrO}}_{6}IrO6​ octahedra. First-principles computation and experimental measurements suggest that the electronic system is gapped, and there should be no magnetic moment as the Ir5+{\mathrm{Ir}}^{5+}Ir5+ ion has no unpaired electrons. However, significant magnetism has been observed in the material, and it can be attributed to disorders that are most likely from oxygen vacancies. No magnetic order is found down to 0.05 K, and the low-temperature magnetic properties exhibit power-law behaviors in magnetic susceptibility and zero-field specific heat, and a single-parameter scaling of the specific heat under magnetic fields. These results provide strong evidence for the existence of the random singlet phase in ${\mathrm{SrIr}}_{2}{\mathrm{O}}_{6\ensuremath{-}\ensuremath{\delta}}$, which offers a different member to the family of spin-orbital entangled iridates and Kitaev materials.
Very recently a quantum liquid was reported to form in H_{3}LiIr_{2}O_{6}, an iridate proposed to be a close realization of the Kitaev honeycomb model. To test this assertion we perform detailed quantum chemistry calculations to determine the magnetic interactions between Ir moments. We find that weakly bond dependent ferromagnetic Kitaev exchange dominates over other couplings, but still is substantially lower than in Na_{2}IrO_{3}. This reduction is caused by the peculiar position of the interlayer species: removing hydrogen cations next to a Ir_{2}O_{2} plaquette increases the Kitaev exchange by more than a factor of 3 on the corresponding Ir─Ir link. Consequently, any lack of hydrogen order will have a drastic effect on the magnetic interactions and strongly promote spin disordering.
This is a comprehensive study of the Ru3+{}^{3+}3+-based Kitaev honeycomb compound (H,Li)6{}_{6}6​Ru2{}_{2}2​O6{}_{6}6​ (HLRO), combining magnetization (MMM), magnetic specific heat (Cm{C}_{m}Cm​), and local probes (muon spin relaxation and magnetic resonance). There is clear evidence of a Kitaev quantum spin liquid (KQSL) state. MMM, Cm{C}_{m}Cm​, and magnetic fluctuations (1/T1{T}_{1}T1​) exhibit scaling behavior. The Cm{C}_{m}Cm​ scaling is in good agreement with theory [PRX 11, 011034 (2021)]. A two-step entropy release is taken as a signature of Majorana fermions. HLRO is a realization of a KQSL without magnetic order in zero field, unlike 𝛼-RuCl3{}_{3}3​.
Motivated by recent experiments on $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the $K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model, where KKK and $\mathrm{\ensuremath{\Gamma}}$ represent the Kitaev and symmetric-anisotropic interactions between spin-1/2 moments on the honeycomb lattice. Using the infinite density matrix renormalization group, we provide compelling evidence for the existence of quantum spin liquid phases in an extended region of the phase diagram. In particular, we use transfer-matrix spectra to show the evolution of two-particle excitations with well-defined two-dimensional dispersion, which is a strong signature of a quantum spin liquid. These results are compared with predictions from Majorana mean-field theory and used to infer the quasiparticle excitation spectra. Further, we compute the dynamical structure factor using finite-size cluster computations and show that the results resemble the scattering continuum seen in neutron-scattering experiments on $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$. We discuss these results in light of recent and future experiments.