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arXiv:1811.04397 · Physical Review Letters

Strong Effect of Hydrogen Order on Magnetic Kitaev Interactions in H3LiIr2O6

Ravi Yadav, Rajyavardhan Ray, Mohamed S. Eldeeb, Satoshi Nishimoto, Liviu Hozoi, Jeroen van den Brink

Published Nov 9, 2018• 53 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.121.197203

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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.
The recently synthesized Ag3LiIr2O6{\mathrm{Ag}}_{3}{\mathrm{LiIr}}_{2}{\mathrm{O}}_{6}Ag3​LiIr2​O6​ has been proposed as a Kitaev magnet in proximity to the quantum spin liquid phase. We explore its microscopic Hamiltonian and magnetic ground state using many-body quantum chemistry methods and exact diagonalization techniques. Our calculations establish a dominant bond dependent ferromagnetic Kitaev exchange between Ir sites and find that the inclusion of Ag 4d4d4d orbitals in the configuration interaction calculations strikingly enhances the Kitaev exchange. Furthermore, using exact diagonalization of the nearest-neighbor fully anisotropic $J\text{\ensuremath{-}}K\text{\ensuremath{-}}\mathrm{\ensuremath{\Gamma}}$ Hamiltonian, we obtain the magnetic phase diagram as a function of further neighbor couplings. We find that the antiferromagnetic off-diagonal coupling stabilizes long range order, but the structure factor calculations suggest that the material is very close to the quantum spin liquid phase and the ordered state can easily collapse into a liquid by small perturbations such as structural distortion or bond disorder.
The recently discovered three-dimensional hyperhoneycomb iridate, β -Li 2 IrO 3 , has raised hopes for the realization of the 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, , correctly captures the low-energy electronic structure. The effective spin model derived in the strong-coupling limit supplemented by the ab initio results is shown to be dominated by the Kitaev interaction. We demonstrated that the possible range of parameters is consistent with a non-coplanar spiral magnetic order found in a recent experiment. All of these analyses suggest that β -Li 2 IrO 3 may be the closest among known materials to the Kitaev spin-liquid regime.
We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling K 2 , which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na 2 IrO 3 , and may also play a role in α-RuCl 3 and Li 2 IrO 3 .This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na 2 IrO 3 .Moreover, the minimal K 1 -K 2 model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.
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 $C/T\ensuremath{\sim}1/\sqrt{T}$ in zero magnetic field and $C/T\ensuremath{\sim}T/{B}^{3/2}$ with finite magnetic field BBB 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 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 $v\ensuremath{\sim}{B}^{3/4}$. 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.
Iridium oxides with a honeycomb lattice have been identified as platforms for the much anticipated Kitaev topological spin liquid: the spin-orbit entangled states of Ir(4+) in principle generate precisely the required type of anisotropic exchange. However, other magnetic couplings can drive the system away from the spin-liquid phase. With this in mind, here we disentangle the different magnetic interactions in Li2IrO3, a honeycomb iridate with two crystallographically inequivalent sets of adjacent Ir sites. Our ab initio many-body calculations show that, while both Heisenberg and Kitaev nearest-neighbour couplings are present, on one set of Ir-Ir bonds the former dominates, resulting in the formation of spin-triplet dimers. The triplet dimers frame a strongly frustrated triangular lattice and by exact cluster diagonalization we show that they remain protected in a wide region of the phase diagram.
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.