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arXiv:2103.05820 · Physical review. B./Physical review. B

Evidence for the random singlet phase in the honeycomb iridate SrIr 2 O 6

Peng-Bo Song, Kejia Zhu, Fan Yang, Yuan Wei, Lu Zhang, Huaixin Yang, Xian‐Lei Sheng, Yang Qi, Jiamin Ni, Shiyan Li, Yanchun Li, Guang‐Han Cao, Zi Yang Meng, Wei Li, Youguo Shi, Shiliang Li

Published Jun 23, 2021• 11 citations
arXivHTMLPDF

Abstract

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 ${\mathrm{IrO}}_{6}$ octahedra. First-principles computation and experimental measurements suggest that the electronic system is gapped, and there should be no magnetic moment as the ${\mathrm{Ir}}^{5+}$ 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.

DOI
10.1103/physrevb.103.l241114

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•Jan 1, 2015•1 citation
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 SrIr2O6\ensuremath−\ensuremathδ{\mathrm{SrIr}}_{2}{\mathrm{O}}_{6\ensuremath{-}\ensuremath{\delta}}SrIr2​O6\ensuremath−\ensuremathδ​ with \ensuremathδ\ensuremath≈0.25\ensuremath{\delta}\ensuremath{\approx}0.25\ensuremathδ\ensuremath≈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 SrIr2O6\ensuremath−\ensuremathδ{\mathrm{SrIr}}_{2}{\mathrm{O}}_{6\ensuremath{-}\ensuremath{\delta}}SrIr2​O6\ensuremath−\ensuremathδ​, which offers a different member to the family of spin-orbital entangled iridates and Kitaev materials.
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.
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.
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.
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 magnetic-field response of the Mott-insulating honeycomb iridate Na2IrO3{\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}Na2​IrO3​ is investigated using torque magnetometry measurements in magnetic fields up to 60 T. A peak-dip structure is observed in the torque response at magnetic fields corresponding to an energy scale close to the zigzag ordering ($\ensuremath{\approx}15\phantom{\rule{0.28em}{0ex}}\mathrm{K}$) temperature. Using exact diagonalization calculations, we show that such a distinctive signature in the torque response constrains the effective spin models for these classes of Kitaev materials to ones with dominant ferromagnetic Kitaev interactions, while alternative models with dominant antiferromagnetic Kitaev interactions are excluded. We further show that, at high magnetic fields, long range spin correlation functions decay rapidly, pointing to a transition to a long-sought-after field-induced quantum spin liquid beyond the peak-dip structure, suggesting this to be a common feature of the family of Kitaev systems. Kitaev systems are thus revealed to be excellent candidates for field-induced quantum spin liquids, similar physics having been suggested in another Kitaev system $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$.
In this doctoral dissertation, we consider the significance of spin-orbit coupling for the phases of matter which arise for strongly correlated electrons. We explore emergent behavior in quantum many-body systems, including symmetry-breaking orders, quantum spin liquids, and unconventional superconductivity. Our study is cemented by a particular class of Mott-insulating materials, centered around a family of two- and three-dimensional iridium oxides, whose honeycomb-like lattice structure admits peculiar magnetic interactions, the so-called Kitaev exchange. By analyzing recent experiments on these compounds, we show that this unconventional exchange is the key ingredient in describing their magnetism, and then use a combination of numerical and analytical techniques to investigate the implications for the phase diagram as well as the physics of the proximate three-dimensional quantum spin liquid phases. These long-ranged-entangled fractionalized phases should exhibit special features, including finite-temperature stability as well as unconventional high-Tc superconductivity upon charge-doping, which should aid future experimental searches for spin liquid physics. Our study explores the nature of frustration and fractionalization which can arise in quantum systems in the presence of strong spin-orbit coupling.