Searching for an ideal Kitaev spin liquid candidate with anyonic excitations and long-range entanglement has motivated the synthesis of a new family of intercalated Kitaev magnets such as H$_{3}$LiIr$_{2}$O$_{6}$, Cu$_{2}$IrO$_{3}$, and Ag$_{3}$LiIr$_{2}$O$_{6}$. The absence of a susceptibility peak and a two-step release of the magnetic entropy in these materials has been proposed as evidence of proximity to the Kitaev spin liquid. Here we present a comparative study of the magnetic susceptibility, heat capacity, and muon spin relaxation ($μ$SR) between two samples of Ag$_{3}$LiIr$_{2}$O$_{6}$ in the clean and disordered limits. In the disordered limit, the absence of a peak in either susceptibility or heat capacity and a weakly depolarizing $μ$SR signal may suggest a proximate spin liquid ground state. In the clean limit, however, we resolve a peak in both susceptibility and heat capacity data, and observe clear oscillations in $μ$SR that confirm long-range antiferromagnetic ordering. The $μ$SR oscillations fit to a Bessel function, characteristic of an incommensurate order, as reported in the parent compound $α$-Li$_{2}$IrO$_{3}$. Our results clarify the role of structural disorder in the intercalated Kitaev magnets.
A new quantum spin liquid (QSL) candidate material H$_{3}$LiIr$_{2}$O$_{6}$ was synthesized recently and was found not to show any magnetic order or phase transition down to low temperatures. In this work, we study the quantum dynamics of the hydrogen ions, i.e., protons, in this material by combining first-principles calculations and theoretical analysis. We show that each proton and its adjacent oxygen ions form an electric dipole. The dipole interactions and the proton tunneling are captured by a transverse-field Ising model with a quantum disordered paraelectric ground state. The dipole ex…
Kitaev magnets are materials with bond-dependent Ising interactions between localized spins on a honeycomb lattice. Such interactions could lead to a quantum spin-liquid (QSL) ground state at zero temperature. Recent theoretical studies suggest two potential signatures of a QSL at finite temperatures, namely a scaling behavior of thermodynamic quantities in the presence of quenched disorder, and a two-step release of the magnetic entropy. Here, we present both signatures in Ag$_{3}$LiIr$_{2}$O$_{6}$ which is synthesized from $α$-Li$_{2}$IrO$_{3}$ by replacing the inter-layer Li atoms with Ag a…
Recently, there have been contrary claims of Kitaev spin-liquid behaviour and ordered behavior in the honeycomb compound Ag$_3$LiIr$_2$O$_6$ based on various experimental signatures. Our investigations on this system reveal a low-temperature ordered state with persistent dynamics down to the lowest temperatures. Magnetic order is confirmed by clear oscillations in the muon spin relaxation ($μ$SR) time spectrum below 9 K till 52 mK. Coincidentally in $^7$Li nuclear magnetic resonance, a wipe-out of the signal is observed below $\sim$ 10 K which again strongly indicates magnetic order in the low…
The bond-disordered Kitaev model attracts much attention due to the experimental relevance in $α$-RuCl$_3$ and $A_3$LiIr$_2$O$_6$ ($A=$ H, D, Ag, $\textit{etc.}$). Applying a magnetic field to break the time-reversal symmetry leads to a strong modulation in mass terms for Dirac cones. Because of the smallness of the flux gap of the Kitaev model, a small bond disorder can have large influence on itinerant Majorana fermions, and Majorana fermions will be in the Anderson localization state immediately. We call this immobile liquid state Anderson-Kitaev liquid state with two localized Majorana fer…
Nearly two decades ago, Alexei Kitaev proposed a model for spin-$1/2$ particles with bond-directional interactions on a two-dimensional honeycomb lattice which had the potential to host a quantum spin-liquid ground state. This work initiated numerous investigations to design and synthesize materials that would physically realize the Kitaev Hamiltonian. The first-generation of such materials, such as Na$_{2}$IrO$_{3}$, $α$-Li$_{2}$IrO$_{3}$, and $α$-RuCl$_{3}$, revealed the presence of non-Kitaev interactions such as the Heisenberg and off-diagonal exchange. Both physical pressure and chemical …
$α$-RuCl$_3$ has been extensively studied recently because of potential bond-dependent Kitaev magnetic exchange interactions and the resulting quantum spin liquid phase that can be realized therein. It has been known that the covalency between Ru 4$d$- and Cl $p$-orbitals is crucial to induce large Kitaev interactions in this compound, therefore replacing Cl into heavier halogen elements such as Br or I can be a promising way to promote the Kitaev interaction even further. In a timely manner, there have been reports on synthesis of $α$-RuBr$_3$ and $α$-RuI$_3$, which are expected to host the s…
Emergence of quantum spin liquid and spin-flop phase in Kitaev antiferromagnets in a [111] magnetic field
College of Physics, Nanjing University of Aeronautics and Astronautics（南京航空航天大学物理学院）；Key Laboratory of Aerospace Information Materials and Physics (NUAA), MIIT（工业和信息化部航空航天信息材料与物理重点实验室（南航））；School of Physics and Institute for Advanced Study in Physics, Zhejiang University（浙江大学物理学院与高等研究院）
A polycrystalline sample of the hyperhoneycomb iridate $β$-ZnIrO$_3$ was synthesized via a topochemical reaction, and its structural, magnetic, and thermodynamic properties were investigated. The magnetization and heat capacity data show the absence of long-range magnetic order at least down to 2 K. A positive Curie-Weiss temperature $θ_W \sim 45$ K probed by the temperature dependence of magnetic susceptibility indicates that a Kitaev interaction is dominant. These observations suggest that a quantum spin liquid may have been realized. Furthermore, the observation of linear temperature-depend…
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 G. Jackeli and G. 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 (Na$_2$IrO$_3$, $α$-Li$_2$IrO$_3$, and $α$-RuCl$_3$)…
Candidate materials for Kitaev spin liquid phase have been intensively studied recently because of their potential applications in fault-tolerant quantum computing. Although most of the studies on Kitaev spin liquid have been done in 4$d$ and 5$d$ based transition metal compounds, recently there has been a growing research interest in Co-based quasi-two-dimensional honeycomb magnets, such as BaCo$_2$(AsO$_4$)$_2$ because of formation of spin-orbit-entangled $J_{\rm eff}$ = 1/2 pseudospin moments at Co$^{2+}$ sites and potential realizations of Kitaev-like magnetism therein. Here, we obtain hig…
The ruthenium halide $α$-RuCl$_{3}$ is a promising candidate for a Kitaev spin liquid. However, the microscopic model describing $α$-RuCl$_{3}$ is still debated partly because of a lack of analogue materials for $α$-RuCl$_{3}$, which prevents tracking of electronic properties as functions of controlled interaction parameters. Here, we report a successful synthesis of RuBr$_{3}$. The material RuBr$_{3}$~possesses BiI$_3$-type structure (space group: $R\overline{3}$) where Ru$^{3+}$ form an ideal honeycomb lattice. Although RuBr$_{3}$ has a negative Weiss temperature, it undergoes a zigzag antif…
We investigate the thermal Hall effect in a Kitaev-Heisenberg system, a model for Kitaev candidate $α$-RuCl$_3$, in the presence of the coupling between spin and phonon arising from chlorine atoms' vibration. We observe that the coupling modifies the relative stability between different magnetic states under a magnetic field, especially stabilizing a canted zigzag antiferromagnetic state. Remarkably, the spin-phonon interaction has distinct effects on the thermal Hall conductivity in different magnetically ordered states. For the canted zigzag state, which is relevant to $α\text{-RuCl}_3$, the…
We study the Kitaev-Heisenberg-$Γ$ model with antiferromagnetic Kitaev exchanges in the strong anisotropic (toric code) limit to understand the phases and the intervening phase transitions between the gapped $Z_2$ quantum spin liquid and the spin-ordered (in the Heisenberg limit) as well as paramagnetic phases (in the pseudo-dipolar, $Γ$, limit). We find that the paramagnetic phase obtained in the large $Γ$ limit has no topological entanglement entropy and is proximate to a gapless critical point of a system described by an equal superposition of differently oriented stacked one-dimensional $Z…
Anyonic excitations emerging from a Kitaev spin liquid can form a basis for quantum computers. Searching for such excitations motivated intense research on the honeycomb iridate materials. However, access to a spin liquid ground state has been hindered by magnetic ordering. Cu2IrO3 is a new honeycomb iridate without thermodynamic signatures of a long-range order. Here, we use muon spin relaxation to uncover the magnetic ground state of Cu2IrO3. We find a two-component depolarization with slow and fast relaxation rates corresponding to distinct regions with dynamic and static magnetism, respect…
Despite the exciting implications of the Kitaev spin-Hamiltonian, finding and confirming the quantum spin liquid state has proven incredibly difficult. Recently the applicability of the model has been expanded through the development of a microscopic description of a spin-1 Kitaev interaction. Here we explore a candidate spin-1 honeycomb system, KNiAsO$_4$ , which meets many of the proposed criteria to generate such an interaction. Bulk measurements reveal an antiferromagnetic transition at $\sim$ 19 K which is generally robust to applied magnetic fields. Neutron diffraction measurements show …
Beyond Kitaev exchange: $Γ'$-driven magnetism in Ag$_3$LiRh$_2$O$_6$
Felix Bloch Institute for Solid-State Physics, University of Leipzig（莱比锡大学菲利克斯·布洛赫固体物理研究所）；Technical University of Munich, TUM School of Natural Sciences, Physics Department（慕尼黑工业大学自然科学学院物理系）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Department of Physics and Center for Functional Materials, Wake Forest University（维克森林大学物理与功能材料中心）；Department of Physics, Loughborough University（拉夫堡大学物理系）；Blackett Laboratory, Imperial College London（帝国理工学院布莱克特实验室）
Magnetoelastic interaction couples spin and lattice degrees of freedom and plays a key role in thermal transport properties of magnetic insulators. In the Kitaev quantum spin liquid, the low energy excitations are charge neutral Majorana fermions, which transform the magnetoelasctic interaction into Majorana-phonon scattering. Motivated by anomalous thermal properties of the Kitaev quantum spin liquid candidate RuCl$_3$, in this letter, we combine meV resolution inelastic x-ray scattering and theoretical calculation to examine the Majorana-phonon scattering. We analytically derive the velocity…
While phase transitions between magnetic analogs of three states of matter --- a long-range ordered state, paramagnet, and spin liquid --- have been extensively studied, the possibility of "liquid-liquid" transitions, namely, between different spin liquids, remains elusive. By introducing the additional Ising coupling into the honeycomb Kitaev model with bond asymmetry, we discover that the Kitaev spin liquid turns into a spin-nematic quantum paramagnet before a magnetic order is established by the Ising coupling. The quantum phase transition between the two liquid states accompanies a topolog…
We point out that the Kitaev materials may not necessarily support Kitaev spin liquid. It is well-known that having a Kitaev term in the spin interaction is not the sufficient condition for the Kitaev spin liquid ground state. Many other spin liquids may be stabilized by the competing spin interactions of the systems. We thus explore the possibilities of non-Kitaev spin liquids in the honeycomb Kitaev materials. We carry out a systematic classification of gapped $\mathbb{Z}_2$ spin liquids using the Schwinger boson representation for the spin variables. The presence of strong spin-orbit coupli…
Leveraging coherent light-matter interaction in solids is a promising new direction towards control and functionalization of quantum materials, to potentially realize regimes inaccessible in equilibrium and stabilize new or useful states of matter. We show how driving the strongly spin-orbit coupled proximal Kitaev magnet $α$-RuCl$_3$ with circularly-polarized light can give rise to a novel ligand-mediated magneto-electric effect that both photo-induces a large dynamical effective magnetic field and dramatically alters the interplay of competing isotropic and anisotropic exchange interactions.…
University of Munich（慕尼黑大学）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；Shanghai Jiao Tong University（上海交通大学）
We use a recently developed interpretable and unsupervised machine-learning method, the tensorial kernel support vector machine (TK-SVM), to investigate the low-temperature classical phase diagram of a generalized Heisenberg-Kitaev-$Γ$ ($J$-$K$-$Γ$) model on a honeycomb lattice. Aside from reproducing phases reported by previous quantum and classical studies, our machine finds a hitherto missed nested zigzag-stripy order and establishes the robustness of a recently identified modulated $S_3 \times Z_3$ phase, which emerges through the competition between the Kitaev and $Γ$ spin liquids, agains…
Recently, there have been increasingly hot debates on whether there exists a quantum spin liquid in the Kitaev honeycomb magnet $α$-RuCl$_3$ in high magnetic field. To investigate this issue, we perform the ultralow-temperature thermal conductivity measurements on the single crystals of $α$-RuCl$_3$ down to 80 mK and up to 9 T. Our experiments clearly show a field-induced phase transition occurring at $H_c$ $\approx$ 7.5 T, above which the zigzag magnetic order is completely suppressed. The minimum of thermal conductivity at 7.5 T is attributed to the strong scattering of phonons by the magnet…
University of Munich（慕尼黑大学）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；Shanghai Jiao Tong University（上海交通大学）
Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the honeycomb Kitaev-$Γ$ model in a magnetic field. Our machine learns the global classical phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic $S_3$ magnets, and two modulated $S_3 \times Z_3$ magnets. We find that the extension of Kitaev spin liquids and a field-in…
