Thermodynamic Evidence of Proximity to a Kitaev Spin Liquid in Ag_{3}LiIr_{2}O_{6}

High-temperature magnetic anomaly via suppression of antisite disorder through synthesis route modification in a Kitaev candidate Cu2IrO3

By incorporating inert KCl into the Na2IrO3+ 2CuCl → Cu2IrO3+ 2NaCl topochemical reaction, we significantly reduced the synthesis temperature of Cu2IrO3from the 350 °C reported in previous studies to 170 °C. This adjustment decreased the Cu/Ir antisite disorder concentration in Cu2IrO3from ∼19% to ∼5%. Furthermore, magnetic susceptibility measurements of the present Cu2IrO3sample revealed a weak ferromagnetic-like anomaly with hysteresis at a magnetic transition temperature of ∼70 K. Our research indicates that the spin-disordered ground state reported in chemically disordered Cu2IrO3is an extrinsic phenomenon, rather than an intrinsic one, underscoring the pivotal role of synthetic chemistry in understanding the application of Kitaev model to realistic materials.

Beyond Kitaev physics in strong spin-orbit coupled magnets

We review the recent advances and current challenges in the field of strong spin-orbit coupled Kitaev materials, with a particular emphasis on the physics beyond the exactly-solvable Kitaev spin liquid point. To this end, we present a comprehensive overview of the key exchange interactions in candidate materials with a specific focus on systems featuring effectiveJeff=1/2magnetic moments. This includes, but not limited to,5d5iridates,4d5ruthenates and3d7cobaltates. Our exploration covers the microscopic origins of these interactions, along with a systematic attempt to map out the most intriguing correlated regimes of the multi-dimensional parameter space. Our approach is guided by robust symmetry and duality transformations as well as insights from a wide spectrum of analytical and numerical studies. We also survey higher spin Kitaev models and recent exciting results on quasi-one-dimensional models and discuss their relevance to higher-dimensional models. Finally, we highlight some of the key questions in the field as well as future directions.

Electronic and Magnetic Properties of Spin-Orbit-Entangled Honeycomb Lattice Iridates MIrO3 (M = Cd, Zn, and Mg)

By means of density functional theory calculations with the inclusion of spin-orbit coupling, we present a comprehensive investigation of the structural, electronic, and magnetic properties of the novel series of ilmenite-type honeycomb lattice iridates MIrO₃ (M = Cd, Zn, and Mg), the potential candidates for realizing the quantum spin liquid. Our findings are as follows: (i) the structural relaxations could not properly capture the abnormal thin two-dimensional honeycomb IrO₆ layers in CdIrO₃, making the experimentally proposed crystal structure questionable. Furthermore, the calculations within the experimental structure could not correctly determine the magnetic ground state; however, the results within the optimized one rectify this scenario and provide a precise and reasonable description of its electronic and magnetic properties, which is in good agreement with the experimental observations and that of Zn and Mg analogues. In this regard, we hope that our report will inspire additional studies on this issue and eventually resolve the crystal structure of CdIrO₃. (ii) We identified that the magnetic ground state of this series of iridates MIrO₃ is the zigzag antiferromagnetic ordering, where ferromagnetic zigzag chains are coupling antiferromagnetically across the bridging bonds within a hexagon. (iii) Though it is widely assumed that all the iridates can be well described based on the spin-orbit-assisted J_eff = 1/2 Mott insulating state model, detailed analysis of electronic band structures indicates that the formation of quasimolecular orbitals (QMOs) within a hexagon plays a non-negligible role in appropriately depicting the electronic and magnetic properties. Finally, (iv) we found that all the antiferromagnetic patterns are insulating with finite band gaps. Clarifying the effect of magnetic ordering on the electronic structures is important because it reminds us of potential erroneous identification/prediction of the ground state. The results suggest that precisely determining the magnetic ground state and adopting it in the simulations are imperative for faithfully rendering the electronic properties of a compound. Our results underline the importance of structural factor, spin-orbit coupling, correlation correction, the formation of the QMOs within the hexagon, as well as magnetic ordering in elucidating the electronic structure of a series of ilmenite-type honeycomb lattice iridates MIrO₃.

First demonstration of tuning between the Kitaev and Ising limits in a honeycomb lattice

Recent observations of novel spin-orbit coupled states have generated interest in 4d/5d transition metal systems. A prime example is the [Formula: see text] state in iridate materials and α-RuCl₃ that drives Kitaev interactions. Here, by tuning the competition between spin-orbit interaction (λ_SOC) and trigonal crystal field (Δ_T), we restructure the spin-orbital wave functions into a previously unobserved [Formula: see text] state that drives Ising interactions. This is done via a topochemical reaction that converts Li₂RhO₃ to Ag₃LiRh₂O₆. Using perturbation theory, we present an explicit expression for the [Formula: see text] state in the limit Δ_T ≫ λ_SOC realized in Ag₃LiRh₂O₆, different from the conventional [Formula: see text] state in the limit λ_SOC ≫ Δ_T realized in Li₂RhO₃. The change of ground state is followed by a marked change of magnetism from a 6 K spin-glass in Li₂RhO₃ to a 94 K antiferromagnet in Ag₃LiRh₂O₆.

Metastable Kitaev Magnets

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 Na2IrO3, α-Li2IrO3, and α-RuCl3, revealed the presence of non-Kitaev interactions such as the Heisenberg and off-diagonal exchange. Both physical pressure and chemical doping were used to tune the relative strength of the Kitaev and competing interactions; however, little progress was made towards achieving a purely Kitaev system. Here, we review the recent breakthrough in modifying Kitaev magnets via topochemical methods that has led to the second generation of Kitaev materials. We show how structural modifications due to the topotactic exchange reactions can alter the magnetic interactions in favor of a quantum spin-liquid phase.

Theoretical scheme for finite-temperature dynamics of Kitaev's spin liquids

In this article, we review the theoretical formulation of finite temperature dynamics of Kitaev's spin liquid. We present the exact analytical solution of the dynamical spin correlation function at the integrable limit of Kitaev's model, on the basis of (2018Phys. Rev. B98220404). By combining the analytical solution with the equilibrium classical Monte-Carlo scheme, we construct a formulation to access the finite temperature dynamics of Kitaev's spin liquid exactly, with a reasonable amount of computational cost. This formulation is based on the real-time representation, which enables us to directly access the experimental observables defined in real frequency, without analytical continuation. The real-time scheme is essential to capturing the resonant features of the spectrum accurately, which occurs e.g. in the chiral spin liquid phase with isolated Majorana zero modes. Accordingly, this scheme provides an effective approach to address the nature of fractional excitations in Kitaev's spin liquid. As an application, we address the detection of zero mode around the site vacancy through the local resonant spectrum and discuss how the character of Kitaev's spin liquid emerges in its dynamical signature.

Thermodynamic behavior of modified integer-spin Kitaev models on the honeycomb lattice

We study the thermodynamic behavior of modified spin-S Kitaev models introduced by Baskaran, Sen, and Shankar [Phys. Rev. B 78, 115116 (2008)PRBMDO1098-012110.1103/PhysRevB.78.115116]. These models have the property that for half-odd-integer spins their eigenstates map on to those of spin-1/2 Kitaev models, with well-known highly entangled quantum spin-liquid states and Majorana fermions. For integer spins, the Hamiltonian is made out of commuting local operators. Thus, the eigenstates can be chosen to be completely unentangled between different sites, though with a significant degeneracy for each eigenstate. For half-odd-integer spins, the thermodynamic properties can be related to the spin-1/2 Kitaev models apart from an additional degeneracy. Hence we focus here on the case of integer spins. We use transfer matrix methods, high-temperature expansions, and Monte Carlo simulations to study the thermodynamic properties of ferromagnetic and antiferromagnetic models with spin S=1 and S=2. Apart from large residual entropies, which all the models have, we find that they can have a variety of different behaviors. Transfer matrix calculations show that for the different models, the correlation lengths can be finite as T→0, become critical as T→0, or diverge exponentially as T→0. The Z_{2} flux variable associated with each hexagonal plaquette saturates at the value +1 as T→0 in all models except the S=1 antiferromagnet where the mean flux remains zero as T→0. We provide qualitative explanations for these results.

Competing antiferromagnetic-ferromagnetic states in a d7 Kitaev honeycomb magnet

The Kitaev model is a rare example of an analytically solvable and physically instantiable Hamiltonian yielding a topological quantum spin liquid ground state. Here we report signatures of Kitaev spin liquid physics in the honeycomb magnet Li3Co2SbO6, built of high-spin d 7 (Co2+) ions, in contrast to the more typical low-spin d 5 electron configurations in the presence of large spin-orbit coupling. Neutron powder diffraction measurements, heat capacity, and magnetization studies support the development of a long-range antiferromagnetic order space group of C C 2/ m , below T N   =   11 K at μ 0 H   =   0 T . The magnetic entropy recovered between T   =   2 and 50 K is estimated to be 0.6 R ln2 , in good agreement with the value expected for systems close to a Kitaev quantum spin liquid state. The temperature-dependent magnetic order parameter demonstrates a β value of 0.19(3), consistent with XY anisotropy and in-plane ordering, with Ising-like interactions between layers. Further, we observe a spin-flop-driven crossover to ferromagnetic order with space group of C 2/ m under an applied magnetic field of μ 0 H   ≈   0.7 T at T   =   2   K . Magnetic structure analysis demonstrates these magnetic states are competing at finite applied magnetic fields even below the spin-flop transition. Both the d 7 compass model, a quantitative comparison of the specific heat of Li3Co2SbO6, and related honeycomb cobaltates to the anisotropic Kitaev model further support proximity to a Kitaev spin liquid state. This material demonstrates the rich playground of high-spin d 7 systems for spin liquid candidates and complements known d 5 Ir- and Ru-based materials.

Universal signatures of Majorana-like quasiparticles in strongly correlated Landau-Fermi liquids

Motivated by recent experiments in the Kitaev honeycomb lattice, Kondo insulators, and the 'Luttinger's theorem-violating' Fermi liquid phase of the underdoped cuprates, we extend the theoretical machinery of Landau-Fermi liquid theory to a system of itinerant, interacting Majorana-like particles. Building upon a previously introduced model of 'nearly self-conjugate' fermionic polarons, a Landau-Majorana kinetic equation is introduced to describe the collective modes and Fermi surface instabilities in a fluid of particles whose fermionic degrees of freedom obey the Majorana reality condition. At large screening, we show that the Landau-Majorana liquid harbors a Lifshitz transition for specific values of the driving frequency. Moreover, we find the dispersion of the zero sound collective mode in such a system, showing that there exists a specific limit where the Landau-Majorana liquid harbors a stability against Pomeranchuk deformations unseen in the conventional Landau-Fermi liquid. With these results, our work paves the way for possible extensions of the Landau quasiparticle paradigm to nontrivial metallic phases of matter.

Accessing new magnetic regimes by tuning the ligand spin-orbit coupling in van der Waals magnets

Van der Waals (VdW) materials have opened new directions in the study of low dimensional magnetism. A largely unexplored arena is the intrinsic tuning of VdW magnets toward new ground states. Chromium trihalides provided the first such example with a change of interlayer magnetic coupling emerging upon exfoliation. Here, we take a different approach to engineer previously unknown ground states, not by exfoliation, but by tuning the spin-orbit coupling (SOC) of the nonmagnetic ligand atoms (Cl, Br, I). We synthesize a three-halide series, CrCl3 - x - y Br x I y , and map their magnetic properties as a function of Cl, Br, and I content. The resulting triangular phase diagrams unveil a frustrated regime near CrCl3. First-principles calculations confirm that the frustration is driven by a competition between the chromium and halide SOCs. Furthermore, we reveal a field-induced change of interlayer coupling in the bulk of CrCl3 - x - y Br x I y crystals at the same field as in the exfoliation experiments.