Realization of a three-dimensional spin–anisotropic harmonic honeycomb iridate

Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids

We investigate the nature of the topological quantum phase transition between the gapless and gapped Kitaev quantum spin liquid phases away from the exactly solvable point. The transition is driven by anisotropy of the Kitaev couplings. At the critical point, the two Dirac points of the gapless Majorana modes merge, resulting in the formation of a semi-Dirac point with quadratic and linear band touching directions. We derive an effective Gross-Neveu-Yukawa-type field theory that describes the topological phase transition in the presence of additional magnetic interactions. We obtain the infrared scaling form of the propagator of the dynamical Ising order parameter field and perform a renormalization-group analysis. The universality of the transition is found to be different from that of symmetry-breaking phase transitions of semi-Dirac electrons. However, as in the electronic case, the Majorana fermions acquire an anomalous dimension, indicative of the breakdown of the fractionalized quasiparticle description.

Selective Synthesis and Crystal Chemistry of Candidate Rare-Earth Kitaev Materials: Honeycomb and Hyperhoneycomb Na2PrO3

Rare-earth oxides have attracted interest as a platform for studying frustrated magnetism arising from bond-dependent anisotropic interactions. Ordered rock salt compounds Na2PrO3 crystallize in two polymorphs (α and β) comprising honeycomb and hyperhoneycomb lattices of octahedrally coordinated Pr4+ (4f1). Although possible realization of antiferromagnetic Kitaev interactions is anticipated for these phases on the basis of ab initio models, the air sensitivity of the two polymorphs has hampered reliable crystal growth and physical property measurements. Here, we have succeeded in preparing powder and single crystals of both α- and β-Na2PrO3 using modified synthetic procedures. Revised crystal structures for both polymorphs are obtained from refinement of untwinned single-crystal X-ray diffraction data.

Two-Dimensional Cobalt(II) Benzoquinone Frameworks for Putative Kitaev Quantum Spin Liquid Candidates

The realization and discovery of quantum spin liquid (QSL) candidate materials are crucial for exploring exotic quantum phenomena and applications associated with QSLs. Most existing metal-organic two-dimensional (2D) quantum spin liquid candidates have structures with spins arranged on the triangular or kagome lattices, whereas honeycomb-structured metal-organic compounds with QSL characteristics are rare. Here, we report the use of 2,5-dihydroxy-1,4-benzoquinone (X2dhbq, X = Cl, Br, H) as the linkers to construct cobalt(II) honeycomb lattices (NEt4)2[Co2(X2dhbq)3] as promising Kitaev-type QSL candidate materials. The high-spin d7 Co2+ has pseudospin-1/2 ground-state doublets, and benzoquinone-based linkers not only provide two separate superexchange pathways that create bond-dependent frustrated interactions but also allow for chemical tunability to mediate magnetic coupling. Our magnetization data show antiferromagnetic interactions between neighboring metal centers with Weiss constants from -5.1 to -8.5 K depending on the X functional group in X2dhbq linkers (X = Cl, Br, H). No magnetic transition or spin freezing could be observed down to 2 K. Low-temperature susceptibility (down to 0.3 K) and specific heat (down to 0.055 K) of (NEt4)2[Co2(H2dhbq)3] were further analyzed. Heat capacity measurements confirmed no long-range order down to 0.055 K, evidenced by the broad peak instead of the λ-like anomaly. Our results indicate that these 2D cobalt benzoquinone frameworks are promising Kitaev QSL candidates with chemical tunability through ligands that can vary the magnetic coupling and frustration.

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.

Observation of the possible magnetic correction above the Curie temperature in Cr2Si2Te6 single crystals

Intrinsic magnetic semiconductors hold great promise in the fields of fundamental magnetization and spintronics. One such semiconductor is Cr2Si2Ti6 (CST), a quasi two-dimensional (2D) magnetic semiconductor with potential applications in future magnetic devices. However, the origin of ferromagnetism in CST remains a mystery. To investigate this, ac/dc susceptibility and electronic spin resonance (ESR) measurements were conducted. Based on ac susceptibility scaling, the critical temperature (TC) for the ferromagnetic (FM) to paramagnetic (PM) phase transition was found to be ∼32.5 K, with a critical exponent of δ = 6.7 from the critical isotherm, β + γ = 1.72 from the temperature dependence of the crossover line, and γ = 1.43 from the temperature dependence of susceptibility along the same line. All critical exponents were found to be consistent with the dc magnetization scaling method. However, above and below TC, the origin of magnetism cannot be explained by a single theory. To explore the origin of abnormal magnetic critical behavior, ESR measurements were performed. Below T* ∼ 130 K, the ESR measurements revealed that the resonance field width (ΔH) tends to increase and decrease for the applied magnetic field H parallel and perpendicular to the c axis, respectively, indicating the onset of magnetic interaction even in the PM state. Meanwhile, the deviation from Curie-Weiss behavior below T* also confirmed the occurrence of magnetic correlation above the TC in CST. These observations suggest that the competition and cooperation among the direct and indirect interactions, the structural distortion and the van der Waals interaction at high temperature should be considered to investigate the origin of anomalous magnetism in CST. The present results provide valuable insights into the nature of ferromagnetism in 2D magnetic semiconductors.

Spin-to-Charge Conversion in All-Oxide La2/3Sr1/3MnO3/SrIrO3 Heterostructures

Spin injection and spin-charge conversion processes in all-oxide La_2/3Sr_1/3MnO₃/SrIrO₃ (LSMO/SIO) heterostructures with different SIO layer thickness and interfacial features have been studied. Ferromagnetic resonance (FMR) technique has been used to generate pure spin currents by spin pumping (SP) in ferromagnetic (FM) half-metallic LSMO. The change of the resonance linewidth in bare LSMO layers and LSMO/SIO heterostructures suggests a successful spin injection into the SIO layers. However, low values of the spin mixing conductance, compared to more traditional permalloy (Py)/Pt or yttrium iron garnet (YIG)/Pt systems, are found. A thorough analysis of the interfaces by high-resolution scanning transmission electron microscopy (HR-STEM) imaging suggests that they are structurally clean and atomic sharp, but a compositional analysis by energy-dispersive X-ray spectroscopy (EDS) reveals the interdiffusion of La, Ir, and Mn atomic species in the first atomic layers close to the interface. Inverse spin Hall effect (ISHE) measurements evidence that interfacial features play a very relevant role in controlling the effectiveness of the spin injection process and low transversal ISHE voltage signals are detected. In addition, it is found that larger voltage signals are detected for the lowest SIO layer thickness highlighting the role of the spin diffusion length (λ_sd)/SIO layer thickness ratio. The values of ISHE voltage are rather low but allow us to determine the spin Hall angle of SIO (θ_SH ≈ 1.12% at T = 250 K), which is remarkably similar to that obtained for the well-known Py/Pt system, therefore suggesting that SIO could be a promising spin-Hall material.

Spin-orbital entangled state and realization of Kitaev physics in 3dcobalt compounds: a progress report

The realization of Kitaev's honeycomb magnetic model in real materials has become one of the most pursued topics in condensed matter physics and materials science. If found, it is expected to host exotic quantum phases of matter and offers potential realizations of fault-tolerant quantum computations. Over the past years, much effort has been made on 4d- or 5d-heavy transition metal compounds because of their intrinsic strong spin-orbit coupling. But more recently, there have been growing shreds of evidence that the Kitaev model could also be realized in 3d-transition metal systems with much weaker spin-orbit coupling. This review intends to serve as a guide to this fast-developing field focusing on systems withd⁷transition metal occupation. It overviews the current theoretical and experimental progress on realizing the Kitaev model in those systems. We examine the recent experimental observations of candidate materials with Co²⁺ions: e.g., CoPS₃, Na₃Co₂SbO₆, and Na₂Co₂TeO₆, followed by a brief review of theoretical backgrounds. We conclude this article by comparing experimental observations with density functional theory calculations. We stress the importance of inter-t_2ghopping channels and Hund's coupling in the realization of Kitaev interactions in Co-based compounds, which has been overlooked in previous studies. This review suggests future directions in the search for Kitaev physics in 3dcobalt compounds and beyond.

Revisiting Sodium Hexafluoroiridates: Perspective Precursors for Electronic, Quantum, and Related Materials

The following salts have been synthesized and structurally characterized: Na₂[IrF₆]·2H₂O (C2/m, a = 6.6327(4), b = 10.0740(6), c = 5.9283(5) Å, β = 122.3880(10)°) and Na₃[IrF₆]·2H₂O (R-3, a = 7.5963(3), b = 7.5963(3), c = 9.8056(4) Å) (for the first time) by single-crystal X-ray diffraction; the unit cell parameters of a tetragonal phase (P4 ₂/mnm, a = 5.005(2), c = 10.074(4) Å) of the stable α-Na₂[IrF₆] were determined for the first time; and the unit cell parameters of β-Na₂[IrF₆] (P321, a = 9.332(4), c = 5.136(2) Å) and Na₃[IrF₆] (P2₁/n, a = 5.567(4), b = 5.778(4), c = 8.017(2) Å, β = 90.41(2)°) were determined using powder X-ray diffraction (PXRD). The data of the thermal stability was obtained by differential thermal analysis (DTA) for all substances. The presence of Na₃[IrF₆]·H₂O monohydrate is predicted. H₂[IrF₆] was prepared in a solution and was demonstrated to behave as a strong dibasic acid.

Stripe-yzmagnetic order in the triangular-lattice antiferromagnet KCeS2

Yb- and Ce-based delafossites were recently identified as effective spin-1/2 antiferromagnets on the triangular lattice. Several Yb-based systems, such as NaYbO2, NaYbS2, and NaYbSe2, exhibit no long-range order down to the lowest measured temperatures and therefore serve as putative candidates for the realization of a quantum spin liquid. However, their isostructural Ce-based counterpart KCeS2exhibits magnetic order belowTN= 400 mK, which was so far identified only in thermodynamic measurements. Here we reveal the magnetic structure of this long-range ordered phase using magnetic neutron diffraction. We show that it represents the so-called 'stripe-yz' type of antiferromagnetic order with spins lying approximately in the triangular-lattice planes orthogonal to the nearest-neighbor Ce-Ce bonds. No structural lattice distortions are revealed belowTN, indicating that the triangular lattice of Ce3+ions remains geometrically perfect down to the lowest temperatures. We propose an effective Hamiltonian for KCeS2, based on a fit to the results ofab initiocalculations, and demonstrate that its magnetic ground state matches the experimental spin structure.

Honeycomb layered oxides: structure, energy storage, transport, topology and relevant insights

The advent of nanotechnology has hurtled the discovery and development of nanostructured materials with stellar chemical and physical functionalities in a bid to address issues in energy, environment, telecommunications and healthcare. In this quest, a class of two-dimensional layered materials consisting of alkali or coinage metal atoms sandwiched between slabs exclusively made of transition metal and chalcogen (or pnictogen) atoms arranged in a honeycomb fashion have emerged as materials exhibiting fascinatingly rich crystal chemistry, high-voltage electrochemistry, fast cation diffusion besides playing host to varied exotic electromagnetic and topological phenomena. Currently, with a niche application in energy storage as high-voltage materials, this class of honeycomb layered oxides serves as ideal pedagogical exemplars of the innumerable capabilities of nanomaterials drawing immense interest in multiple fields ranging from materials science, solid-state chemistry, electrochemistry and condensed matter physics. In this review, we delineate the relevant chemistry and physics of honeycomb layered oxides, and discuss their functionalities for tunable electrochemistry, superfast ionic conduction, electromagnetism and topology. Moreover, we elucidate the unexplored albeit vastly promising crystal chemistry space whilst outlining effective ways to identify regions within this compositional space, particularly where interesting electromagnetic and topological properties could be lurking within the aforementioned alkali and coinage-metal honeycomb layered oxide structures. We conclude by pointing towards possible future research directions, particularly the prospective realisation of Kitaev-Heisenberg-Dzyaloshinskii-Moriya interactions with single crystals and Floquet theory in closely-related honeycomb layered oxide materials.

Orbital Effects in Solids: Basics, Recent Progress, and Opportunities

The properties of transition metal compounds are largely determined by nontrivial interplay of different degrees of freedom: charge, spin, lattice, and also orbital ones. Especially rich and interesting effects occur in systems with orbital degeneracy. For example, they result in the famous Jahn-Teller effect, leading to a plethora of consequences for static and dynamic properties, including nontrivial quantum effects. In the present review, we discuss the main phenomena in the physics of such systems, paying central attention to the novel manifestations of those. After shortly summarizing the basic phenomena and their descriptions, we concentrate on several specific directions in this field. One of them is the reduction of effective dimensionality in many systems with orbital degrees of freedom due to the directional character of orbitals, with the concomitant appearance of some instabilities that lead in particular to the formation of dimers, trimers, and similar clusters in a material. The properties of such cluster systems, which are largely determined by their orbital structure, are discussed in detail, and many specific examples of those in different materials are presented. Another big field that has acquired special significance relatively recently is the role of the relativistic spin-orbit interaction. The mutual influence of this interaction and the more traditional Jahn-Teller physics is treated in detail in the second part of the review. In discussing all of these questions, special attention is paid to novel quantum effects.

Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism

The Kitaev spin liquid provides a rare example of well-established quantum spin liquids in more than one dimension. It is obtained as the exact ground state of the Kitaev spin model with bond-dependent anisotropic interactions. The peculiar interactions can be yielded by the synergy of spin-orbit coupling and electron correlations for specific electron configuration and lattice geometry, which is known as the Jackeli-Khaliullin mechanism. Based on this mechanism, there has been a fierce race for the materialization of the Kitaev spin liquid over the last decade, but the candidates have been still limited mostly to 4d- and 5d-electron compounds including cations with the low-spind5electron configuration, such as Ir4+and Ru3+. Here we discuss recent efforts to extend the material perspective beyond the Jackeli-Khaliullin mechanism, by carefully reexamining the two requisites, formation of thejeff= 1/2 doublet and quantum interference between the exchange processes, for not onlyd- but alsof-electron systems. We present three examples: the systems including Co2+and Ni3+with the high-spind7electron configuration, Pr4+with thef1-electron configuration, and polar asymmetry in the lattice structure. In particular, the latter two are intriguing since they may realize the antiferromagnetic Kitaev interactions, in contrast to the ferromagnetic ones in the existing candidates. This partial overview would stimulate further material exploration of the Kitaev spin liquids and its topological properties due to fractional excitations.

Resonant inelastic x-ray scattering study of [Formula: see text]-RuCl3: a progress report

Ru M₃-edge resonant inelastic x-ray scattering (RIXS) measurements of [Formula: see text] with 27 meV resolution reveals a spin-orbit exciton without noticeable splitting. We extract values for the spin-orbit coupling constant ([Formula: see text] meV) and trigonal distortion field energy ([Formula: see text] meV) which support the [Formula: see text] nature of [Formula: see text]. We demonstrate the feasibility of M-edge RIXS for 4d systems, which allows ultra high-resolution RIXS of 4d systems until instrumentation for L-edge RIXS improves.

Magnon bound states versus anyonic Majorana excitations in the Kitaev honeycomb magnet α-RuCl3

The pure Kitaev honeycomb model harbors a quantum spin liquid in zero magnetic fields, while applying finite magnetic fields induces a topological spin liquid with non-Abelian anyonic excitations. This latter phase has been much sought after in Kitaev candidate materials, such as α-RuCl₃. Currently, two competing scenarios exist for the intermediate field phase of this compound (B = 7 − 10 T), based on experimental as well as theoretical results: (i) conventional multiparticle magnetic excitations of integer quantum number vs. (ii) Majorana fermionic excitations of possibly non-Abelian nature with a fractional quantum number. To discriminate between these scenarios a detailed investigation of excitations over a wide field-temperature phase diagram is essential. Here, we present Raman spectroscopic data revealing low-energy quasiparticles emerging out of a continuum of fractionalized excitations at intermediate fields, which are contrasted by conventional spin-wave excitations. The temperature evolution of these quasiparticles suggests the formation of bound states out of fractionalized excitations.

α-RuCl₃ has properties consistent with predictions of a phase hosting fractionalized Majorana fermions but that could also be explained by conventional magnetic excitations. Here the authors find evidence for fractionalized quasiparticles by studying magnetic excitations across the field-temperature phase diagram.

Possible Quantum Paramagnetism in Compressed Sr_{2}IrO_{4}

The effect of compression on the magnetic ground state of Sr_{2}IrO_{4} is studied with x-ray resonant techniques in the diamond anvil cell. The weak interlayer exchange coupling between square-planar 2D IrO_{2} layers is readily modified upon compression, with a crossover between magnetic structures around 7 GPa mimicking the effect of an applied magnetic field at ambient pressure. Higher pressures drive an order-disorder magnetic phase transition with no magnetic order detected above 17-20 GPa. The persistence of strong exchange interactions between J_{eff}=1/2 magnetic moments within the insulating IrO_{2} layers up to at least 35 GPa points to a highly frustrated magnetic state in compressed Sr_{2}IrO_{4}, opening the door for realization of novel quantum paramagnetic phases driven by extended 5d orbitals with entangled spin and orbital degrees of freedom.

Pressure-Tuned Interactions in Frustrated Magnets: Pathway to Quantum Spin Liquids?

Quantum spin liquids are prime examples of strongly entangled phases of matter with unconventional exotic excitations. Here, strong quantum fluctuations prohibit the freezing of the spin system. On the other hand, frustrated magnets, the proper platforms to search for the quantum spin liquid candidates, still show a magnetic ground state in most of the cases. Pressure is an effective tuning parameter of structural properties and electronic correlations. Nevertheless, the ability to influence the magnetic phases should not be forgotten. We review experimental progress in the field of pressure-tuned magnetic interactions in candidate systems. Elaborating on the possibility of tuned quantum phase transitions, we further show that chemical or external pressure is a suitable parameter in these exotic states of matter.

Nonsymmorphic-Symmetry-Protected Topological Magnons in Three-Dimensional Kitaev Materials

Topological phases in magnetic materials offer novel tunability of topological properties via varying the underlying magnetism. We show that three-dimensional Kitaev materials with nonsymmorphic symmetries can provide a great opportunity for controlling symmetry-protected topological nodal magnons. These materials are originally considered as strong candidates for the Kitaev quantum spin liquid due to the bond-dependent frustrating spin-exchange interactions. As a concrete example, we consider the symmetry and topology of the magnons in the canted zigzag ordered state in the hyperhoneycomb β-Li_{2}IrO_{3}, which can be obtained by applying a magnetic field in the counter-rotating spiral state at zero field. It is shown that the magnetic glide symmetries and the non-Hermitian nature of the bosonic magnons lead to unique topological protection that is different from the case of their fermionic counterparts. We investigate how such topological magnons can be controlled by changing the symmetry of the underlying spin-exchange interactions.

Heisenberg-Kitaev physics in magnetic fields

Magnetic insulators in the regime of strong spin-orbit coupling exhibit intriguing behaviors in external magnetic fields, reflecting the frustrated nature of their effective interactions. We review the recent advances in understanding the field responses of materials that are described by models with strongly bond-dependent spin exchange interactions, such as Kitaev's celebrated honeycomb model and its extensions. We discuss the field-induced phases and the complex magnetization processes found in these theories and compare with experimental results in the layered Mott insulators [Formula: see text]-RuCl₃ and Na₂IrO₃, which are believed to realize this fascinating physics.

Nonpolar-to-Polar Trimerization Transitions in the S = 1 Kagomé Magnet Na2Ti3Cl8

Kagomé lattice magnets have emerged as a versatile platform on which to discover and explore the underlying physics of quantum-spin liquids and related states of matter, although experimental examples of ideal kagomé lattices remain rare. Here we report that Na₂Ti₃Cl₈ is an ideal realization of an insulating S = 1 kagomé magnet. This material undergoes a discrete two-step trimerization upon cooling, transforming from a centrosymmetric, paramagnetic high-temperature (HT) R3m phase to noncentrosymmetric, polar, and trimerized intermediate- (IT) and low-temperature (LT) R3m phases via two successive first-order phase transitions. Symmetry mode decomposition analysis shows that trimerization requires activation of the proper polar order parameter Γ₂^- and that this mode becomes active at the HT → IT phase transition. The magnitude of this order parameter approximately doubles at the IT → LT transition, with possible activation of a second polar mode, corresponding to Na₂ and Ti₃Cl₈ displacing layers toward each other, at the IT → LT transition. Specific heat measurements reveal comparable changes in entropy between the LT → IT transition, 18.6(1.0) J (mol of f.u.)^-1 K^-1, and the IT → LT transition, 16.8(1.0) J (mol of f.u.)^-1 K^-1, demonstrating loss of the magnetic degrees of freedom and constraining possible models for the magnetic and electronic structures of the IT and LT phases. Thus, Na₂Ti₃Cl₈ demonstrates a novel mechanism to obtain polar structures driven by geometrically frustrated lattices and metal-metal bonding and highlights the rich physics arising from kagomé lattice materials.

Hidden Plaquette Order in a Classical Spin Liquid Stabilized by Strong Off-Diagonal Exchange

We report a new classical spin liquid in which the collective flux degrees of freedom break the translation symmetry of the honeycomb lattice. This exotic phase exists in the frustrated spin-orbit magnets where a dominant off-diagonal exchange, the so-called Γ term, results in a macroscopic ground-state degeneracy at the classical level. We demonstrate that the system undergoes a phase transition driven by thermal order by disorder at a critical temperature T_{c}≈0.04|Γ|. This transition reduces the emergent spherical spin symmetry to a cubic one: spins point predominantly toward the cubic axes, yet seem to remain disordered at T<T_{c}. Importantly, we show that the phase transition corresponds to a hidden plaquette ordering of hexagonal fluxes, which explicitly breaks the cubic symmetry, a scenario that is confirmed by our extensive Monte Carlo simulations. We further compute the dynamical structure factors of the spin-liquid phase and reveal unusual dynamical properties of the hexagonal flux parameters.

Theory of the field-revealed Kitaev spin liquid

Elementary excitations in entangled states such as quantum spin liquids may exhibit exotic statistics different from those obeyed by fundamental bosons and fermions. Non-Abelian anyons exist in a Kitaev spin liquid-the ground state of an exactly solvable model. A smoking-gun signature of these excitations, namely a half-integer quantized thermal Hall conductivity, was recently reported in α-RuCl₃. While fascinating, a microscopic theory for this phenomenon remains elusive because the pure Kitaev model cannot display this effect in an intermediate magnetic field. Here we present a microscopic theory of the Kitaev spin liquid emerging between the low- and high-field states. Essential to this result is an antiferromagnetic off-diagonal symmetric interaction which allows the Kitaev spin liquid to protrude from the ferromagnetic Kitaev limit under a magnetic field. This generic model displays a strong field anisotropy, and we predict a wide spin liquid regime when the field is perpendicular to the honeycomb plane.

Sawtooth Torque in Anisotropic j_{eff}=1/2 Magnets: Application to α-RuCl_{3}

The so-called "Kitaev candidate" materials based on 4d^{5} and 5d^{5} metals have recently emerged as magnetic systems displaying strongly anisotropic exchange interactions reminiscent of the Kitaev's honeycomb model. Recently, these materials have been shown to commonly display a distinct sawtooth angular dependence of the magnetic torque over a wide range of magnetic fields. While higher order chiral spin interactions have been considered as a source of this observation, we show here that bilinear anisotropic interactions and/or g anisotropy are each sufficient to explain the observed torque response, which may be distinguished on the basis of high-field measurements. These findings unify the understanding of magnetic torque experiments in a variety of Kitaev candidate materials.

Exotic Low-Energy Excitations Emergent in the Random Kitaev Magnet Cu_{2}IrO_{3}

We report on magnetization M(H), dc and ac magnetic susceptibility χ(T), specific heat C_{m}(T) and muon spin relaxation (μSR) measurements of the Kitaev honeycomb iridate Cu_{2}IrO_{3} with quenched disorder. In spite of the chemical disorders, we find no indication of spin glass down to 260 mK from the C_{m}(T) and μSR data. Furthermore, a persistent spin dynamics observed by the zero-field muon spin relaxation evidences an absence of static magnetism. The remarkable observation is a scaling relation of χ[H,T] and M[H,T] in H/T with the scaling exponent α=0.26-0.28, expected from bond randomness. However, C_{m}[H,T]/T disobeys the predicted universal scaling law, pointing towards the presence of additional low-lying excitations on the background of bond-disordered spin liquid. Our results signify a many-faceted impact of quenched disorder in a Kitaev spin system due to its peculiar bond character.

Ni2Mo3O8: Complex antiferromagnetic order on a honeycomb lattice

Theoretical studies have predicted the existence of topological magnons in honeycomb compounds with stripy or zigzag antiferromagnetic (AFM) order. Here we report the discovery of AFM order in the layered and noncentrosymmetric honeycomb nickelate Ni2Mo3O8 through a combination of magnetization, specific heat, x-ray and neutron diffraction, and electron paramagnetic resonance measurements. The AFM order is complex, with a mixture of stripy and zigzag character on an integer spin noncentrosymmetric honeycomb lattice (P63 mc). Further, each of the two sublattices of the bipartite honeycomb lattice is comprised of a different crystal field environment, i.e., octahedral and tetrahedral Ni2+, respectively, enabling independent substitution on each. Replacement of Ni by Mg on the octahedral site suppresses the long-range magnetic order and results in a weakly ferromagnetic state. Conversely, substitution of Fe for Ni enhances the strength of the AFM exchange and increases the ordering temperature. Thus, Ni2Mo3O8 provides a platform on which to explore the rich physics of S = 1 on the honeycomb lattice in the presence of competing magnetic interactions with a noncentrosymmetric, formally piezopolar, crystal structure.

Role of Hydrogen in the Spin-Orbital-Entangled Quantum Liquid Candidate H_{3}LiIr_{2}O_{6}

Motivated by recent reports of H_{3}LiIr_{2}O_{6} as a spin-orbital-entangled quantum liquid, we investigate via a combination of density functional theory and nonperturbative exact diagonalization the microscopic nature of its magnetic interactions. We find that while the interlayer O─H─O bond geometry strongly affects the local magnetic couplings, these bonds are likely to remain symmetrical due to large zero-point fluctuations of the H positions. In this case, the estimated magnetic model lies close to the classical tricritical point between ferromagnetic, zigzag, and incommensurate spiral orders, what may contribute to the lack of magnetic ordering. However, we also find that substitution of H by D (deuterium) as well as disorder-induced inhomogeneities destabilizes the O─H or D─O bonds, modifying strongly the local magnetic couplings. These results suggest that the magnetic response in H_{3}LiIr_{2}O_{6} is likely sensitive to both the stoichiometry and the microstructure of the samples and emphasize the importance of a careful treatment of hydrogen for similar systems.

Strong Effect of Hydrogen Order on Magnetic Kitaev Interactions in H_{3}LiIr_{2}O_{6}

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.

Resonant torsion magnetometry in anisotropic quantum materials

Unusual behavior in quantum materials commonly arises from their effective low-dimensional physics, reflecting the underlying anisotropy in the spin and charge degrees of freedom. Here we introduce the magnetotropic coefficient k = ∂²F/∂θ², the second derivative of the free energy F with respect to the magnetic field orientation θ in the crystal. We show that the magnetotropic coefficient can be quantitatively determined from a shift in the resonant frequency of a commercially available atomic force microscopy cantilever under magnetic field. This detection method enables part per 100 million sensitivity and the ability to measure magnetic anisotropy in nanogram-scale samples, as demonstrated on the Weyl semimetal NbP. Measurement of the magnetotropic coefficient in the spin-liquid candidate RuCl₃ highlights its sensitivity to anisotropic phase transitions and allows a quantitative comparison to other thermodynamic coefficients via the Ehrenfest relations.

Uniaxial and hydrostatic pressure effects in α-RuCl3 single crystals via thermal-expansion measurements

We present high-resolution thermal-expansion and specific-heat measurements of single crystalline α-RuCl₃. An extremely hysteretic structural transition expanding over 100 K is observed by thermal-expansion along both crystallographic axes, which we attribute to a change of stacking sequence of the RuCl₃ layers. Three magnetic transitions are observed, which we link to the different stacking sequences. Using our data and thermodynamic relations, we derive the uniaxial and hydrostatic pressure derivatives of all three magnetic transitions. Our results demonstrate that magnetic order of the major transition at  ∼7 K should be totally suppressed by very moderate pressures of 0.3 GPa. Finally, we discuss why our results differ from recent hydrostatic pressure measurements and suggest a possible route to reaching the spin-liquid state in α-RuCl₃.

Emergent SU(4) Symmetry in α-ZrCl_{3} and Crystalline Spin-Orbital Liquids

While the enhancement of spin-space symmetry from the usual SU(2) to SU(N) is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here, we propose a new mechanism by which SU(4) symmetry emerges in the strong spin-orbit coupling limit. In d^{1} transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently SU(4)-breaking hopping between the J_{eff}=3/2 quartets. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit at quarter filling, as realized in α-ZrCl_{3}, the low-energy effective model is the SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. By generalizing this model to other three-dimensional lattices, we also propose crystalline spin-orbital liquids protected by this emergent SU(4) symmetry and space group symmetries.

Breakdown of Magnetic Order in the Pressurized Kitaev Iridate β-Li_{2}IrO_{3}

Temperature-pressure phase diagram of the Kitaev hyperhoneycomb iridate β-Li_{2}IrO_{3} is explored using magnetization, thermal expansion, magnetostriction, and muon spin rotation measurements, as well as single-crystal x-ray diffraction under pressure and ab initio calculations. The Néel temperature of β-Li_{2}IrO_{3} increases with the slope of 0.9  K/GPa upon initial compression, but the reduction in the polarization field H_{c} reflects a growing instability of the incommensurate order. At 1.4 GPa, the ordered state breaks down upon a first-order transition, giving way to a new ground state marked by the coexistence of dynamically correlated and frozen spins. This partial freezing in the absence of any conspicuous structural defects may indicate the classical nature of the resulting pressure-induced spin liquid, an observation paralleled to the increase in the nearest-neighbor off-diagonal exchange Γ under pressure.

Unraveling the Nature of Magnetism of the 5d^{4} Double Perovskite Ba_{2}YIrO_{6}

We report electron spin resonance (ESR) spectroscopy results on the double perovskite Ba_{2}YIrO_{6}. On general grounds, this material is expected to be nonmagnetic due to the strong coupling of the spin and orbital momenta of Ir^{5+} (5d^{4}) ions. However, controversial experimental reports on either strong antiferromagnetism with static order at low temperatures or just a weakly paramagnetic behavior have triggered a discussion on the breakdown of the generally accepted scenario of the strongly spin-orbit coupled ground states in the 5d^{4} iridates and the emergence of a novel exotic magnetic state. Our data evidence that the magnetism of the studied material is solely due to a few percent of Ir^{4+} and Ir^{6+} magnetic defects while the regular Ir^{5+} sites remain nonmagnetic. Remarkably, the defect Ir^{6+} species manifest magnetic correlations in the ESR spectra at T≲20  K, suggesting a long-range character of superexchange in the double perovskites as proposed by recent theories.

Barrier tunneling of the loop-nodal semimetal in the hyperhoneycomb lattice

We theoretically investigate the barrier tunneling in the 3D model of the hyperhoneycomb lattice, which is a nodal-line semimetal with a Dirac loop at zero energy. In the presence of a rectangular potential, the scattering amplitudes for different injecting states around the nodal loop are calculated, by using analytical treatments of the effective model, as well as numerical simulations of the tight binding model. In the low energy regime, states with remarkable transmissions are only concentrated in a small range around the loop plane. When the momentum of the injecting electron is coplanar with the nodal loop, nearly perfect transmissions can occur for a large range of injecting azimuthal angles if the potential is not high. For higher potential energies, the transmission shows a resonant oscillation with the potential, but still with peaks being perfect transmissions that do not decay with the potential width. These strikingly robust transports of the loop-nodal semimetal can be approximately explained by a momentum dependent Dirac Hamiltonian.

The challenge of spin-orbit-tuned ground states in iridates: a key issues review

Effects of spin-orbit interactions in condensed matter are an important and rapidly evolving topic. Strong competition between spin-orbit, on-site Coulomb and crystalline electric field interactions in iridates drives exotic quantum states that are unique to this group of materials. In particular, the 'J _eff  =  ½' Mott state served as an early signal that the combined effect of strong spin-orbit and Coulomb interactions in iridates has unique, intriguing consequences. In this Key Issues Review, we survey some current experimental studies of iridates. In essence, these materials tend to defy conventional wisdom: absence of conventional correlations between magnetic and insulating states, avoidance of metallization at high pressures, 'S-shaped' I-V characteristic, emergence of an odd-parity hidden order, etc. It is particularly intriguing that there exist conspicuous discrepancies between current experimental results and theoretical proposals that address superconducting, topological and quantum spin liquid phases. This class of materials, in which the lattice degrees of freedom play a critical role seldom seen in other materials, evidently presents some profound intellectual challenges that call for more investigations both experimentally and theoretically. Physical properties unique to these materials may help unlock a world of possibilities for functional materials and devices. We emphasize that, given the rapidly developing nature of this field, this Key Issues Review is by no means an exhaustive report of the current state of experimental studies of iridates.

Polarized-neutron investigation of magnetic ordering and spin dynamics in BaCo2(AsO4)2 frustrated honeycomb-lattice magnet

The magnetic properties of the cobaltite BaCo2(AsO4)2, a good realization of the quasi two-dimensional frustrated honeycomb-lattice system with strong planar anisotropy, have been reinvestigated by means of spherical neutron polarimetry with CRYOPAD. From accurate measurements of polarization matrices both on elastic and inelastic contributions as a function of the scattering vector Q, we have been able to determine the low-temperature magnetic structure of BaCo2(AsO4)2 and reveal its puzzling in-plane spin dynamics. Surprisingly, the ground-state structure (described by an incommensurate propagation vector [Formula: see text], with [Formula: see text] and [Formula: see text]) appears to be a quasi-collinear structure, and not a simple helix, as previously determined. In addition, our results have revealed the existence of a non-negligible out-of-plane moment component [Formula: see text]/Co2+, representing about 10% of the in-plane component, as demonstrated by the presence of finite off-diagonal elements [Formula: see text] and [Formula: see text] of the polarization matrix, both on elastic and inelastic magnetic contributions. Despite a clear evidence of the existence of a slightly inelastic contribution of structural origin superimposed to the magnetic excitations at the scattering vectors [Formula: see text] and [Formula: see text] (energy transfer [Formula: see text] meV), no strong inelastic nuclear-magnetic interference terms could be detected so far, meaning that the nuclear and magnetic degrees of freedom have very weak cross-correlations. The strong inelastic [Formula: see text] and [Formula: see text] matrix elements can be understood by assuming that the magnetic excitations in BaCo2(AsO4)2 are spin waves associated with trivial anisotropic precessions of the magnetic moments involved in the canted incommensurate structure.

Models and materials for generalized Kitaev magnetism

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 Jackeli and 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 (Na₂IrO₃, α-Li₂IrO₃, and α-RuCl₃), three-dimensional Kitaev materials (β- and γ-Li₂IrO₃), and other potential candidates, completing the review with the list of open questions awaiting new insights.

Antiferromagnetic Resonance and Terahertz Continuum in α-RuCl_{3}

We report measurements of optical absorption in the zigzag antiferromagnet α-RuCl_{3} as a function of temperature T, magnetic field B, and photon energy ℏω in the range ∼0.3-8.3 meV, using time-domain terahertz spectroscopy. Polarized measurements show that threefold rotational symmetry is broken in the honeycomb plane from 2 to 300 K. We find a sharp absorption peak at 2.56 meV upon cooling below the Néel temperature of 7 K at B=0 that we identify as the magnetic-dipole excitation of a zero-wave-vector magnon, or antiferromagnetic resonance (AFMR). With the application of B, the AFMR broadens and shifts to a lower frequency as long-range magnetic order is lost in a manner consistent with transitioning to a spin-disordered phase. From a direct, internally calibrated measurement of the AFMR spectral weight, we place an upper bound on the contribution to the dc susceptibility from a magnetic excitation continuum.

Correlated states in β-Li2IrO3 driven by applied magnetic fields

Magnetic honeycomb iridates are thought to show strongly spin-anisotropic exchange interactions which, when highly frustrated, lead to an exotic state of matter known as the Kitaev quantum spin liquid. However, in all known examples these materials magnetically order at finite temperatures, the scale of which may imply weak frustration. Here we show that the application of a relatively small magnetic field drives the three-dimensional magnet β-Li₂IrO₃ from its incommensurate ground state into a quantum correlated paramagnet. Interestingly, this paramagnetic state admixes a zig-zag spin mode analogous to the zig-zag order seen in other Mott-Kitaev compounds. The rapid onset of the field-induced correlated state implies the exchange interactions are delicately balanced, leading to strong frustration and a near degeneracy of different ground states.

Materials with a Kitaev spin liquid ground state are sought after as models of quantum phases but candidates so far form either zig-zag or incommensurate magnetic order. Ruiz et al. find a crossover between these states in β-Li₂IrO₃ under weak magnetic fields, indicating strongly frustrated spin interactions.

Probing Spinon Nodal Structures in Three-Dimensional Kitaev Spin Liquids

We propose that resonant inelastic x-ray scattering (RIXS) is an effective probe of the fractionalized excitations in three-dimensional (3D) Kitaev spin liquids. While the non-spin-conserving RIXS responses are dominated by the gauge-flux excitations and reproduce the inelastic-neutron-scattering response, the spin-conserving (SC) RIXS response picks up the Majorana-fermion excitations and detects whether they are gapless at Weyl points, nodal lines, or Fermi surfaces. As a signature of symmetry fractionalization, the SC RIXS response is suppressed around the Γ point. On a technical level, we calculate the exact SC RIXS responses of the Kitaev models on the hyperhoneycomb, stripyhoneycomb, hyperhexagon, and hyperoctagon lattices, arguing that our main results also apply to generic 3D Kitaev spin liquids beyond these exactly solvable models.

Robust spin correlations at high magnetic fields in the harmonic honeycomb iridates

The complex antiferromagnetic orders observed in the honeycomb iridates are a double-edged sword in the search for a quantum spin-liquid: both attesting that the magnetic interactions provide many of the necessary ingredients, while simultaneously impeding access. Focus has naturally been drawn to the unusual magnetic orders that hint at the underlying spin correlations. However, the study of any particular broken symmetry state generally provides little clue about the possibility of other nearby ground states. Here we use magnetic fields approaching 100 Tesla to reveal the extent of the spin correlations in γ-lithium iridate. We find that a small component of field along the magnetic easy-axis melts long-range order, revealing a bistable, strongly correlated spin state. Far from the usual destruction of antiferromagnetism via spin polarization, the high-field state possesses only a small fraction of the total iridium moment, without evidence for long-range order up to the highest attainable magnetic fields.The complex antiferromagnetic orders observed in the honeycomb iridates prevent access to a spin-liquid ground state. Here the authors apply extremely high magnetic fields to destroy the antiferromagnetic order in γ-lithium iridate and reveal a bistable, strongly correlated spin state.

Evidence for a Field-Induced Quantum Spin Liquid in α-RuCl_{3}

We report a ^{35}Cl nuclear magnetic resonance study in the honeycomb lattice α-RuCl_{3}, a material that has been suggested to potentially realize a Kitaev quantum spin liquid (QSL) ground state. Our results provide direct evidence that α-RuCl_{3} exhibits a magnetic-field-induced QSL. For fields larger than ∼10  T, a spin gap opens up while resonance lines remain sharp, evidencing that spins are quantum disordered and locally fluctuating. The spin gap increases linearly with an increasing magnetic field, reaching ∼50  K at 15 T, and is nearly isotropic with respect to the field direction. The unusual rapid increase of the spin gap with increasing field and its isotropic nature are incompatible with conventional magnetic ordering and, in particular, exclude that the ground state is a fully polarized ferromagnet. The presence of such a field-induced gapped QSL phase has indeed been predicted in the Kitaev model.

Evidence for anionic redox activity in a tridimensional-ordered Li-rich positive electrode β-Li2IrO3

Lithium-ion battery cathode materials have relied on cationic redox reactions until the recent discovery of anionic redox activity in Li-rich layered compounds which enables capacities as high as 300 mAh g^-1. In the quest for new high-capacity electrodes with anionic redox, a still unanswered question was remaining regarding the importance of the structural dimensionality. The present manuscript provides an answer. We herein report on a β-Li₂IrO₃ phase which, in spite of having the Ir arranged in a tridimensional (3D) framework instead of the typical two-dimensional (2D) layers seen in other Li-rich oxides, can reversibly exchange 2.5 e^- per Ir, the highest value ever reported for any insertion reaction involving d-metals. We show that such a large activity results from joint reversible cationic (Mⁿ⁺) and anionic (O₂)^n- redox processes, the latter being visualized via complementary transmission electron microscopy and neutron diffraction experiments, and confirmed by density functional theory calculations. Moreover, β-Li₂IrO₃ presents a good cycling behaviour while showing neither cationic migration nor shearing of atomic layers as seen in 2D-layered Li-rich materials. Remarkably, the anionic redox process occurs jointly with the oxidation of Ir⁴⁺ at potentials as low as 3.4 V versus Li⁺/Li⁰, as equivalently observed in the layered α-Li₂IrO₃ polymorph. Theoretical calculations elucidate the electrochemical similarities and differences of the 3D versus 2D polymorphs in terms of structural, electronic and mechanical descriptors. Our findings free the structural dimensionality constraint and broaden the possibilities in designing high-energy-density electrodes for the next generation of Li-ion batteries.

Classical Spin Liquid Instability Driven By Off-Diagonal Exchange in Strong Spin-Orbit Magnets

We show that the off-diagonal exchange anisotropy drives Mott insulators with strong spin-orbit coupling to a classical spin liquid regime, characterized by an infinite number of ground states and Ising variables living on closed or open strings. Depending on the sign of the anisotropy, quantum fluctuations either fail to lift the degeneracy down to very low temperatures, or select noncoplanar magnetic states with unconventional spin correlations. The results apply to all 2D and 3D tricoordinated materials with bond-directional anisotropy and provide a consistent interpretation of the suppression of the x-ray magnetic circular dichroism signal reported recently for β-Li_{2}IrO_{3} under pressure.

Quantum spin liquids: a review

Quantum spin liquids may be considered 'quantum disordered' ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.

Kitaev exchange and field-induced quantum spin-liquid states in honeycomb α-RuCl3

Large anisotropic exchange in 5d and 4d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4d⁵ honeycomb halide α-RuCl₃. From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5d⁵ iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d⁵ halides and oxides in general.

Magnetic Structures of Orthorhombic Li2M(SO4)2 (M = Co, Fe) and LixFe(SO4)2 (x = 1, 1.5) Phases

We report herein on the magnetic properties and structures of orthorhombic Li₂M(SO₄)₂ (M = Co, Fe) and their oxidized phases Li_xFe(SO₄)₂ (x = 1, 1.5), which were previously studied as potential cathode materials for Li-ion batteries. The particular structure of these orthorhombic compounds (space group Pbca) consists of a three-dimensional network of isolated MO₆ octahedra enabling solely super-super-exchange interactions between transition metals. We studied the magnetic properties of these phases via temperature-dependent susceptibility measurements and applied neutron powder diffraction experiments to solve their magnetic structures. All compounds present an antiferromagnetic long-range ordering of the magnetic spins below their Néel temperature. Their magnetic structures are collinear and follow a spin sequence (+ + - - - - + +), with the time reversal associated with the inversion center, a characteristic necessary for a linear magneto-electric effect. We found that the orientation of the magnetic moments varies with the nature of M. While Li₂Co(SO₄)₂ and Li₁Fe(SO₄)₂ adopt the magnetic space group Pb'c'a', the magnetic space group for Li₂Fe(SO₄)₂ and Li_1.5Fe(SO₄)₂ is P112₁'/a, which might hint for a possible monoclinic distortion of their nuclear structure. Moreover we compared the orthorhombic phases to their monoclinic counterparts as well as to the isostructural orthorhombic Li₂Ni(SO₄)₂ compound. Finally, we show that this possible magneto-electric feature is driven by the topology of the magnetic interactions.

Structure and Magnetic Behavior of Layered Honeycomb Tellurates, BiM(III)TeO6 (M = Cr, Mn, Fe)

New layered honeycomb tellurates, BiM(III)TeO₆ (M = Cr, Mn, Fe) were synthesized and characterized. BiM(III)TeO₆ (M = Cr, Fe) species crystallize in a trigonal space group, P3̅1c (No. 163), of edge-sharing M³⁺/Te⁶⁺O₆ octahedra, which form honeycomb-like double layers in the ab plane with Bi³⁺ cations located between the layers. Interestingly, the structure of BiMnTeO₆ is similar to those of the Cr/Fe analogues, but with monoclinic space group, P2₁/c (No. 14), attributed to the strong Jahn-Teller distortion of Mn³⁺ cations. The crystal structure of BiM(III)TeO₆ is a superstructure of PbSb₂O₆-related materials (ABB'O₆). The Cr³⁺ and Fe³⁺ cations are ordered 80% and 90%, respectively, while the Mn³⁺ ions are completely ordered on the B-site of the ABB'O₆ structure. BiCrTeO₆ shows a broad antiferromagnetic transition (AFM) at ∼17 K with a Weiss temperature (θ) of -59.85 K, while BiFeTeO₆ and BiMnTeO₆ show sharp AFM transitions at ∼11 K with θ of -27.56 K and at ∼9.5 K with θ of -17.57 K, respectively. These differences in the magnetic behavior are ascribed to the different concentration of magnetic nearest versus next-nearest neighbor interactions of magnetic cations due to the relative differences in the extent of M/Te ordering.

Single crystal growth from separated educts and its application to lithium transition-metal oxides

Thorough mixing of the starting materials is the first step of a crystal growth procedure. This holds true for almost any standard technique, whereas the intentional separation of educts is considered to be restricted to a very limited number of cases. Here we show that single crystals of α-Li₂IrO₃ can be grown from separated educts in an open crucible in air. Elemental lithium and iridium are oxidized and transported over a distance of typically one centimeter. In contrast to classical vapor transport, the process is essentially isothermal and a temperature gradient of minor importance. Single crystals grow from an exposed condensation point placed in between the educts. The method has also been applied to the growth of Li₂RuO₃, Li₂PtO₃ and β-Li₂IrO₃. A successful use of this simple and low cost technique for various other materials is anticipated.