Disorder-Enriched Magnetic Excitations in a Heisenberg-Kitaev Quantum Magnet Na_{2}Co_{2}TeO_{6}.

Using optical magnetospectroscopy, we investigate the magnetic excitations of Na_{2}Co_{2}TeO_{6} in a broad magnetic field range (0 T≤B≤17.5 T) at low temperature. Our measurements reveal rich spectra of in-plane magnetic excitations with a surprisingly large number of modes, even in the high-field spin-polarized state. Theoretical calculations find that the Na-occupation disorder in Na_{2}Co_{2}TeO_{6} plays a crucial role in generating these modes. Our Letter demonstrates the necessity to consider disorder in the spin environment in the search for Kitaev quantum spin liquid states in practicable materials.

Magnetic anisotropy reversal driven by structural symmetry-breaking in monolayer α-RuCl3.

Layered α-RuCl3 is a promising material to potentially realize the long-sought Kitaev quantum spin liquid with fractionalized excitations. While evidence of this state has been reported under a modest in-plane magnetic field, such behaviour is largely inconsistent with theoretical expectations of spin liquid phases emerging only in out-of-plane fields. These predicted field-induced states have been largely out of reach due to the strong easy-plane anisotropy of bulk crystals, however. We use a combination of tunnelling spectroscopy, magnetotransport, electron diffraction and ab initio calculations to study the layer-dependent magnons, magnetic anisotropy, structure and exchange coupling in atomically thin samples. Due to picoscale distortions, the sign of the average off-diagonal exchange changes in monolayer α-RuCl3, leading to a reversal of spin anisotropy to easy-axis anisotropy, while the Kitaev interaction is concomitantly enhanced. Our work opens the door to the possible exploration of Kitaev physics in the true two-dimensional limit.

Spin Vortex Crystal Order in Organic Triangular Lattice Compound.

Organic salts represent an ideal experimental playground for studying the interplay between magnetic and charge degrees of freedom, which has culminated in the discovery of several spin-liquid candidates such as κ-(ET)_{2}Cu_{2}(CN)_{3} (κ-Cu). Recent theoretical studies indicate the possibility of chiral spin liquids stabilized by ring exchange, but the parent states with chiral magnetic order have not been observed in this material family. In this Letter, we discuss the properties of the recently synthesized κ-(BETS)_{2}Mn[N(CN)_{2}]_{3} (κ-Mn). Based on analysis of specific heat, magnetic torque, and NMR measurements combined with ab initio calculations, we identify a spin-vortex crystal order. These observations definitively confirm the importance of ring exchange in these materials and support the proposed chiral spin-liquid scenario for triangular lattice organics.

Low temperature insights into the crystal and magnetic structure of a neutral radical ferromagnet.

The crystal structure of the radical ferromagnet 1a at 2 K reveals a contraction in the unit cell c constant which, at the molecular level, translates into a decrease in slippage of the radical π-stacks and an increase in ferromagnetic exchange interactions along the stacking axis. The results of BS-DFT calculations using long-range corrected functionals are consistent with an overall ferromagnetic topology.

Erratum: Lattice Dynamics Coupled to Charge and Spin Degrees of Freedom in the Molecular Dimer-Mott Insulator κ-(BEDT-TTF)_{2}Cu[N(CN)_{2}]Cl [Phys. Rev. Lett. 123, 027601 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.123.027601.

Electronic Properties of α-RuCl_{3} in Proximity to Graphene.

In the pursuit of developing routes to enhance magnetic Kitaev interactions in α-RuCl_{3}, as well as probing doping effects, we investigate the electronic properties of α-RuCl_{3} in proximity to graphene. We study α-RuCl_{3}/graphene heterostructures via ab initio density functional theory calculations, Wannier projection, and nonperturbative exact diagonalization methods. We show that α-RuCl_{3} becomes strained when placed on graphene and charge transfer occurs between the two layers, making α-RuCl_{3} (graphene) lightly electron doped (hole doped). This gives rise to an insulator-to-metal transition in α-RuCl_{3} with the Fermi energy located close to the bottom of the upper Hubbard band of the t_{2g} manifold. These results suggest the possibility of realizing metallic and even exotic superconducting states. Moreover, we show that in the strained α-RuCl_{3} monolayer the Kitaev interactions are enhanced by more than 50% compared to the unstrained bulk structure. Finally, we discuss scenarios related to transport experiments in α-RuCl_{3}/graphene heterostructures.

Lattice Dynamics Coupled to Charge and Spin Degrees of Freedom in the Molecular Dimer-Mott Insulator κ-(BEDT-TTF)_{2}Cu[N(CN)_{2}]Cl.

Inelastic neutron scattering measurements on the molecular dimer-Mott insulator κ-(BEDT-TTF)_{2}Cu[N(CN)_{2}]Cl reveal a phonon anomaly in a wide temperature range. Starting from T_{ins}∼50-60 K where the charge gap opens, the low-lying optical phonon modes become overdamped upon cooling towards the antiferromagnetic ordering temperature T_{N}=27 K, where also a ferroelectric ordering at T_{FE}≈T_{N} occurs. Conversely, the phonon damping becomes small again when spins and charges are ordered below T_{N}, while no change of the lattice symmetry is observed across T_{N} in neutron diffraction measurements. We assign the phonon anomalies to structural fluctuations coupled to charge and spin degrees of freedom in the BEDT-TTF molecules.

Critical spin liquid versus valence-bond glass in a triangular-lattice organic antiferromagnet.

In the quest for materials with unconventional quantum phases, the organic triangular-lattice antiferromagnet κ-(ET)2Cu2(CN)3 has been extensively discussed as a quantum spin liquid (QSL) candidate. The description of its low temperature properties has become, however, a particularly challenging task. Recently, an intriguing quantum critical behaviour was suggested from low-temperature magnetic torque experiments. Here we highlight significant deviations of the experimental observations from a quantum critical scenario by performing a microscopic analysis of all anisotropic contributions, including Dzyaloshinskii-Moriya and multi-spin scalar chiral interactions. Instead, we show that disorder-induced spin defects provide a comprehensive explanation of the low-temperature properties. These spins are attributed to valence bond defects that emerge spontaneously as the QSL enters a valence-bond glass phase at low temperature. This theoretical treatment is applicable to a general class of frustrated magnetic systems and has important implications for the interpretation of magnetic torque, nuclear magnetic resonance, thermal transport and thermodynamic experiments.

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.

The Importance of Electronic Dimensionality in Multiorbital Radical Conductors.

The exceptional performance of oxobenzene-bridged bis-1,2,3-dithiazolyls 6 as single-component neutral radical conductors arises from the presence of a low-lying π-lowest unoccupied molecular orbital, which reduces the potential barrier to charge transport and increases the kinetic stabilization energy of the metallic state. As part of ongoing efforts to modify the solid-state structures and transport properties of these so-called multiorbital materials, we report the preparation and characterization of the acetoxy, methoxy, and thiomethyl derivatives 6 (R = OAc, OMe, SMe). The crystal structures are based on ribbonlike arrays of radicals laced together by S···N' and S···O' secondary bonding interactions. The steric and electronic effects of the exocyclic ligands varies, affording one-dimensional (1D) π-stacked radicals for R = OAc, 1D cofacial dimer π-stacks for R = SMe, and a pseudo two-dimensional (2D) brick-wall arrangement for R = OMe. Variable-temperature magnetic and conductivity measurements reveal strong antiferromagnetic interactions and Mott insulating behavior for the two radical-based structures (R = OAc, OMe), with lower room-temperature conductivities (σRT ≈ 1 × 10-4 and ∼1 × 10-3 S cm-1, respectively) and higher thermal activation energies ( Eact = 0.24 and 0.21 eV, respectively) than found for the ideal 2D brick-wall structure of 6 (R = F), where σRT ≈ 1 × 10-2 S cm-1 and Eact = 0.10 eV. The performance of R = OMe, OAc relative to that of R = F, is consistent with the results of density functional theory band electronic structure calculations, which indicate a lower kinetic stabilization energy of the putative metallic state arising from their reduced electronic dimensionality.

Three-Dimensional Magnetic Exchange Networks in Trigonal Bisdithiazolyl Radicals.

The N-methyl-4-phenyl-pyridine-bridged bisdithiazolyl radical PhBPMe is polymorphic, crystallizing from cold acetonitrile in a trigonal α-phase, space group P3121, and from hot dichloroethane in an orthorhombic ß-phase, space group Pca21. The crystal structures of both phases consist of slipped π-stacks of undimerized radicals aligned laterally into herringbone arrays. In the ß-phase, there are two independent radicals in the asymmetric unit, and the resulting π-stacks form corrugated layers interspersed by methyl and phenyl groups which block the approach of neighboring radicals. In the α-phase, the methyl/phenyl groups and the radical π-stacks separately form spirals about 31 axes, the latter giving rise to a 3D network of close radical/radical contacts. Variable temperature magnetic susceptibility measurements on the ß-phase indicate strong antiferromagnetic coupling. Weaker but predominantly antiferromagnetic interactions (θ = -20.7 K) are observed in the α-phase. A high temperature series expansion analysis of the magnetic data for the α-phase affords antiferromagnetic exchange energies for the one- and two-step radical/radical interactions about the 31 spirals ( J1 = -1.2 K, J2 = -10.9 K, respectively), with weak ferromagnetic interactions along the π-stacks ( Jπ = +1.8 K). Despite the presence of a 3D network based on the dominant J2 interactions, which affords two independent bipartite sublattices, no evidence of bulk antiferromagnetic order has been observed above T = 2 K. The magnetic results are discussed in light of exchange energies calculated using density functional theory broken symmetry methods.

Evidence for Electronically Driven Ferroelectricity in a Strongly Correlated Dimerized BEDT-TTF Molecular Conductor.

By applying measurements of the dielectric constants and relative length changes to the dimerized molecular conductor κ-(BEDT-TTF)_{2}Hg(SCN)_{2}Cl, we provide evidence for order-disorder type electronic ferroelectricity that is driven by the charge order within the (BEDT-TTF)_{2} dimers and stabilized by a coupling to the anions. According to our density functional theory calculations, this material is characterized by a moderate strength of dimerization. This system thus bridges the gap between strongly dimerized materials, often approximated as dimer-Mott systems at 1/2 filling, and nondimerized or weakly dimerized systems at 1/4 filling, exhibiting a charge order. Our results indicate that intradimer charge degrees of freedom are of particular importance in correlated κ-(BEDT-TTF)_{2}X salts and can create novel states, such as electronically driven multiferroicity or charge-order-induced quasi-one-dimensional spin liquids.

Probing α-RuCl_{3} Beyond Magnetic Order: Effects of Temperature and Magnetic Field.

Recent studies have brought α-RuCl_{3} to the forefront of experimental searches for materials realizing Kitaev spin-liquid physics. This material exhibits strongly anisotropic exchange interactions afforded by the spin-orbit coupling of the 4d Ru centers. We investigate the dynamical response at finite temperature and magnetic field for a realistic model of the magnetic interactions in α-RuCl_{3}. These regimes are thought to host unconventional paramagnetic states that emerge from the suppression of magnetic order. Using exact diagonalization calculations of the quantum model complemented by semiclassical analysis, we find a very rich evolution of the spin dynamics as the applied field suppresses the zigzag order and stabilizes a quantum paramagnetic state that is adiabatically connected to the fully polarized state at high fields. At finite temperature, we observe large redistributions of spectral weight that can be attributed to the anisotropic frustration of the model. These results are compared to recent experiments and provide a road map for further studies of these regimes.

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.

Breakdown of magnons in a strongly spin-orbital coupled magnet.

The description of quantized collective excitations stands as a landmark in the quantum theory of condensed matter. A prominent example occurs in conventional magnets, which support bosonic magnons-quantized harmonic fluctuations of the ordered spins. In striking contrast is the recent discovery that strongly spin-orbital-coupled magnets, such as α-RuCl3, may display a broad excitation continuum inconsistent with conventional magnons. Due to incomplete knowledge of the underlying interactions unraveling the nature of this continuum remains challenging. The most discussed explanation refers to a coherent continuum of fractional excitations analogous to the celebrated Kitaev spin liquid. Here, we present a more general scenario. We propose that the observed continuum represents incoherent excitations originating from strong magnetic anharmonicity that naturally occurs in such materials. This scenario fully explains the observed inelastic magnetic response of α-RuCl3 and reveals the presence of nontrivial excitations in such materials extending well beyond the Kitaev state.

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 (ß- and γ-Li2IrO3), and other potential candidates, completing the review with the list of open questions awaiting new insights.

The Power of Packing: Metallization of an Organic Semiconductor.

Benzoquino-bis-1,2,3-dithiazole 5 is a closed shell, antiaromatic 16π-electron zwitterion with a small HOMO-LUMO gap. Its crystal structure consists of planar ribbon-like molecular arrays packed into offset layers to generate a "brick-wall" motif with strong 2D interlayer electronic interactions. The spread of the valence and conduction bands, coupled with the narrow HOMO-LUMO gap, affords a small band gap semiconductor with σRT = 1 × 10-3 S cm-1 and Eact = 0.14 eV for transport within the brick-wall arrays. Closure of the band gap to form an all-organic molecular metal with σRT > 101 S cm-1 can be achieved by the application of pressure to 8 GPa.

Fine Tuning the Performance of Multiorbital Radical Conductors by Substituent Effects.

A critical feature of the electronic structure of oxobenzene-bridged bisdithiazolyl radicals 2 is the presence of a low-lying LUMO which, in the solid state, improves charge transport by providing additional degrees of freedom for electron transfer. The magnitude of this multiorbital effect can be fine-tuned by variations in the π-electron releasing/accepting nature of the basal ligand. Here we demonstrate that incorporation of a nitro group significantly stabilizes the LUMO, and hence lowers Ueff, the effective Coulombic barrier to charge transfer. The effect is echoed, at the molecular level, in the observed trend in Ecell, the electrochemical cell potential for 2 with R = F, H and NO2. The crystal structures of the MeCN and EtCN solvates of 2 with R = NO2 have been determined. In the EtCN solvate the radicals are dimerized, but in the MeCN solvate the radicals form superimposed and evenly spaced π-stacked arrays. This highly 1D material displays Pauli-like temperature independent paramagnetic behavior, with χTIP = 6 × 10-4 emu mol-1, but its charge transport behavior, with σRT near 0.04 S cm-1 and Eact = 0.05 eV, is more consistent with a Mott insulating ground state. High pressure crystallographic measurements confirm uniform compression of the π-stacked architecture with no phase change apparent up to 8 GPa. High pressure conductivity measurements indicate that the charge gap between the Mott insulator and metallic states can be closed near 6 GPa. These results are discussed in the light of DFT band structure calculations.

Pushing TC to 27.5 K in a heavy atom radical ferromagnet.

In the solid state the iodo-substituted bisdiselenazolyl radical 1c orders as a ferromagnet with TC = 10.5 K. With the application of pressure TC rises rapidly, reaching a value of 27.5 K at 2.4 GPa. The accompanying structural and magnetic changes have been examined by high resolution powder X-ray diffraction and by DFT calculations of magnetic exchange interactions.