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BaCo$_2$(AsO$_4$)$_2$ (BCAO), a honeycomb cobaltate, is considered a promising candidate for materials displaying the Kitaev quantum spin liquid state. This assumption is based on the distinctive characteristics of Co$^{2+}$ ions (3$d^7$) within an octahedral crystal environment, resulting in spin-orbit-coupled $J_{\rm eff}$~=~1/2 doublet states. However, recent experimental observations and theoretical analyses have raised questions regarding this hypothesis. Despite these uncertainties, reports of continuum excitations reminiscent of spinon excitations have prompted further investigations. In this study, we explore the magnetic phases of BCAO under both in-plane and out-of-plane magnetic fields, employing dc and ac magnetic susceptibilities, capacitance, and torque magnetometry measurement. Our results affirm the existence of multiple field-induced magnetic phases, with strong anisotropy of the phase boundaries between in-plane and out-of-plane fields. To elucidate the nature of these phases, we develop a minimal anisotropic exchange model. This model, supported by combined first principles calculations and theoretical modeling, quantitatively reproduces our experimental data. In BCAO, the combination of strong bond-independent XXZ anisotropy and geometric frustration leads to significant quantum order by disorder effects that stabilize collinear phases under both zero and finite magnetic fields., Comment: 14 pages, 5 main + 5 supplementary figures

We apply a recently developed first-principles based approach for treating generic spin-phonon couplings in materials with strong spin-orbit coupling to study $\alpha$-RuCl$_3$. Of particular focus is the potential for this material to exhibit a phonon thermal Hall effect induced by spin-phonon interactions. We find that spin-orbit coupling significantly enriches the form of these interactions, and imbues them with chirality that is conducive to generating finite phonon Berry curvatures. We show that this leads to a phonon thermal Hall effect that qualitatively reproduces the measured field dependence of $\kappa_{xy}$ without requiring a field-induced spin liquid., Comment: 22 pages, 10 figures including supplemental material. Changes from v1 summarized on first page

Spin-phonon coupling underlies a number of diverse range of phenomena of recent interest, particularly in transition metal insulators with strong spin-orbit effects, where it may give rise to hybrid magnetoelastic excitations, and the controversial phonon thermal Hall effect. In this work, we describe a general approach to the first principles estimation of generic spin-orbit-phonon couplings suitable for investigating these diverse effects. The method is demonstrated by application to study the temperature-dependent optical phonon lineshapes in MnPSe$_3$, for which we find quantitative agreement with recent experiments., Comment: 21 pages, 7 figures

In this study, a novel material from the rare-earth based breathing pyrochlore family, Ba3Tm2Zn5O11, was successfully synthesized. Powder X-ray diffraction and high-resolution powder neutron diffraction confirmed phase purity and crystal structure, while thermogravimetric analysis revealed incongruent melting behavior compared to its counterpart, Ba3Yb2Zn5O11. High-quality single crystals of Ba3Tm2Zn5O11 were grown using the traveling solvent floating zone technique and assessed using Laue diffractometer and single crystal X-ray diffraction. Thermodynamic characterization indicated paramagnetic behavior down to 0.05 K, and inelastic neutron scattering measurements identified distinct crystal electric field bands. Additional low-energy excitation studies on single crystals revealed dispersionless bands at 0.8 and 1 meV. Computed phonon dispersions from first principles calculations ruled out phonons as the source of these modes, further illustrating the puzzling and unique properties of Ba3Tm2Zn5O11.

Motivated by the on-going discussion on the nature of magnetism in the quantum Ising chain CoNb$_2$O$_6$, we present a first-principles-based analysis of its exchange interactions by applying an \textit{ab initio} approach with additional modelling that accounts for various drawbacks of a purely density functional theory ansatz. With this method we are able to extract and understand the origin of the magnetic couplings under inclusion of all symmetry-allowed terms, and to resolve the conflicting model descriptions in CoNb$_2$O$_6$. We find that the twisted Kitaev chain and the transverse-field ferromagnetic Ising chain views are mutually compatible, although additional off-diagonal exchanges are necessary to provide a complete picture. We show that the dominant exchange interaction is a ligand-centered exchange process - involving the $e_g$ electrons -, which is rendered anisotropic by the low-symmetry crystal fields environments in CoNb$_2$O$_6$, giving rise to the dominant Ising exchange, while the smaller bond-dependent anisotropies are found to originate from $d-d$ kinetic exchange processes involving the $t_{2g}$ electrons. We demonstrate the validity of our approach by comparing the predictions of the obtained low-energy model to measured THz and inelastic neutron scattering spectra., Comment: 14 pages, 6 figures

Co-based materials have recently been explored due to potential to realise complex bond-dependent anisotropic magnetism. Prominent examples include Na$_2$Co$_2$TeO$_6$, BaCo$_2$(AsO$_4$)$_2$, Na$_2$BaCo(PO$_4$)$_2$, and CoX$_2$ (X = Cl, Br, I). In order to provide insight into the magnetic interactions in these compounds, we make a comparative analysis of their local crystal electric field excitations spectra via Raman scattering measurements. Combining these measurements with theoretical analysis confirms the validity of $j_{\rm eff} = 1/2$ single-ion ground states for all compounds, and provides accurate experimental estimates of the local crystal distortions, which play a prominent role in the magnetic couplings between spin-orbital coupled Co moments., Comment: 11 pages, 7 figures

FePS3 is a layered van der Waals (vdW) Ising antiferromagnet that has recently been studied in the context of true 2D magnetism, and emerged as an ideal material platform for investigating strong spin-phonon coupling, and non-linear magneto-optical phenomena. In this work, we demonstrate an important unresolved role of spin-orbit coupling (SOC) in the ground state and excitations of this compound. Combining first principles calculations with Linear Flavor Wave Theory (LFWT), we find strong mixing and spectral overlap of different spin-orbital single-ion states. As such, the low-lying excitations form complex mixtures of local degrees of freedom most accurately viewed as hybrid spin-orbit exciton-magnon modes. Complete parameterization of the resulting low-energy model including all such degrees of freedom requires nearly half a million coupling constants. Despite this complexity, we show that such a model can be inexpensively derived using local many-body-based approaches, which yield quantitative agreement with recent experiments. The results highlight the importance of SOC even in first row transition metals, and provide essential insight into the properties of 2D magnets with unquenched orbital moments., Comment: Fixed typos and replaced figure 4 to show correct ordering of states

Recent advances in the study of cobaltites have unveiled their potential as a promising platform for realizing Kitaev physics in honeycomb systems and the Ising model in weakly coupled chain materials. In this manuscript, we explore the magnetic properties of pyroxene SrCoGe$_2$O$_6$ using a combination of neutron scattering, {\it ab initio} methods, and linear spin-wave theory. Through careful examination of inelastic neutron scattering powder spectra, we propose a modified Kitaev model to accurately describe the twisted chains of edge-sharing octahedra surrounding Co$^{2+}$ ions. The extended Kitaev-Heisenberg model, including a significant anisotropic bond-dependent exchange term with $K/|J|=0.96$, is identified as the key descriptor of the magnetic interactions in SrCoGe$_2$O$_6$. Furthermore, our heat capacity measurements reveal an effect of an external magnetic field (approximately 13~T) which shifts the system from a fragile antiferromagnetic ordering with $T_{\mathrm{N}}=9$~K to a field-induced state. We argue that pyroxenes, particularly those modified by substituting Ge with Si and its less extended $p$ orbitals, emerge as a novel platform for the Kitaev model. This opens up possibilities for advancing our understanding of Kitaev physics., Comment: 11 + 2 pages, 7 + 3 figures

Using a combination of resistance fluctuation (noise) and dielectric spectroscopy we investigate the nature of relaxor-type electronic ferroelectricity in the organic conductor $\kappa$-(BETS)$_2$Mn[N(CN)$_2$]$_3$, a system representative for a wider class of materials, where strong correlations of electrons on a lattice of dimerized molecules results in an insulating ground state. The two complementary spectroscopies reveal a distinct low-frequency dynamics. By dielectric spectroscopy we detect an intrinsic relaxation that is typical for relaxor ferroelectrics below the metal-to-insulator transition at $T_{\rm{MI}}\sim 25\,$K. Resistance noise spectroscopy reveals fluctuating two-level processes above $T_{\rm MI}$ which strongly couple to the applied electric field, a signature of fluctuating polar nanoregions (PNR), i.e. clusters of quantum electric dipoles fluctuating collectively. The PNR preform above the metal insulator transition. Upon cooling through $T_{\rm MI}$, a drastic increase of the low-frequency $1/f$-type fluctuations and slowing down of the charge carrier dynamics is accompanied by the onset of strong non-equilibrium dynamics indicating a glassy transition of interacting dipolar clusters, the scaling properties of which are consistent with a droplet model. The freezing of nano-scale polar clusters and non-equilibrium dynamics is suggested to be a common feature of organic relaxor-type electronic ferroelectrics and needs to be considered in theoretical models describing these materials.

We present results of the coefficient of thermal expansion for the frustrated quasi-two-dimensional molecular conductor $\theta$-(BEDT-TTF)$_2$RbZn(SCN)$_4$ for temperatures 1.5 K $\leq T \leq$ 290 K. A pronounced first-order phase transition anomaly is observed at the combined charge-order/structural transition at 215 K. Furthermore, clear evidence is found for two separate glasslike transitions at $T_{\mathrm{g}}$ = 90-100 K and $T_{\mathrm{g}}^\dagger$ = 120-130 K, similar to previous findings for $\theta$-(BEDT-TTF)$_2$CsZn(SCN)$_4$ and $\theta$-(BEDT-TTF)$_2$CsCo(SCN)$_4$, reported in T. Thomas et al., Phys. Rev. B 105, L041114 (2022), both of which lack the charge-order/structural transition. Our findings indicate that these glasslike transitions are common features for the $\theta$-(BEDT-TTF)$_2MM^\prime$(SCN)$_4$ family with $M$ = (Rb, Cs) and $M^\prime$ = (Co, Zn), irrespective of the presence or absence of charge order. These results are consistent with our model calculations on the glasslike dynamics associated with the flexible ethylene endgroups of the BEDT-TTF molecules for various $\theta$-(BEDT-TTF)$_2MM^\prime$(SCN)$_4$ salts, predicting two different conformational glass transitions. Moreover, calculations of the hopping integrals show a substantial degree of dependence on the endgroups' conformation, suggesting a significant coupling to the electronic degrees of freedom. Our findings support the possibility that the glassy freezing of the ethylene endgroups could drive or enhance glassy charge dynamics., Comment: 11 pages, 10 figures, 1 table

A spin-1/2 triangular-lattice antiferromagnet is a prototypical frustrated quantum magnet, which exhibits remarkable quantum many-body effects that arise from the synergy between geometric spin frustration and quantum fluctuations. It can host quantum frustrated magnetic topological phenomena like quantum spin liquid (QSL) states, highlighted by the presence of fractionalized quasiparticles within a continuum of magnetic excitations. In this work, we use neutron scattering to study CoZnMo$_3$O$_8$, which has a triangular lattice of Jeff = 1/2 Co2+ ions with octahedral coordination. We found a wave-vector-dependent excitation continuum at low energy that disappears with increasing temperature. Although these excitations are reminiscent of a spin excitation continuum in a QSL state, their presence in CoZnMo$_3$O$_8$ originates from magnetic intersite disorder-induced dynamic spin states with peculiar excitations. Our results, therefore, give direct experimental evidence for the presence of a disorder-induced spin excitation continuum.

Using optical magneto-spectroscopy, we investigate the magnetic excitations of Na$_2$Co$_2$TeO$_6$ in a broad magnetic field range ($0\ \rm{T}\leq B\leq 17.5\ \rm{T}$) 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 \NCTO plays a crucial role in generating these modes. Our work demonstrates the necessity to consider disorder in the spin environment in the search for Kitaev quantum spin liquid states in practicable materials.

Layered {\alpha}-RuCl3 is a promising material to potentially realize the long-sought Kitaev quantum spin liquid with fractionalized excitations. While evidence of this exotic state has been reported under a modest in-plane magnetic field, such behavior is largely inconsistent with theoretical expectations of Kitaev phases emerging only in out-of-plane fields. These predicted field-induced states have been mostly out of reach due to the strong easy-plane anisotropy of bulk crystals, however. We use a combination of tunneling spectroscopy, magnetotransport, electron diffraction, and ab initio calculations to study the layer-dependent magnons, anisotropy, structure, and exchange coupling in atomically thin samples. Due to structural distortions, the sign of the average off-diagonal exchange changes in monolayer {\alpha}-RuCl3, leading to a reversal of magnetic anisotropy to easy-axis. Our work provides a new avenue to tune the magnetic interactions in {\alpha}-RuCl3 and allows theoretically predicted quantum spin liquid phases for out-of-plane fields to be more experimentally accessible.

The realization of the stable structure of Heusler compounds and the study of different properties is an important step for their potential application in spintronics and magnetoelectronic devices. In this paper, using the plane-wave pseudopotential method within the framework of density functional theory (DFT), we investigate 25 Quaternary Heusler compounds for their electronic, magnetic, and mechanical properties. The Open Quantum Materials Database (OQMD) is used to screen a large number of compounds to narrow down the possible synthesizable materials. The convex-hull distance and elastic constants are exploited to confirm the thermodynamic and mechanical stability of the compounds. The careful study of the different structures suggests that 5 of the compounds crystallize in type-1 structure whereas 20 compounds adopt type-3 structure. The possible explanation for the observed behavior is made by invoking electronegativity arguments and through the study of individual spin magnetic moments in different structures. The compounds with diverse electronic and magnetic properties such as half-metallicity, spin gapless semiconducting behavior, and non-magnetic semi-conducting property have been identified.

Motivated by the recent wealth of exotic magnetic phases emerging in two-dimensional frustrated lattices, we investigate the origin of possible magnetism in the monolayer family of triangular lattice materials $MX_2$ ($M$={V, Mn, Ni}, $X$={Cl, Br, I}). We first show that consideration of general properties such as filling and hybridization enables to formulate trends for the most relevant magnetic interaction parameters. In particular, we observe that the effects of spin-orbit coupling (SOC) can be effectively tuned through the ligand elements as the considered 3$d$ transition metal ions do not strongly contribute to the anisotropic component of the inter-site exchange interaction. Consequently, we find that the corresponding SOC matrix-elements differ significantly from the atomic limit. In a next step and by using two complementary approaches based on first principles, we extract realistic effective spin models and find that in the case of heavy ligand elements, SOC effects manifest in anisotropic exchange and single-ion anisotropy only for specific fillings.

High-spin $d^7$ Co(II) compounds have recently been identified as possible platforms for realising highly anisotropic and bond-dependent couplings featured in quantum-compass models such as the celebrated Kitaev model. In order to evaluate this potential, we consider all symmetry-allowed contributions to the magnetic exchange for ideal edge-sharing bonds. Though a combination of ab-initio and cluster many-body calculations we conclude that bond-dependent couplings are generally suppressed in favor of Heisenberg exchange for real materials. Consequences for several prominent materials including Na$_2$Co$_2$TeO$_6$ and BaCo$_2$(AsO$_4$)$_2$ are discussed., Comment: 15 pages, 10 figures; v3 corrects an error in v2 where "trigonal elongation" and "trigonal compression" were accidentally reversed. The published version has always been correct

By considering two {\it ab initio}-based complementary approaches, we analyze the electronic structure and extract effective spin models of BaCo$_2$(AsO$_4$)$_2$, a honeycomb material which has been proposed as a candidate for Kitaev physics. Both methods show that the dominant direct hopping makes the bond-dependent Kitaev term negligible averting the material away from the sought-after spin-liquid regime. As a result, we present a simple three-parameter exchange model to describe the interactions of the lowest doublet of the honeycomb cobaltate BaCo$_2$(AsO$_4$)$_2$. Remarkably, it is the third-neighbor interactions, both isotropic and anisotropic, that are responsible for the standout double-zigzag ground state of BaCo$_2$(AsO$_4$)$_2$, stabilized by quantum fluctuations. A significantly large third-nearest neighbor hopping, observed in {\it ab initio}, supports the importance of the third-neighbor interactions in the stabilization of the unique ground state of BaCo$_2$(AsO$_4$)$_2$., Comment: 8 pages, 4 figures

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 $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$ ($\kappa$-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 work, we discuss the properties of the recently synthesized $\kappa$-(BETS)$_2$Mn[N(CN)$_2$]$_3$ ($\kappa$-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.

We discuss the applicability of elementary band representations (EBRs) to diagnose spatial- and time-reversal-symmetry protected topological phases in interacting insulators in terms of their single-particle Green's functions. We do so by considering an auxiliary non-interacting system $H_{\textrm{T}}(\mathbf{k}) = -G^{-1}(0, \mathbf{k})$, known as the topological Hamiltonian, whose bands can be labeled by EBRs. This labeling is stable if neither (i) the gap in the spectral function at zero frequency closes, (ii) the Green's function has a zero at zero frequency or (iii) the Green's function breaks a protecting symmetry. We demonstrate the use of EBRs applied to the Green's function on the one-dimensional Su-Schrieffer-Heeger model with Hubbard interactions, which we solve by exact diagonalization for a finite number of unit cells. Finally, the use of EBRs for the Green's function to diagnose so-called symmetry protected topological phases is discussed, but remains an open question., Comment: 12 pages, 6 figures

In spin-orbit-coupled magnetic materials, the usually applied Curie-Weiss law can break down. This is due to potentially sharp temperature-dependence of the local magnetic moments. We therefore propose a modified Curie-Weiss formula suitable for analysis of experimental susceptibility. We show for octahedrally coordinated materials of $d^5$ filling that the Weiss constant obtained from the improved formula is in excellent agreement with the calculated Weiss constant from microscopic exchange interactions. Reanalyzing the measured susceptibility of several Kitaev candidate materials with the modified formula resolves apparent discrepancies between various experiments regarding the magnitude and anisotropies of the underlying magnetic couplings.

In recent years, the notion of Quantum Materials has emerged as a powerful unifying concept across diverse fields of science and engineering, from condensed-matter and cold atom physics to materials science and quantum computing. Beyond traditional quantum materials such as unconventional superconductors, heavy fermions, and multiferroics, the field has significantly expanded to encompass topological quantum matter, two-dimensional materials and their van der Waals heterostructures, Moire materials, Floquet time crystals, as well as materials and devices for quantum computation with Majorana fermions. In this Roadmap collection we aim to capture a snapshot of the most recent developments in the field, and to identify outstanding challenges and emerging opportunities. The format of the Roadmap, whereby experts in each discipline share their viewpoint and articulate their vision for quantum materials, reflects the dynamic and multifaceted nature of this research area, and is meant to encourage exchanges and discussions across traditional disciplinary boundaries. It is our hope that this collective vision will contribute to sparking new fascinating questions and activities at the intersection of materials science, condensed matter physics, device engineering, and quantum information, and to shaping a clearer landscape of quantum materials science as a new frontier of interdisciplinary scientific inquiry., Comment: 93 pages, 27 figures

The recently introduced topological quantum chemistry (TQC) framework has provided a description of universal topological properties of all possible band insulators in all space groups based on crystalline unitary symmetries and time reversal. While this formalism filled the gap between the mathematical classification and the practical diagnosis of topological materials, an obvious limitation is that it only applies to weakly interacting systems-which can be described within band theory. It is an open question to which extent this formalism can be generalized to correlated systems that can exhibit symmetry protected topological phases which are not adiabatically connected to any band insulator. In this work we address the many facettes of this question by considering the specific example of a Hubbard diamond chain. This model features a Mott insulator, a trivial insulating phase and an obstructed atomic limit phase. Here we discuss the nature of the Mott insulator and determine the phase diagram and topology of the interacting model with infinite density matrix renormalization group calculations, variational Monte Carlo simulations and with many-body topological invariants. We then proceed by considering a generalization of the TQC formalism to Green's functions combined with the concept of topological Hamiltonian to identify the topological nature of the phases, using cluster perturbation theory to calculate the Green's functions. The results are benchmarked with the above determined phase diagram and we discuss the applicability and limitations of the approach and its possible extensions., Comment: 16 pages, 13 figures

We present first-principles results on the magnetoelastic coupling in $\alpha$-RuCl$_3$ and uncover a striking dependence of the magnetic coupling constants on strain effects. Different magnetic interactions are found to respond very unequally to variations in the lattice, with the Kitaev interaction being the most sensitive. Exact diagonalization results on our magnetoelastic model reproduce recent measurements of the structural Gr\"uneisen parameter and explain the origin of the negative magnetostriction of $\alpha$-RuCl$_3$, disentangling contributions related to different anisotropic interactions and g factors. Uniaxial strain perpendicular to the honeycomb planes is predicted to reorganize the relative coupling strengths, strongly enhancing the Kitaev interaction while simultaneously weakening the other anisotropic exchanges under compression. Uniaxial strain may therefore pose a fruitful route to experimentally tune $\alpha$-RuCl$_3$ nearer to the Kitaev limit., Comment: final published version; 5 pages, 4 figures + supplemental

We investigate via exact diagonalization of finite clusters the electronic structure and magnetism of M$_2$O$_9$ dimers in the mixed-valence hexagonal perovskites A$_3$B'M$_2$O$_9$ for various different fillings of 4$d$ and 5$d$ transition-metal M ions. We find that the magnetic moments of such dimers are determined by a subtle interplay of spin-orbit coupling, Hund's coupling, and Coulomb repulsion, as well as the electron filling of the M ions. Most importantly, the magnetic moments are anisotropic and temperature-dependent. This behavior is a result of spin-orbit coupling, magnetic field effects, and the existence of several nearly-degenerate electronic configurations whose proximity allows occupation of excited states already at room temperature. This analysis is consistent with experimental susceptibility measurements for a variety of dimer-based materials. Furthermore, we perform a survey of A$_3$B'M$_2$O$_9$ materials and propose ground-state phase diagrams for the experimentally relevant M fillings of $d^{4.5}$, $d^{3.5}$ and $d^{2.5}$. Finally, our results show that the usually applied Curie-Weiss law with a constant magnetic moment cannot be used in these spin-orbit-coupled materials.

In the pursuit of developing routes to enhance magnetic Kitaev interactions in {\alpha}-RuCl3, as well as probing doping effects, we investigate the electronic properties of {\alpha}-RuCl3 in proximity to graphene. We study {\alpha}-RuCl3/graphene heterostructures via ab initio density functional theory calculations, Wannier projection and non-perturbative exact diagonalization methods. We show that {\alpha}-RuCl3 becomes strained when placed on graphene and charge transfer occurs between the two layers, making {\alpha}-RuCl3 (graphene) lightly electron-doped (hole-doped). This gives rise to an insulator to metal transition in {\alpha}-RuCl3 with the Fermi energy located close to the bottom of the upper Hubbard band of the t2g manifold. These results suggest the possibility of realizing metallic and even exotic superconducting states. Moreover, we show that in the strained {\alpha}-RuCl3 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 {\alpha}-RuCl3/graphene heterostructures., Comment: 11 pages, 3 figures Further calculation details included

Inelastic neutron scattering measurements on the molecular dimer-Mott insulator $\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Cl reveal a phonon anomaly in a wide temperature range. Starting from $T_{\rm ins}\sim50$-$60$ K where the charge gap opens, the low-lying optical phonon modes become overdamped upon cooling towards the antiferromagnetic ordering temperature $T_\mathrm{N} = 27$ K, where also a ferroelectric ordering at $T_{\rm FE} \approx T_{\rm N}$ occurs. Conversely, the phonon damping becomes small again when spins and charges are ordered below $T_\mathrm{N}$, while no change of the lattice symmetry is observed across $T_\mathrm{N}$ 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., Comment: 6 pages, 3 figures with Erratum ( 4 pages, 2 figures) and supplemental material (4 pages, 4 figures)

Motivated by recent reports of a field-induced intermediate phase (IP) in the antiferromagnetic honeycomb Kitaev model that may be a spin liquid whose nature is distinct from the Kitaev Z2 phase, we present a detailed numerical study on the nature and dynamical response (such as dynamical spin-structure factors and resonant inelastic x-ray scattering intensities) of this field-induced IP and neighboring phases in a family of Kitaev-based models related by hidden symmetries and duality transformations. We further show that the same field-induced IP can appear in models relevant for $\alpha$-RuCl${_3}$, which exhibit a ferromagnetic Kitaev coupling and additional interactions. In $\alpha$-RuCl${_3}$, the IP represents a new phase, that is likely independent from the putative field-induced (spin-liquid) phase recently reported from thermal Hall conductivity measurements., Comment: 13 pages

Implicit in the study of magnetic materials is the concept of spin Hamiltonians, which emerge as the low-energy theories of correlation-driven insulators. In order to predict and establish such Hamiltonians for real materials, a variety of first principles $ab$-$initio$ methods have been developed, based on density functional theory and wavefunction methodologies. In this review, we provide a basic introduction to such methods and the essential concepts of low-energy Hamiltonians, with a focus on their practical capabilities and limitations. We further discuss our recent efforts toward understanding a variety of complex magnetic systems that present unique challenges from the perspective of $ab$-$initio$ approaches., Comment: Submitted to the SFB/TRR49 special issue of Physica Status Solidi B

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 saw-tooth 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., Comment: v3 includes a more explicit discussion of the different field regions and a more general ansatz for the scaling behaviour. Updated Supplemental Information included

In the quest for materials with unconventional quantum phases, the organic triangular-lattice antiferromagnet $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$ has been extensively discussed as a quantum spin liquid (QSL) candidate. Recently, an intriguing quantum critical behaviour was suggested from low-temperature magnetic torque experiments. Through microscopic analysis of all anisotropic contributions, including Dzyaloshinskii-Moriya and multi-spin scalar chiral interactions, we highlight significant deviations of the experimental observations from a quantum critical scenario. 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., Comment: v3 includes improved readability with several additional comments and a more detailed discussion of the origin and consequences of local moments

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 non-perturbative 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 destabilize the O-H/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 microstructure of the samples and emphasize the importance of a careful treatment of hydrogen for similar systems., Comment: accepted in Phys. Rev. Lett

The honeycomb Mott insulator $\alpha$-RuCl$_3$ loses its low-temperature magnetic order by pressure. We report clear evidence for a dimerized structure at $P>1$ GPa and observe the breakdown of the relativistic $j_{\rm eff}$ picture in this regime strongly affecting the electronic properties. A pressure-induced Kitaev quantum spin liquid cannot occur in this broken symmetry state. We shed light on the new phase by broad-band infrared spectroscopy of the low-temperature properties of $\alpha$-RuCl$_{3}$ and ab initio density functional theory calculations, both under hydrostatic pressure., Comment: 5 pages, 4 figures

By applying measurements of the dielectric constants and relative length changes to the dimerized molecular conductor $\kappa$-(BEDT-TTF)$_2$Hg(SCN)$_2$Cl, we provide evidence for order-disorder type electronic ferroelectricity which is driven by 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 non- or weakly dimerized systems at 1/4 filling exhibiting charge order. Our results indicate that intra-dimer charge degrees of freedom are of particular importance in correlated $\kappa$-(BEDT-TTF)$_2$X salts and can create novel states, such as electronically-driven multiferroicity or charge-order-induced quasi-1D spin liquids., Comment: 6 pages, 4 figures + Supplementary Information (8 pages, 8 figures)

We present high-resolution measurements of the relative length change as a function of temperature of the organic charge-transfer salt $\kappa$-(BEDT-TTF)$_2$Hg(SCN)$_2$Cl. We identify anomalous features at $T_g \approx\,63$ K which can be assigned to a kinetic glass-like ordering transition. By determining the activation energy $E_A$, this glass-like transition can be related to conformational degrees of freedom of the ethylene endgroups of the organic building block BEDT-TTF. As opposed to other $\kappa$-(BEDT-TTF)$_2X$ salts, we identify a peculiar ethylene endgroup ordering in the present material in which only one of the two crystallographically inequivalent ethylene endgroups is subject to glass-like ordering. This experimental finding is fully consistent with our predictions from $ab\,initio$ calculations from which we estimate the energy differences $\Delta E$ and the activation energies $E_A$ between different conformations. The present results indicate that the specific interaction between the ethylene endgroups and the nearby anion layers leads to different energetics of the inequivalent ethylene endgroups, as evidenced by different ratios $E_A/\Delta E$. We infer that the ratio $E_A/\Delta E$ is a suitable parameter to identify the tendency of ethylene endgroups towards glass-like freezing., Comment: 10 pages, 6 figures, Supplementary Information (2 pages)

Recent studies have brought $\alpha$-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 $\alpha$-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 semi-classical 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 roadmap for further studies of these regimes., Comment: final published version; 5 pages, 4 figures + supplemental

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$_3$, $\alpha$-Li$_2$IrO$_3$, and $\alpha$-RuCl$_3$), three-dimensional Kitaev materials ($\beta$- and $\gamma$-Li$_2$IrO$_3$), and other potential candidates, completing the review with the list of open questions awaiting new insights., Comment: updated references, published version

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 $\alpha$-RuCl$_3$, 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 anharmoniticity that naturally occurs in such materials. This scenario fully explains the observed inelastic magnetic response of $\alpha$-RuCl$_3$ and reveals the presence of nontrivial excitations in such materials extending well beyond the Kitaev state., Comment: Final version; supplemental information included

We investigate the spin-orbit coupling (SOC) effects in $\alpha$- and $\kappa$-phase BEDT-TTF and BEDT-TSF organic salts. Contrary to the assumption that SOC in organics is negligible due to light C, S, H atoms, we show the relevance of such an interaction in a few representative cases. In the weakly correlated regime, SOC manifests primarily in the opening of energy gaps at degenerate band touching points. This effect becomes especially important for Dirac semimetals such as $\alpha$-(ET)$_2$I$_3$. Furthermore, in the magnetic insulating phase, SOC results in additional anisotropic exchange interactions, which provide a compelling explanation for the controversial field-induced behaviour of the quantum spin-liquid candidate $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$. We conclude by discussing the importance of SOC for the description of low-energy properties in organics.

We investigate the electronic properties of the three-dimensional stripyhoneycomb $\gamma$-Li$_2$IrO$_3$ via relativistic density functional theory calculations as well as exact diagonalization of finite clusters and explore the details of the optical conductivity. Our analysis of this quantity reveals the microscopic origin of the experimentally observed (i) optical transitions and (ii) anisotropic behavior along the various polarization directions. In particular we find that the optical excitations are overall dominated by transitions between $j_\text{eff}$ = 1/2 and 3/2 states and the weight of transitions between $j_\text{eff}$ = 1/2 states at low frequencies can be correlated to deviations from a pure Kitaev description. We furthermore reanalyze within this approach the electronic excitations in the known two-dimensional honeycomb systems $\alpha$-Li$_2$IrO$_3$ and Na$_2$IrO$_3$ and discuss the results in comparison to $\gamma$-Li$_2$IrO$_3$., Comment: replaced results for $\alpha$-Li$_2$IrO$_3$ with new single-crystal data; corrected typos; reorganized sections

In this study, we reanalyze the magnetic interactions in the Kitaev spin liquid candidate materials Na$_2$IrO$_3$, $\alpha$-RuCl$_3$, and $\alpha$-Li$_2$IrO$_3$ using nonperturbative exact diagonalization methods. These methods are more appropriate given the relatively itinerant nature of the systems suggested in previous works. We treat all interactions up to third neighbours on equal footing. The computed terms reveal significant long range coupling, bond-anisotropy, and/or off-diagonal couplings which we argue naturally explain the observed ordered phases in these systems. Given these observations, the potential for realizing the spin-liquid state in real materials is analyzed, and synthetic challenges are defined and explained.