Spin-Glass Ground State in a Triangular-Lattice Compound YbZnGaO_{4}

Ba6RE2Ti4O17 (RE = Nd, Sm, Gd, Dy-Yb): A Family of Rare-Earth-Based Layered Triangular Lattice Magnets

The exploration of new rare-earth (RE)-based triangular-lattice materials plays a significant role in motivating the discovery of exotic magnetic states. Herein, we report a family of hexagonal perovskite compounds Ba6RE2Ti4O17 (RE = Nd, Sm, Gd, Dy-Yb) with a space group of P63/mmc, where magnetic RE3+ ions are distributed on the parallel triangular-lattice layers within the ab-plane and stacked in an 'AA'-type fashion along the c-axis. The low-temperature magnetic characterizations indicate that all synthesized Ba6RE2Ti4O17 compounds exhibit dominant antiferromagnetic (AFM) interactions and the absence of magnetic order down to 1.8 K. The isothermal magnetization and electron spin resonance results reveal the distinct magnetic anisotropy for the compounds with different RE ions. Moreover, the as-grown Ba6Nd2Ti4O17 single crystals exhibit Ising-like magnetic anisotropy with a magnetic easy-axis perpendicular to the triangle-lattice plane and no long-range magnetic order down to 80 mK, as the quantum spin liquid candidate with dominant Ising-type interactions.

Robust Spin Liquidity in 2D Metal-Organic Framework Cu3 (HHTP)2 with S=1 /2 Kagome Lattice

On one hand electron or hole doping of quantum spin liquid (QSL) may unlock high-temperature superconductivity and on the other hand it can disrupt the spin liquidity, giving rise to a magnetically ordered ground state. Recently, a 2D MOF, Cu3 (HHTP)2 (HHTP - 2,3,6,7,10,11-hexahydroxytriphenylene), containing Cu(II) S=1 / 2 ${{ 1/2 }}$ frustrated spins in the Kagome lattice is emerging as a promising QSL candidate. Herein, we present an elegant in situ redox-chemistry strategy of anchoring Cu3 (HHTP)2 crystallites onto diamagnetic reduced graphene oxide (rGO) sheets, resulting in the formation of electron-doped Cu3 (HHTP)2 -rGO composite which exhibited a characteristic semiconducting behavior (5 K to 300 K) with high electrical conductivity of 70 S ⋅ m-1 and a carrier density of ~1.1×1018  cm-3 at 300 K. Remarkably, no magnetic transition in the Cu3 (HHTP)2 -rGO composite was observed down to 1.5 K endorsing the robust spin liquidity of the 2D MOF Cu3 (HHTP)2 . Specific heat capacity measurements led to the estimation of the residual entropy values of 28 % and 34 % of the theoretically expected value for the pristine Cu3 (HHTP)2 and Cu3 (HHTP)2 -rGO composite, establishing the presence of strong quantum fluctuations down to 1.5 K (two times smaller than the value of the exchange interaction J).

Continuous Spin Excitations in the Three-Dimensional Frustrated Magnet K_{2}Ni_{2}(SO_{4})_{3}

Continuous spin excitations are widely recognized as one of the hallmarks of novel spin states in quantum magnets, such as quantum spin liquids (QSLs). Here, we report the observation of such kind of excitations in K_{2}Ni_{2}(SO_{4})_{3}, which consists of two sets of intersected spin-1 (Ni^{2+}) trillium lattices. Our inelastic neutron scattering measurement on single crystals clearly shows a dominant excitation continuum, which exhibits a distinct temperature-dependent behavior from that of spin waves, and is rooted in strong quantum spin fluctuations. Further using the self-consistent-Gaussian-approximation method, we determine that the fourth- and fifth-nearest-neighbor exchange interactions are dominant. These two bonds together form a unique three-dimensional network of corner-sharing tetrahedra, which we name as a "hypertrillium" lattice. Our results provide direct evidence for the existence of QSL features in K_{2}Ni_{2}(SO_{4})_{3} and highlight the potential for the hypertrillium lattice to host frustrated quantum magnetism.

Fluctuating magnetic droplets immersed in a sea of quantum spin liquid

The search of quantum spin liquid (QSL), an exotic magnetic state with strongly fluctuating and highly entangled spins down to zero temperature, is a main theme in current condensed matter physics. However, there is no smoking gun evidence for deconfined spinons in any QSL candidate so far. The disorders and competing exchange interactions may prevent the formation of an ideal QSL state on frustrated spin lattices. Here we report comprehensive and systematic measurements of the magnetic susceptibility, ultralow-temperature specific heat, muon spin relaxation (μSR), nuclear magnetic resonance (NMR), and thermal conductivity for NaYbSe2 single crystals, in which Yb3+ ions with effective spin-1/2 form a perfect triangular lattice. All these complementary techniques find no evidence of long-range magnetic order down to their respective base temperatures. Instead, specific heat, μSR, and NMR measurements suggest the coexistence of quasi-static and dynamic spins in NaYbSe2. The scattering from these quasi-static spins may cause the absence of magnetic thermal conductivity. Thus, we propose a scenario of fluctuating ferrimagnetic droplets immersed in a sea of QSL. This may be quite common on the way pursuing an ideal QSL, and provides a brand new platform to study how a QSL state survives impurities and coexists with other magnetically ordered states.

Depletion-driven antiferromagnetic, paramagnetic, and ferromagnetic behavior in quasi-two-dimensional buckled colloidal solids

We investigate quasi-two-dimensional buckled colloidal monolayers on a triangular lattice with tunable depletion interactions. Without depletion attraction, the experimental system provides a colloidal analog of the well-known geometrically frustrated Ising antiferromagnet [Y. Han et al., Nature 456, 898-903 (2008)]. In this contribution, we show that the added depletion attraction can influence both the magnitude and sign of an Ising spin coupling constant. As a result, the nearest-neighbor Ising "spin" interactions can be made to vary from antiferromagnetic to para- and ferromagnetic. Using a simple theory, we compute an effective Ising nearest-neighbor coupling constant, and we show how competition between entropic effects permits for the modification of the coupling constant. We then experimentally demonstrate depletion-induced modification of the coupling constant, including its sign, and other behaviors. Depletion interactions are induced by rod-like surfactant micelles that change length with temperature and thus offer means for tuning the depletion attraction in situ. Buckled colloidal suspensions exhibit a crossover from an Ising antiferromagnetic to paramagnetic phase as a function of increasing depletion attraction. Additional dynamical experiments reveal structural arrest in various regimes of the coupling-constant, driven by different mechanisms. In total, this work introduces novel colloidal matter with "magnetic" features and complex dynamics rarely observed in traditional spin systems.

Emergent Glassy Behavior in a Kagome Rydberg Atom Array

We present large-scale quantum Monte Carlo simulation results on a realistic Hamiltonian of kagome-lattice Rydberg atom arrays. Although the system has no intrinsic disorder, intriguingly, our analyses of static and dynamic properties on large system sizes reveal emergent glassy behavior in a region of parameter space located between two valence bond solid phases. The extent of this glassy region is demarcated using the Edwards-Anderson order parameter, and its phase transitions to the two proximate valence bond solids-as well as the crossover towards a trivial paramagnetic phase-are identified. We demonstrate the intrinsically slow (imaginary) time dynamics deep inside the glassy phase and discuss experimental considerations for detecting such a quantum disordered phase with numerous nearly degenerate local minima. Our proposal paves a new route to the study of real-time glassy phenomena and highlights the potential for quantum simulation of a distinct phase of quantum matter beyond solids and liquids in current-generation Rydberg platforms.

Mapping AC susceptibility with quantum diamond microscope

We present a technique for determining the micro-scale AC susceptibility of magnetic materials. We use the magnetic field sensing properties of nitrogen-vacancy (NV-) centers in diamond to gather quantitative data about the magnetic state of the magnetic material under investigation. A quantum diamond microscope with an integrated lock-in camera is used to perform pixel-by-pixel, lock-in detection of NV- photo-luminescence for high-speed magnetic field imaging. In addition, a secondary sensor is employed to isolate the effect of the excitation field from fields arising from magnetic structures on NV- centers. We demonstrate our experimental technique by measuring the AC susceptibility of soft permalloy micro-magnets at excitation frequencies of up to 20 Hz with a spatial resolution of 1.2 µm and a field of view of 100 µm. Our work paves the way for microscopic measurement of AC susceptibilities of magnetic materials relevant to physical, biological, and material sciences.

Active learning-assisted neutron spectroscopy with log-Gaussian processes

Neutron scattering experiments at three-axes spectrometers (TAS) investigate magnetic and lattice excitations by measuring intensity distributions to understand the origins of materials properties. The high demand and limited availability of beam time for TAS experiments however raise the natural question whether we can improve their efficiency and make better use of the experimenter's time. In fact, there are a number of scientific problems that require searching for signals, which may be time consuming and inefficient if done manually due to measurements in uninformative regions. Here, we describe a probabilistic active learning approach that not only runs autonomously, i.e., without human interference, but can also directly provide locations for informative measurements in a mathematically sound and methodologically robust way by exploiting log-Gaussian processes. Ultimately, the resulting benefits can be demonstrated on a real TAS experiment and a benchmark including numerous different excitations.

Ground-State Spin Dynamics in d1 Kagome-Lattice Titanium Fluorides

Many quantum magnetic materials suffer from structural imperfections. The effects of structural disorder on bulk properties are difficult to assess systematically from a chemical perspective due to the complexities of chemical synthesis. The recently reported S = 1/2 kagome lattice antiferromagnet, (CH₃NH₃)₂NaTi₃F₁₂, 1-Ti, with highly symmetric kagome layers and disordered interlayer methylammonium cations, shows no magnetic ordering down to 0.1 K. To study the impact of structural disorder in the titanium fluoride kagome compounds, (CH₃NH₃)₂KTi₃F₁₂, 2-Ti, was prepared. It presents no detectable structural disorder and only a small degree of distortion of the kagome lattice. The methylammonium disorder model of 1-Ti and order in 2-Ti were confirmed by atomic-resolution transmission electron microscopy. The antiferromagnetic interactions and band structures of both compounds were calculated based on spin-polarized density functional theory and support the magnetic structure analysis. Three spin-glass-like (SGL) transitions were observed in 2-Ti at 0.5, 1.4, and 2.3 K, while a single SGL transition can be observed in 1-Ti at 0.8 K. The absolute values of the Curie-Weiss temperatures of both 1-Ti (-139.5(7) K) and 2-Ti (-83.5(7) K) are larger than the SGL transition temperatures, which is indicative of geometrically frustrated spin glass (GFSG) states. All the SGL transitions are quenched with an applied field >0.1 T, which indicates novel magnetic phases emerge under small applied magnetic fields. The well-defined structure and the lack of structural disorder in 2-Ti suggest that 2-Ti is an ideal model compound for studying GFSG states and the potential transitions between spin liquid and GFSG states.

Unravelling the signatures of effective spin1/2moments in CeVO4: magnetization and heat capacity study

The realization of an effective spin (J_eff) ½ state at low temperatures offers a platform to study the enthralling physics behind the disordered states in certain systems. Here, we report the signatures of magnetic ground state associated withJ_eff= ½ in CeVO₄. Our studies confirm the absence of any ordering or freezing down to 1.8 K. In the low temperature region, the Curie-Weiss fit of the inverse DC susceptibility indicate towards the presence of antiferromagnetic correlations among the Ce³⁺spins. The calculated value of effective moment (∼1.16μB) corresponds toJ= ½ withg_J∼ 1.20. Further, the field dependent magnetization curve at 2 K follows a behaviour corresponding toJ= ½ Brillouin function withg_J∼ 1.13. Magnetic field dependent heat capacity fits very well with two-level Schottky scheme. Our investigations suggest that CeVO₄can be a promising candidate to realiseJ_eff= ½ properties among 3D spin systems.

Non-magnetic ion site disorder effects on the quantum magnetism of a spin-1/2 equilateral triangular lattice antiferromagnet

With the motivation to study how non-magnetic ion site disorder affects the quantum magnetism of Ba₃CoSb₂O₉, a spin-1/2 equilateral triangular lattice antiferromagnet, we performed DC and AC susceptibility, specific heat, elastic and inelastic neutron scattering measurements on single crystalline samples of Ba_2.87Sr_0.13CoSb₂O₉with Sr doping on non-magnetic Ba²⁺ion sites. The results show that Ba_2.87Sr_0.13CoSb₂O₉exhibits (i) a two-step magnetic transition at 2.7 K and 3.3 K, respectively; (ii) a possible canted 120 degree spin structure at zero field with reduced ordered moment as 1.24μ_B/Co; (iii) a series of spin state transitions for bothH∥ab-plane andH∥c-axis. ForH∥ab-plane, the magnetization plateau feature related to the up-up-down phase is significantly suppressed; (iv) an inelastic neutron scattering spectrum with only one gapped mode at zero field, which splits to one gapless and one gapped mode at 9 T. All these features are distinctly different from those observed for the parent compound Ba₃CoSb₂O₉, which demonstrates that the non-magnetic ion site disorder (the Sr doping) plays a complex role on the magnetic properties beyond the conventionally expected randomization of the exchange interactions. We propose the additional effects including the enhancement of quantum spin fluctuations and introduction of a possible spatial anisotropy through the local structural distortions.

Fractionalized conductivity and emergent self-duality near topological phase transitions

The experimental discovery of the fractional Hall conductivity in two-dimensional electron gases revealed new types of quantum particles, called anyons, which are beyond bosons and fermions as they possess fractionalized exchange statistics. These anyons are usually studied deep inside an insulating topological phase. It is natural to ask whether such fractionalization can be detected more broadly, say near a phase transition from a conventional to a topological phase. To answer this question, we study a strongly correlated quantum phase transition between a topological state, called a [Formula: see text] quantum spin liquid, and a conventional superfluid using large-scale quantum Monte Carlo simulations. Our results show that the universal conductivity at the quantum critical point becomes a simple fraction of its value at the conventional insulator-to-superfluid transition. Moreover, a dynamically self-dual optical conductivity emerges at low temperatures above the transition point, indicating the presence of the elusive vison particles. Our study opens the door for the experimental detection of anyons in a broader regime, and has ramifications in the study of quantum materials, programmable quantum simulators, and ultra-cold atomic gases. In the latter case, we discuss the feasibility of measurements in optical lattices using current techniques.

Survival of itinerant excitations and quantum spin state transitions in YbMgGaO4 with chemical disorder

A recent focus of quantum spin liquid (QSL) studies is how disorder/randomness in a QSL candidate affects its true magnetic ground state. The ultimate question is whether the QSL survives disorder or the disorder leads to a “spin-liquid-like” state, such as the proposed random-singlet (RS) state. Since disorder is a standard feature of most QSL candidates, this question represents a major challenge for QSL candidates. YbMgGaO₄, a triangular lattice antiferromagnet with effective spin-1/2 Yb³⁺ions, is an ideal system to address this question, since it shows no long-range magnetic ordering with Mg/Ga site disorder. Despite the intensive study, it remains unresolved as to whether YbMgGaO₄ is a QSL or in the RS state. Here, through ultralow-temperature thermal conductivity and magnetic torque measurements, plus specific heat and DC magnetization data, we observed a residual κ₀/T term and series of quantum spin state transitions in the zero temperature limit for YbMgGaO₄. These observations strongly suggest that a QSL state with itinerant excitations and quantum spin fluctuations survives disorder in YbMgGaO₄.

It remains an open question as to whether the quantum spin liquid state survives material disorder, or is replaced by some spin-liquid like state. Here, Rao et al succeed in resolving a resolving a κ₀/T residual in the thermal conductivity of YbMgGaO₄ strongly suggesting the survival of the quantum spin liquid state.

Structure and Magnetic Properties of Melilite-Type Compounds RE2Be2GeO7 (RE = Pr, Nd, Gd-Yb) with Rare-Earth Ions on Shastry-Sutherland Lattice

Rare-earth (RE)-based frustrated magnets, such as typical systems of combining strong spin-orbit coupling (SOC), geometric frustration, and anisotropic exchange interaction, can give rise to diverse exotic magnetic ground states such as quantum spin liquid. The discovery of new RE-based frustrated materials is crucial for exploring the exotic magnetic phases. Herein, we report the synthesis, structure, and magnetic properties of a family of melilite-type RE₂Be₂GeO₇ (RE = Pr, Nd, and Gd-Yb) compounds crystallized in a tetragonal P4̅2₁m structure, where magnetic RE³⁺ ions lay out on the Shastry-Sutherland lattice (SSL) within the ab plane and are well separated by nonmagnetic [GeBe₂O₇]^6- polyhedrons along the c-axis. Temperature (T)-dependent susceptibilities χ(T) and isothermal magnetization M(H) measurements reveal that most RE₂Be₂GeO₇ compounds except RE = Tb show no magnetic ordering down to 2 K despite the dominant antiferromagnetic (AFM) interactions, where Tb₂Be₂GeO₇ undergoes AFM transition with Néel temperature T_N ∼ 2.5 K and field-induced spin flop behaviors (T < T_N). In addition, the calculated magnetic entropy change ΔS_m from the isothermal M(H) curves reveals viable magnetocaloric effect for RE₂Be₂GeO₇ (RE = Gd and Dy) in liquid helium temperature regimes; Gd₂Be₂GeO₇ shows the maximum ΔS_m up to 54.8 J K^-1 kg^-1 at ΔH = 7 T and Dy₂Be₂GeO₇ has the largest value ΔS_m = 16.1 J K^-1 kg^-1 at ΔH = 2 T in this family. More excitingly, the rich diversity of RE ions in this family enables an archetype for exploring exotic quantum magnetic phenomena with large variability of spin located on the SSL lattice.

Extreme Suppression of Antiferromagnetic Order and Critical Scaling in a Two-Dimensional Random Quantum Magnet

Sr_{2}CuTeO_{6} is a square-lattice Néel antiferromagnet with superexchange between first-neighbor S=1/2 Cu spins mediated by plaquette centered Te ions. Substituting Te by W, the affected impurity plaquettes have predominantly second-neighbor interactions, thus causing local magnetic frustration. Here we report a study of Sr_{2}CuTe_{1-x}W_{x}O_{6} using neutron diffraction and μSR techniques, showing that the Néel order vanishes already at x=0.025±0.005. We explain this extreme order suppression using a two-dimensional Heisenberg spin model, demonstrating that a W-type impurity induces a deformation of the order parameter that decays with distance as 1/r^{2} at temperature T=0. The associated logarithmic singularity leads to loss of order for any x>0. Order for small x>0 and T>0 is induced by weak interplane couplings. In the nonmagnetic phase of Sr_{2}CuTe_{1-x}W_{x}O_{6}, the μSR relaxation rate exhibits quantum critical scaling with a large dynamic exponent, z≈3, consistent with a random-singlet state.

Dynamical ground state in the XY pyrochlore Yb2GaSbO7

The magnetic ground state of the pyrochlore Yb2GaSbO7 has remained an enigma for nearly a decade. The persistent spin fluctuations observed by muon spin relaxation measurements at low temperatures have not been adequately explained for this material using existing theories for quantum magnetism. Here we report on the synthesis and characterisation of Yb2GaSbO7 to elucidate the central physics at play. Through DC and AC magnetic susceptibility, heat capacity, and neutron scattering experiments, we observe evidence for a dynamical ground state that makes Yb2GaSbO7 a promising candidate for disorder-induced spin-liquid or spin-singlet behaviour. This state is quite fragile, being tuned to a splayed ferromagnet in a modest magnetic field μ 0 H c ∼ 1.5 T .

Synthesis of a d1-titanium fluoride kagome lattice antiferromagnet

The kagome lattice, composed of a planar array of corner-sharing triangles, is one of the most geometrically frustrated lattices. The realization of a spin S = 1/2 kagome lattice antiferromagnet is of particular interest because it may host an exotic form of matter, a quantum spin liquid state, which shows long-range entanglement and no magnetic ordering down to 0 K. A few S = 1/2 kagome lattice antiferromagnets exist, typically based on Cu²⁺, d⁹ compounds, though they feature structural imperfections. Herein, we present the synthesis of (CH₃NH₃)₂NaTi₃F₁₂, which comprises an S = 1/2 kagome layer that exhibits only one crystallographically distinct Ti³⁺, d¹ site, and one type of bridging fluoride. A static positional disorder is proposed for the interlayer CH₃NH₃⁺. No structural phase transitions were observed from 1.8 K to 523 K. Despite its spin-freezing behaviour, other features-including its negative Curie-Weiss temperature and a lack of long-range ordering-imply that this compound is a highly frustrated magnet with unusual magnetic phase behaviours.

Spin liquids in geometrically perfect triangular antiferromagnets

The cradle of quantum spin liquids, triangular antiferromagnets show strong proclivity to magnetic order and require deliberate tuning to stabilize a spin-liquid state. In this brief review, we juxtapose recent theoretical developments that trace the parameter regime of the spin-liquid phase, with experimental results for Co-based and Yb-based triangular antiferromagnets. Unconventional spin dynamics arising from both ordered and disordered ground states are discussed, and the notion of a geometrically perfect triangular system is scrutinized to demonstrate non-trivial imperfections that may assist magnetic frustration in stabilizing dynamic spin states with peculiar excitations.

Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4

Frustrated magnets hold the promise of material realizations of exotic phases of quantum matter, but direct comparisons of unbiased model calculations with experimental measurements remain very challenging. Here we design and implement a protocol of employing many-body computation methodologies for accurate model calculations—of both equilibrium and dynamical properties—for a frustrated rare-earth magnet TmMgGaO₄ (TMGO), which explains the corresponding experimental findings. Our results confirm TMGO is an ideal realization of triangular-lattice Ising model with an intrinsic transverse field. The magnetic order of TMGO is predicted to melt through two successive Kosterlitz–Thouless (KT) phase transitions, with a floating KT phase in between. The dynamical spectra calculated suggest remnant images of a vanishing magnetic stripe order that represent vortex–antivortex pairs, resembling rotons in a superfluid helium film. TMGO therefore constitutes a rare quantum magnet for realizing KT physics, and we further propose experimental detection of its intriguing properties.

TmMgGaO₄ is one of a number of recently-synthesized quantum magnets that are proposed to realize important theoretical models. Here the authors demonstrate the agreement between detailed experimental measurements and state-of-the-art predictions based on the 2D transverse-field triangular lattice Ising model.

Weak-field induced nonmagnetic state in a Co-based honeycomb

Layered honeycomb magnets are of interest as potential realizations of the Kitaev quantum spin liquid (KQSL), a quantum state with long-range spin entanglement and an exactly solvable Hamiltonian. Conventional magnetically ordered states are present for all currently known candidate materials, however, because non-Kitaev terms in the Hamiltonians obscure the Kitaev physics. Current experimental studies of the KQSL are focused on 4d or 5d transition metal-based honeycombs, in which strong spin-orbit coupling can be expected, yielding Kitaev interaction that dominates in an applied magnetic field. In contrast, for 3d-based layered honeycomb magnets, spin-orbit coupling is weak, and thus, Kitaev physics should be substantially less accessible. Here, we report our studies on BaCo₂(AsO₄)₂, for which we find that the magnetic order associated with the non-Kitaev interactions can be fully suppressed by a relatively low magnetic field, yielding a nonmagnetic material and implying the presence of strong magnetic frustration and weak non-Kitaev interactions.

Nature of the randomness-induced quantum spin liquids in two dimensions

The nature of the randomness-induced quantum spin liquid state, the random-singlet state, is investigated in two dimensions (2D) by means of the exact-diagonalization and the Hams-de Raedt methods for several frustrated lattices, e.g. the triangular, the kagome and the J ₁-J ₂ square lattices. Properties of the ground state, the low-energy excitations and the finite-temperature thermodynamic quantities are investigated. The ground state and the low-lying excited states consist of nearly isolated singlet-dimers, clusters of resonating singlet-dimers, and orphan spins. Low-energy excitations are either singlet-to-triplet excitations, diffusion of orphan spins accompanied by the recombination of nearby singlet-dimers, creation or destruction of resonating singlet-dimers clusters. The latter two excitations give enhanced dynamical 'liquid-like' features to the 2D random-singlet state. Comparison is made with the random-singlet state in a 1D chain without frustration, the similarity and the difference between in 1D and in 2D being highlighted. Frustration in a wide sense, not only the geometrical one but also including the one arising from the competition between distinct types of interactions, play an essential role in stabilizing this frustrated random singlet state. Recent experimental situations on both organic and inorganic materials are reviewed and discussed.

Absence of Magnetic Thermal Conductivity in the Quantum Spin Liquid Candidate EtMe_{3}Sb[Pd(dmit)_{2}]_{2}

We present the ultralow-temperature specific heat and thermal conductivity measurements on single crystals of triangular-lattice compound EtMe_{3}Sb[Pd(dmit)_{2}]_{2}, which has long been considered as a gapless quantum spin liquid candidate. In specific heat measurements, a finite linear term is observed, consistent with the previous work [S. Yamashita et al., Nat. Commun. 2, 275 (2011)NCAOBW2041-172310.1038/ncomms1274]. However, we do not observe a finite residual linear term in the thermal conductivity measurements, and the thermal conductivity does not change in a magnetic field of 6 T. These results are in sharp contrast to previous thermal conductivity measurements on EtMe_{3}Sb[Pd(dmit)_{2}]_{2} [M. Yamashita et al., Science 328, 1246 (2010)SCIEAS0036-807510.1126/science.1188200], in which a huge residual linear term was observed and attributed to highly mobile gapless excitations, likely the spinons of a quantum spin liquid. In this context, the true ground state of EtMe_{3}Sb[Pd(dmit)_{2}]_{2} has to be reconsidered.

Intertwined dipolar and multipolar order in the triangular-lattice magnet TmMgGaO4

A phase transition is often accompanied by the appearance of an order parameter and symmetry breaking. Certain magnetic materials exhibit exotic hidden-order phases, in which the order parameters are not directly accessible to conventional magnetic measurements. Thus, experimental identification and theoretical understanding of a hidden order are difficult. Here we combine neutron scattering and thermodynamic probes to study the newly discovered rare-earth triangular-lattice magnet TmMgGaO₄. Clear magnetic Bragg peaks at K points are observed in the elastic neutron diffraction measurements. More interesting, however, is the observation of sharp and highly dispersive spin excitations that cannot be explained by a magnetic dipolar order, but instead is the direct consequence of the underlying multipolar order that is "hidden" in the neutron diffraction experiments. We demonstrate that the observed unusual spin correlations and thermodynamics can be accurately described by a transverse field Ising model on the triangular lattice with an intertwined dipolar and ferro-multipolar order.

A poor man's coherent Ising machine based on opto-electronic feedback systems for solving optimization problems

Coherent Ising machines (CIMs) constitute a promising approach to solve computationally hard optimization problems by mapping them to ground state searches of the Ising model and implementing them with optical artificial spin-networks. However, while CIMs promise speed-ups over conventional digital computers, they are still challenging to build and operate. Here, we propose and test a concept for a fully programmable CIM, which is based on opto-electronic oscillators subjected to self-feedback. Contrary to current CIM designs, the artificial spins are generated in a feedback induced bifurcation and encoded in the intensity of coherent states. This removes the necessity for nonlinear optical processes or large external cavities and offers significant advantages regarding stability, size and cost. We demonstrate a compact setup for solving MAXCUT optimization problems on regular and frustrated graphs with 100 spins and can report similar or better performance compared to CIMs based on degenerate optical parametric oscillators.

Strong quantum fluctuations in a quantum spin liquid candidate with a Co-based triangular lattice

Currently under active study in condensed matter physics, both theoretically and experimentally, are quantum spin liquid (QSL) states, in which no long-range magnetic ordering appears at low temperatures due to strong quantum fluctuations of the magnetic moments. The existing QSL candidates all have their intrinsic disadvantages, however, and solid evidence for quantum fluctuations is scarce. Here, we report a previously unreported compound, [Formula: see text], a geometrically frustrated system with effective spin-1/2 local moments for Co²⁺ ions on an isotropic 2-dimensional (2D) triangular lattice. Magnetic susceptibility and neutron scattering experiments show no magnetic ordering down to 0.05 K. Thermodynamic measurements show that there is a tremendous amount of magnetic entropy present below 1 K in 0-applied magnetic field. The presence of localized low-energy spin fluctuations is revealed by inelastic neutron measurements. At low applied fields, these spin excitations are confined to low energy and contribute to the anomalously large specific heat. In larger applied fields, the system reverts to normal behavior as evident by both neutron and thermodynamic results. Our experimental characterization thus reveals that this material is an excellent candidate for the experimental realization of a QSL state.

Spin-liquid-like state in pure and Mn-doped TbInO3 with a nearly triangular lattice

Inelastic neutron scattering studies in single crystals of TbInO3 and TbIn0.95Mn0.05O3 with nearly triangular antiferromagnetic lattice are reported. At low energies, a broad and apparently gapless continuum of magnetic excitations, located at the triangular lattice (TL) Brillouin zone boundary, is observed. The data are well described by the uncorrelated nearest-neighbor valence bonds model. At higher energies, a broad excitation branch dispersing from the TL zone boundary is observed. No signs of static magnetic order are found down to the temperatures two orders of magnitude smaller than the effective interaction energy. The fluctuating magnetic moment exceeds two-thirds of the Tb3+ free-ion value and is confined to the TL plane. These observations are consistent with a TL-based spin liquid state in TbInO3.

Rearrangement of Uncorrelated Valence Bonds Evidenced by Low-Energy Spin Excitations in YbMgGaO_{4}

dc-magnetization data measured down to 40 mK speak against conventional freezing and reinstate YbMgGaO_{4} as a triangular spin-liquid candidate. Magnetic susceptibility measured parallel and perpendicular to the c axis reaches constant values below 0.1 and 0.2 K, respectively, thus indicating the presence of gapless low-energy spin excitations. We elucidate their nature in the triple-axis inelastic neutron scattering experiment that pinpoints the low-energy (E≤J_{0}∼0.2  meV) part of the excitation continuum present at low temperatures (T<J_{0}/k_{B}), but completely disappearing upon warming the system above T≫J_{0}/k_{B}. In contrast to the high-energy part at E>J_{0} that is rooted in the breaking of nearest-neighbor valence bonds and persists to temperatures well above J_{0}/k_{B}, the low-energy one originates from the rearrangement of the valence bonds and thus from the propagation of unpaired spins. We further extend this picture to herbertsmithite, the spin-liquid candidate on the kagome lattice, and argue that such a hierarchy of magnetic excitations may be a universal feature of quantum spin liquids.

Scaling and data collapse from local moments in frustrated disordered quantum spin systems

Recently measurements on various spin–1/2 quantum magnets such as H₃LiIr₂O₆, LiZn₂Mo₃O₈, ZnCu₃(OH)₆Cl₂ and 1T-TaS₂—all described by magnetic frustration and quenched disorder but with no other common relation—nevertheless showed apparently universal scaling features at low temperature. In particular the heat capacity C[H, T] in temperature T and magnetic field H exhibits T/H data collapse reminiscent of scaling near a critical point. Here we propose a theory for this scaling collapse based on an emergent random-singlet regime extended to include spin-orbit coupling and antisymmetric Dzyaloshinskii-Moriya (DM) interactions. We derive the scaling C[H, T]/T ~ H^−γF_q[T/H] with F_q[x] = x^q at small x, with q ∈ {0, 1, 2} an integer exponent whose value depends on spatial symmetries. The agreement with experiments indicates that a fraction of spins form random valence bonds and that these are surrounded by a quantum paramagnetic phase. We also discuss distinct scaling for magnetization with a q-dependent subdominant term enforced by Maxwell’s relations.

There are many proposals for new forms of quantum matter in frustrated magnets but in practice disorder prevents the realisation of theoretically-tractable idealised models. Kimchi et al. show that recently observed scaling behavior common to several disordered quantum magnets can be understood as the emergence of a universal random-singlet regime.

Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4

Quantum spin liquids (QSLs) are exotic states of matter characterized by emergent gauge structures and fractionalized elementary excitations. The recently discovered triangular lattice antiferromagnet YbMgGaO₄ is a promising QSL candidate, and the nature of its ground state is still under debate. Here we use neutron scattering to study the spin excitations in YbMgGaO₄ under various magnetic fields. Our data reveal a dispersive spin excitation continuum with clear upper and lower excitation edges under a weak magnetic field (H = 2.5 T). Moreover, a spectral crossing emerges at the Γ point at the Zeeman-split energy. The corresponding redistribution of the spectral weight and its field-dependent evolution are consistent with the theoretical prediction based on the inter-band and intra-band spinon particle-hole excitations associated with the Zeeman-split spinon bands, implying the presence of fractionalized excitations and spinon Fermi surfaces in the partially magnetized QSL state in YbMgGaO₄.

Recent experiments have indicated that YbMgGaO₄ may be a quantum spin liquid with spinon Fermi surfaces but additional evidence is needed to support this interpretation. Shen et al. show weak magnetic fields cause changes in the excitation continuum that are consistent with spin liquid predictions.

Dynamical Signature of Symmetry Fractionalization in Frustrated Magnets

The nontriviality of quantum spin liquids (QSLs) typically manifests in the nonlocal observables that signify their existence; however, this fact actually casts a shadow on detecting QSLs with experimentally accessible probes. Here, we provide a solution by unbiasedly demonstrating a dynamical signature of anyonic excitations and symmetry fractionalization in QSLs. Employing large-scale quantum Monte Carlo simulation and stochastic analytic continuation, we investigate the extended XXZ model on the kagome lattice, and find out that, across the phase transitions from Z_{2} QSLs to different symmetry breaking phases, spin spectral functions can reveal the presence and condensation of emergent anyonic spinon and vison excitations, in particular, the translational symmetry fractionalization of the latter, which can be served as the dynamical signature of the seemingly ephemeral QSLs in spectroscopic techniques such as inelastic neutron or resonance (inelastic) x-ray scatterings.

Topography of Spin Liquids on a Triangular Lattice

Spin systems with frustrated anisotropic interactions are of significant interest due to possible exotic ground states. We have explored their phase diagram on a nearest-neighbor triangular lattice using the density-matrix renormalization group and mapped out the topography of the region that can harbor a spin liquid. We find that this spin-liquid phase is continuously connected to a previously discovered spin-liquid phase of the isotropic J_{1}-J_{2} model. The two limits show nearly identical spin correlations, making the case that their respective spin liquids are isomorphic to each other.