Spin liquids in frustrated magnets

Emergent quantum state unveiled by ultrafast collective dynamics in 1T-TaS2

Charge density wave (CDW) material 1T-TaS2 was proposed as a quantum spin liquid candidate, on which a cluster Mott insulator comes into being below the transition temperature. We report an experimental ultrafast generation and detection of the coherent amplitude mode (AM) of its CDW state. A salient feature emerges: The coherent CDW mode AM exhibits an unusual T3.56 temperature dependence below 65 K, in addition to the T2 temperature dependence observed in the 65 to 200 K range. This behavior suggests the enhancement of in-gap electronic excitations below 65 K and the emergence of a new phase of matter. Consequently, the intriguing quantum state leads to a crossover. Our investigation provides insights into understanding the interplay among various degrees of freedom in quantum materials.

Spin-Frustrated Metal-Organic Frameworks

Metal-organic frameworks (MOFs) are a fascinating class of structured materials with diverse functionality originating from their distinctive physicochemical properties. This review focuses on the specific chemical design of geometrically frustrated MOFs along with the origin of the intriguing magnetic properties. We have discussed the arrangement of spin centres (metal and ligand) which are responsible for the unusual magnetic phenomena in MOFs. Both two-dimensional (2D) and three-dimensional (3D) MOFs with frustrated magnetism, their synthetic routes, and evaluation of magnetic properties are highlighted. Such spin-frustrated MOFs may find applications in the field of memory devices, transistors, sensors, and the development of unconventional superconductors.

Spectroscopic Evidence for Possible Quantum Spin Liquid Behavior in a Two-Dimensional Mott Insulator

Mott insulators with localized magnetic moments will exhibit a quantum spin liquid state when the quantum fluctuations are strong enough to suppress the ordering of the spins. Such an entangled state will give rise to collective excitations, in which spin and charge information are carried separately. Our angle-resolved photoemission spectroscopy measurements on single-layer 1T-TaS_{2} show a flat band around the zone center and a gap opening of about 200 meV in the low temperature, indicating 2D Mott insulating nature in the system. This flat band is dispersionless in momentum space but shows anomalously broad width around the zone center and the spectral weight decays rapidly as momentum increases. The observation is described as a spectral continuum from electron fractionalization, corroborated by a low energy effective model. The intensity of the flat band is reduced by surface doping with magnetic adatoms and the gap is closing, a result from the interaction between spin impurities coupled with spinons and the chargons, which gives rise to a charge redistribution. Doping with nonmagnetic impurities behaves differently as the chemical potential shift dominates. These findings provide insight into the quantum spin liquid states of strongly correlated electrons on 2D triangular lattices.

Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids

Classical spin liquids (CSLs) are intriguing states of matter that do not exhibit long-range magnetic order and are characterized by an extensive ground-state degeneracy. Adding quantum fluctuations, which induce dynamics between these different classical ground states, can give rise to quantum spin liquids (QSLs). QSLs are highly entangled quantum phases of matter characterized by fascinating emergent properties, such as fractionalized excitations and topological order. One such exotic quantum liquid is the [Formula: see text] QSL, which can be regarded as a resonating valence bond (RVB) state formed from superpositions of dimer coverings of an underlying lattice. In this work, we unveil a hidden large-scale structural property of archetypal CSLs and QSLs known as hyperuniformity, i.e., normalized infinite-wavelength density fluctuations are completely suppressed in these systems. In particular, we first demonstrate that classical ensembles of close-packed dimers and their corresponding quantum RVB states are perfectly hyperuniform in general. Subsequently, we focus on a ruby-lattice spin liquid that was recently realized in a Rydberg-atom quantum simulator, and show that the QSL remains effectively hyperuniform even in the presence of a finite density of spinon and vison excitations, as long as the dimer constraint is still largely preserved. Moreover, we demonstrate that metrics based on the framework of hyperuniformity can be used to distinguish the QSL from other proximate quantum phases. These metrics can help identify potential QSL candidates, which can then be further analyzed using more advanced, computationally intensive quantum numerics to confirm their status as true QSLs.

Capturing Strong Correlation in Molecules with Phaseless Auxiliary-Field Quantum Monte Carlo Using Generalized Hartree-Fock Trial Wave Functions

Generalized Hartree-Fock (GHF) is a long-established electronic structure method that can lower the energy (compared to spin-restricted variants) by breaking physical wave function symmetries, namely S ^ 2 and S ^ z . After an exposition of GHF theory, we assess the use of GHF trial wave functions in phaseless auxiliary field quantum Monte Carlo (ph-AFQMC-G) calculations of strongly correlated molecular systems including symmetrically stretched hydrogen rings, carbon dioxide, and dioxygen. Imaginary time propagation is able to restore S ^ 2 symmetry and yields energies of comparable or better accuracy than CCSD(T) with unrestricted HF and GHF references, and consistently smooth dissociation curves─a remarkable result given the relative scalability of ph-AFQMC-G to larger system sizes. The present exploration of model strongly correlated systems marks a promising starting point for future studies of more chemically relevant molecules, and demonstrates that ph-AFQMC-G provides a highly accurate (and, in contrast to active-space-based trials, relatively black box and always size-consistent) description of challenging systems exhibiting, e.g., antiferromagnetic coupling and/or geometric spin frustration.

Observation of Robust Compressed CuO6 Octahedra and Exotic Spin Structure in CaCuFe2O5

CuO6 octahedra usually show elongated distortion, leading to active dx2-y2 orbitals and planar exchange interactions, while compressed CuO6 octahedra with active d3z2-r2 orbitals and unidirectional exchange interactions are exceptionally rare. Here, we design and synthesize a new frustrated antiferromagnet CaCuFe2O5 through a high-pressure and high-temperature approach, in which robust compressed CuO6 octahedra are realized, separating the Fe2O5 sheets that comprise zigzag spin ladders. Magnetic susceptibility and specific heat measurements exhibit a long-range antiferromagnetic order below the Néel temperature of 165 K, which is further confirmed by neutron diffraction. Detailed magnetic refinement reveals a C-type spin structure, with its spin arrangement and orientation distinct from that of the isostructural CaFe3O5. By constructing a Heisenberg model, we find that this is due to the exchange redistribution between the CuO6 octahedra and Fe2O5 sheets, during which some of the exchange interactions are selectively annihilated due to the specific orientation of the Cu d3z2-r2 orbitals in the compressed CuO6 octahedra. Our results provide a unique example of robust compressed CuO6 octahedra and show that it can selectively annihilate some of the exchange interactions and completely modify the spin structure and magnetic frustration accordingly.

On-Surface Synthesis and Characterization of Radical Spins in Kagome Graphene

Flat bands in Kagome graphene might host strong electron correlations and frustrated magnetism upon electronic doping. However, the porous nature of Kagome graphene opens a semiconducting gap due to quantum confinement, preventing its fine-tuning by electrostatic gates. Here we induce zero-energy states into a semiconducting Kagome graphene by inserting π-radicals at selected locations. We utilize the on-surface reaction of tribromotrioxoazatriangulene molecules to synthesize carbonyl-functionalized Kagome graphene on Au(111), thereafter modified in situ by exposure to atomic hydrogen. Atomic force microscopy and tunneling spectroscopy unveil the stepwise chemical transformation of the carbonyl groups into radicals, which creates local magnetic defects of spin state S = 1/2 and zero-energy states as confirmed by density functional theory. The ability to imprint local magnetic moments opens up prospects to study the interplay between topology, magnetism, and electron correlation in Kagome graphene.

Triply Ordered 6H Halide Perovskites: A Family of Triangular Lattice Antiferromagnets

Three new hexagonal perovskites with Cs3M+M2+RhCl9 (M+ = Na+, Ag+; M2+ = Mn2+, Fe2+) stoichiometry have been synthesized from solution precipitation reactions. These air-stable compounds crystallize as triply cation-ordered variants of the 6H perovskite structure. This structure contains octahedra that share a common face to form M2+RhCl94- dimers that are arranged on a two-dimensional triangular network. M+ cations reside in octahedral holes located between dimer layers and connect M2+RhCl94- dimers through corner-sharing linkages. The cation sites in the corner-sharing layers are fully occupied by Na+/Ag+, except for Cs3AgMnRhCl9, where a small amount of Ag+/Mn2+ antisite disorder is observed. The M2+RhCl94- dimers adopt an ordered configuration that lowers the symmetry from P63/mmc to P63mc. Optical absorption in the near ultraviolet (UV) and visible regions is dominated by Rh d-to-d transitions and metal-to-metal charge transfer transitions. Variable temperature magnetic susceptibility measurements show no sign of long-range magnetic order down to 2 K. Curie-Weiss fits reveal relatively weak antiferromagnetic interactions between M2+ ions, with Weiss constants that range from -2.3 to -5.4 K. The strength of the antiferromagnetic interactions between M2+ ions increases as the covalency of the M2+-Cl bond increases. The ordering of three different cations in the 6H perovskite structure diminishes magnetic coupling between layers, leading to a new family of two-dimensional triangular lattice antiferromagnets.

Review of honeycomb-based Kitaev materials with zigzag magnetic ordering

The search for a Kitaev quantum spin liquid in crystalline magnetic materials has fueled intense interest in the two-dimensional honeycomb systems. Many promising candidate Kitaev systems are characterized by a long-range-ordered magnetic structure with an antiferromagnetic zigzag-type order, where the static moments form alternating ferromagnetic chains. Recent experiments on high-quality single crystals uncovered the existence of intriguing multi-k magnetic structures, which evolved from zigzag structures. Those discoveries have sparked new theoretical developments and amplified interest in these materials. We present an overview of the honeycomb materials known to display this type of magnetic structure and provide detailed crystallographic information for the possible single- and multi-k variants.

Polymorphism and magnetism in a Kitaev honeycomb cobaltate KCoAsO4

We report the synthesis, crystal structure, and magnetic properties of a new Kitaev honeycomb cobaltate, KCoAsO4, which crystallizes in two distinct forms: P2/c and R[Formula: see text] space groups. Magnetic measurements reveal ordering temperatures of ~ 14 K for the P2/c structure and ~ 10.5 K for the R[Formula: see text] structure. The P2/c-type KCoAsO4 sample exhibits a complex temperature-field phase diagram, including a field-induced phase, while the R[Formula: see text]-type KCoAsO4 shows a simpler phase diagram with a single magnetically ordered phase. The observed differences in magnetic properties are attributed to subtle structural variations, strongly suggesting that local structural changes play a crucial role in determining the magnetism of cobaltate-based Kitaev materials.

Spin Glass Transition of Magnetic Ionic Liquids Induced by Self-Assembly

Spin glass (SG), in which the spins are glassy, has attracted broad attention for theoretical study and prospective application. SG states are generally related to disordered or frustrated spin systems, which are usually observed in inorganic magnets. Herein, supramolecular magnetic ionic liquid (TMTBDI[FeCl4]) self-assemblies are prepared by solution self-assembly via hydrophobic and π-π stacking interactions. The supramolecular self-assemblies are in short-range lattice ordering and long-range disordering structures, as the lattice self-assemblies with the tens of nanometer scale are distributed randomly to form a long-range disorder. The shortest Fe(III)-Fe(III) distance is calculated to be ca. 2.4 Å from transmission electron microscopy (TEM) results. The magnetic properties of the supramolecular self-assemblies are studied via direct current (DC) and alternating current (AC) magnetic susceptibility characterizations. It is noted that TMTBDI[FeCl4] is paramagnetic before self-assembly. However, the supramolecular self-assemblies exhibit a strong ferromagnetic interaction due to the short Fe(III)-Fe(III) distance. The AC results show that the supramolecular self-assemblies are in the SG state at low temperatures as the imaginary part of the susceptibility moves to high temperatures with frequency. The self-assembly-induced spin glass transition of TMTBDI[FeCl4] is due to the long-range disordering and short-range ordering structures of the self-assemblies, which induces a frustrated spin system.

Frustrated Magnetism and Spin Anisotropy in a Buckled Square Net YbTaO4

The interplay between quantum effects from magnetic frustration, low-dimensionality, spin-orbit coupling, and crystal electric field in rare-earth materials leads to nontrivial ground states with unusual magnetic excitations. Here, we investigate YbTaO4, which hosts a buckled square net of Yb3+ ions with Jeff = 1/2 moments. The observed Curie-Weiss temperature is about -1 K, implying an antiferromagnetic coupling between the Yb3+ moments. The heat capacity shows no long-range ordering down to 0.10 K, instead shows a field-dependent broad maximum indicative of short-range correlations. The magnetic entropy recovered and magnetization measurements confirm a spin-orbit driven Jeff = 1/2 Kramers doublet ground state. Point charge calculations show that the Yb3+ ions do not host the quintessential XY spin anisotropy observed in typical Yb-based quantum magnets like NaYbO2, YbMgGaO4, and pyrochlores but rather exhibit an almond-shaped anisotropy with an easy axis. Thus, YbTaO4 can serve as a model system to study frustrated magnetism in a square lattice using the J1-J2 Heisenberg model. This work also emphasizes the significance of small perturbations to the local crystal electric field that can alter the spin anisotropy and change the collective behavior of the system.

Reviving the Lieb-Schultz-Mattis theorem in open quantum systems

In closed systems, the celebrated Lieb-Schultz-Mattis (LSM) theorem states that a one-dimensional locally interacting half-integer spin chain with translation and spin rotation symmetries cannot have a non-degenerate gapped ground state. However, the applicability of this theorem is diminished when the system interacts with a bath and loses its energy conservation. In this letter, we propose that the LSM theorem can be revived in the entanglement Hamiltonian when the coupling to the bath renders the system short-range correlated. Specifically, we argue that the entanglement spectrum cannot have a non-degenerate minimum, isolated by a gap from other states. We further support the results with numerical examples where a spin-[Formula: see text] system is coupled to another spin-[Formula: see text] chain serving as the bath. Compared with the original LSM theorem that primarily addresses UV-IR correspondence, our findings reveal that the UV data and topological constraints also play a pivotal role in shaping the entanglement in open quantum many-body systems.

ASb3Mn9O19 (A = K or Rb): New Mn-Based 2D Magnetoplumbites with Geometric and Magnetic Frustration

Magnetoplumbites are one of the most broadly studied families of hexagonal ferrites, typically with high magnetic ordering temperatures, making them excellent candidates for permanent magnets. However, magnetic frustration is rarely observed in magnetoplumbites. Herein, the discovery, synthesis, and characterization of the first Mn-based magnetoplumbite, as well as the first magnetoplumbite involving pnictogens (Sb), ASb3Mn9O19 (A = K or Rb) are reported. The Mn3+ (S = 2) cations, further confirmed by DC magnetic susceptibility and X-ray photoelectron spectroscopy, construct three geometrically frustrated sublattices, including Kagome, triangular, and puckered honeycomb lattices. Magnetic properties measurements revealed strong antiferromagnetic spin-spin coupling as well as multiple low-temperature magnetic features. Heat capacity data does not show any prominent λ-anomaly, suggesting minimal associated magnetic entropy. Moreover, neutron powder diffraction (NPD) implied the absence of long-range magnetic ordering in KSb3Mn9O19 down to 3 K. However, several magnetic peaks are observed in RbSb3Mn9O19 at 3 K, corresponding to an incommensurate magnetic structure. Interestingly, strong diffuse scattering is seen in the NPD patterns of both compounds at low angles and is analyzed by reverse Monte Carlo refinements, indicating short-range spin ordering related to frustrated magnetism as well as 2D magnetic correlations in ASb3Mn9O19 (A = K or Rb).

Evidence of Dirac Quantum Spin Liquid in YbZn_{2}GaO_{5}

The emergence of a quantum spin liquid (QSL), a state of matter that can result when electron spins are highly correlated but do not become ordered, has been the subject of a considerable body of research in condensed matter physics [1,2]. Spin liquid states have been proposed as hosts for high-temperature superconductivity [3] and can host topological properties with potential applications in quantum information science [4]. The excitations of most quantum spin liquids are not conventional spin waves but rather quasiparticles known as spinons, whose existence is well established experimentally only in one-dimensional systems; the unambiguous experimental realization of QSL behavior in higher dimensions remains challenging. Here, we investigate the novel compound YbZn_{2}GaO_{5}, which hosts an ideal triangular lattice of effective spin-1/2 moments with no detectable inherent chemical disorder. Thermodynamic and inelastic neutron scattering measurements performed on high-quality single crystal samples of YbZn_{2}GaO_{5} exclude the possibility of long-range magnetic ordering down to 0.06 K, demonstrate a quadratic power law for the specific heat and reveal a continuum of magnetic excitations in parts of the Brillouin zone. Both low-temperature thermodynamics and inelastic neutron scattering spectra suggest that YbZn_{2}GaO_{5} is a U(1) Dirac QSL with spinon excitations concentrated at certain points in the Brillouin zone. We advanced these results by performing additional specific heat measurements under finite fields, further confirming the theoretical expectations for a Dirac QSL on the triangular lattice of YbZn_{2}GaO_{5}.

Phase Switch Driven by the Hidden Half-Ice, Half-Fire State in a Ferrimagnet

The notion of "half fire, half ice" was recently introduced to describe an exotic macroscopic ground-state degeneracy emerging in a ferrimagnet under the critical magnetic field, in which the "hot" spins are fully disordered on the sublattice with smaller magnetic moments and the "cold" spins are fully ordered on the sublattice with larger magnetic moments. Here, we further point out that this state has a twin named "half ice, half fire" in which the hot and cold spins switch positions. The new state is an excited state-thus hidden in the ground-state phase diagram-and is robust with respect to the interactions that destroy the half-fire, half-ice state. We demonstrate with exact results how this hidden state can drive phase switching at desirable finite temperature, even for the one-dimensional Ising model where phase transition at finite temperature is forbidden. We suggest that our findings may open a new door to the understanding and controlling of phase competition and transition in unconventional frustrated systems.

Revealing exchange bias in spin compensated systems for spintronics applications

Antiferromagnetic materials offer potential for spintronic applications due to their resilience to magnetic field perturbations and lack of stray fields. Achieving exchange bias in these materials is crucial for certain applications; however, discovering such materials remains challenging due to their compensated spin structure. The quest for antiferromagnetic materials with exchange bias became a reality through our experimental study and theoretical simulation onSr 2 FeIrO 6 andSr 2 CoIrO 6 . This study also unveils the impact of ionic disorder and lattice distortion on magnetic properties. The presence of exchange bias in both materials, given their antiferromagnetic nature, is intriguing. This study opens up new avenues for achieving exchange bias in spin-compensated systems, offering potential for low power and ultra fast antiferromagnetic spintronic applications in future research endeavors.

Transformation of Kagomé and Breathing Kagomé Lattices Induced by Ion Replacement

PbOCu3(SeO3)2(NO3)(OH) was synthesized by means of a replacement of (OH)- groups for F- ions of PbOCu3(SeO3)2(NO3)F, showing a transformation of kagomé and breathing kagomé lattices. Such a replacement did not change their intralayer ferromagnetic interactions and interlayer antiferromagnetic (AFM) interactions but slightly affected the Néel temperature and critical field, where PbOCu3(SeO3)2(NO3)(OH) possesses an AFM ordering at TN = 29.3 K, and a field-induced metamagnetic transition can occur at 2 K while a critical magnetic field of 1.45 T is applied.

Effect of Fe doping on the electronic properties of CoSn Kagome semimetal

Quantum phenomena in two-dimensional Kagome materials lead to exotic topological states and complex magnetism. Here, we have investigated the detailed electronic properties of Co1-xFexSn as a function of composition (x) to explore the competing electronic interactions for the origin of complex magnetism and topological properties. We find that the screening effect in the valence electrons increases while the correlation effect decreases with an increase in the Fe doping. Valence fluctuations observed at Co and FeL2,3edges showed systematic changes in the magnitude of divalent and trivalent states with the increase inx. Fe 3dstates are found to be more screened by the conduction electrons than the Co 3dstates. A comparison of the theoretical and experimental density of states showed different natures of localized states with strong screening effects on the surface and dominating correlation effects in the bulk forx>0. We have observed localized flat bands on the CoSn (001) surface while quasi-localized flat bands on the Co0.94Fe0.06Sn (001) surface. The distinct character of the bulk and surface band structure is confirmed in the Fe-doped composition. Hence, the bulk-surface interaction present in Co1-xFexSn gives rise to the origin of valence fluctuation, complex magnetism, and topological properties.

Two new tellurite compounds ACu3Te2O8 (A = Ca, Cd) with ferromagnetic spin-1/2 kagomé layers

Two new tellurite compounds ACu3Te2O8 (A = Ca, Cd) have been synthesized by a typical hydrothermal method, exhibiting a similar 2D layered structure in the trigonal system of space group R3̄m, where Cu2+ ions construct a spin-1/2 regular kagomé lattice via corner-sharing. Magnetic measurements confirmed that ACu3Te2O8 (A = Ca, Cd) possesses antiferromagnetic ordering at low temperature, while exchange interactions between magnetic ions within layers are ferromagnetic.

A new S = 1/2 stacked kagomé lattice compound showing two successive ferromagnetic transitions

A new V4+-based selenite compound Na6V7(SeO3)8O6F6 was synthesized by the hydrothermal method, exhibiting a rare S = 1/2 stacked kagomé lattice built by corner-sharing VO6 zigzag chains along the c-axis, while face-shared VF6 linear chains are located inside the hexagonal channels. Magnetic measurements indicate that this compound possesses two successive ferromagnetic transitions at low temperature.

Low-Temperature Glassy Behavior of Sr2Ni3(C2O4)3(OH)4·3H2O with Frustrated Spin Hexamers

In this paper, we studied the synthesis, crystal structure, magnetism, and memory effect of a spin hexamer compound Sr2Ni3(C2O4)3(OH)4·3H2O. The basic magnetic unit of this compound is a ringed spin hexamer (Ni6 cluster). These Ni6 clusters are connected by an oxalate group, constituting a two-dimensional framework along the ab plane. With decreasing temperature, three anomalies are detected in susceptibility curves, corresponding to the formation of short-range spin correlation around 42.5 K, the onset of an antiferromagnetic ordering at 21.4 K, and a reentrant cluster spin-glass state below 12 K. A strong spin frustration is demonstrated with a frustrated factor f ∼ 11. The dominant exchange interactions are J1/kB = -17.1 K and J2/kB = -81.1 K, evaluated by exact diagonalization analysis with an isolated Ni6 cluster model. A nonequilibrium dynamics study of magnetic memory effect indicates the evolution of several intermediate metastable states.

Spiral Spin Liquid in a Frustrated Honeycomb Antiferromagnet: A Single-Crystal Study of GdZnPO

The frustrated honeycomb spin model can stabilize a subextensively degenerate spiral spin liquid with nontrivial topological excitations and defects, but its material realization remains rare. Here, we report the experimental realization of this model in the structurally disorder-free compound GdZnPO. Using a single-crystal sample, we find that spin-7/2 rare-earth Gd^{3+} ions form a honeycomb lattice with dominant second-nearest-neighbor antiferromagnetic and first-nearest-neighbor ferromagnetic couplings, along with easy-plane single-site anisotropy. This frustrated model stabilizes a unique spiral spin liquid with a degenerate contour around the K{1/3,1/3} point in reciprocal space, consistent with our experiments down to 30 mK, including the observation of a giant residual specific heat. Our results establish GdZnPO as an ideal platform for exploring the stability of spiral spin liquids and their novel properties, such as the emergence of low-energy topological defects on the sublattices.

Quasi-One-Dimensional Spin Dynamics in a Molecular Spin Liquid System

The molecular triangular lattice system, β^{'}-EtMe_{3}Sb[Pd(dmit)_{2}]_{2}, is considered as a candidate material for the quantum spin liquid state, although ongoing debates arise from recent controversial results. Here, the results of electron spin resonance and muon-spin relaxation measurements on β^{'}-EtMe_{3}Sb[Pd(dmit)_{2}]_{2} are presented. Both results indicate characteristic behaviors related to quasi-one-dimensional spin dynamics, whereas the direction of anisotropy found in electron spin resonance is in contradiction with previous theories. We succeed in interpreting the experiments by combining density-functional theory calculations and analysis of the effective model taking into account the multiorbital nature of the system. While the quantum-spin-liquid-like origin of β^{'}-EtMe_{3}Sb[Pd(dmit)_{2}]_{2} was initially attributed to the magnetic frustration of the triangular lattice, it appears that the primary origin is a 1D spin liquid resulting from the dimensional reduction effect.

Exact Deconfined Gauge Structures in the Higher-Spin Yao-Lee Model: A Quantum Spin-Orbital Liquid with Spin Fractionalization and Non-Abelian Anyons

The nonintegrable higher spin Kitaev honeycomb model has an exact Z_{2} gauge structure, which exclusively identifies quantum spin liquid in the half-integer spin Kitaev model. But its constraints for the integer-spin Kitaev model are much limited, and even trivially gapped insulators cannot be excluded. The physical implications of exact Z_{2} gauge structure, especially Z_{2} fluxes, in integer-spin models remain largely unexplored. In this Letter, we theoretically show that a spin-S Yao-Lee model [a spin-orbital model with SU(2) spin-rotation symmetry] possesses a topologically nontrivial quantum spin-orbital liquid ground state for any spin (both integer and half-integer spin) by constructing exact deconfined fermionic Z_{2} gauge charges. We further show that the conserved Z_{2} flux can also demonstrate the intriguing spin fractionalization phenomena in the non-Abelian topological order phase of the spin-1 Yao-Lee model. Its deconfined Z_{2} vortex excitation carries fractionalized spin-1/2 quantum number in the low-energy subspace, which is also a non-Abelian anyon. Our exact manifestation of spin fractionalization in an integer-spin model is rather rare in previous studies, and is absent in the Kitaev honeycomb model.

Uncommon Magnetic Ordering in the Quantum Magnet Yb_{3}Ga_{5}O_{12}

The antiferromagnetic structure of Yb_{3}Ga_{5}O_{12} is identified by neutron diffraction experiments below the previously known transition at T_{λ}=54  mK. The magnetic propagation vector is found to be k=(1/2,1/2,0), an unusual wave vector in the garnet structure. The associated complex magnetic structure highlights the role of exchange interactions in a nearly isotropic system dominated by dipolar interactions and finds echoes with exotic structures theoretically proposed. Reduced values of the ordered moments may indicate significant quantum fluctuations in this effective spin-1/2 geometrically frustrated magnet.

Tunable topological phases in nanographene-based spin-1/2 alternating-exchange Heisenberg chains

Unlocking the potential of topological order in many-body spin systems has been a key goal in quantum materials research. Despite extensive efforts, the quest for a versatile platform enabling site-selective spin manipulation, essential for tuning and probing diverse topological phases, has persisted. Here we utilize on-surface synthesis to construct spin-1/2 alternating-exchange Heisenberg chains by covalently linking Clar's goblets-nanographenes each hosting two antiferromagnetically coupled spins. Using scanning tunnelling microscopy, we exert atomic-scale control over chain lengths, parities and exchange-coupling terminations, and probe their magnetic response via inelastic tunnelling spectroscopy. Our investigation confirms the gapped nature of bulk excitations in the chains, known as triplons. Their dispersion relation is extracted from the spatial variation of tunnelling spectral amplitudes. Depending on the parity and termination of chains, we observe varying numbers of in-gap spin-1/2 edge excitations, reflecting the degeneracy of distinct topological ground states in the thermodynamic limit. By monitoring interactions between these edge spins, we identify the exponential decay of spin correlations. Our findings present a phase-controlled many-body platform, opening avenues toward spin-based quantum devices.

A Frustrated Antipolar Phase Analogous to Classical Spin Liquids

The study of magnetic frustration in classical spin systems is motivated by the prediction and discovery of classical spin liquid states. These uncommon magnetic phases are characterized by a massive degeneracy of their ground state implying a finite magnetic entropy at zero temperature. While the classical spin liquid state is originally predicted in the Ising triangular lattice antiferromagnet in 1950, this state has never been experimentally observed in any triangular magnets. The discovery of an electric analogue of classical spin liquids on a triangular lattice of uniaxial electric dipoles in EuAl12O19 is reported here. This new type of frustrated antipolar phase is characterized by a highly-degenerate state at low temperature implying an absence of long-range antiferroelectric order, despite short-range antipolar correlations. Its dynamics are governed by a thermally activated process, slowing down upon cooling toward a complete freezing at zero temperature.

Signatures of Spinon Dynamics and Phase Structure of Dipolar-Octupolar Quantum Spin Ices in Two-Dimensional Coherent Spectroscopy

We study how sharp signatures of fractionalization emerge in nonlinear spectroscopy experiments on spin liquids with separated energy scales. Our model is that of dipolar-octupolar rare earth pyrochlore materials, prime candidates for realizing quantum spin ice. This family of three-dimensional quantum spin liquids exhibits fractionalization of spin degrees of freedom into spinons charged under an emergent U(1) gauge field. We show that the technique of two-dimensional coherent spectroscopy can identify clear signatures of fractionalized spinon dynamics in dipolar-octupolar quantum spin ices. However, at intermediate temperatures, spinon dynamics are heavily constrained in the presence of an incoherent spin background, leading to a broad two-dimensional coherent spectroscopy response. At lower temperatures, a sharp signal emerges as the system enters a coherent spin liquid state. This lower temperature signal can in turn distinguish between zero-flux and π-flux forms of quantum spin ice.

Vacancies in Generic Kitaev Spin Liquids

The Kitaev honeycomb model supports gapless and gapped quantum spin liquid phases. Its exact solvability relies on extensively many locally conserved quantities. Any real-world manifestation of these phases would include imperfections in the form of disorder and interactions that break integrability. We show that the latter qualitatively alters the properties of vacancies in the gapless Kitaev spin liquid: (i) Isolated vacancies carry a magnetic moment, which is absent in the exactly solvable case. (ii) Pairs of vacancies on even or opposite sublattices gap each other with distinct power laws that reveal the presence of emergent gauge flux.

A classical chiral spin liquid from chiral interactions on the pyrochlore lattice

Classical spin liquids are paramagnetic phases that feature nontrivial patterns of spin correlations within their ground-state manifold whose degeneracy scales with system size. Often they harbor fractionalized excitations, and their low-energy fluctuations are described by emergent gauge theories. In this work, we discuss a model composed of chiral three-body spin interactions on the pyrochlore lattice that realizes a novel classical chiral spin liquid whose excitations are fractonalized while also displaying a fracton-like behavior. We demonstrate that the ground-state manifold of this spin liquid is given by a subset of the so-called color-ice states. We show that the low-energy states are captured by an effective gauge theory which possesses a divergence-free condition and an additional chiral term that constrains the total flux of the fields through a single tetrahedron. The divergence-free constraint on the gauge fields results in two-fold pinch points in the spin structure factor and the identification of bionic charges as excitations of the system.

Accelerated Exploration of Empty Material Compositional Space: Mg-Fe-B Ternary Metal Borides

Borides are a family of materials with valuable properties for various applications. Their diverse structures and compositions, yet disparity in the constituent chemical elements for the known compounds, give elemental substitutions for prototypes great potential for material discovery. To explore uncharted material compositional space, we develop a workflow that joins high-throughput crystal structure prediction and automated diffraction pattern matching to discover new compounds with significant prediction and synthesis hurdles. Utilizing the workflow, we explore the empty Mg-Fe-B ternary compositional space, previously uncharted largely due to the immiscibility of Mg and Fe, as a paradigm. A total of 275 ternary boride prototypes are classified, using which we predict 23 (158) stable and metastable ternary phases within 50 (200) meV/atom above the convex hull. We identify Gd2(FeB)7-type Mg2Fe7B7 and ZrCo3B2-type MgFe3B2 to match previously unsolved experimental powder X-ray diffraction (PXRD) patterns. The discovered Mg2Fe7B7 and related channeled structures feature mismatched Mg and (FeB) sublattice periods, for which we conduct structural analyses with respect to the PXRD. They are predicted to exhibit exceptionally fast superionic transport of Mg and outstanding electrochemical performance, which serve as post-Li-ion battery candidate electrode materials. This result opens a new avenue for borides' potential applications as electrode materials and fast ionic conductors. This work also portrays the map and landscape of ternary metal borides with similar chemical environments. With high efficiency, the prototype- and PXRD-assisted crystal structure prediction workflow opens a new avenue for exploring various material compositional spaces across the periodic table.

Continuum Excitations in a Spin Supersolid on a Triangular Lattice

Magnetic, thermodynamic, neutron diffraction and inelastic neutron scattering are used to study spin correlations in the easy-axis XXZ triangular lattice magnet K_{2}Co(SeO_{3})_{2}. Despite the presence of quasi-2D "supersolid" magnetic order, the low-energy excitation spectrum contains no sharp modes and is instead a broad and structured multiparticle continuum. Applying a weak magnetic field drives the system into an m=1/3 fractional magnetization plateau phase and restores sharp spin wave modes. To some extent, the behavior at zero field can be understood in terms of spin wave decay. However, the presence of clear excitation minima at the M points of the Brillouin zone suggest that the spinon language may provide a more adequate description, and signals a possible proximity to a Dirac spin liquid state.

Higher-Magnesium-Doping Effects on the Singlet Ground State of the Shastry-Sutherland SrCu2(BO3)2

Doping of quantum antiferromagnets is an established approach to investigate the robustness of their ground state against the competing phases. Predictions of doping effects on the ground state of the Shastry-Sutherland dimer model are here verified experimentally on Mg-doped SrCu2(BO3)2. A partial incorporation of Mg2+ on the Cu2+ site in the SrCu2(BO3)2 structure leads to a subtle but systematic lattice expansion with the increasing Mg-doping concentration, which is accompanied by a slight decrease in the spin gap, the Curie-Weiss temperature, and the peak temperature of the susceptibility. These findings indicate a doping-induced breaking of Cu2+ spin-1/2 dimers that is also corroborated by X-band EPR spectroscopy that points to a systematic increase in the intensity of free Cu2+ sites with increasing Mg-doping concentration. Extending the Mg-doping up to nominal x = 0.10 yielding SrCu1.9Mg0.1(BO3)2, in the magnetization measurements taken up to 35 T, a suppression of the pseudo-1/8 plateau is found along with a clear presence of an anomaly at an onset critical field μ0H'C0 ≈ 9 T. The latter, absent in pure SrCu2(BO3)2, emerges due to the pairwise coupling of liberated Cu2+ spin-1/2 entities in the vicinity of Mg-doping induced impurities.

Incommensurate Order with Translationally Invariant Projected Entangled-Pair States: Spiral States and Quantum Spin Liquid on the Anisotropic Triangular Lattice

Simulating strongly correlated systems with incommensurate order poses significant challenges for traditional finite-size-based approaches. Confining such a phase to a finite-size geometry can induce spurious frustration, with spin spirals in frustrated magnets being a typical example. Here, we introduce an Ansatz based on infinite projected entangled-pair states which overcomes these limitations and enables the direct search for the optimal spiral in the thermodynamic limit, with a computational cost that is independent of the spiral's wavelength. Leveraging this method, we simulate the Heisenberg model on the anisotropic triangular lattice, which interpolates between the square and isotropic triangular lattice limits. Besides accurately reproducing the magnetically ordered phases with arbitrary wavelength, the simulations reveal a quantum spin liquid phase emerging between the Néel and spin spiral phases.

Discovering Classical Spin Liquids by Topological Search of High Symmetry Nets

Spin liquids are a paradigmatic example of a nontrivial state of matter. The search for new spin liquids is a key interdisciplinary challenge. Geometrical frustration-where the geometry of the net that the spins occupy precludes the generation of a simple ordered state-is a particularly fruitful way to generate these intrinsically disordered states. Prior focus has been on a handful of high symmetry nets. There are, however, many three-dimensional nets, each of which has the potential to form unique states. In this paper, we investigate the high symmetry nets-those which are both vertex- and edge-transitive-for the simplest possible interaction sets: nearest-neighbor couplings of antiferromagnetic Heisenberg and Ising spins. While the well-known crs (pyrochlore) net is the only nearest-neighbor Heisenberg antiferromagnet which does not order, we identify two new frustrated nets (lcx and thp) possessing finite temperature Heisenberg spin-liquid states with strongly suppressed magnetic ordering and noncollinear ground states. With Ising spins, we identify three new classical spin liquids that do not order down to T/J = 0.01. We highlight materials that contain these high symmetry nets, and which could, if substituted with appropriate magnetic ions, potentially host these unusual states. Our systematic survey will guide searches for novel magnetic phases.

Chemical Design of Spin Frustration to Realize Topological Spin Glasses

Patterning spins to generate collective behavior is at the core of condensed matter physics. Physicists develop techniques, including the fabrication of magnetic nanostructures and precision layering of materials specifically to engender frustrated lattices. As chemists, we can access such exotic materials through targeted chemical synthesis and create new lattice types by chemical design. Here, we introduce a new approach to induce magnetic frustration on a modified honeycomb lattice through a competition of alternating antiferromagnetic (AFM) and ferromagnetic (FM) nearest-neighbor interactions. By subtly modulating these two types of interactions through facile synthetic modifications, we created two systems: (1) a topological spin glass and (2) a frustrated spin-canted magnet with low-temperature exchange bias. To design this unconventional magnetic lattice, we used a metal-organic framework (MOF) platform, Ni3(pymca)3X3 (NipymcaX where pymca = pyrimidine-2-carboxylato and X = Cl, Br). We isolated two MOFs, NipymcaCl and NipymcaBr, featuring canted Ni2+-based moments. Despite this similarity, differences in the single-ion anisotropies of the Ni2+ spins result in distinct magnetic properties for each material. NipymcaCl is a topological spin glass, while NipymcaBr is a rare frustrated magnet with low-temperature exchange bias. Density functional theory calculations and Monte Carlo simulations on the NipymcaX lattice support the presence of magnetic frustration as a result of alternating AFM and FM interactions. Our calculations enabled us to determine the ground-state spin configuration and the distribution of spin-spin correlations relative to paradigmatic kagomé and triangular lattices. This modified honeycomb lattice is similar to the electronic Kekulé-O phase in graphene and provides a highly tunable platform to realize unconventional spin physics.

Highly Tunable 2D Silicon Quantum Dot Array with Coupling beyond Nearest Neighbors

Scaling up quantum dots to two-dimensional (2D) arrays is a crucial step for advancing semiconductor quantum computation. However, maintaining excellent tunability of quantum dot parameters, including both nearest-neighbor and next-nearest-neighbor couplings, during 2D scaling is challenging, particularly for silicon quantum dots due to their relatively small size. Here, we present a highly controllable and interconnected 2D quantum dot array in planar silicon, demonstrating independent control over electron fillings and the tunnel couplings of nearest-neighbor dots. More importantly, we also demonstrate the wide tuning of tunnel couplings between next-nearest-neighbor dots, which play a crucial role in 2D quantum dot arrays. This excellent tunability enables us to alter the coupling configuration of the array as needed. These results open up the possibility of utilizing silicon quantum dot arrays as versatile platforms for quantum computing and quantum simulation.

Deciphering competing interactions of Kitaev-Heisenberg-Γ system in clusters: II. Dynamics of Majorana fermions

We perform a systematic and exact study of Majorana fermion dynamics in the Kitaev-Heisenberg-Γ model in a few finite-size clusters increasing in size up to twelve sites. We employ exact Jordan-Wigner transformations to evaluate certain measures of Majorana fermion correlation functions, which effectively capture matter and gauge Majorana fermion dynamics in different parameter regimes. An external magnetic field is shown to produce a profound effect on gauge fermion dynamics. Depending on certain non-zero choices of other non-Kitaev interactions, it can stabilise it to its non-interacting Kitaev limit. For all the parameter regimes, gauge fermions are seen to have slower dynamics, which could help build approximate decoupling schemes for appropriate mean-field theory. The probability of Majorana fermions returning to their original starting site shows that the Kitaev model in small clusters can be used as a test bed for the quantum speed limit.

Variational benchmarks for quantum many-body problems

The continued development of computational approaches to many-body ground-state problems in physics and chemistry calls for a consistent way to assess its overall progress. In this work, we introduce a metric of variational accuracy, the V-score, obtained from the variational energy and its variance. We provide an extensive curated dataset of variational calculations of many-body quantum systems, identifying cases where state-of-the-art numerical approaches show limited accuracy and future algorithms or computational platforms, such as quantum computing, could provide improved accuracy. The V-score can be used as a metric to assess the progress of quantum variational methods toward a quantum advantage for ground-state problems, especially in regimes where classical verifiability is impossible.

Evidence of high electron mobility in magnetic kagome topological metal FeSn thin films

We present a systematic study of the low-energy electrodynamics of the magnetic FeSn kagome metal, which hosts both topological (Dirac) and non-trivial states. Our results reveal that the optical conductivity of FeSn shows two Drude contributions that can be associated with the linear (Dirac) and parabolic (massive) bands, with a dominance of the former to the DC conductivity at low temperatures. The weight of the Drude response shifts toward lower frequencies upon cooling due to a rapid increase in the Dirac electron mobility, which we associate with a temperature suppression of e-ph scattering. The experimental interband dielectric function is in very good agreement with that calculated within Density Functional Theory (DFT). These results provide a full description of the charge dynamics in FeSn kagome topological metal, opening the road for its use in photonic and plasmonic applications.

A New Spin on Material Properties: Local Magnetic Structure in Functional and Quantum Materials

The past few decades have made clear that the properties and performances of emerging functional and quantum materials can depend strongly on their local atomic and/or magnetic structure, particularly when details of the local structure deviate from the long-range structure averaged over space and time. Traditional methods of structural refinement (e.g., Rietveld) are typically sensitive only to the average structure, creating a need for more advanced structural probes suitable for extracting information about structural correlations on short length- and time-scales. In this Perspective, we describe the importance of local magnetic structure in several classes of emerging materials and present the magnetic pair distribution function (mPDF) technique as a powerful tool for studying short-range magnetism from neutron total-scattering data. We then provide a selection of examples of mPDF analysis applied to magnetic materials of recent technological and fundamental interest, including the antiferromagnetic semiconductor MnTe, geometrically frustrated magnets, and iron-oxide magnetic nanoparticles. The rapid development of mPDF analysis since its formalization a decade ago puts this technique in a strong position for making continued impact in the study of local magnetism in emerging materials.

Spinon Pairing Induced by Chiral In-Plane Exchange and the Stabilization of Odd-Spin Chern Number Spin Liquid in Twisted MoTe_{2}

The unusual structure and symmetry of low-energy states in twisted transition metal dichalcogenides leads to large in-plane spin-exchange interactions between spin-valley locked holes. We demonstrate that this exchange interaction can stabilize a gapped spin-liquid phase with a quantized spin-Chern number of 3 when the twist angle is sufficiently small and the system lies in a Mott insulating phase. The gapped spin liquid may be understood as arising from spinon pairing in the DIII Altland-Zirnbauer symmetry class. Applying an out-of-plane electric field or increasing the twist angle is shown to drive a transition, respectively, to an anomalous Hall insulator or an in-plane antiferromagnet. Recent experiments indicate that a spin-Chern number 3 phase occurs in twisted MoTe_{2} at small twist angles with a transition to a quantum anomalous Hall phase as the twist angle is increased above a critical value of about 2.5° in the absence of an applied electric field.

Stabilization of Short- and Long-Range Magnetic Ordering through the Cooperative Effect of 1D [CuO4]∞ Chains and [CuO2X2] Quadrilateral in Quasi-1D Spin-1/2 Systems

Quasi-1D chain antiferromagnets with reduced structural dimensionality are a rich playground for investigating novel quantum phenomena. We report the synthesis, crystal structure, and magnetism of two novel quasi-1D antiferromagnets, β-PbCu2(TeO3)2Cl2 (I) and PbCu2(TeO3)2Br2 (II). Their magnetic frameworks are constructed via Cu-based quasi-1D [Cu(2)O4]∞ zigzag chains with square-planar [Cu(1)O2X2] (X=Cl or Br) separated among 1D chains. Specific heat measurements show λ peaks at ~9 K and ~19 K for I and II, respectively. Moreover, both broad maximums (χmax=90 K for I and 80 K for II) and small kinks (TN≈9 K for I and 19 K for II) have been observed in magnetic susceptibility measurements of I and II. Bonner-Fisher model fitting, and theoretical analyses were performed to evaluate the magnetic exchange interactions. Our experimental and theoretical results and structure-properties relationship analysis reveal the coexistence of short- and long-range magnetic ordering from the cooperative effect of 1D [CuO4]∞ chains and [CuO2X2] quadrilateral.

Pressure-tuning of α-RuCl3 towards a quantum spin liquid

The layered material α-RuCl3 is a promising candidate to realize the Kitaev quantum spin liquid (QSL) state. However, at ambient pressure, deviations from the perfect Kitaev geometry prevent the existence of the QSL state at low temperatures. Here we present the discovery of a pressure-induced high-symmetry phase in α-RuCl3, which creates close to ideal conditions for the emergence of a QSL. Employing a novel approach based on Bragg and diffuse scattering of synchrotron radiation, we reveal a pressure-induced reorganization of the RuCl3-layers. Most importantly, this reorganization affects the structure of the layers themselves, which acquire a high trigonal symmetry. For this trigonal phase the largest ratio between the Kitaev (K) and the Heisenberg exchange (J) ever encountered is found: K/J = 124. Additionally, we demonstrate that this phase can also be stabilized by a slight biaxial pressure. This not only resolves the conflicting reports of low-temperature structures in the literature, but also facilitates the investigation of the high-symmetry phase and its potential QSL using a range of experimental techniques.

Growth of Ba2CoWO6single crystals and their magnetic, thermodynamic and electronic properties

This study explores the bulk crystal growth, structural characterization, and physical property measurements of the cubic double perovskite Ba2CoWO6(BCWO). In BCWO, Co2+ions form a face-centred cubic lattice with non-distorted cobalt octahedra. The compound exhibits long-range antiferromagnetic order belowTN= 14 K. Magnetization data indicated a slight anisotropy along with a spin-flop transition at 10 kOe, a saturation field of 310 kOe and an ordered moment of 2.17µB atT= 1.6 K. Heat capacity measurements indicate an effectivej= 1/2 ground state configuration, resulting from the combined effects of the crystal electric field and spin-orbit interaction. Surface photovoltage analysis reveals two optical gaps in the UV-Visible region, suggesting potential applications in photocatalysis and photovoltaics. The magnetic and optical properties highlight the significant role of orbital contributions within BCWO, indicating various other potential applications.

Giant Anisotropic Magnetoresistance in Few-Layer α-RuCl3 Tunnel Junctions

The spin-orbit-assisted Mott insulator α-RuCl3 is proximate to the coveted quantum spin liquid (QSL) predicted by the Kitaev model. In the search for the pure Kitaev QSL, reducing the dimensionality of this frustrated magnet by exfoliation has been proposed as a way to enhance magnetic fluctuations and Kitaev interactions. Here, we perform angle-dependent tunneling magnetoresistance (TMR) measurements on ultrathin α-RuCl3 crystals with various layer numbers to probe their magnetic, electronic, and crystal structures. We observe a giant change in resistance, as large as ∼2500%, when the magnetic field rotates either within or out of the α-RuCl3 plane, a manifestation of the strongly anisotropic spin interactions in this material. In combination with scanning transmission electron microscopy, this tunneling anisotropic magnetoresistance (TAMR) reveals that few-layer α-RuCl3 crystals remain in the high-temperature monoclinic phase at low temperatures. It also shows the presence of a zigzag antiferromagnetic order below the critical temperature TN ≃ 14 K, which is twice the one typically observed in bulk samples with rhombohedral stacking. Our work offers valuable insights into the relation between the stacking order and magnetic properties of this material, which helps lay the groundwork for creating and electrically probing exotic magnetic phases such as QSLs via van der Waals engineering.

Low-Temperature Ferromagnetic Order in a Two-Level Layered Co2+ Material

The magnetic properties of a 2D layered material consisting of high-spin Co2+ complexes, [Co(NH3NH2)2(H2O)2Cl2]Cl2 (CoHyd 2 Cl 4 ), have been extensively characterized using electron paramagnetic resonance, magnetic susceptibility, and low-temperature heat capacity measurements. Electron paramagnetic resonance spectroscopy studies suggest that below 50 K, the J = 3/2 orbital triplet state of Co is gradually depopulated in favor of the J = 1/2 spin state, which is dominant below 20 K. In light of this, the magnetic susceptibility has been fitted with a two-level model, indicating that the interactions in this material are much weaker than previously thought. This two-level model is unable to fit the data at low temperatures and, combined with electron paramagnetic resonance spectroscopy, suggests that ferromagnetic interactions between Co2+ cations in the J = 1/2 state become significant approaching 2 K. Heat capacity measurements suggest the emergence of a long-range ordered state below 246 mK, which neutron diffraction confirms to be ferromagnetic.

Crystal Growth, Structure, and Diverse Magnetic Behaviors in Frustrated Triangular Lattice REBO3 (RE = Tb-Yb)

Triangular lattice (TL) materials are a rich playground for investigating exotic quantum spin states and related applications in quantum computing and quantum information. Millimeter-level single crystals of REBO3 (RE = Tb-Yb) with a nearly perfect RE-based TL have been successfully grown via a high-temperature flux method and structurally characterized via single-crystal X-ray diffraction. These 113-type materials crystallize in a monoclinic crystal system with a C2/c space group. Anisotropic magnetism and dominant antiferromagnetic interactions are found for the above materials based on DC magnetic susceptibility measurements. The comprehensive low-temperature specific heat data of REBO3 (RE = Tb-Tm) are characterized on single crystals for the first time, which exhibit diverse magnetic behaviors. Specifically, two weak-field-induced transitions could be found in the case of DyBO3 based on the specific heat measurements. Our results suggest that REBO3 (RE = Tb-Yb) is a TL magnetic system for investigating potential quantum magnetism.

Irrational Moments and Signatures of Higher-Rank Gauge Theories in Diluted Classical Spin Liquids

Classical spin liquids (CSLs) have proved to be a fruitful setting for the emergence of exotic gauge theories. Vacancy clusters in CSLs can introduce gauge charges into the system, and the resulting behavior in turn reveals the nature of the underlying theory. We study these effects for a series of CSLs on the honeycomb lattice. We find that dilution leads to the emergence of effective free spins with tuneable, and generally irrational, size. For a specific higher-rank CSL, described by a symmetric tensor gauge fields, dilution produces nondecaying spin textures with a characteristic quadrupolar angular structure and infinite-ranged interactions between dilution clusters.