Spin liquids in frustrated magnets

Magnetocaloric effect of topological excitations in Kitaev magnets

Traditional magnetic sub-Kelvin cooling relies on the nearly free local moments in hydrate paramagnetic salts, whose utility is hampered by the dilute magnetic ions and low thermal conductivity. Here we propose to use instead fractional excitations inherent to quantum spin liquids (QSLs) as an alternative, which are sensitive to external fields and can induce a very distinctive magnetocaloric effect. With state-of-the-art tensor-network approach, we compute low-temperature properties of Kitaev honeycomb model. For the ferromagnetic case, strong demagnetization cooling effect is observed due to the nearly free Z2 vortices via spin fractionalization, described by a paramagnetic equation of state with a renormalized Curie constant. For the antiferromagnetic Kitaev case, we uncover an intermediate-field gapless QSL phase with very large spin entropy, possibly due to the emergence of spinon Fermi surface and gauge field. Potential realization of topological excitation magnetocalorics in Kitaev materials is also discussed, which may offer a promising pathway to circumvent existing limitations in the paramagnetic hydrates.

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

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

Disordered magnetic ground state in a quasi-1-Dd4columnar iridate Sr3LiIrO6

Spin-orbit coupling offers a large variety of novel and extraordinary magnetic and electronic properties in otherwise 'ordinary pool' of heavy ion oxides. Here we present a detailed study on an apparently isolated hexagonal 2Hspin-chaind4iridate Sr3LiIrO6with geometric frustration. Our structural studies reveal Li-Ir chemical order with desired stoichiometry in this compound, while x-ray absorption together with x-ray photoemission spectroscopic characterizations establish pure 5+ valence of Ir. We have established a magnetic ground state with finite Ir5+magnetic moments in this compound, contrary to the anticipated nonmagneticJeff= 0 state, through combined dc susceptibility,7Li nuclear magnetic resonance (NMR), muon spin relaxation (µSR) andab-initioelectronic structure studies. These investigations together with ac magnetic susceptibility and specific heat measurements reveal that despite having noticeable antiferromagnetic correlation among the Ir5+local moments, this system does not magnetically order down to at least 0.05 K, possibly due to geometrical exchange frustration, arising from the comparable nearest- and next-nearest-neighbor interchain Ir-O-O-Ir superexchange interaction strengths with opposite signs. However, the zero-fieldµSR analysis shows emergence of a considerable proportion of spin-freezing on top of a spin-fluctuating dynamic magnetic background down to the lowest measured temperature of 1.7 K, possibly due to some inhomogeneity and/or the much stronger intra-column Ir-Ir magnetic exchange interaction strength relative to the inter-column Ir-Ir ones. The linear temperature dependence of the magnetic specific heat (Cm) in both zero and applied magnetic fields, plus the power-law behavior of the NMR spin-lattice relaxation rate suggest a gapless spinon density of states in this charge gapped disordered magnetic ground state of Sr3LiIrO6.

Phonon excitations in Eu2Ir2O7probed by inelastic x-ray scattering

The study of phonon dynamics and its interplay with magnetic ordering is crucial for understanding the unique quantum phases in the pyrochlore iridates. Here, through inelastic x-ray scattering on a single crystal sample of the pyrochlore iridate Eu2Ir2O7, we map out the phonon excitation spectra in Eu2Ir2O7and compare them with the theoretical phonon spectra calculated using the density functional theory. Possible phonon renormalization across the magnetic long-range order transition is observed in our experiments, which is consistent with the results of the previous Raman scattering experiments.

Periodic DFT calculations to compute the attributes of a quantum material: honeycomb ruthenium trichloride

Quantum spin liquids (QSLs) have become prominent materials of interest in the pursuit of fault-tolerant materials for quantum computing applications. This is due to the fact that these materials are theorized to host an interesting variety of quantum phenomena such as quasi-particles that may behave as anyons as a result of the high entangled nature of the spin states within the systems. Computing the electronic and magnetic properties of these materials is necessary in order to understand the underlying interactions of the materials. In this paper, the structural, electronic, and magnetic properties including lattice parameters, bandgap, Heisenberg coupling constants, and Curie temperatures for α-RuCl3, a promising candidate for the Kitaev QSL model, are computed using periodic density functional theory. Furthermore, various parameters of the calculations (i.e. functional choice, basis set, k-point density, and Hubbard correction) are varied in order to determine what effect, if any, the computational setup has on the computed properties. The results of this study indicate that PBE functional with Hubbard corrections of 1.5-2.5 eV with a k-point density of 3.0 points per Å-1 appear to be the best parameters to compute Heisenberg coupling constants for α-RuCl3. These parameters with the addition of spin orbit coupling works well for computing Curie temperatures for α-RuCl3. Distinct differences are noted in the computations of the bulk structure vs. monolayer structures, indicating that interactions between the layers play a role in the material properties and changes to the inter-layer spacing may result in interesting and unique magnetic properties that require further investigation.

High-temperature magnetic anomaly via suppression of antisite disorder through synthesis route modification in a Kitaev candidate Cu2IrO3

By incorporating inert KCl into the Na2IrO3+ 2CuCl → Cu2IrO3+ 2NaCl topochemical reaction, we significantly reduced the synthesis temperature of Cu2IrO3from the 350 °C reported in previous studies to 170 °C. This adjustment decreased the Cu/Ir antisite disorder concentration in Cu2IrO3from ∼19% to ∼5%. Furthermore, magnetic susceptibility measurements of the present Cu2IrO3sample revealed a weak ferromagnetic-like anomaly with hysteresis at a magnetic transition temperature of ∼70 K. Our research indicates that the spin-disordered ground state reported in chemically disordered Cu2IrO3is an extrinsic phenomenon, rather than an intrinsic one, underscoring the pivotal role of synthetic chemistry in understanding the application of Kitaev model to realistic materials.

Twisted graphene superlattices: resonating valence bond states and magnetic properties

Resonating valence bond (RVB) states are fundamental for understanding quantum spin liquids in two-dimensional (2D) systems. The RVB state is a collective phenomenon in which spins are uncoupled. 2D lattices such as triangular, honeycomb, and dice lattices were investigated using the Hubbard model and exact diagonalization method. We analyzed the total spin, spin-spin correlation functions, local magnetic moments, and spin and charge gaps as a function of on-site Coulomb repulsion, electron concentration, and electronic hopping parameters. Phase diagrams showed that RVB states can live in half-filled and hole-doped anisotropic triangular lattices. We found two types of RVB states: one in the honeycomb sublattice and the other in the centered hexagons in the triangular lattices. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene and transition metal dichalcogenide systems, our results provide physical insights into the onset of magnetism and possible spin liquid states in these layered materials.

Interpenetrated Lattices of Quaternary Chalcogenides Displaying Magnetic Frustration, High Na-Ion Conductivity, and Cation Redox in Na-Ion Batteries

A series of quaternary selenides, NaxMGaSe4 (M = Mn, Fe, and mixed Zn/Fe), have been synthesized for the first time employing a high-temperature solid-state synthesis route through stochiometric or polychalcogenide flux reactions. Along with the selenides, a previously reported sulfide analogue, NaxFeGaS4, is also revisited with new findings. These compounds form an interpenetrated structure made up of a supertetrahedral unit. The electrochemical evaluations exhibit a reversible (de)intercalation of ∼0.6 and ∼0.45 Na-ions, respectively, from Na2.87FeGaS4 (1a) and Na2.5FeGaSe4 (2) involving Fe2+/Fe3+ redox when cycled between 1.5 and 2.5 V. Mössbauer spectroscopy of 1a shows the existence of a mixed oxidation state of Fe2+/3+ in the pristine compound and reversible oxidation of Fe2+ to Fe3+ during the electrochemical cycles. Na2.79Zn0.6Fe0.4GaSe4 possesses a reasonably high room temperature ionic conductivity of 0.077 ms/cm with an activation energy of 0.30 eV. The preliminary magnetic measurements show a bifurcation of FC-ZFC at 4.5 and 2.5 K, respectively, for 1a and Na3MnGaSe4 (4) arising most likely from a spin-glass like transition. The high negative values of the Weiss constants -368.15 and -308.43 K for 1a and 4, respectively, indicate strong antiferromagnetic interactions between the magnetic ions and also emphasize the presence of a high degree of magnetic frustration in these compounds.

Gd substitution induced incommensurate antiferromagnetism in B20 noncentrosymmetric CoSi

Rare-earth element Gd doped CoSi, Co1-xGdxSi (x= 0.01), is investigated using x-ray diffraction and magnetization. It crystallizes in B20 cubic structure with lattice parameter ofa= 4.4429 Å. The alloy exhibits two antiferromagnetic transitions AFM-I at 38.44 K and AFM-II at 21.87 K followed by an upturn of magnetization belowTut= 9.79 K as illustrated through the temperature-magnetic fieldT-Hphase diagram. AFM-I state is incommensurate. AFM-II state is weakly correlated as inferred from field-induced transition to AFM-I state. Further, AFM-I state is reported to transform to ferromagnetic state in high magnetic fields. The present study stimulates an approach to derive novel and exotic magnetic materials by substituting rare-earth in transition metal monosilicides.

Thermodynamics of resonating-valence-bond states toward the understanding of quantum spin liquid phenomena

A quantum spin liquid (QSL) is a state of matter in which spins do not exhibit magnetic order. In contrast to paramagnets, the spins in a QSL interact strongly, similar to conventional ordered magnets; however the thermodynamic stability of QSLs is rarely studied. Here, the thermodynamic properties of centered hexagon nanoclusters were investigated using the Hubbard model, which was solved using exact numerical diagonalization. The total spin, spin-spin correlation functions, local magnetic moments, charge and spin gaps, and magnetocaloric effect were analyzed for a half-filled band as a function of the ratio between the on-site Coulomb repulsion and electronic hopping (U/t). The centered hexagon nanocluster exhibited an antiferromagnetic (AFM) behavior with exotic magnetic ordering. Resonating-valence-bond (RVB) states were observed for intermediate values of U/t, in which short-range spin-spin correlation functions were suppressed to minimize spin frustration. The AFM order was examined in terms of the Néel-like temperature derived from the temperature dependence of the magnetic susceptibility. An interesting result is that the systems under external magnetic fields exhibited an inverse magnetocaloric effect, which was remarkable for intermediate values of U/t, where the RVB state was observed. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene (TBLG) systems, these results provide insights into the onset of magnetism and the possible spin liquid states in these graphene moiré materials.

Kagomerization of transition metal monolayers induced by two-dimensional hexagonal boron nitride

The kagome lattice is an exciting solid state physics platform for the emergence of nontrivial quantum states driven by electronic correlations: topological effects, unconventional superconductivity, charge and spin density waves, and unusual magnetic states such as quantum spin liquids. While kagome lattices have been realized in complex multi-atomic bulk compounds, here we demonstrate from first-principles a process that we dub kagomerization, in which we fabricate a two-dimensional kagome lattice in monolayers of transition metals utilizing an hexagonal boron nitride (h-BN) overlayer. Surprisingly, h-BN induces a large rearrangement of the transition metal atoms supported on a fcc(111) heavy-metal surface. This reconstruction is found to be rather generic for this type of heterostructures and has a profound impact on the underlying magnetic properties, ultimately stabilizing various topological magnetic solitons such as skyrmions and bimerons. Our findings call for a reconsideration of h-BN as merely a passive capping layer, showing its potential for not only reconstructing the atomic structure of the underlying material, e.g. through the kagomerization of magnetic films, but also enabling electronic and magnetic phases that are highly sought for the next generation of device technologies.

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

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

Unveiling a Family of Dimerized Quantum Magnets, Conventional Antiferromagnets, and Nonmagnets in Ternary Metal Borides

Dimerized quantum magnets are exotic crystalline materials where Bose-Einstein condensation of magnetic excitations can happen. However, known dimerized quantum magnets are limited to only a few oxides and halides. Here, we unveil 9 dimerized quantum magnets and 11 conventional antiferromagnets in ternary metal borides MTB4 (M = Sc, Y, La, Ce, Lu, Mg, Ca, and Al; T = V, Cr, Mn, Fe, Co, and Ni), where T atoms are arranged in structural dimers. Quantum magnetism in these compounds is dominated by strong antiferromagnetic (AFM) interactions between Cr (Cr and Mn for M = Mg and Ca) atoms within the dimers, with much weaker interactions between the dimers. These systems are proposed to be close to a quantum critical point between a disordered singlet spin-dimer phase, with a spin gap, and the ordered conventional Néel AFM phase. They greatly enrich the materials inventory that allows investigations of the spin-gap phase. Conventional antiferromagnetism in these compounds is dominated by ferromagnetic Mn (Fe for M = Mg and Ca) interactions within the dimers. The predicted stable and nonmagnetic (NM) YFeB4 phase is synthesized and characterized, providing a scarce candidate to study Fe dimers and Fe ladders in borides. The identified quantum, conventional, and NM systems provide a platform with abundant possibilities to tune the magnetic exchange coupling by doping and study the unconventional quantum phase transition and conventional magnetic transitions. This work opens new avenues for studying novel magnetism in borides arising from spin dimers and establishes a theoretical workflow for future searches for dimerized quantum magnets in other families of materials.

Noncentrosymmetric Triangular Magnet CaMnTeO6: Strong Quantum Fluctuations and Role of s0 versus s2 Electronic States in Competing Exchange Interactions

Noncentrosymmetric triangular magnets offer a unique platform for realizing strong quantum fluctuations. However, designing these quantum materials remains an open challenge attributable to a knowledge gap in the tunability of competing exchange interactions at the atomic level. Here, a new noncentrosymmetric triangular S = 3/2 magnet CaMnTeO6 is created based on careful chemical and physical considerations. The model material displays competing magnetic interactions and features nonlinear optical responses with the capability of generating coherent photons. The incommensurate magnetic ground state of CaMnTeO6 with an unusually large spin rotation angle of 127°(1) indicates that the anisotropic interlayer exchange is strong and competing with the isotropic interlayer Heisenberg interaction. The moment of 1.39(1) µB, extracted from low-temperature heat capacity and neutron diffraction measurements, is only 46% of the expected value of the static moment 3 µB. This reduction indicates the presence of strong quantum fluctuations in the half-integer spin S = 3/2 CaMnTeO6 magnet, which is rare. By comparing the spin-polarized band structure, chemical bonding, and physical properties of AMnTeO6 (A = Ca, Sr, Pb), how quantum-chemical interpretation can illuminate insights into the fundamentals of magnetic exchange interactions, providing a powerful tool for modulating spin dynamics with atomically precise control is demonstrated.

Superconducting diode effect and interference patterns in kagome CsV3Sb5

The interplay among frustrated lattice geometry, non-trivial band topology and correlation yields rich quantum states of matter in kagome systems1,2. A series of recent members in this family, AV3Sb5 (A = K, Rb or Cs), exhibit a cascade of symmetry-breaking transitions3, involving the 3Q chiral charge ordering4-8, electronic nematicity9,10, roton pair density wave11 and superconductivity12. The nature of the superconducting order is yet to be resolved. Here we report an indication of dynamic superconducting domains with boundary supercurrents in intrinsic CsV3Sb5 flakes. The magnetic field-free superconducting diode effect is observed with polarity modulated by thermal histories, suggesting that there are dynamic superconducting order domains in a spontaneous time-reversal symmetry-breaking background. Strikingly, the critical current exhibits double-slit superconductivity interference patterns when subjected to an external magnetic field. The characteristics of the patterns are modulated by thermal cycling. These phenomena are proposed as a consequence of periodically modulated supercurrents flowing along certain domain boundaries constrained by fluxoid quantization. Our results imply a time-reversal symmetry-breaking superconducting order, opening a potential for exploring exotic physics, for example, Majorana zero modes, in this intriguing topological kagome system.

A single crystal study of Kagome metals U2Mn3Ge and U2Fe3Ge

Single crystals of U2Mn3Ge and U2Fe3Ge with a Kagome lattice structure were synthesized using a high-temperature self-flux crystal growth method. The physical properties of these crystals were characterized through measurements of resistivity, magnetism, and specific heat. U2Fe3Ge exhibits ferromagnetic ground state and anomalous Hall effect, and U2Mn3Ge demonstrates a complex magnetic structure. Both compounds exhibit large Sommerfeld coefficient, indicating coexistence of heavy Fermion behaviour with magnetism. Our results suggest that this U2TM3Ge (TM = Mn, Fe, Co) family is a promising platform to investigate the interplay of magnetism, Kondo physics and the Kagome lattice.

N-Heterocyclic Carbene-Derived 1,3,5-Trimethylenebenzene: On-Surface Synthesis and Electronic Structure

1,3,5-Trimethylenebenzene (1,3,5-TMB), a 3-fold-symmetric triradical with a high-spin ground state, is an attractive platform for investigating the unique spin properties of π-conjugated triangular triradicals. Here, we report the on-surface synthesis of N-heterocyclic carbene (NHC)-derived 1,3,5-TMB (N-TMB) via surface-assisted C-C and C-N coupling reactions on Au(111). The chemical and electronic structures of N-TMB on the Au(111) surface are revealed with atomic precision using scanning tunneling microscopy and noncontact atomic force microscopy, combined with density functional theory (DFT) calculations. It is demonstrated that there is substantial charge transfer between N-TMB and the substrate, resulting in a positively charged N-TMB on Au(111). DFT calculations at the UB3LYP/def2-TZVP level of theory and multireference method, e.g., CASSCF/NEVPT2, indicate that N-TMB possesses a doublet ground state with reduced Cs symmetry in the gas phase, contrasting the quartet ground state of 1,3,5-TMB with D3h symmetry, and exhibits a doublet-quartet energy gap of -0.80 eV. The incorporation of NHC structures and the extended π-conjugation promote the spin-orbital overlaps in N-TMB, leading to Jahn-Teller distortion and the formation of a robust doublet state. Our results not only demonstrate the fabrication of polyradicals based on NHC but also shed light on the effect of NHC and π-conjugation on the electronic structure and spin coupling, which opens up new possibilities for precisely regulating the spin-spin exchange coupling of organic polyradicals.

Anatomy of Hidden Dzyaloshinskii-Moriya Interactions and Topological Spin Textures in Centrosymmetric Crystals

The Dzyaloshinskii-Moriya interaction (DMI) is understood to be forbidden by the symmetry of centrosymmetric systems, thus restricting the candidate types for investigating many correlated physical phenomena. Here, we report the hidden DMI existing in centrosymmetric magnets driven by the local inversion symmetry breaking of specific spin sublattices. The opposite DMI spatially localized on the inverse spin sublattice favors the separated spin spiral with opposite chirality. Furthermore, we elucidate that hidden DMI widely exists in many potential candidates, from the first-principles calculations on the mature crystal database. Interestingly, novel topological spin configurations, such as the anti-chirality-locked merons and antiferromagnetic-ferromagnetic meron chains, are stabilized as a consequence of hidden DMI. Our understanding enables the effective control of DMI by symmetry operations at the atomic level and enlarges the range of currently useful magnets for topological magnetism.

Low-temperature behaviors of the dipolar magnet Dy3Sb3Zn2O14with a strongly site-mixing disordered kagome lattice

Interesting behaviors may emerge in the magnetic frustrated materials with significant site-mixing disorder. We present the results of the structural, magnetic susceptibility, and specific heat measurements of Dy3Sb3Zn2O14with ∼20%Dy/Zn site-mixing disorder, which results in either a diluted 2D triangular lattice, or an intermediate structure between the kagome and pyrochlore lattice. In addition to the sharp anomaly of the temperature dependence of specific heat atT∼0.35 K, which was attributed to the emergent charge order state for the sample with less disorder, a broad peak atT∼1.5 K, and a small hump belowT∼0.1 K are observed. The measured temperature dependence of specific heat and the Monte Carlo simulation suggest that the magnetic frustration persists despite of a strong site-mixing disorder.

Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

Observation of Nagaoka polarons in a Fermi-Hubbard quantum simulator

Quantum interference can deeply alter the nature of many-body phases of matter1. In the case of the Hubbard model, Nagaoka proved that introducing a single itinerant charge can transform a paramagnetic insulator into a ferromagnet through path interference2-4. However, a microscopic observation of this kinetic magnetism induced by individually imaged dopants has been so far elusive. Here we demonstrate the emergence of Nagaoka polarons in a Hubbard system realized with strongly interacting fermions in a triangular optical lattice5,6. Using quantum gas microscopy, we image these polarons as extended ferromagnetic bubbles around particle dopants arising from the local interplay of coherent dopant motion and spin exchange. By contrast, kinetic frustration due to the triangular geometry promotes antiferromagnetic polarons around hole dopants7. Our work augurs the exploration of exotic quantum phases driven by charge motion in strongly correlated systems and over sizes that are challenging for numerical simulation8-10.

Large magnetic anisotropy of a decorated spin-chain system K2Co3(MoO4)3(OH)2

The magnetic structure of K2Co3(MoO4)3(OH)2 is studied in detail. The material has a half-sawtooth one-dimensional (1-D) structure containing two unique Co2+ ions, one in the chain backbone and one on the apex of the sawtooth creating a series of isosceles triangles along the b-axis. These triangles can be a source of magnetic frustration. The ability to grow large single crystals enables detailed magnetic measurements with the crystals oriented in a magnetic field along the respective axes. It has a Curie-Weiss temperature θCW of 5.3(2) K with an effective magnetic moment of 4.8(3)μB/Co. The material is highly anisotropic with a sharp antiferromagnetic ordering transition at 7 K with a metamagnetic transition at 2 kOe. Neutron diffraction was used to determine the magnetic structure and revealed a magnetic structure with canted spins along the backbone of the chain while spins along the sawtooth caps maintained a colinear orientation, arranging antiferromagnetically relative to the backbone spins. The parallel chains arrange antiferromagnetically relative to each other along the c-axis and ferromagnetically along the a-axis.

Frustrated Extended Bose-Hubbard Model and Deconfined Quantum Critical Points with Optical Lattices at the Antimagic Wavelength

The study of geometrically frustrated many-body quantum systems is of central importance to uncover novel quantum mechanical effects. We design a scheme where ultracold bosons trapped in a one-dimensional state-dependent optical lattice are modeled by a frustrated Bose-Hubbard Hamiltonian. A derivation of the Hamiltonian parameters based on Cesium atoms, further show large tunability of contact and nearest-neighbor interactions. For pure contact repulsion, we discover the presence of two phases peculiar to frustrated quantum magnets: the bond-order-wave insulator with broken inversion symmetry and a chiral superfluid. When the nearest-neighbor repulsion becomes sizable, a further density-wave insulator with broken translational symmetry can appear. We show that the phase transition between the two spontaneously symmetry-broken phases is continuous, thus representing a one-dimensional deconfined quantum critical point not captured by the Landau-Ginzburg-Wilson symmetry-breaking paradigm. Our results provide a solid ground to unveil the novel quantum physics induced by the interplay of nonlocal interactions, geometrical frustration, and quantum fluctuations.

Charge density waves in two-dimensional transition metal dichalcogenides

Charge density wave (CDW is one of the most ubiquitous electronic orders in quantum materials. While the essential ingredients of CDW order have been extensively studied, a comprehensive microscopic understanding is yet to be reached. Recent research efforts on the CDW phenomena in two-dimensional (2D) materials provide a new pathway toward a deeper understanding of its complexity. This review provides an overview of the CDW orders in 2D with atomically thin transition metal dichalcogenides (TMDCs) as the materials platform. We mainly focus on the electronic structure investigations on the epitaxially grown TMDC samples with angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy as complementary experimental tools. We discuss the possible origins of the 2D CDW, novel quantum states coexisting with them, and exotic types of charge orders that can only be realized in the 2D limit.

Observation of Topological Hall Effect in a Chemically Complex Alloy

The topological Hall effect (THE) is the transport response of chiral spin textures and thus can serve as a powerful probe for detecting and understanding these unconventional magnetic orders. So far, the THE is only observed in either noncentrosymmetric systems where spin chirality is stabilized by Dzyaloshinskii-Moriya interactions, or triangular-lattice magnets with Ruderman-Kittel-Kasuya-Yosida-type interactions. Here, a pronounced THE is observed in a Fe-Co-Ni-Mn chemically complex alloy with a simple face-centered cubic (fcc) structure across a wide range of temperatures and magnetic fields. The alloy is shown to have a strong magnetic frustration owing to the random occupation of magnetic atoms on the close-packed fcc lattice and the direct Heisenberg exchange interaction among atoms, as evidenced by the appearance of a reentrant spin glass state in the low-temperature regime and the first principles calculations. Consequently, THE is attributed to the nonvanishing spin chirality created by strong spin frustration under the external magnetic field, which is distinct from the mechanism responsible for the skyrmion systems, as well as geometrically frustrated magnets.

Exceptional Magnetocaloric Responses in a Gadolinium Silicate with Strongly Correlated Spin Disorder for Sub-Kelvin Magnetic Cooling

The development of magnetocaloric materials with a significantly enhanced volumetric cooling capability is highly desirable for the application of adiabatic demagnetization refrigerators in confined spatial environments. Here, the thermodynamic characteristics of a magnetically frustrated spin-7/2 Gd9.33[SiO4]6O2 is presented, which exhibits strongly correlated spin disorder below ≈1.5 K. A quantitative model is proposed to describe the magnetization results by incorporating nearest-neighbor Heisenberg antiferromagnetic and dipolar interactions. Remarkably, the recorded magnetocaloric responses are unprecedentedly large and applicable below 1.0 K. It is proposed that the S = 7/2 spin liquids serve as versatile platforms for investigating high-performance magnetocaloric materials in the sub-kelvin regime, particularly those exhibiting a superior cooling power per unit volume.

Construction of Ideal One-Dimensional Spin Chains by Topochemical Dehydration/Rehydration Route

One-dimensional (1D) Heisenberg antiferromagnets are of great interest due to their intriguing quantum phenomena. However, the experimental realization of such systems with large spin S remains challenging because even weak interchain interactions induce long-range ordering. In this study, we present an ideal 1D S = 5/2 spin chain antiferromagnet achieved through a multistep topochemical route involving dehydration and rehydration. By desorbing three water molecules from (2,2'-bpy)FeF3(H2O)·2H2O (2,2'-bpy = 2,2'-bipyridyl) at 150 °C and then intercalating two water molecules at room temperature (giving (2,2'-bpy)FeF3·2H2O 1), the initially isolated FeF3ON2 octahedra combine to form corner-sharing FeF4N2 octahedral chains, which are effectively separated by organic and added water molecules. Mössbauer spectroscopy reveals significant dynamical fluctuations down to 2.7 K, despite the presence of strong intrachain interactions. Moreover, results from electron spin resonance (ESR) and heat capacity measurements indicate the absence of long-range order down to 0.5 K. This controlled topochemical dehydration/rehydration approach is further extended to (2,2'-bpy)CrF3·2H2O with S = 3/2 1D chains, thus opening the possibility of obtaining other low-dimensional spin lattices.

Proximity effect of emergent field from spin ice in an oxide heterostructure

Geometrical frustration endows magnets with degenerate ground states, resulting in exotic spin structures and quantum phenomena. Such magnets, called quantum magnets, can display non-coplanar spin textures and be a viable platform for the topological Hall effect driven by "emergent field." However, most quantum magnets are insulators, making it challenging to electrically detect associated fluctuations and excitations. Here, we probe magnetic transitions in the spin ice insulator Dy2Ti2O7, a prototypical quantum magnet, as emergent magnetotransport phenomena at the heterointerface with the nonmagnetic metal Bi2Rh2O7. Angle-dependent longitudinal resistivity exhibits peaks at the magnetic phase boundaries of spin ice due to domain boundary scattering. In addition, the anomalous Hall resistivity undergoes a sign change with the magnetic transition in Dy2Ti2O7, reflecting the inversion of the emergent field. These findings, on the basis of epitaxial techniques, connect the fundamental research on insulating quantum magnets to their potential electronic applications, possibly leading to transformative innovations in quantum technologies.

Quantum spin liquid signatures in monolayer 1T-NbSe2

Quantum spin liquids (QSLs) are in a quantum disordered state that is highly entangled and has fractional excitations. As a highly sought-after state of matter, QSLs were predicted to host spinon excitations and to arise in frustrated spin systems with large quantum fluctuations. Here we report on the experimental observation and theoretical modeling of QSL signatures in monolayer 1T-NbSe2, which is a newly emerging two-dimensional material that exhibits both charge-density-wave (CDW) and correlated insulating behaviors. By using scanning tunneling microscopy and spectroscopy (STM/STS), we confirm the presence of spin fluctuations in monolayer 1T-NbSe2 by observing the Kondo resonance as monolayer 1T-NbSe2 interacts with metallic monolayer 1H-NbSe2. Subsequent STM/STS imaging of monolayer 1T-NbSe2 at the Hubbard band energy further reveals a long-wavelength charge modulation, in agreement with the spinon modulation expected for QSLs. By depositing manganese-phthalocyanine (MnPc) molecules with spin S = 3/2 onto monolayer 1T-NbSe2, new STS resonance peaks emerge at the Hubbard band edges of monolayer 1T-NbSe2. This observation is consistent with the spinon Kondo effect induced by a S = 3/2 magnetic impurity embedded in a QSL. Taken together, these experimental observations indicate that monolayer 1T-NbSe2 is a new promising QSL material.

Pressure-induced structural and magnetic ordering transitions in the J1-J2 square lattice antiferromagnets AMoOPO4Cl (A = K, Rb)

By means of ab initio density functional theory calculations taking into account electronic correlation and van der Waals force, we conducted comprehensive studies of the electronic and magnetic properties, as well as structural and magnetic ordering evolution under pressure of the square lattice antiferromagnets AMoOPO4Cl (A = K, Rb) containing Mo5+ ions with , theoretically predicted as the potential candidates for achieving quantum phases, existing in the boundary regimes for square lattice magnets. Our results indicate that the columnar antiferromagnetic ordering, experimentally determined, is the magnetic ground state of the ambient P4/nmm phase, stabilized by the predominant antiferromagnetic next nearest neighbor interaction J2 in the diagonal directions of the square lattice, regardless of the effective Hubbard amendment values. More importantly, the P4/n phase, involving the mutual twisting of the MoO5Cl and PO4 polyhedra, satisfactorily reproduces the experimentally observed structural transition and the subsequent magnetic ordering transition from columnar antiferromagnetic ordering to Néel antiferromagnetic one, identified to be the appropriate high pressure structure. Furthermore, the mechanism underlined responsible for the magnetic ordering transition at high pressure has been disclosed in terms of density of states and spin density isosurface analysis across the transition. The loss of mirror plane symmetry in the P4/n phase activates the P 3s orbitals to participate in the magnetic interaction, giving rise to a competitive ferromagnetic superexchange interaction, in addition to antiferromagnetic direct one, and consequently initiating the magnetic ordering transition. The insights revealed here not only deepen our understanding of the electronic properties and structural and magnetic ordering transitions under high pressure of square lattice antiferromagnets AMoOPO4Cl (A = K, Rb), but also push the boundaries of knowledge by recognizing the role of nonmagnetic ions P 3s in magnetic exchange coupling.

Structural and magnetic studies of the frustratedS = 1 kagome magnet NH4Ni2Mo2O10H3

The strong geometric frustration of the kagome antiferromagnets (KAFMs) can destabilise conventional magnetic order and lead to exotic electronic states, such as the quantum spin-liquid state observed in someS=12KAFM materials. However, the ground state ofS = 1 KAFM systems are less well understood. Spin nematic phases and valence bond solid ground states have been predicted to form but a paucity of experimental realisations restricts understanding. Here, theS = 1 KAFM NH4Ni2Mo2O10H3is presented, which has the 3-fold symmetry of the kagome lattice but significant site depletion, with∼64%site occupancy. Frustration and a competition between exchange interactions are evidenced through the suppression of order below the Weiss temperature|θW|and observation of ferromagnetic and antiferromagnetic characteristics in the magnetisation data. A semi spin glass ground state is predicted based on the ac-field frequency dependence of the magnetic transition and ferromagnetic signal.

Pinalites: Optical Properties and Quantum Magnetism of Heteroanionic A3MO5X2 Compounds

Heteroanionic compounds, which contain two or more types of anions, have emerged as a promising class of materials with diverse properties and functionalities. In this paper, I review the experimental findings on Ca3ReO5Cl2 and related compounds that exhibit remarkable pleochroism and novel quantum magnetism. I discuss how the heteroanionic coordination affects the optical and magnetic properties by modulating the d-orbital states of the transition metal ions. Subsequently, I compare these materials with other heteroanionic and monoanionic compounds and highlight the potential of A3MO5X2 materials for future exploration of materials and phenomena.

Low temperature Raman spectroscopic study of anharmonic and spin-phonon coupled quasi-two dimensional rare earth based francisites

Mineral francisites Cu3Bi(SeO3)2O2Cl are unique compounds with interesting quasi two-dimensional structure along with fascinating magnetic properties. The magnetic properties can be fine-tuned when non-magnetic Bi is replaced by a suitable rare earth (RE) metal. It is because of the inclusion of additional magnetic sub-centre RE apart from Cu. Temperature dependent Raman spectroscopy measurements in RE based francisites [Cu3RE(SeO3)2O2Cl, shortly RECufr] were performed in the range of 11 K-295 K. Among the three studied RECufr (LaCufr, NdCufr, and DyCufr) compounds, the properties of phonon vibration vary from moderate (in DyCufr) to weak (in LaCufr) spin phonon coupled and the absence of spin phonon coupling (SPC) (i.e. strictly anharmonic in nature) was observed in NdCufr and the reason for this observation has been provided. More specifically, two Raman-active phonons soften below the antiferromagnetic ordering temperature ofTN≈ 39 K in DyCufr compound, indicating the existence of moderate SPC. This trend of phonon vibration is correlated with magnetic properties, particularly field induced metamagnetic transition (MMT). Strong MMT enabled DyCufr develops SPC, while weak MMT enabled NdCufr is unable to develop SPC.

Intertwining of Localized (d) and Delocalized (π) Spins in Magnetically Frustrated Two-Dimensional Metal-Organic Frameworks

Two-dimensional metal-organic frameworks (2D MOFs) are emerging as a new class of multifunctional materials for diversified applications, although magnetic properties have not been widely explored. The metal ions and organic ligands in some of the 2D MOFs are arranged in the well-known Kagome lattice, leading to geometric spin frustration. Hence, such systems could be the potential candidates to exhibit an exotic quantum spin liquid (QSL) state, as was observed in Cu3(HHTP)2 (HHTP = hexahydroxytriphenylene), with no magnetic transition down to 38 mK. Hereto, we have investigated the spin intertwining in a bimetallic 2D MOF system, M3(HHTP)2 (M = Cu/Zn), arising from the localized (d-electron) and delocalized (π-electron) S = 1/2 spins from the Cu(II) ions and the HHTP radicals, respectively. The origin of the spin frustration (down to 5K) was critically examined by varying the metal composition in bimetallic systems, CuxZn3-x(HHTP)2 (x = 1, 1.5, 2), containing both S = 1/2 and S = 0 spins. Additionally, to gain a deeper understanding, we studied the spin interaction in the pristine Zn3(HHTP)2 system containing only S = 0 Zn(II) ions. In view of the quantitative estimate of the localized and delocalized spins, the d-π spin correlation appears essential in understanding the unusual magnetic and/or other physical properties of such hybrid organic-inorganic 2D crystalline solids.

Entropy driven incommensurate structures in the frustrated kagome staircase Co3V2O8

Co3V2O8features spin-3/2 moments arrayed on a kagome staircase lattice. A spin density wave with a continuously evolving propagation vector ofk⃗=(0,δ,0), showing both incommensurate states and multiple commensurate lock-ins, is observed at temperatures above the ferromagnetic ground state. Previous work has suggested that this changing propagation vector could be driven by changes in exchange interactions due to Co atom displacements. We present a straightforward model showing that a Hamiltonian with competing (but temperature independent) interactions can semi-quantitatively reproduce this behavior using a mean field approximation. The simulated spin density wave magnetic structures feature buckled kagome planes that are either ferromagnetically or antiferromagnetically ordered. Propagation vectors that differ fromδ=1/2will have multiple different ways of arranging these ferromagnetic layers that have very similar energies. This classical stacking entropy appears to be crucial in stabilizing the temperature-dependent propagation vector.

Luminescent Radicals

Organic radicals are attracting increasing interest as a new class of molecular emitters. They demonstrate electronic excitation and relaxation dynamics based on their doublet or higher multiplet spin states, which are different from those based on singlet-triplet manifolds of conventional closed-shell molecules. Recent studies have disclosed luminescence properties and excited state dynamics unique to radicals, such as highly efficient electron-photon conversion in OLEDs, NIR emission, magnetoluminescence, an absence of heavy atom effect, and spin-dependent and spin-selective dynamics. These are difficult or sometimes impossible to achieve with closed-shell luminophores. This review focuses on luminescent organic radicals as an emerging photofunctional molecular system, and introduces the material developments, fundamental properties including luminescence, and photofunctions. Materials covered in this review range from monoradicals, radical oligomers, and radical polymers to metal complexes with radical ligands demonstrating radical-involved emission. In addition to stable radicals, transiently formed radicals generated in situ by external stimuli are introduced. This review shows that luminescent organic radicals have great potential to expand the chemical and spin spaces of luminescent molecular materials and thus broaden their applicability to photofunctional systems.

Spectroscopic Signatures of Fractionalization in Octupolar Quantum Spin Ice

Recent investigations on the dipolar-octupolar compounds Ce_{2}Zr_{2}O_{7} and Ce_{2}Sn_{2}O_{7} suggest that they may stabilize so-called π-flux octupolar quantum spin ice (π-O-QSI), a novel three-dimensional quantum spin liquid hosting emergent photons. Confirmation of such an exotic phase would require the prediction of a distinctive signature and its subsequent experimental observation. So far, however, theoretical predictions for any such sharp smoking-gun signatures are lacking. In this Letter, we thoroughly investigate O-QSI using an extension of gauge mean-field theory. This framework produces a phase diagram consistent with previous work and an energy-integrated neutron scattering signal with intensity-modulated rod motifs, as reported in experiments and numerical studies. We predict that the dynamical spin structure factor of π-O-QSI is characterized by a broad continuum with three distinctive peaks as a consequence of the two mostly flat spinon bands. These three peaks should be measurable by high-resolution inelastic neutron scattering. Such spectroscopic signatures would be clear evidence for the realization of π-flux quantum spin ice.

Field-Induced Non-BEC Transitions in Frustrated Magnets

Frustrated spin systems have traditionally proven challenging to understand, owing to a scarcity of controlled methods for their analyses. By contrast, under strong magnetic fields, certain aspects of spin systems admit simpler and universal description in terms of hardcore bosons. The bosonic formalism is anchored by the phenomenon of Bose-Einstein condensation (BEC), which has helped explain the behaviors of a wide range of magnetic compounds under applied magnetic fields. Here, we focus on the interplay between frustration and externally applied magnetic field to identify instances where the BEC paradigm is no longer applicable. As a representative example, we consider the antiferromagnetic J_{1}-J_{2}-J_{3} model on the square lattice in the presence of a uniform external magnetic field, and demonstrate that the frustration-driven suppression of the Néel order leads to a Lifshitz transition for the hardcore bosons. In the vicinity of the Lifshitz point, the physics becomes unmoored from the BEC paradigm, and the behavior of the system, both at and below the saturation field, is controlled by a Lifshitz multicritical point. We obtain the resultant universal scaling behaviors, and provide strong evidence for the existence of a frustration and magnetic-field driven correlated bosonic liquid state along the entire phase boundary separating the Néel phase from other magnetically ordered states.

From caged compounds with isolated U atoms to frustrated magnets with 2- or 3-atom clusters: a review of Al-rich uranium aluminides with transition metals

Crystal structures and physical properties of four families of Al-rich ternary uranium compounds with transition metals (TE) are reviewed, namely UTE2Al20, UTE2Al10, U6TE4Al43, and U3TE4Al12. The compounds can be described as consisting of 1 (isolated), 2 (dumbbells) or 3 (triangles) uranium atom clusters, surrounded (1-2-20, 1-2-10 and 6-4-43) or not (3-4-12) by large cages, which strongly influence their magnetic and related properties. Indeed, the ground states of the described systems evolve from Curie-like paramagnetism in the case of the phases with well-isolated, single U-atoms, to complex magnetic order or possible frustrated magnetism in the case of the systems with uranium triangles forming a breathing kagome lattice. We argue that the four families of uranium aluminides described in this review provide a unique opportunity to study magnetic interactions between U magnetic moments while gradually increasing the number of their nearest magnetic neighbors, and may also be helpful in understanding the fundamental origin of magnetic freezing phenomena.

Effectiveness of the recursive-lattice technique in the investigation of magnetic systems with the pyrochlore structure

A well-defined higher recursive approximation of the pyrochlore lattice is introduced and its relevance and effectiveness for the systematic investigation of magnetic systems with the pyrochlore structure is studied within the classical antiferromagnetic as well as ferromagnetic spin-1/2 Ising model in the presence of the external magnetic field. The exact solution of the model is found with the explicit analytic expression for the free energy per site of the lattice. The magnetization and entropy properties of all ground states of the antiferromagnetic model are determined and compared to those obtained within the lower recursive approximation of the model on the recursive tetrahedral lattice. The exact analysis of the residual entropies of the model on the introduced recursive lattice explicitly shows that the well-known Pauling entropy of the water ice cannot represent the true residual entropy of the antiferromagnetic model on the regular pyrochlore lattice in the zero external magnetic field. The improvement of the value of the critical temperature of the ferromagnetic model obtained within the introduced higher recursive approximation is also discussed. The analysis performed demonstrates the great efficiency of recursive approximations in the investigation of various magnetic systems with the pyrochlore structure, especially for frustrated antiferromagnetic systems.

Concurrence distribution in excited states of the one-dimensional spin-1/2 transverse-field XY model: Two different regions

We investigate the variation of concurrence in a spin-1/2 transverse field XY chain system in an excited state. Initially, we precisely solve the eigenvalue problem of the system Hamiltonian using the fermionization technique. Subsequently, we calculate the concurrence between nearest-neighbor pairs of spins in all excited states with higher energy than the ground state. Below the factorized field, denoted as h_{f}=sqrt[J^{2}-(Jδ)^{2}], we find no pairwise entanglement between nearest neighbors in excited states. At the factorized field, corresponding to a factorized state, we observe weak concurrence in very low energy states. Beyond h_{f}, the concurrence strengthens, entangling all excited states. The density of entangled states peaks at the center of the excited spectrum. Additionally, the distribution of concurrence reveals that the midpoint of the nonzero concurrence range harbors the most entangled excited states.

Persistence of weak ferromagnetism in antiferromagnetic systems on the body-centered octahedral lattice

The possibility of existence of weak ferromagnetism in antiferromagnetic systems on the body-centered octahedral lattice is investigated in the framework of the corresponding spin-1/2J_{1}-J_{2} model in the recursive-lattice approach. The exact solution of the model is found and its phase diagram is determined. The magnetic and thermodynamic properties of all phases are studied, the nature of all phase transitions is established, and an equation that determines the positions of all second-order phase transitions of the model is found. The magnetic and entropy properties of all ground states of the model are also determined. It is shown that the weak ferromagnetism predicted earlier in the pure spin-1/2 antiferromagnetic system on the octahedral lattice remains present even in the case of the model on the body-centered octahedral lattice with antiferromagnetic as well as ferromagnetic interactions between the central site of each elementary octahedron and each of its vertices. However, the presence of the interacting central site suppresses the weak ferromagnetism at very low temperatures, where the standard antiferromagnetic phase emerges. At the same time, the temperature region with the antiferromagnetic phase increases with simultaneous decreasing of the region, where the weak ferromagnetism can be observed, when the strength of the interaction between the central site of each elementary octahedron and each of its vertices increases. Moreover, the phenomenon of weak ferromagnetism disappears completely when this interaction becomes sufficiently stronger than the nearest-neighbor antiferromagnetic interaction between spin variables placed in vertices of each elementary octahedron of the lattice. Moreover, the possibility of the existence of the classical spin-liquid behavior in such magnetic systems is also discussed.

Correlated order at the tipping point in the kagome metal CsV3Sb5

Spontaneously broken symmetries are at the heart of many phenomena of quantum matter and physics more generally. However, determining the exact symmetries that are broken can be challenging due to imperfections such as strain, in particular when multiple electronic orders are competing. This is exemplified by charge order in some kagome systems, where evidence of nematicity and flux order from orbital currents remains inconclusive due to contradictory measurements. Here we clarify this controversy by fabricating highly symmetric samples of a member of this family, CsV3Sb5, and measuring their transport properties. We find that a measurable anisotropy is absent at any temperature in the unperturbed material. However, a pronounced in-plane transport anisotropy appears when either weak magnetic fields or strains are present. A symmetry analysis indicates that a perpendicular magnetic field can indeed lead to in-plane anisotropy by inducing a flux order coexisting with more conventional bond order. Our results provide a unifying picture for the controversial charge order in kagome metals and highlight the need for materials control at the microscopic scale in the identification of broken symmetries.

Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions

In the past few decades, tremendous efforts have been made toward understanding the exotic physics emerging from competition between various ordering tendencies in strongly correlated systems. Employing state-of-the-art quantum Monte Carlo simulation, we investigate an interacting SU(N) fermionic model with varying interaction strength and value of N, and we unveil the ground-state phase diagram of the model exhibiting a plethora of exotic phases. For small values of N-namely, N=2, 3-the ground state is an antiferromagnetic (AFM) phase, whereas in the large-N limit, a staggered valence bond solid (VBS) order is dominant. For intermediate values of N such as N=4, 5, remarkably, our study reveals that distinct VBS orders appear in the weak and strong coupling regimes. More fantastically, the competition between staggered and columnar VBS ordering tendencies gives rise to a Mott insulating phase without spontaneous symmetry breaking (SSB), existing in a large interacting parameter regime, which is consistent with a gapped quantum spin liquid. Our study not only provides a platform to investigate the fundamental physics of quantum many-body systems-it also offers a novel route toward searching for exotic states of matter such as quantum spin liquid in realistic quantum materials.

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).

Possible quantum-spin-liquid state in van der Waals cluster magnet Nb3Cl8

The cluster magnet Nb3Cl8consists of Nb3trimmers that form an emergentS= 1/2 two-dimensional triangular layers, which are bonded by weak van der Waals interactions. Recent studies show that its room-temperature electronic state can be well described as a single-band Mott insulator. However, the magnetic ground state is non-magnetic due to a structural transition below about 100 K. Here we show that there exists a thickness threshold below which the structural transition will not happen. For a bulk crystal, a small fraction of the sample maintains the high-temperature structure at low temperatures and such remnant gives rise to linear-temperature dependence of the specific heat at very low temperatures. This is further confirmed by the measurements on ground powder sample orc-axis pressed single crystals, which prohibits the formation of the non-magnetic state. Moreover, the intrinsic magnetic susceptibility also tends to be constant with decreasing temperature. Our results suggest that Nb3Cl8with the high-temperature structure may host a quantum-spin-liquid ground state with spinon Fermi surfaces, which can be achieved by making the thickness of a sample smaller than a certain threshold.

Structure, Spin Correlations, and Magnetism of the S = 1/2 Square-Lattice Antiferromagnet Sr2CuTe1-xWxO6 (0 ≤ x ≤ 1)

Quantum spin liquids are highly entangled magnetic states with exotic properties. The S = 1/2 square-lattice Heisenberg model is one of the foundational models in frustrated magnetism with a predicted, but never observed, quantum spin liquid state. Isostructural double perovskites Sr2CuTeO6 and Sr2CuWO6 are physical realizations of this model but have distinctly different types of magnetic order and interactions due to a d10/d0 effect. Long-range magnetic order is suppressed in the solid solution Sr2CuTe1-xWxO6 in a wide region of x = 0.05-0.6, where the ground state has been proposed to be a disorder-induced spin liquid. Here, we present a comprehensive neutron scattering study of this system. We show using polarized neutron scattering that the spin liquid-like x = 0.2 and x = 0.5 samples have distinctly different local spin correlations, which suggests that they have different ground states. Low-temperature neutron diffraction measurements of the magnetically ordered W-rich samples reveal magnetic phase separation, which suggests that the previously ignored interlayer coupling between the square planes plays a role in the suppression of magnetic order at x ≈ 0.6. These results highlight the complex magnetism of Sr2CuTe1-xWxO6 and hint at a new quantum critical point between 0.2 < x < 0.4.

Tuneable Short-Range Antiferromagnetic Correlation in Fe-Containing Entropy Stabilized Oxides

To elucidate the impact of a high entropy elemental distribution of the lattice site on the magnetic properties in oxide compounds, a series of complex perovskites BaBO3 (B = Y, Fe, Ti, Zr, Hf, Nb, and Ta) with different Fe content ratios (0, 0.2, 0.3, and 0.4) have been synthesized and thoroughly characterized. In this complex oxide series, superconducting quantum interference device magnetometry reveals a gradual change of a well-defined magnetic phase transition and B-site magnetic moment, which correlates with the Fe content. More importantly, a comprehensive analysis of the sample with a 0.4-Fe content (40% on the B-site) including magnetization, heat capacity, neutron diffraction, and muon-spin rotation measurements suggests that in the low-temperature state, a short-range antiferromagnetic correlation may exist, which could result from the magnetic interaction of Fe ions and consequent redistribution of associated d-electrons.

Spin Frustration in Organic Radicals

Spin frustration, which results from geometric frustration and a systematical inability to satisfy all antiferromagnetic (AF) interactions between unpaired spins simultaneously, is under the spotlight for its importance in physics and materials science. Spin frustration is treated as the structural basis of quantum spin liquids (QSLs). Featuring flexible chemical structures, organic radical species exhibit great potential in building spin-frustrated molecules and lattices. So far, the reported examples of spin-frustrated organic radical compounds include triradicals, tetrathiafulvalene (TTF) radicals and derivatives, [Pd(dmit)2 ] compounds (dmit=1,3-dithiol-2-thione-4,5-dithiolate), nitronyl nitroxides, fullerenes, polycyclic aromatic hydrocarbons (PAHs), and other heterocyclic compounds where the spin frustration is generated intra- or intermolecularly. In this Minireview, we provide a brief summary of the reported radical compounds that possess spin frustration. The related data, including magnetic exchange coupling parameters, spin models, frustration parameters, and crystal lattices, are summarized and discussed.

Spinon Heat Transport in the Three-Dimensional Quantum Magnet PbCuTe_{2}O_{6}

Quantum spin liquids (QSLs) are novel phases of matter which remain quantum disordered even at the lowest temperature. They are characterized by emergent gauge fields and fractionalized quasiparticles. Here we show that the sub-kelvin thermal transport of the three-dimensional S=1/2 hyperhyperkagome quantum magnet PbCuTe_{2}O_{6} is governed by a sizeable charge-neutral fermionic contribution which is compatible with the itinerant fractionalized excitations of a spinon Fermi surface. We demonstrate that this hallmark feature of the QSL state is remarkably robust against sample crystallinity, large magnetic field, and field-induced magnetic order, ruling out the imitation of QSL features by extrinsic effects. Our findings thus reveal the characteristic low-energy features of PbCuTe_{2}O_{6} which qualify this compound as a true QSL material.