Spin liquid state in the S = 1/2 triangular lattice Ba3CuSb2O9

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.

Ba4RuMn2O10: A Noncentrosymmetric Polar Crystal Structure with Disordered Trimers

Phase-pure polycrystalline Ba4RuMn2O10 was prepared and determined to adopt the noncentrosymmetric polar crystal structure (space group Cmc21) based on results of second harmonic generation, convergent beam electron diffraction, and Rietveld refinements using powder neutron diffraction data. The crystal structure features zigzag chains of corner-shared trimers, which contain three distorted face-sharing octahedra. The three metal sites in the trimers are occupied by disordered Ru/Mn with three different ratios: Ru1:Mn1 = 0.202(8):0.798(8), Ru2:Mn2 = 0.27(1):0.73(1), and Ru3:Mn3 = 0.40(1):0.60(1), successfully lowering the symmetry and inducing the polar crystal structure from the centrosymmetric parent compounds Ba4T3O10 (T = Mn, Ru; space group Cmca). The valence state of Ru/Mn is confirmed to be +4 according to X-ray absorption near-edge spectroscopy. Ba4RuMn2O10 is a narrow bandgap (∼0.6 eV) semiconductor exhibiting spin-glass behavior with strong magnetic frustration and antiferromagnetic interactions.

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

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

Coexistence of spin liquid state and magnetic correlations in 3d-5dbased triangular-lattice antiferromagnet Sr3CuIr2O9

Here, we report detailed lattice structure, magnetization (dc and ac) and specific heat measurements on a 3d-5dbased new triple-perovskite material Sr3CuIr2O9. The Sr/Cu forms a layered structure of triangular-lattice while the Ir forms Ir2O9dimers which lie in chain as well as simultaneously makes layered triangular-lattice with neighboring atoms. Due to random site-sharing with Sr2+, the Cu2+(3d9, spin-1/2) forms a diluted magnetic lattice, thus giving a disordered in-plane exchange interaction. Opposed to conventionalJeffmodel, the Ir5+(5d4,Jeff= 0) is believed to be magnetic here which participates both in-chain and in-plane magnetic interactions. This complex lattice structure driven competing exchange interaction leads the ground state to a gapless quantum-spin-liquid state which coexists with (weak) ferromagnetic spin correlations. While underling the importance of spin state (spin-1/2), we believe that the combined effect of lattice structure, geometric frustration, spin-orbit coupling and spin state has given rise this interesting ground state in this material.

Angular dependence of spin-flop transition in triangular lattice antiferromagnet Cu2(OH)3Br

We report angular dependence of spin-flop transition in triangular lattice antiferromagnet Cu₂(OH)₃Br by angle-dependent magnetization and ESR measurements. The results show that the antiferromagnetic easy magnetization axis is the diagonal direction (θ= 45°) of theac^*plane, i.e., the orientation of Cu1 spins based on the magnetic structure (2020Phys. Rev. Lett.125037204), whereas the spin-flop axis is thebaxis. A phenomenological model is proposed to describe the angle-dependent spin-flop transitions. Based on this model, Cu1 spins are sensitive to external magnetic field, while Cu2 spins are robust against to the field, showing partial decoupling. The model is expected to be used in other uniaxial antiferromagnets with a more general easy axis and complex spin-flop transitions.

Chemistry of Quantum Spin Liquids

Quantum spin liquids are an exciting playground for exotic physical phenomena and emergent many-body quantum states. The realization and discovery of quantum spin liquid candidate materials and associated phenomena lie at the intersection of solid-state chemistry, condensed matter physics, and materials science and engineering. In this review, we provide the current status of the crystal chemistry, synthetic techniques, physical properties, and research methods in the field of quantum spin liquids. We highlight a number of specific quantum spin liquid candidate materials and their structure-property relationships, elucidating their fascinating behavior and connecting it to the intricacies of their structures. Furthermore, we share our thoughts on defects and their inevitable presence in materials, of which quantum spin liquids are no exception, which can complicate the interpretation of characterization of these materials, and urge the community to extend their attention to materials preparation and data analysis, cognizant of the impact of defects. This review was written with the intention of providing guidance on improving the materials design and growth of quantum spin liquids, and to paint a picture of the beauty of the underlying chemistry of this exciting class of materials.

Gapless Quantum Spin Liquid in the Triangular System Sr_{3}CuSb_{2}O_{9}

We report gapless quantum spin liquid behavior in the layered triangular Sr_{3}CuSb_{2}O_{9} system. X-ray diffraction shows superlattice reflections associated with atomic site ordering into triangular Cu planes well separated by Sb planes. Muon spin relaxation measurements show that the S=1/2 moments at the magnetically active Cu sites remain dynamic down to 65 mK in spite of a large antiferromagnetic exchange scale evidenced by a large Curie-Weiss temperature θ_{CW}≃-143  K as extracted from the bulk susceptibility. Specific heat measurements also show no sign of long-range order down to 0.35 K. The magnetic specific heat (C_{m}) below 5 K reveals a C_{m}=γT+αT^{2} behavior. The significant T^{2} contribution to the magnetic specific heat invites a phenomenology in terms of the so-called Dirac spinon excitations with a linear dispersion. From the low-T specific heat data, we estimate the dominant exchange scale to be ∼36  K using a Dirac spin liquid ansatz which is not far from the values inferred from microscopic density functional theory calculations (∼45  K) as well as high-temperature susceptibility analysis (∼70  K). The linear specific heat coefficient is about 18  mJ/mol K^{2} which is somewhat larger than for typical Fermi liquids.

Synthesis of the Elusive S = 1/2 Star Structure: A Possible Quantum Spin Liquid Candidate

Materials with two-dimensional, geometrically frustrated, spin-¹/₂ lattices provide a fertile playground for the study of intriguing magnetic phenomena such as quantum spin liquid (QSL) behavior, but their preparation has been a challenge. In particular, the long-sought, exotic spin-¹/₂ star structure has not been experimentally realized to date. Here we report the synthesis of [(CH₃)₂(NH₂)]₃[Cu^II₃(μ₃-OH)(μ₃-SO₄)(μ₃-SO₄)₃]·0.24H₂O with an S = ¹/₂ star lattice. On the basis of the magnetic susceptibility and heat capacity measurements, the layered Cu-based compound exhibits antiferromagnetic interactions but no magnetic ordering or spin freezing down to 2 K. The spin-frustrated material appears to be a promising QSL candidate.

Frustrated Magnetism in Triangular Lattice TlYbS2 Crystals Grown via Molten Flux

The triangular lattice compound TlYbS₂ was prepared as large single crystals via a molten flux growth technique using sodium chloride. Anisotropic magnetic susceptibility measurements down to 0.4 K indicate a complete absence of long-range magnetic order. Despite this lack of long-range order, short-range antiferromagnetic interactions are evidenced through broad transitions, suggesting frustrated behavior. Variable magnetic field measurements reveal metamagnetic behavior at temperatures ≤2 K. Complex low temperature field-tunable magnetic behavior, in addition to no observable long-range order down to 0.4 K, suggest that TlYbS₂ is a frustrated magnet and a possible quantum spin liquid candidate.

Quantum magnetisms in uniform triangular lattices Li2AMo3O8 (A = In, Sc)

Molecular based spin-1/2 triangular lattice systems such as LiZn2Mo3O8 have attracted research interest. Distortions, defects, and intersite disorder are suppressed in such molecular-based magnets, and intrinsic geometrical frustration gives rise to unconventional and unexpected ground states. Li2AMo3O8 (A = In or Sc) is such a compound where spin-1/2 Mo3O13 clusters in place of Mo ions form the uniform triangular lattice. Their ground states are different according to the A site. Li2InMo3O8 undergoes conventional 120° long-range magnetic order below TN = 12 K whereas isomorphic Li2ScMo3O8 exhibits no long-range magnetic order down to 0.5 K. Here, we report exotic magnetisms in Li2InMo3O8 and Li2ScMo3O8 investigated by muon spin rotation (μSR) and inelastic neutron scattering (INS) spectroscopies using polycrystalline samples. Li2InMo3O8 and Li2ScMo3O8 show completely different behaviors observed in both μSR and INS measurements, representing their different ground states. Li2InMo3O8 exhibits spin wave excitation which is quantitatively described by the nearest neighbor anisotropic Heisenberg model based on the 120° spin structure. In contrast, Li2ScMo3O8 undergoes short-range magnetic order below 4 K with quantum-spin-liquid-like magnetic fluctuations down to the base temperature. Origin of the different ground states is discussed in terms of anisotropies of crystal structures and magnetic interactions.

Spin-orbital entangled liquid state in the copper oxide Ba3CuSb2O9

Structure with orbital degeneracy is unstable toward spontaneous distortion. Such orbital correlation usually has a much higher energy scale than spins, and therefore, magnetic transition takes place at a much lower temperature, almost independently from orbital ordering. However, when the energy scales of orbitals and spins meet, there is a possibility of spin-orbital entanglement that would stabilize novel ground state such as spin-orbital liquid and random singlet state. Here we review on such a novel spin-orbital magnetism found in the hexagonal perovskite oxide Ba₃CuSb₂O₉, which hosts a self-organized honeycomblike short-range order of a strong Jahn-Teller ion Cu²⁺. Comprehensive structural and magnetic measurements have revealed that the system has neither magnetic nor Jahn-Teller transition down to the lowest temperatures, and Cu spins and orbitals retain the hexagonal symmetry and paramagnetic state. Various macroscopic and microscopic measurements all indicate that spins and orbitals remain fluctuating down to low temperatures without freezing, forming a spin-orbital entangled liquid state.

Emergent SU(4) Symmetry in α-ZrCl_{3} and Crystalline Spin-Orbital Liquids

While the enhancement of spin-space symmetry from the usual SU(2) to SU(N) is promising for finding nontrivial quantum spin liquids, its realization in magnetic materials remains challenging. Here, we propose a new mechanism by which SU(4) symmetry emerges in the strong spin-orbit coupling limit. In d^{1} transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently SU(4)-breaking hopping between the J_{eff}=3/2 quartets. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit at quarter filling, as realized in α-ZrCl_{3}, the low-energy effective model is the SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. By generalizing this model to other three-dimensional lattices, we also propose crystalline spin-orbital liquids protected by this emergent SU(4) symmetry and space group symmetries.

Syntheses, Structure, and 2/5 Magnetization Plateau of a 2D Layered Fluorophosphate Na3Cu5(PO4)4F·4H2O

A new two-dimensional (2D) fluorophosphate compound Na₃Cu₅(PO₄)₄F·4H₂O with a Cu₅ cluster has been synthesized using a conventional hydrothermal method. The compound crystallizes in the orthorhombic crystal system with space group Pnma. The 2D layered structure is formed by cap-like {Cu₅(PO₄)₄F} building units consisting of a Cu₄O₁₂F cluster plus a residual cap Cu²⁺ ion. Magnetic susceptibility exhibits a broad maximum at T₂ = 19.2 K due to low-dimensional character followed by a long-range antiferromagnetic ordering at T₁ = 11.5 K, which is further confirmed by the specific heat data. High-field magnetization measurement demonstrates a 2/5 quantum magnetization plateau above 40 T. The ESR data indicate the presence of magnetic anisotropy, in accordance with the 2D structure of the system.

Spin-liquid-like state in a spin-1/2 square-lattice antiferromagnet perovskite induced by d10-d0 cation mixing

A quantum spin liquid state has long been predicted to arise in spin-1/2 Heisenberg square-lattice antiferromagnets at the boundary region between Néel (nearest-neighbor interaction dominates) and columnar (next-nearest-neighbor interaction dominates) antiferromagnetic order. However, there are no known compounds in this region. Here we use d¹⁰-d⁰ cation mixing to tune the magnetic interactions on the square lattice while simultaneously introducing disorder. We find spin-liquid-like behavior in the double perovskite Sr₂Cu(Te_0.5W_0.5)O₆, where the isostructural end phases Sr₂CuTeO₆ and Sr₂CuWO₆ are Néel and columnar type antiferromagnets, respectively. We show that magnetism in Sr₂Cu(Te_0.5W_0.5)O₆ is entirely dynamic down to 19 mK. Additionally, we observe at low temperatures for Sr₂Cu(Te_0.5W_0.5)O₆-similar to several spin liquid candidates-a plateau in muon spin relaxation rate and a strong T-linear dependence in specific heat. Our observations for Sr₂Cu(Te_0.5W_0.5)O₆ highlight the role of disorder in addition to magnetic frustration in spin liquid physics.

Highly Spin-Frustrated Magnetism in the Topochemically Prepared Triangular Lattice Cluster Magnets Na3 A2 (MoO4 )2 Mo3 O8 (A=In, Sc)

The physical properties of novel cluster-based triangular lattice antiferromagnets Na₃ A₂ (MoO₄ )₂ Mo₃ O₈ (A=In, Sc), synthesized through a topochemical Na-intercalation to nonmagnetic Na₂ A₂ (MoO₄ )₂ Mo₃ O₈ , are reported. The S=1/2 [Mo₃ ]¹¹⁺ clusters form a regular triangular lattice, which gives the magnetic system a strong geometrical spin frustration effect. Despite the strong antiferromagnetic couplings among [Mo₃ ]¹¹⁺ clusters, they show no long-range magnetic orderings down to 0.5 K with the finite residual magnetic entropy. The ground states of Na₃ A₂ (MoO₄ )₂ Mo₃ O₈ have been characterized as a quantum spin liquid, owing to the strong spin frustration of cluster spins on the triangular lattice.

Crystal structures, magnetic properties, and DFT calculation of B-site defected 12L-perovskites Ba2La2MW2O12 (M = Mn, Co, Ni, Zn)

The synthesis, crystal structures and magnetic properties of Ba₂La₂MW₂O₁₂ (M  =  Mn, Co, Ni, Zn) were investigated. They crystallize in the 12-layer polytype of the perovskite structure with a regular cation defect in the B-site. The results of neutron diffraction measurements reveal that they adopt a rhombohedral structure with a space group R  -  3 and have a cation ordering between Ba and La ions in the A-site. In these compounds, the magnetic M ions form the 2D triangular lattice. From the results of magnetic measurements, the ferromagnetic ordering of M²⁺ ions for M  =  Co (T _C  =  1.3 K) and Ni (6.2 K) and the paramagnetic behavior (T  >  1.8 K) with an antiferromagnetic interaction for M  =  Mn are observed. From the DFT calculation, their band structures and magnetic interactions are discussed.

3D Spin-Liquid State in an Organic Hyperkagome Lattice of Mott Dimers

We report the first 3D spin liquid state of isotropic organic spins. Structural analysis, and magnetic and heat-capacity measurements were carried out for a chiral organic radical salt, (TBA)_{1.5}[(-)-NDI-Δ] (TBA denotes tetrabutylammonium and NDI denotes naphthalene diimide), in which (-)-NDI-Δ forms a K_{4} structure due to its triangular molecular structure and an intermolecular π-π overlap between the NDI moieties. This lattice was identical to the hyperkagome lattice of S=1/2 Mott dimers, and should exhibit 3D spin frustration. In fact, even though the high-temperature magnetic susceptibility followed the Curie-Weiss law with a negative Weiss constant of θ=-15  K, the low-temperature magnetic measurements revealed no long-range magnetic ordering down to 70 mK, and suggested the presence of a spin liquid state with a large residual paramagnetism χ_{0} of 8.5×10^{-6}  emu g^{-1} at the absolute zero temperature. This was supported by the ^{14}N NMR measurements down to 0.38 K. Further, the low-temperature heat capacities c_{p} down to 68 mK clearly indicated the presence of c_{p} for the spin liquid state, which can be fitted to the power law of T^{0.62} in the wide temperature range 0.07-4.5 K.

Thermal Hall Effect in a Phonon-Glass Ba_{3}CuSb_{2}O_{9}

A distinct thermal Hall signal is observed in a quantum spin liquid candidate Ba_{3}CuSb_{2}O_{9}. The transverse thermal conductivity shows a power-law temperature dependence below 50 K, where a spin gap opens. We suggest that because of the very low longitudinal thermal conductivity and the thermal Hall signals, a phonon Hall effect is induced by strong phonon scattering of orphan Cu^{2+} spins formed in the random domains of the Cu^{2+}-Sb^{5+} dumbbells in Ba_{3}CuSb_{2}O_{9}.

Double phase transition in the triangular antiferromagnet Ba3CoTa2O9

Here, we report the synthesis and magnetic properties of a new triangular lattice antiferromagnet Ba₃CoTa₂O₉. The effective spin of Co²⁺ is found to be J  =  1/2 at low temperatures due to the combined effect of crystal field and spin-orbit coupling. Ba₃CoTa₂O₉ undergoes two successive magnetic phase transitions at [Formula: see text] K and [Formula: see text] K in zero applied field, which is typical for triangular antiferromagnets with the easy-axis magnetic anisotropy. With increasing field, the transition anomalies are found to shift toward low temperatures, confirming the antiferromagnetic nature of the transitions. At higher fields, the transition peaks in the heat capacity data disappear and give way to a broad maximum, which can be ascribed to a Schottky anomaly due to the Zeeman splitting of spin levels. The H  -  T phase diagram of the compound shows three distinct phases. The possible nature of these phases is discussed.

Rearrangement of van der Waals stacking and formation of a singlet state at T = 90 K in a cluster magnet

A change of van der Waals stacking occurs spontaneously at 90 K in a cluster magnet.

Anomalous vacuum energy and stability of a quantum liquid

We show that the vacuum (zero-point) energy of a low-temperature quantum liquid is a variable property which changes with the state of the system, in notable contrast to the static vacuum energy in solids commonly considered. We further show that this energy is inherently anomalous: it decreases with temperature and gives a negative contribution to a system's heat capacity. This effect operates in an equilibrium and macroscopic system, in marked contrast to small or out-of-equilibrium configurations discussed previously. We find that the negative contribution is over-compensated by the positive term from the excitation of longitudinal fluctuations and demonstrate how the overall positive heat capacity is related to the stability of a condensed phase at the microscopic level.

Origin of the Spin-Orbital Liquid State in a Nearly J=0 Iridate Ba_{3}ZnIr_{2}O_{9}

We show using detailed magnetic and thermodynamic studies and theoretical calculations that the ground state of Ba_{3}ZnIr_{2}O_{9} is a realization of a novel spin-orbital liquid state. Our results reveal that Ba_{3}ZnIr_{2}O_{9} with Ir^{5+} (5d^{4}) ions and strong spin-orbit coupling (SOC) arrives very close to the elusive J=0 state but each Ir ion still possesses a weak moment. Ab initio density functional calculations indicate that this moment is developed due to superexchange, mediated by a strong intradimer hopping mechanism. While the Ir spins within the structural Ir_{2}O_{9} dimer are expected to form a spin-orbit singlet state (SOS) with no resultant moment, substantial frustration arising from interdimer exchange interactions induce quantum fluctuations in these possible SOS states favoring a spin-orbital liquid phase down to at least 100 mK.

Disorder-Driven Spin-Orbital Liquid Behavior in the Ba3XSb2O9 Materials

Recent experiments on the Ba(3)XSb(2)O(9) family have revealed materials that potentially realize spin- and spin-orbital liquid physics. However, the lattice structure of these materials is complicated due to the presence of charged X(2+)-Sb(5+) dumbbells, with two possible orientations. To model the lattice structure, we consider a frustrated model of charged dumbbells on the triangular lattice, with long-range Coulomb interactions. We study this model using Monte Carlo simulation, and find a freezing temperature, T(frz), at which the simulated structure factor matches well to low-temperature x-ray diffraction data for Ba(3)CuSb(2)O(9). At T=T(frz) we find a complicated "branching" structure of superexchange-linked X(2+) clusters, which form a fractal pattern with fractal dimension d(f)=1.90. We show that this gives a natural explanation for the presence of orphan spins. Finally we provide a plausible mechanism by which such dumbbell disorder can promote a spin-orbital resonant state with delocalized orphan spins.

Absence of Jahn-Teller transition in the hexagonal Ba3CuSb2O9 single crystal

With decreasing temperature, liquids generally freeze into a solid state, losing entropy in the process. However, exceptions to this trend exist, such as quantum liquids, which may remain unfrozen down to absolute zero owing to strong quantum entanglement effects that stabilize a disordered state with zero entropy. Examples of such liquids include Bose-Einstein condensation of cold atoms, superconductivity, quantum Hall state of electron systems, and quantum spin liquid state in the frustrated magnets. Moreover, recent studies have clarified the possibility of another exotic quantum liquid state based on the spin-orbital entanglement in FeSc2S4. To confirm this exotic ground state, experiments based on single-crystalline samples are essential. However, no such single-crystal study has been reported to date. Here, we report, to our knowledge, the first single-crystal study on the spin-orbital liquid candidate, 6H-Ba3CuSb2O9, and we have confirmed the absence of an orbital frozen state. In strongly correlated electron systems, orbital ordering usually appears at high temperatures in a process accompanied by a lattice deformation, called a static Jahn-Teller distortion. By combining synchrotron X-ray diffraction, electron spin resonance, Raman spectroscopy, and ultrasound measurements, we find that the static Jahn-Teller distortion is absent in the present material, which indicates that orbital ordering is suppressed down to the lowest temperatures measured. We discuss how such an unusual feature is realized with the help of spin degree of freedom, leading to a spin-orbital entangled quantum liquid state.

Effect of divalent Ba cation substitution with Sr on coupled 'multiglass' state in the magnetoelectric multiferroic compound Ba3NbFe3Si2O14

(Ba/Sr)₃NbFe₃Si₂O₁₄ is a magneto-electric multiferroic with an incommensurate antiferromagnetic spiral magnetic structure which induces electric polarization at 26 K. Structural studies show that both the compounds have similar crystal structure down to 6 K. They exhibit a transition, T_N at 26 K and 25 K respectively, as indicated by heat capacity and magnetization, into an antiferromagnetic state. Although Ba and Sr are isovalent, they exhibit very different static and dynamic magnetic behaviors. The Ba-compound exhibits a glassy behavior with critical slowing dynamics with a freezing temperature of ~35 K and a critical exponent of 3.9, a value close to the 3-D Ising model above T_N, in addition to the invariant transition into an antiferromagnetic state. The Sr-compound however does not exhibit any dispersive behavior except for the invariant transition at T_N. The dielectric constant reflects magnetic behavior of the two compounds: the Ba-compound has two distinct dispersive peaks while the Sr-compound has a single dispersive peak. Thus the compounds exhibit coupled ‘multiglass’ behavior. The difference in magnetic properties between the two compounds is found to be due to modifications to super exchange path angle and length as well as anti-site defects which stabilize either ferromagnetic or antiferromagnetic interactions.

Gapless quantum spin liquid in an organic spin-1/2 triangular-lattice κ-H3(Cat-EDT-TTF)2

We report the results of SQUID and torque magnetometry of an organic spin-1/2 triangular-lattice κ-H(3)(Cat-EDT-TTF)(2). Despite antiferromagnetic exchange coupling at 80-100 K, we observed no sign of antiferromagnetic order down to 50 mK owing to spin frustration on the triangular lattice. In addition, we found nearly temperature-independent susceptibility below 3 K associated with Pauli paramagnetism. These observations suggest the development of gapless quantum spin liquid as the ground state. On the basis of a comparative discussion, we point out that the gapless quantum spin liquid states in organic systems share a possible mechanism, namely the formation of a band with a Fermi surface possibly attributed to spinons.

Theory of a competitive spin liquid state for weak Mott insulators on the triangular lattice

We propose a novel quantum spin liquid state that can explain many of the intriguing experimental properties of the low-temperature phase of the organic spin liquid candidate materials κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2. This state of paired fermionic spinons preserves all symmetries of the system, and it has a gapless excitation spectrum with quadratic bands that touch at momentum k[over →]=0. This quadratic band touching is protected by symmetries. Using variational Monte Carlo techniques, we show that this state has highly competitive energy in the triangular lattice Heisenberg model supplemented with a realistically large ring-exchange term.

Singlet ground state of the quantum antiferromagnet Ba(3)CuSb(2)O(9)

We present local probe results on the honeycomb lattice antiferromagnet Ba(3)CuSb(2)O(9). Muon spin relaxation measurements in a zero field down to 20 mK show unequivocally that there is a total absence of spin freezing in the ground state. Sb NMR measurements allow us to track the intrinsic susceptibility of the lattice, which shows a maximum at around 55 K and drops to zero in the low-temperature limit. The spin-lattice relaxation rate shows two characteristic energy scales, including a field-dependent crossover to exponential low-temperature behavior, implying gapped magnetic excitations.

Physics. The impact of ionic frustration on electronic order

The frustrated ordering of dipoles created by copper and antimony ions in an oxide material may help to create an exotic quantum electronic state.

Spin liquid phases for spin-1 systems on the triangular lattice

Motivated by recent experiments on material Ba3NiSb2O9, we propose two novel spin liquid phases (A and B) for spin-1 systems on a triangular lattice. At the mean field level, both spin liquid phases have gapless fermionic spinon excitations with quadratic band touching; thus, in both phases the spin susceptibility and γ=C(v)/T saturate to a constant at zero temperature, which are consistent with the experimental results on Ba3NiSb2O9. On the lattice scale, these spin liquid phases have Sp(4)~SO(5) gauge fluctuation, while in the long wavelength limit this Sp(4) gauge symmetry is broken down to U(1)×Z(2) in the type A spin liquid phase, and broken down to Z(4) in the type B phase. We also demonstrate that the A phase is the parent state of the ferroquadrupole state, nematic state, and the noncollinear spin density wave state.

High-pressure sequence of Ba3NiSb2O9 structural phases: new S = 1 quantum spin liquids based on Ni2+

Two new gapless quantum spin-liquid candidates with S = 1 (Ni(2+)) moments: the 6H-B phase of Ba(3)NiSb(2)O(9) with a Ni(2+)-triangular lattice and the 3C phase with a Ni(2/3)Sb(1/3)-three-dimensional edge-shared tetrahedral lattice were obtained under high pressure. Both compounds show no magnetic order down to 0.35 K despite Curie-Weiss temperatures θ(CW) of -75.5 (6H-B) and -182.5 K (3C), respectively. Below ~25 K, the magnetic susceptibility of the 6H-B phase saturates to a constant value χ(0) = 0.013 emu/mol, which is followed below 7 K by a linear-temperature-dependent magnetic specific heat (C(M)) displaying a giant coefficient γ = 168 mJ/mol K(2). Both observations suggest the development of a Fermi-liquid-like ground state. For the 3C phase, the C(M) perpendicular T(2) behavior indicates a unique S = 1, 3D quantum spin-liquid ground state.

Unconventional magnetism in a nitrogen-containing analog of cupric oxide

We have investigated the magnetic properties of CuNCN, the first nitrogen-based analog of cupric oxide CuO. Our muon-spin relaxation, nuclear magnetic resonance, and electron-spin resonance studies reveal that classical magnetic ordering is absent down to the lowest temperatures. However, a large enhancement of spin correlations and an unexpected inhomogeneous magnetism have been observed below 80 K. We attribute this to a peculiar fragility of the electronic state against weak perturbations due to geometrical frustration, which selects between competing spin-liquid and more conventional frozen states.