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.

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.

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.

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.

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).

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.

Frustration- and doping-induced magnetism in a Fermi-Hubbard simulator

Geometrical frustration in strongly correlated systems can give rise to a plethora of novel ordered states and intriguing magnetic phases, such as quantum spin liquids1-3. Promising candidate materials for such phases4-6 can be described by the Hubbard model on an anisotropic triangular lattice, a paradigmatic model capturing the interplay between strong correlations and magnetic frustration7-11. However, the fate of frustrated magnetism in the presence of itinerant dopants remains unclear, as well as its connection to the doped phases of the square Hubbard model12. Here we investigate the local spin order of a Hubbard model with controllable frustration and doping, using ultracold fermions in anisotropic optical lattices continuously tunable from a square to a triangular geometry. At half-filling and strong interactions U/t ≈ 9, we observe at the single-site level how frustration reduces the range of magnetic correlations and drives a transition from a collinear Néel antiferromagnet to a short-range correlated 120° spiral phase. Away from half-filling, the triangular limit shows enhanced antiferromagnetic correlations on the hole-doped side and a reversal to ferromagnetic correlations at particle dopings above 20%, hinting at the role of kinetic magnetism in frustrated systems. This work paves the way towards exploring possible chiral ordered or superconducting phases in triangular lattices8,13 and realizing t-t' square lattice Hubbard models that may be essential to describe superconductivity in cuprate materials14.

Observation of flat band, Dirac nodal lines and topological surface states in Kagome superconductor CsTi3Bi5

Kagome lattices of various transition metals are versatile platforms for achieving anomalous Hall effects, unconventional charge-density wave orders and quantum spin liquid phenomena due to the strong correlations, spin-orbit coupling and/or magnetic interactions involved in such a lattice. Here, we use laser-based angle-resolved photoemission spectroscopy in combination with density functional theory calculations to investigate the electronic structure of the newly discovered kagome superconductor CsTi3Bi5, which is isostructural to the AV3Sb5 (A = K, Rb or Cs) kagome superconductor family and possesses a two-dimensional kagome network of titanium. We directly observe a striking flat band derived from the local destructive interference of Bloch wave functions within the kagome lattice. In agreement with calculations, we identify type-II and type-III Dirac nodal lines and their momentum distribution in CsTi3Bi5 from the measured electronic structures. In addition, around the Brillouin zone centre, [Formula: see text] nontrivial topological surface states are also observed due to band inversion mediated by strong spin-orbit coupling.

Amorphous and Polycrystalline Routes toward a Chiral Spin Liquid

We show that a chiral spin liquid spontaneously emerges in partially amorphous, polycrystalline, or ion-irradiated Kitaev materials. In these systems, time-reversal symmetry is broken spontaneously due to a nonzero density of plaquettes with an odd number of edges n_{odd}. This mechanism opens a sizable gap, at small n_{odd} compatible with that of typical amorphous materials and polycrystals, and which can alternatively be induced by ion irradiation. We find that the gap is proportional to n_{odd}, saturating at n_{odd}∼40%. Using exact diagonalization, we find that the chiral spin liquid is approximately as stable to Heisenberg interactions as Kitaev's honeycomb spin-liquid model. Our results open up a significant number of noncrystalline systems where chiral spin liquids can emerge without external magnetic fields.

Spin-Liquid Insulators Can Be Landau's Fermi Liquids

The long search for insulating materials that possess low-energy quasiparticles carrying electron's quantum numbers except charge-inspired by the neutral spin-1/2 excitations, the so-called spinons, exhibited by Anderson's resonating-valence-bond state-seems to have reached a turning point after the discovery of several Mott insulators displaying the same thermal and magnetic properties as metals, including quantum oscillations in a magnetic field. Here, we show that such anomalous behavior is not inconsistent with Landau's Fermi liquid theory of quasiparticles at a Luttinger surface. That is the manifold of zeros within the Brillouin zone of the single-particle Green's function at zero frequency, and which thus defines the spinon Fermi surface conjectured by Anderson.

Flat band ferromagnetism in Pb[Formula: see text]Sb[Formula: see text]O[Formula: see text] via a self-doped mechanism

Electron systems with strong geometrical frustrations have flat bands, and their unusual band dispersions are expected to induce a wide variety of physical properties. However, for the emergence of such properties, the Fermi level must be pinned within the flat band. In this study, we performed first-principles calculations on pyrochlore oxide Pb[Formula: see text]Sb[Formula: see text]O[Formula: see text] and theoretically clarified that the self-doping mechanism induces pinning of the Fermi level in the flat band in this system. Therefore, a very high density of states is realized at the Fermi level, and the ferromagnetic state transforms into the ground state via a flat band mechanism, although the system does not contain any magnetic elements. This compound has the potential to serve as a new platform for projecting the properties of flat band systems in the real world.

Emergent Z_{2} Gauge Theories and Topological Excitations in Rydberg Atom Arrays

Strongly interacting arrays of Rydberg atoms provide versatile platforms for exploring exotic many-body phases and dynamics of correlated quantum systems. Motivated by recent experimental advances, we show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to emergent Z_{2} gauge theories endowed with matter fields. Based on this mapping, we describe how Rydberg platforms could realize two distinct classes of topological Z_{2} quantum spin liquids, which differ in their patterns of translational symmetry fractionalization. We also discuss the natures of the fractionalized excitations of these Z_{2} spin liquid states using both fermionic and bosonic parton theories and illustrate their rich interplay with proximate solid phases.

Controlling magnetic frustration in 1T-TaS2via Coulomb engineered long-range interactions

Magnetic frustrations in two-dimensional materials provide a rich playground to engineer unconventional phenomena. However, despite intense efforts, a realization of tunable frustrated magnetic order in two-dimensional materials remains an open challenge. Here we propose Coulomb engineering as a versatile strategy to tailor magnetic ground states in layered materials. Using the frustrated van der Waals monolayer 1T-TaS₂as an example, we show how long-range Coulomb interactions renormalize the low energy nearly flat band structure, leading to a Heisenberg model which depends on the Coulomb interactions. Based on this, we show that superexchange couplings in the material can be precisely tailored by means of environmental dielectric screening, ultimately allowing to externally drive the material towards a tunable frustrated regime. Our results put forward Coulomb engineering as a powerful tool to manipulate magnetic properties of van der Waals materials.

Frustration in a generalized kagomé Ising antiferromagnet: Exact results

We obtain the exact ground-state phase diagram of a generalized kagomé antiferromagnet with both pair and triplet interactions, J_{2} and J_{3}, respectively, in the presence of a magnetic field h appropriately tuned. We find that when the pair interaction J_{2}<0 dominates, the ground state is geometrically frustrated; on the other hand, the ground state is disordered but not frustrated when the triplet interaction J_{3} dominates, the boundaries between the two cases being at J_{3}=±J_{2}. The exact ground-state crossover lines between the two distinct types of disorder remain identifiable crossover curves at finite temperatures. In the frustrated domain, the ground state of the three-parameter model is identical to the ground state of the prototype one-parameter (J_{2}<0) model of geometrical frustration. Towards further understanding the frustration domain of the three-parameter model, a closed-form approximation (exact at zero temperature) determines solutions on a two-parameter subspace for induced magnetization and parallel magnetic susceptibility at finite fields h and temperatures T, the inverse susceptibility showing a Curie-Weiss behavior. We argue that the existence of an exact T=0 threshold magnetic field, below which the magnetization remains zero, indicates the existence of a gapped spectrum attributable to the presence of the triplet interaction J_{3}.

A Geometrically Frustrated Family of MIIMIIIF5(H2O)2 Mixed-Metal Fluorides with Complex Magnetic Interactions

Inverse weberites are of interest as geometrically frustrated magnetic materials due to their unique cation arrangement. We have synthesized nine isostructural materials that adopt the inverse weberite crystal structure, which consists of cross-linked kagome layers. These materials, having the general formula M^IIM^IIIF₅(H₂O)₂ (M^II = Co, Mn, Ni, Zn; M^III = Ga, Cr, Fe, V), were synthesized using mild hydrothermal conditions, which yielded phase-pure samples after optimization of the reaction conditions. Their crystal structures and optical, thermal, and magnetic behavior were characterized using single-crystal X-ray diffraction, UV-vis spectroscopy, thermogravimetric analysis, and measurement of the magnetic susceptibility and isothermal magnetization data, respectively. Three distinct types of magnetism were observed, including simple paramagnetism, antiferromagnetism, and canted antiferromagnetism; the last type is accompanied by a high frustration index fin the range 4.16-8.09. We demonstrated that the magnetic behavior of inverse weberites depends on the presence or absence of unpaired-electron-containing cations on the two distinct crystallographic sites, which can be employed for the prediction of the magnetic properties of other compounds in this rich and diverse family.

Magnetic properties and signatures of ordering in triangular lattice antiferromagnet KCeO2

The magnetic ground state and the crystalline electric field level scheme of the triangular lattice antiferromagnet KCeO 2 are investigated. Below T N = 300 mK, KCeO 2 develops signatures of magnetic order in specific heat measurements and low energy inelastic neutron scattering data. Trivalent Ce 3 + ions in the D 3 d local environment of this compound exhibit large splittings among the lowest three 4 f 1 Kramers doublets defining for the free ion the J = 5 / 2 sextet and a ground state doublet with dipole character, consistent with recent theoretical predictions in M. S. Eldeeb et al. Phys. Rev. Materials 4, 124001 (2020). An unexplained, additional local mode appears, and potential origins of this anomalous mode are discussed.

Dynamic fingerprint of fractionalized excitations in single-crystalline Cu3Zn(OH)6FBr

Beyond the absence of long-range magnetic orders, the most prominent feature of the elusive quantum spin liquid (QSL) state is the existence of fractionalized spin excitations, i.e., spinons. When the system orders, the spin-wave excitation appears as the bound state of the spinon-antispinon pair. Although scarcely reported, a direct comparison between similar compounds illustrates the evolution from spinon to magnon. Here, we perform the Raman scattering on single crystals of two quantum kagome antiferromagnets, of which one is the kagome QSL candidate Cu₃Zn(OH)₆FBr, and another is an antiferromagnetically ordered compound EuCu₃(OH)₆Cl₃. In Cu₃Zn(OH)₆FBr, we identify a unique one spinon-antispinon pair component in the E_2g magnetic Raman continuum, providing strong evidence for deconfined spinon excitations. In contrast, a sharp magnon peak emerges from the one-pair spinon continuum in the E_g magnetic Raman response once EuCu₃(OH)₆Cl₃ undergoes the antiferromagnetic order transition. From the comparative Raman studies, we can regard the magnon mode as the spinon-antispinon bound state, and the spinon confinement drives the magnetic ordering.

Proximate Quantum Spin Liquid on Designer Lattice

Complementary to bulk synthesis, here we propose a designer lattice with extremely high magnetic frustration and demonstrate the possible realization of a quantum spin liquid state from both experiments and theoretical calculations. In an ultrathin (111) CoCr₂O₄ slice composed of three triangular and one kagome cation planes, the absence of a spin ordering or freezing transition is demonstrated down to 0.03 K, in the presence of strong antiferromagnetic correlations in the energy scale of 30 K between Co and Cr sublattices, leading to the frustration factor of ∼1000. Persisting spin fluctuations are observed at low temperatures via low-energy muon spin relaxation. Our calculations further demonstrate the emergence of highly degenerate magnetic ground states at the 0 K limit, due to the competition among multiply altered exchange interactions. These results collectively indicate the realization of a proximate quantum spin liquid state on the synthetic lattice.

order in quantum kagome Heisenberg antiferromagnet

We have studied the nearest neighbor Heisenberg model with added Dzyaloshinskii-Moriya interaction using Schwinger boson mean-field theory considering the in-plane component as well as out-of-plane component. Motivated by the experimental result of vesignieite that the ground state is in aQ = 0long-range order state, we first looked at the classical ground state of the model and considered the mean-field ansatz which mimics the classical ground state in the largeSlimit. We have obtained the ground-state phase diagram of this model and calculated properties of different phases. We have also studied the above model numerically using exact diagonalization up to a system sizeN= 30. We have compared the obtained results from these two approaches. Our results are in agreement with the experimental result of the vesignieite.

Frustrated Heisenberg J1-J2 model within the stretched diamond lattice of LiYbO2

We investigate the magnetic properties of LiYbO2, containing a three-dimensionally frustrated, diamond-like lattice via neutron scattering, magnetization, and heat capacity measurements. The stretched diamond network of Yb3+ ions in LiYbO2 enters a long-range incommensurate, helical state with an ordering wave vector k = ( 0.384 , ± 0.384 , 0 ) that "locks-in" to a commensurate k = ( 1 / 3 , ± 1 / 3,0 ) phase under the application of a magnetic field. The spiral magnetic ground state of LiYbO2 can be understood in the framework of a Heisenberg J 1 - J 2 Hamiltonian on a stretched diamond lattice, where the propagation vector of the spiral is uniquely determined by the ratio of J 2 / J 1 . The pure Heisenberg model, however, fails to account for the relative phasing between the Yb moments on the two sites of the bipartite lattice, and this detail as well as the presence of an intermediate, partially disordered, magnetic state below 1 K suggests interactions beyond the classical Heisenberg description of this material.

Tuning Topological Orders by a Conical Magnetic Field in the Kitaev Model

We show that a conical magnetic field H=(1,1,1)H can be used to tune the topological order and hence, anyon excitations of the Z_{2} quantum spin liquid in the isotropic antiferromagnetic Kitaev model. A novel topological order, featured with Chern number C=4 and Abelian anyon excitations, is induced in a narrow range of intermediate fields H_{c1}≤H≤H_{c2}. On the other hand, the C=1 Ising-topological order with non-Abelian anyon excitations, as previously known to be present at small fields, is found here to survive up to H_{c1}. The results are obtained by developing and applying a Z_{2} mean field theory that works at finite fields and is asymptotically exact in the zero field limit and the associated variational quantum Monte Carlo.

Synthesis, crystal structures, and magnetic properties of one-dimensional alkali metal copper chlor-tellurites A(NH4)Cu4Te2O6Cl6 (A = K, Cs), NaCu4Te2Cl5O6 and Rb3(NH4)2Cu12Te6Cl16.5O18(OH)0.5

Four new alkali metal copper chlor-tellurites, [Cs(NH4)]layer[Cu4Te2O6Cl6]layer (I), [Rb3(NH4)2(OH)0.5]layer[Cu12Te6Cl16.5O18]layer (II), [K(NH4)]layer[Cu4Te2O6Cl6]layer (III) and [NaCl]layer[Cu4Te2O6Cl4]layer (IV), have been synthesized via hydrothermal reactions using mixtures of AF (A = Cs, Rb, K, Na), CuCl2·2H2O, TeO2, and hydrazine monohydrate. They have two-dimensional (2D)-layered [Cu4Te2Cl5+x-yO6]∞ (x = 0, 2/3, 1; y = 0, 1/6) structures that are separated by different layers comprised of various cations and anions, including A+, NH4+ Cl- OH-, etc. The blocks feature S-shaped ∞[Cu2O3Cl3-x] chains linked by TeO3 trigonal pyramids. The magnetic susceptibility shows a broad maximum at 220 K for I and 240 K for III, which is well simulated by using an alternating antiferromagnetic chain model. The J2/J1 ratio within the alternating chain is estimated to be 0.60(1), and the spin gaps are refined to be 152 K for I and 136 K for III.

Super-Necking Crystal Growth and Structural and Magnetic Properties of SrTb2O4 Single Crystals

We report on single-crystal growths of the SrTb₂O₄ compound by a super-necking technique with a laser-floating-zone furnace and study the stoichiometry, growth mode, and structural and magnetic properties by scanning electronic microscopy, neutron Laue, X-ray powder diffraction, and the physical property measurement system. We optimized the growth parameters, mainly the growth speed, atmosphere, and the addition of a Tb₄O₇ raw material. Neutron Laue diffraction displays the characteristic feature of a single crystal. Our study reveals an atomic ratio of Sr:Tb = 0.97(2):2.00(1) and a possible layer by layer crystal growth mode. Our X-ray powder diffraction study determines the crystal structure, lattice constants, and atomic positions. The paramagnetic (PM) Curie-Weiss (CW) temperature θ_CW = 5.00(4) K, and the effective PM moment M _mea ^eff = 10.97(1) μ_B per Tb³⁺ ion. The data of magnetization versus temperature can be divided into three regimes, showing a coexistence of antiferromagnetic and ferromagnetic interactions. This probably leads to the magnetic frustration in the SrTb₂O₄ compound. The magnetization at 2 K and 14 T originates from both the Tb1 and Tb2 sites and is strongly frustrated with an expected saturation field at ∼41.5 T, displaying an intricate phase diagram with three ranges.

Topological approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets

We have formulated a twist operator argument for the geometrically frustrated quantum spin systems on the kagome and triangular lattices, thereby extending the application of the Lieb-Schultz-Mattis and Oshikawa-Yamanaka-Affleck theorems to these systems. The equivalent large gauge transformation for the geometrically frustrated lattice differs from that for non-frustrated systems due to the existence of multiple sublattices in the unit cell and non-orthogonal basis vectors. Our study for the S  =  1/2 kagome Heisenberg antiferromagnet at zero external magnetic field gives a criterion for the existence of a two-fold degenerate ground state with a finite excitation gap and fractionalized excitations. At finite field, we predict various plateaux at fractional magnetisation, in analogy with integer and fractional quantum Hall states of the primary sequence. These plateaux correspond to gapped quantum liquid ground states with a fixed number of singlets and spinons in the unit cell. A similar analysis for the triangular lattice predicts a single fractional magnetization plateau at 1/3. Our results are in broad agreement with numerical and experimental studies.

Quantum Disordering of an Antiferromagnetic Order by Quenched Randomness in an Organic Mott Insulator

The behavior of interacting spins subject to randomness is a longstanding issue and the emergence of exotic quantum states is among intriguing theoretical predictions. We show how a quantum-disordered phase emerges from a classical antiferromagnet by controlled randomness. ^{1}H NMR of a successively x-ray-irradiated organic Mott insulator finds that the magnetic order collapses into a spin-glass-like state, immediately after a slight amount of disorder centers are created, and evolves to a gapless quantum-disordered state without spin freezing, spin gap, or critical slowing down, as reported by T. Furukawa et al. [Phys. Rev. Lett. 115, 077001 (2015)]PRLTAO0031-900710.1103/PhysRevLett.115.077001 through sequential reductions in the spin freezing temperature and moment.

Spatial anisotropy of the quantum spin liquid system YbMgGaO4 revealed by ab initio calculations

YbMgGaO₄ was recently proposed as a promising quantum-spin-liquid candidate material. However, some details of its structure, such as those related to a spatial anisotropy, were not completely understood. In this work, we perform ab initio calculations based on density-functional-theory to investigate the structural, the electronic and the magnetic properties of YbMgGaO₄. The geometrical model was constructed to take into account disorder effects produced by the random distribution of Ga and Mg along the lattice. We found a substantial spatial anisotropy revealed by variations up to 8% in the Mg-O and Ga-O bond lengths, which results in variations up to 3% in the Yb-Yb distances along its triangular lattice. Thus, the Yb lattice was not perfectly triangular. Furthermore, we demonstrate an out-of-plane magnetization at the Yb atoms with magnetic anisotropy energy of [Formula: see text] eV/Yb and a small interlayer exchange of [Formula: see text] eV/Yb, demonstrating that the system is only approximately two-dimensional. The presented results provide insights for an atomic-scale understanding of YbMgGaO₄ with density-functional-theory calculations.

Electron-nuclear hyperfine coupling in quantum kagome antiferromagnets from first-principles calculation and a reflection of the defect effect

The discovery of ideal spin-1/2 kagome antiferromagnets Herbertsmithite and Zn-doped Barlowite represents a breakthrough in the quest for quantum spin liquids (QSLs), and nuclear magnetic resonance (NMR) spectroscopy plays a prominent role in revealing the quantum paramagnetism in these compounds. However, interpretation of NMR data that is often masked by defects can be controversial. Here, we show that the most significant interaction strength for NMR, i.e. the hyperfine coupling (HFC) strength, can be reasonably reproduced by first-principles calculations for these proposed QSLs. Applying this method to a supercell containing Cu-Zn defects enables us to map out the variation and distribution of HFC at different nuclear sites. This predictive power is expected to bridge the missing link in the analysis of the low-temperature NMR data.

Order-disorder transition in the S = ½ kagome antiferromagnets claringbullite and barlowite

The transition in the quantum magnets barlowite, Cu4(OH)6FBr, and claringbullite, Cu4(OH)6FCl is of an order-disorder type, where at ambient temperature interlayer Cu2+ ions are dynamically disordered over three equivalent positions. The disorder becomes static as the temperature is decreased, resulting in a lowering of symmetry. Ab initio density functional theory calculations explain this structural phase transition and provide insights regarding the differences between these two materials.

Negative Thermal Expansion in the Plateau State of a Magnetically Frustrated Spinel

We report on negative thermal expansion (NTE) in the high-field, half-magnetization plateau phase of the frustrated magnetic insulator CdCr_{2}O_{4}. Using dilatometry, we precisely map the phase diagram at fields of up to 30 T and identify a strong NTE associated with the collinear half-magnetization plateau for B>27  T. The resulting phase diagram is compared with a microscopic theory for spin-lattice coupling, and the origin of the NTE is identified as a large negative change in magnetization with temperature, coming from a nearly localized band of spin excitations in the plateau phase. These results provide useful guidelines for the discovery of new NTE materials.

Magnetism study on a triangular lattice antiferromagnet Cu2(OH)3Br

Magnetism of Cu₂(OH)₃Br single crystals based on a triangular lattice is studied by means of magnetic susceptibility, pulsed-field magnetization, and specific heat measurements. There are two inequivalent Cu²⁺ sites in an asymmetric unit. Both Cu²⁺ sublattices undergo a long-range antiferromagnetic (AFM) order at [Formula: see text] K. Upon cooling, an anisotropy crossover from Heisenberg to XY behavior is observed below 7.5 K from the anisotropic magnetic susceptibility. The magnetic field applied within the XY plane induces a spin-flop transition of Cu²⁺ ions between 4.9 T and 5.3 T. With further increasing fields, the magnetic moment is gradually increased but is only about half of the saturation of a Cu²⁺ ion even in 30 T. The individual reorientation of the inequivalent Cu²⁺ spins under field is proposed to account for the magnetization behavior. The observed spin-flop transition is likely related to one Cu site, and the AFM coupling among the rest Cu spins is so strong that the 30 T field cannot overcome the anisotropy. The temperature dependence of the magnetic specific heat, which is well described by a sum of two gapped AFM contributions, is a further support for the proposed scenario.

Embedding S = 1/2 Kagome-like Lattice in Reduced Graphene Oxide

An elegant platform to explore frustrated magnetism is the kagome spin lattice. In this work, clinoatacamite, a naturally occurring S = 1/2 kagome-like antiferromagnetic insulator, is synthesized in water at ambient pressure for the first time from a cuprous chloride (CuCl) precursor whereby Cu(I) was spontaneously oxidized to Cu(II) in the form of clinoatacamite [Cu₂(OH)₃Cl] with a simultaneous reduction of graphene oxide (GO) to reduced graphene oxide (rGO) in one pot. A stable nanocomposite of phase-pure clinoatacamite nanocrystals embedded in the rGO matrix was isolated. The clinoatacamite-rGO nanocomposite was determined to be magnetically active with a markedly enhanced coercive field of ∼2500 Oe at 5 K as well as electronically active with a conductivity value of ∼200 S·m^-1 at 300 K. Our results illustrate an avenue of combining exotic magnetic and electronic lattices without impeding their individual characteristics and synergistically generating a new class of magnetic semiconductors.

Unveiling spin-glass transition and antiferromagnetic order by μSR studies in spin-chain Sm2BaNiO5

We report the zero-field and longitudinal field muon spin relaxation studies in a spin-chain compound Sm₂BaNiO₅. Two magnetic transitions, that have not been previously detected by the heat capacity and magnetization measurements, are confirmed at 46 and 9 K. The antiferromagnetic order is suggested at 46 K. Analysis of the muon spin polarization unveils the spin-glass transition at 9 K. Time-field scaling relation of the muon spin polarization verifies the spin-spin autocorrelation function following the cut-off power law, which is approximated by the Ogielski form, as employed numerically for characterizing the spin-glasses.

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

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

First-Principles Design of the Spinel Iridate Ir_{2}O_{4} for High-Temperature Quantum Spin Ice

Insulating magnetic rare-earth pyrochlores related to spin ice host emergent bosonic monopolar spinons, which obey a magnetic analogue of quantum electrodynamics and may open a route to spinonics. However, the energy scales of the interactions among rare-earth moments are so low (∼ 1 K) that the possible quantum coherence can be achieved at a sub-Kelvin scale. Here, we design high-temperature quantum spin ice materials from first principles. It is shown that the A-site deintercalated spinel iridate Ir_{2}O_{4}, which has been experimentally grown as epitaxial thin films, is a promising candidate for quantum spin ice with a spin-ice-rule interaction of a few tens of meV. Controlling electronic structures of Ir_{2}O_{4} through substrates, it is possible to tune magnetic interactions so that a magnetic Coulomb liquid persists at high temperatures.

Trigonal layered rosiaite-related antiferromagnet MnSnTeO6: ion-exchange preparation, structure and magnetic properties

Ion-exchange treatment of Na2SnTeO6 in molten salt mixtures resulted in rosiaite (PbSb2O6)-related MnSnTeO6. Its crystal structure was refined by the Rietveld method. Of the three possible models of Sn/Te distribution, the disordered model (P3[combining macron]1m, a = 5.23093(11) Å, c = 4.62430(16) Å) was preferred based on bond distances. However, it is supposed that each individual (SnTeO6)2- layer retains complete ordering of the precursor and the apparent disorder is only due to stacking faults. Magnetic studies have shown that MnSnTeO6 orders antiferromagnetically at Neél temperature TN = 9.8 K. The effective magnetic moment reasonably agrees with theoretical estimations assuming high-spin configuration of Mn2+ (S = 5/2). Electron spin resonance reveals spin dynamics in accordance with antiferromagnetic ordering. Moreover, critical broadening of ESR linewidth indicates the low-dimensional type of exchange interactions. Based on the temperature and field-dependent magnetization studies, the magnetic phase diagram of the new compound was constructed.

Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4

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

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

Li doped kagome spin liquid compounds

Herbertsmithite and Zn-doped barlowite are two compounds for experimental realization of two-dimensional kagome spin liquids. Theoretically, it has been proposed that charge doping a quantum spin liquid gives rise to exotic metallic states, such as high-temperature superconductivity. However, one recent experiment on herbertsmithite with successful Li-doping surprisingly showed an insulating state even under a heavily doped scenario, which cannot be explained by previous theories. Using first-principles calculations, we performed a comprehensive study on the Li intercalation doping effect of these two compounds. For the Li-doped herbertsmithite, we identified the optimized Li position at the Cl-(OH)3-Cl pentahedron site instead of the previously speculated Cl-(OH)3 tetrahedral site. With increasing Li doping concentration, saturation magnetization decreases linearly due to charge transfer from Li to Cu ions. Moreover, we found that Li forms chemical bonds with nearby (OH)- and Cl- ions, which lowers the surrounding chemical potential and traps electrons, as evidenced by the localized charge distribution, explaining the insulating behavior measured experimentally. Though a different structure from herbertsmithite, Zn-doped barlowite shows the same features upon Li doping. We conclude that Li doping this family of kagome spin liquids cannot realize exotic metallic states, and other methods should be further explored, such as element substitution with those having different valence electrons.

Instabilities of a U(1) Quantum Spin Liquid in Disordered Non-Kramers Pyrochlores

Quantum spin liquids (QSLs) are exotic phases of matter exhibiting long-range entanglement and supporting emergent gauge fields. A vigorous search for experimental realizations of these states has identified several materials with properties hinting at QSL physics. A key issue in understanding these QSL candidates is often the interplay of weak disorder of the crystal structure with the spin liquid state. It has recently been pointed out that in at least one important class of candidate QSLs-pyrochlore magnets based on non-Kramers ions such as Pr^{3+} or Tb^{3+}-structural disorder can actually promote a U(1) QSL ground state. Here we set this proposal on a quantitative footing by analyzing the stability of the QSL state in the minimal model for these systems: a random transverse field Ising model. We consider two kinds of instability, which are relevant in different limits of the phase diagram: condensation of spinons and confinement of the U(1) gauge fields. Having obtained stability bounds on the QSL state, we apply our results directly to the disordered candidate QSL Pr_{2}Zr_{2}O_{7}. We find that the available data for currently studied samples of Pr_{2}Zr_{2}O_{7} are most consistent with it a ground state outside the spin liquid regime, in a paramagnetic phase with quadrupole moments near saturation due to the influence of structural disorder.

Electrodynamics of quantum spin liquids

Quantum spin liquids attract great interest due to their exceptional magnetic properties characterized by the absence of long-range order down to low temperatures despite the strong magnetic interaction. Commonly, these compounds are strongly correlated electron systems, and their electrodynamic response is governed by the Mott gap in the excitation spectrum. Here we summarize and discuss the optical properties of several two-dimensional quantum spin liquid candidates. First we consider the inorganic material herbertsmithite ZnCu₃(OH)₆Cl₂ and related compounds, which crystallize in a kagome lattice. Then we turn to the organic compounds [Formula: see text]-EtMe₃Sb[Pd(dmit)₂]₂, κ-(BEDT-TTF)₂Ag₂(CN)₃ and κ-(BEDT-TTF)₂Cu₂(CN)₃, where the spins are arranged in an almost perfect triangular lattice, leading to strong frustration. Due to differences in bandwidth, the effective correlation strength varies over a wide range, leading to a rather distinct behavior as far as the electrodynamic properties are concerned. We discuss the spinon contributions to the optical conductivity in comparison to metallic quantum fluctuations in the vicinity of the Mott transition.

Charge Fractionalization in the Two-Channel Kondo Effect

The phenomenon of charge fractionalization describes the emergence of novel excitations with fractional quantum numbers, as predicted in strongly correlated systems such as spin liquids. We elucidate that precisely such an unusual effect may occur in the simplest possible non-Fermi liquid, the two-channel Kondo effect. To bring this concept down to experimental test, we study nonequilibrium transport through a device realizing the charge two-channel Kondo critical point in a recent experiment by Iftikhar et al. [Nature (London) 526, 233 (2015)NATUAS0028-083610.1038/nature15384]. The shot noise at low voltages is predicted to result in a universal Fano factor e^{*}/e=1/2. This allows us to experimentally identify elementary transport processes of emergent fermions carrying half-integer charge.

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.

Unusual Phonon Heat Transport in α-RuCl_{3}: Strong Spin-Phonon Scattering and Field-Induced Spin Gap

The honeycomb Kitaev-Heisenberg model is a source of a quantum spin liquid with Majorana fermions and gauge flux excitations as fractional quasiparticles. Here we unveil the highly unusual low-temperature heat conductivity κ of α-RuCl_{3}, a prime candidate for realizing such physics: beyond a magnetic field of B_{c}≈7.5  T, κ increases by about one order of magnitude, both for in-plane as well as out-of-plane transport. This clarifies the unusual magnetic field dependence unambiguously to be the result of severe scattering of phonons off putative Kitaev-Heisenberg excitations in combination with a drastic field-induced change of the magnetic excitation spectrum. In particular, an unexpected, large energy gap arises, which increases linearly with the magnetic field, reaching remarkable ℏω_{0}/k_{B}≈50  K at 18 T.

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.

Theoretical Discovery of a Superconducting Two-Dimensional Metal-Organic Framework

Superconductivity is a fascinating quantum phenomenon characterized by zero electrical resistance and the Meissner effect. To date, several distinct families of superconductors (SCs) have been discovered. These include three-dimensional (3D) bulk SCs in both inorganic and organic materials as well as two-dimensional (2D) thin film SCs but only in inorganic materials. Here we predict superconductivity in 2D and 3D organic metal-organic frameworks by using first-principles calculations. We show that the highly conductive and recently synthesized Cu-benzenehexathial (BHT) is a Bardeen-Cooper-Schrieffer SC. Remarkably, the monolayer Cu-BHT has a critical temperature (T_c) of 4.43 K, while T_c of bulk Cu-BHT is 1.58 K. Different from the enhanced T_c in 2D inorganic SCs which is induced by interfacial effects, the T_c enhancement in this 2D organic SC is revealed to be the out-of-plane soft-mode vibrations, analogous to surface mode enhancement originally proposed by Ginzburg. Our findings not only shed new light on better understanding 2D superconductivity but also open a new direction to search for SCs by interface engineering with organic materials.

1T-TaS2 as a quantum spin liquid

1T-TaS2 is unique among transition metal dichalcogenides in that it is understood to be a correlation-driven insulator, where the unpaired electron in a 13-site cluster experiences enough correlation to form a Mott insulator. We argue, based on existing data, that this well-known material should be considered as a quantum spin liquid, either a fully gapped [Formula: see text] spin liquid or a Dirac spin liquid. We discuss the exotic states that emerge upon doping and propose further experimental probes.

Nearest-neighbour resonating valence bonds in YbMgGaO4

Since its proposal by Anderson, resonating valence bonds (RVB) formed by a superposition of fluctuating singlet pairs have been a paradigmatic concept in understanding quantum spin liquids. Here, we show that excitations related to singlet breaking on nearest-neighbour bonds describe the high-energy part of the excitation spectrum in YbMgGaO₄, the effective spin-1/2 frustrated antiferromagnet on the triangular lattice, as originally considered by Anderson. By a thorough single-crystal inelastic neutron scattering study, we demonstrate that nearest-neighbour RVB excitations account for the bulk of the spectral weight above 0.5 meV. This renders YbMgGaO₄ the first experimental system where putative RVB correlations restricted to nearest neighbours are observed, and poses a fundamental question of how complex interactions on the triangular lattice conspire to form this unique many-body state.

The signature of short range resonating valence bonds (RVB) to understand quantum spin liquids is yet to be explored. Here, Li et al. observe the putative RVB correlations restricted to nearest neighbours in YbMgGaO₄, responsible for the high-energy spin excitations.