Spin dynamics of the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2

High-Pressure Induced Continuous Structural Evolution of Kagome Antiferromagnet MgMn3(OH)6Cl2: A Structural Analogue to Quantum Spin Liquid Herbertsmithite

MgMn3(OH)6Cl2 serves readily as the classical Heisenberg kagome antiferromagnet lattice spin frustration material, due to its similarity to herbertsmithite in composition and crystal structure. In this work, nanosheets of MgMn3(OH)6Cl2 are synthesized through a solid-phase reaction. Low-temperature magnetic measurements revealed two antiferromagnetic transitions, occurring at ∼8 and 55 K, respectively. Utilizing high-pressure synchrotron radiation X-ray diffraction techniques, the topological structural evolution of MgMn3(OH)6Cl2 under pressures up to 24.8 GPa was investigated. The sample undergoes a second-order structural phase transition from the rhombohedral phase to the monoclinic phase at pressures exceeding 7.8 GPa. Accompanying the disappearance of the Fano-like line shape in the high-pressure Raman spectra were the emergence of new Raman active modes and discontinuities in the variations of Raman shifts in the high-frequency region. The phase transition to a structure with lower symmetry was attributed to the pressure-induced enhancement of cooperative Jahn-Teller distortion, which is caused by the mutual substitution of Mn2+ ions from the kagome layer and Mg2+ ions from the triangular interlayer. High-pressure ultraviolet-visible absorption measurements support the structural evolution. This research provides a robust experimental approach and physical insights for further exploration of classical geometrical frustration materials with kagome lattice.

The type-I, III nodal ring, type-I, III quadratic nodal point, and Dirac valley phonons in 2D kagome lattices M2C3(M = As, Bi, Cd, Hg, P, Sb, Zn)

Topological phases in kagome systems have garnered considerable interest since the introduction of the colloidal kagome lattice. Our study employs first-principle calculations and symmetry analysis to predict the existence of ideal type-I, III nodal rings (NRs), type-I, III quadratic nodal points (QNPs), and Dirac valley phonons (DVPs) in a collection of two-dimensional (2D) kagome lattices M2C3(M = As, Bi, Cd, Hg, P, Sb, Zn). Specifically, the Dirac valley points (DVPs) can be observed at two inequivalent valleys with Berry phases of +πand-π, connected by edge arcs along the zigzag and armchair directions. Additionally, the QNP is pinned at the Γ point, and two edge states emerge from its projections. Notably, these kagome lattices also exhibit ideal type-I and III nodal rings protected by time inversion and spatial inversion symmetries. Our work examines the various categories of nodal points and nodal ring phonons within the 2D kagome systems and presents a selection of ideal candidates for investigating topological phonons in bosonic systems.

Structural phase transformation of quantum spin liquid herbertsmithite via pressure induced enhancement of the cooperative Jahn-Teller effect and antisite disorder

Herbertsmithite, Cu3Zn(OH)6Cl2, serves as one of the most promising candidates for quantum spin liquids with a perfect quantum kagome Heisenberg antiferromagnetic system. It can comprise an ideal model system for studying the compression response of the unique structure as well as exotic properties of kagome quantum spin liquid materials, which is of fundamental importance from both scientific and technological viewpoints. In this work, the structural evolution of herbertsmithite was investigated via in situ X-ray diffraction and Raman scattering techniques up to 30 GPa. The trigonal herbertsmithite structure transformed into a monoclinic clinoatacamite-like structure at 12.6 GPa. High pressure seems to act in a reverse way as Zn-doping for herbertsmithite, with the distortion degree of the system changing continuously. The occurrence of the displacive and reversible phase transition between the polymorphs is a consequence of the interplay between the external pressure and cooperative Jahn-Teller (JT) effect, aided by the presence of antisite mutual substitution of magnetic Cu2+ ions and nonmagnetic Zn2+ ions between the kagome layer and interlayer sites.

Fluctuating magnetic droplets immersed in a sea of quantum spin liquid

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

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.

Flat bands, non-trivial band topology and rotation symmetry breaking in layered kagome-lattice RbTi3Bi5

A representative class of kagome materials, AV3Sb5 (A = K, Rb, Cs), hosts several unconventional phases such as superconductivity, [Formula: see text] non-trivial topological states, and electronic nematic states. These can often coexist with intertwined charge-density wave states. Recently, the discovery of the isostructural titanium-based single-crystals, ATi3Bi5 (A = K, Rb, Cs), which exhibit similar multiple exotic states but without the concomitant charge-density wave, has opened an opportunity to disentangle these complex states in kagome lattices. Here, we combine high-resolution angle-resolved photoemission spectroscopy and first-principles calculations to investigate the low-lying electronic structure of RbTi3Bi5. We demonstrate the coexistence of flat bands and several non-trivial states, including type-II Dirac nodal lines and [Formula: see text] non-trivial topological surface states. Our findings also provide evidence for rotational symmetry breaking in RbTi3Bi5, suggesting a directionality to the electronic structure and the possible emergence of pure electronic nematicity in this family of kagome compounds.

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.

Possible realization of three-dimensional quantum spin liquid behavior in HoVO4

The study of geometrically frustrated magnetic systems with unusual crystal field ground states offers a possibility of realizing the new aspects of physics of disordered systems. In this study, we report our results of structural, magnetic susceptibility, heat capacity measurements, along with density functional theory (DFT) calculations on HoVO₄; a compound in which the presence of a distorted kind of HoO₈polyhedral leads to multiple magnetic interaction paths. The observed broad maximum below 10 K in the temperature response of DC susceptibility curves implies the presence of short-range correlations. AC susceptibility rules out the possibility of any kind of spin freezing. Temperature dependent heat capacity measurement at zero field indicate towards the absence of long-range ordering, along with the presence of a broad maximum centered around 14 K. The residual heat capacity exhibits a characteristic power-law (T^α) behavior with the exponentαnearly equal to 2, which is analogous to that observed for other three-dimensional (3D) quantum spin liquid (QSL) systems. The DFT calculations signify the presence of dominant second and third nearest neighbor interactions, which in turn lead to magnetic frustration in our system. Our investigations suggest that HoVO₄can be a candidate for realizing a 3D QSL state.

The kagomé metals RbTi3Bi5 and CsTi3Bi5

The kagomé metals RbTi3Bi5 and CsTi3Bi5 were synthesized both as polycrystalline powders by heating the elements in an argon atmosphere and as single crystals grown using a self-flux method. The compounds crystallize in the hexagonal crystal system isotypically to KV3Sb5 (P6/mmm, Z = 1, CsTi3Bi5: a = 5.7873(1), c = 9.2062(1) Å; RbTi3Bi5: a = 5.773(1), c = 9.065(1) Å). The titanium atoms form a kagomé net with bismuth atoms in the hexagons as well as above and below the triangles. The alkali metal atoms are coordinated by 12 bismuth atoms and form AlB2-like slabs between the kagomé layers. Magnetic susceptibility measurements with CsTi3Bi5 and RbTi3Bi5 single crystals reveal Pauli-paramagnetism and traces of superconductivity caused by CsBi2/RbBi2 impurities. Magnetotransport measurements reveal conventional Fermi liquid behavior and quantum oscillations indicative of a single dominant orbit at low temperature. DFT calculations show the characteristic metallic kagomé band structure similar to that of CsV3Sb5 with reduced band filling. A symmetry analysis of the band structure does not reveal an obvious and unique signature of a nontrivial topology.

Eminuscent phase in frustrated magnets: a challenge to quantum spin liquids

A geometrically frustrated (GF) magnet consists of localised magnetic moments, spins, whose orientation cannot be arranged to simultaneously minimise their interaction energies. Such materials may host novel fascinating phases of matter, such as fluid-like states called quantum spin-liquids. GF magnets have, like all solid-state systems, randomly located impurities whose magnetic moments may “freeze” at low temperatures, making the system enter a spin-glass state. We analyse the available data for spin-glass transitions in GF materials and find a surprising trend: the glass-transition temperature grows with decreasing impurity concentration and reaches a finite value in the impurity-free limit at a previously unidentified, “hidden”, energy scale. We propose a scenario in which the interplay of interactions and entropy leads to a crossover in the permeability of the medium that assists glass freezing at low temperatures. This low-temperature, “eminuscent”, phase may obscure or even destroy the widely-sought spin-liquid states in rather clean systems.

A spin-glass forms in frustrated magnetic systems when at low temperatures impurity sites “freeze” into a random spin configuration. Here, by looking back at previous experimental results, Syzranov and Ramirez show that the glass-transition temperature grows with decreasing impurity concentration.

Freezing of the Lattice in the Kagome Lattice Heisenberg Antiferromagnet Zn-Barlowite ZnCu_{3}(OD)_{6}FBr

We use ^{79}Br nuclear quadrupole resonance (NQR) to demonstrate that ultraslow lattice dynamics set in below the temperature scale set by the Cu-Cu superexchange interaction J (≃160  K) in the kagome lattice Heisenberg antiferromagnet Zn-barlowite. The lattice completely freezes below 50 K, and ^{79}Br NQR line shapes become twice broader due to increased lattice distortions. Moreover, the frozen lattice exhibits an oscillatory component in the transverse spin echo decay, a typical signature of pairing of nuclear spins by indirect nuclear spin-spin interaction. This indicates that some Br sites form structural dimers via a pair of kagome Cu sites prior to the gradual emergence of spin singlets below ∼30  K. Our findings underscore the significant roles played by subtle structural distortions in determining the nature of the disordered magnetic ground state of the kagome lattice.

Structure, magnetism and magnetocaloric effect in a new triangular lattice compound Gd3Cu9(OH)19Br8

A new triangular lattice compound Gd₃Cu₉(OH)₁₉Br₈ has been synthesized by the hydrothermal method. The structure, magnetism and magnetocaloric effect of Gd₃Cu₉(OH)₁₉Br₈ have been studied by X-ray diffraction, magnetic susceptibility, isothermal magnetization and specific heat measurements. In Gd₃Cu₉(OH)₁₉Br₈, the Cu²⁺ ions form a Kagome lattice along the ab plane, and Gd³⁺ ions are located in the center of hexagonal holes of the Kagome layer. The Cu-sublattice and Gd-sublattice overlap and constitute a magnetic triangular lattice. The temperature dependence of susceptibility and specific heat curves indicate no magnetic transition down to 2 K, suggesting a paramagnetic-like behavior at low temperature. The magnetocaloric effect (MCE) at low temperature has been calculated according to Maxwell's equations. The maximum value of magnetic entropy change −ΔS_M is 26.04 J kg⁻¹ K⁻¹ and adiabatic temperature change ΔT_ad is 13.79 K, for a field change of 0–7 T, indicating a potential application of this compound in the field of magnetic refrigeration at low temperature. The influence of 4f–3d interaction on magnetism and MCE is also discussed.

The two-dimensional magnetic lattice of Gd₃Cu₉(OH)₁₉Br₈, where Gd³⁺ ions are located in the center of hexagonal holes of the Cu-Kagome lattice.

Heat Transport in Herbertsmithite: Can a Quantum Spin Liquid Survive Disorder?

One favorable situation for spins to enter the long-sought quantum spin liquid (QSL) state is when they sit on a kagome lattice. No consensus has been reached in theory regarding the true ground state of this promising platform. The experimental efforts, relying mostly on one archetypal material ZnCu_{3}(OH)_{6}Cl_{2}, have also led to diverse possibilities. Apart from subtle interactions in the Hamiltonian, there is the additional degree of complexity associated with disorder in the real material ZnCu_{3}(OH)_{6}Cl_{2} that haunts most experimental probes. Here we resort to heat transport measurement, a cleaner probe in which instead of contributing directly, the disorder only impacts the signal from the kagome spins. For ZnCu_{3}(OH)_{6}Cl_{2}, we observed no contribution by any spin excitation nor obvious field-induced change to the thermal conductivity. These results impose strong constraints on various scenarios about the ground state of this kagome compound: while certain quantum paramagnetic states other than a QSL may serve as natural candidates, a QSL state, gapless or gapped, must be dramatically modified by the disorder so that the kagome spin excitations are localized.

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.

Crystal chemistry criteria of the existence of spin liquids on the kagome lattice

The structural-magnetic models of 25 antiferromagnetic kagome cuprates similar to herbertsmithite (ZnCu₃(OH)₆Cl₂)-a perspective spin liquid-have been calculated and analyzed. Main correlations between the structure and magnetic properties of these compounds were revealed. It has been demonstrated that, in all AFM kagome cuprates, including herbertsmithite, there exists the competition between the exchange interaction and the antisymmetric anisotropic exchange one (the Dzyaloshinskii-Moriya interaction), as magnetic ions are not linked to the center of inversion in the kagome lattice. This competition is strengthened in all the kagome AFM, except herbertsmithite, by one more type of the anisotropy (duality) of the third in lengthJ3 magnetic couplings (strongJ3(J1₂) next-to-nearest-neighbor couplings in linear chains along the triangle edges and very weak FM or AFMJ3(J_d) couplings along the hexagon diagonals). The above couplings are crystallographically identical, but are divided to two types of different in strength magnetic interactions. The existence of duality ofJ3 couplings originated from the structure of the kagome lattice itself. Only combined contributions of dualJ3 couplings with anisotropic Dzyaloshinskii-Moriya interactions are capable to suppress frustration of kagome antiferromagnetics. It has been demonstrated that the possibility of elimination of such a duality in herbertsmithite, which made it a spin liquid, constitutes a rare lucky event in the kagome system. Three crystal chemistry criteria of the existence of spin liquids on the kagome lattice have been identified: first, the presence of frustrated kagome lattices with strong dominant antiferromagnetic nearest-neighborJ1 couplings competing only with each other in small triangles; second, magnetic isolation of these frustrated kagome lattices; and third, the absence of duality of the third in lengthJ3 magnetic couplings.

Chiral flux phase in the Kagome superconductor AV3Sb5

We argue that the topological charge density wave phase in the quasi-2D Kagome superconductor AV₃Sb₅ is a chiral flux phase. Considering the symmetry of the Kagome lattice, we show that the chiral flux phase has the lowest energy among those states which exhibit 2×2 charge orders observed experimentally. This state breaks the time-reversal symmetry and displays anomalous Hall effect. The explicit pattern of the density of state in real space is calculated. These results are supported by recent experiments and suggest that these materials are new platforms to investigate the interplay between topology, superconductivity and electron-electron correlations.

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.

Ground state and stability of the fractional plateau phase in metallic Shastry-Sutherland system TmB4

We present a study of the ground state and stability of the fractional plateau phase (FPP) with M/M_sat = 1/8 in the metallic Shastry-Sutherland system TmB₄. Magnetization (M) measurements show that the FPP states are thermodynamically stable when the sample is cooled in constant magnetic field from the paramagnetic phase to the ordered one at 2 K. On the other hand, after zero-field cooling and subsequent magnetization these states appear to be of dynamic origin. In this case the FPP states are closely associated with the half plateau phase (HPP, M/M_sat = ½), mediate the HPP to the low-field antiferromagnetic (AF) phase and depend on the thermodynamic history. Thus, in the same place of the phase diagram both, the stable and the metastable (dynamic) fractional plateau (FP) states, can be observed, depending on the way they are reached. In case of metastable FP states thermodynamic paths are identified that lead to very flat fractional plateaus in the FPP. Moreover, with a further decrease of magnetic field also the low-field AF phase becomes influenced and exhibits a plateau of the order of 1/1000 M_sat.

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.

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.

Crystal structure and magnetic properties of the magnetically isolated zigzag chain in KGaCu(PO4)2

Magnetism of any material depends on its crystal structure. However, two isostructural compounds such as MCuMoO4(OH) (M = Na, K) can have markedly different magnetic properties. Herein, we introduce a new method to describe the linkages between the O-atoms and their bridged Cu2+ ions in order to clearly illustrate the structure-magnetic property relationships. This new method can account for magnetic differences between the two isostructural MCuMoO4(OH) and is further confirmed by the rational design and development of a new compound KGaCu(PO4)2 with different linkages. The title compound crystalized in a space group of P21/c adopts a one-dimensional (1D) magnetically isolated S = 1/2 zigzag chain composed of elongated [CuO6] octahedra via sharing alternately equatorial and skew edges. O atoms at the skew edges bridge the equatorial and axial orbitals of neighbouring Cu2+ ions (denoted EOA), while those at the equatorial edges bridge the equatorial orbitals of Cu2+ ions (EOE). The nearest-neighbour (NN) magnetic coupling of Cu2+ ions with the EOA linkage at 2.821 Å in the title compound is negligible, whereas the NN magnetic coupling of Cu2+ ions with the EOE linkage at 2.974 Å is essential. Therefore, the zigzag chain containing alternating spin-exchange dimers and no-spin-exchange ones is similar in electronic configuration to the dimerization of the quasi-one-dimensional antiferromagnet. Magnetic investigation of analogous compounds with a 'trans-cis-trans-cis' configuration observed in the title compound may shed light on structural evolutions associated with spin-Peierls (SP) transition.

Signatures of a Spin-1/2 Cooperative Paramagnet in the Diluted Triangular Lattice of Y_{2}CuTiO_{6}

We present a combination of thermodynamic and dynamic experimental signatures of a disorder driven dynamic cooperative paramagnet in a 50% site diluted triangular lattice spin-1/2 system: Y_{2}CuTiO_{6}. Magnetic ordering and spin freezing are absent down to 50 mK, far below the Curie-Weiss scale (-θ_{CW}) of ∼134  K. We observe scaling collapses of the magnetic field and temperature dependent magnetic heat capacity and magnetization data, respectively, in conformity with expectations from the random singlet physics. Our experiments establish the suppression of any freezing scale, if at all present, by more than 3 orders of magnitude, opening a plethora of interesting possibilities such as disorder stabilized long range quantum entangled ground states.

Quantum Spin Liquid State in a Two-Dimensional Semiconductive Metal-Organic Framework

Two-dimensional metal-organic frameworks (2D MOFs) have attracted much attention, as they are the crystalline materials that exhibit both conductivity and microporosity. Numerous efforts have been made to advance their application as chemiresistive sensors or electrochemical capacitors. However, the intrinsic physical properties and spin states of these materials remain poorly understood. Most of these 2D MOFs possess a honeycomb lattice, with a Kagomé lattice arrangement of metal cations. These structural characteristics suggest that these MOFs would be candidates for geometrically frustrated spin systems with unprecedented magnetic phenomena. Herein, by performing magnetic susceptibility and specific heat measurements at an ultralow temperature down to 38mK on a 2D semiconductive MOF, Cu₃(HHTP)₂, a quantum spin liquid state that arises from the geometrical frustration was suggested. This result illustrates the potential of strongly correlated MOFs as systems with emergent phenomena induced by unusual structural topologies.

Synthesis of a d1-titanium fluoride kagome lattice antiferromagnet

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

Co3(SeO3)(SO4)(OH)2: A Selenite-Sulfate Compound with a Distorted Kagomé Lattice

A new selenite-sulfate compound Co₃(SeO₃)(SO₄)(OH)₂ was prepared using a typical hydrothermal reaction. This compound is found to crystallize in an orthorhombic space group of Pnma, featuring a 2D distorted kagomé structure composed of linear and zigzag Co-chains, in which the magnetic ions construct different isosceles-triangles. Our results of magnetic and specific heat measurements confirm a canted antiferromagnetic order at T_N ∼ 29 K. Further, the successive field-induced metamagnetic transitions can be observed at H_c1 ∼ 1 T, H_c2 ∼ 23 T, and H_c3 ∼ 27 T, respectively. A clear magnetic hysteresis loop with a coercive field (H_c) of ∼1.4 T is also observed.

Spin-lattice Coupling and the Emergence of the Trimerized Phase in the S=1 Kagome Antiferromagnet Na_{2}Ti_{3}Cl_{8}

Spin-1 antiferromagnets are abundant in nature, but few theories exist to understand their properties and behavior when geometric frustration is present. Here we study the S=1 kagome compound Na_{2}Ti_{3}Cl_{8} using a combination of density functional theory, exact diagonalization, and density matrix renormalization group approaches to achieve a first principles supported explanation of its exotic magnetic phases. We find that the effective magnetic Hamiltonian includes essential non-Heisenberg terms that do not stem from spin-orbit coupling, and both trimerized and spin-nematic magnetic phases are relevant. The experimentally observed structural transition to a breathing kagome phase is driven by spin-lattice coupling, which favors the trimerized magnetic phase against the quadrupolar one. We thus show that lattice effects can be necessary to understand the magnetism in frustrated magnetic compounds and surmise that Na_{2}Ti_{3}Cl_{8} is a compound that cannot be understood from only electronic or only lattice Hamiltonians, very much like VO_{2}.

Absence of magnetic ordering in the spin liquid candidate Ca3Cu2GeV2O12

Typically, quantum spin liquid candidates can be found in materials with a combination of geometrical frustration along with low spin. Due to its spin of S  =  1/2 the copper (II) ion is often present in the discussion on spin liquid candidates. The solid state compound Ca3Cu2GeV2O12 is a material that crystallizes in the garnet structure (s.g. #230, Ia-3d), where 3D frustration is known to occur. Heat capacity has shown a lack of magnetic ordering down to 0.35 K, confirmed with low temperature neutron diffraction to 0.07 K. This system displays a Weiss temperature of  -0.93(1) K indicating net antiferromagnetic interactions and significant J 1-J 2 competition causing frustration. Using both neutron and x-ray diffraction along with heat capacity and magnetometry, the work presented here shows Ca3Cu2GeV2O12 has potential as a new spin liquid candidate.

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.

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.

Spin transition nanoparticles made electrochemically

Materials displaying novel magnetic ground states signify the most exciting prospects for nanoscopic devices for nanoelectronics and spintronics. Spin transition materials, e.g., spin liquids and spin glasses, are at the forefront of this pursuit; but the few synthesis routes available do not produce them at the nanoscale. Thus, it remains an open question if and how their spin transition nature persists at such small dimensions. Here we demonstrate a new route to synthesize nanoparticles of spin transition materials, gas-diffusion electrocrystallization (GDEx), wherein the reactive precipitation of soluble metal ions with the products of the oxygen reduction reaction (ORR), i.e., in situ produced H₂O₂, OH^-, drives their formation at the electrochemical interface. Using mixtures of Cu²⁺ and Zn²⁺ as the metal precursors, we form spin transition materials of the herbertsmithite family-heralded as the first experimental material known to exhibit the properties of a quantum spin liquid (QSL). Single-crystal nanoparticles of ∼10-16 nm were produced by GDEx, with variable Cu/Zn stoichiometry at the interlayer sites of Zn_xCu_4-x(OH)₆Cl₂. For x = 1 (herbertsmithite) the GDEx nanoparticles demonstrated a quasi-QSL behavior, whereas for x = 0.3 (0.3 < x < 1 for paratacamite) and x = 0 (clinoatacamite) a spin-glass behavior was evidenced. Finally, our discovery not only confirms redox reactions as the driving force to produce spin transition nanoparticles, but also proves a simple way to switch between these magnetic ground states within an electrochemical system, paving the way to further explore its reversibility and overarching implications.

Raman spectroscopic diagnostic of quantum spin liquids

Quantum spin liquids are outstanding examples of highly quantum entangled phases of matter and serve as a testbed to gauge central concepts of strongly correlated materials. Enormous research efforts in the past few decades have brought an in-depth understanding of these novel phases, although their conundrums have not yet been solved completely. In this review, we give an overview of the three different classes of spin-liquid materials: (i) a one-dimensional spin chain system KCuF₃, (ii) a kagome antiferromagnet ZnCu₃(OH)₆Cl₂, and (iii) a Kitaev honeycomb material [Formula: see text]-RuCl₃. The emphasis is on demonstrating the success of the Raman scattering technique for probing fractionalized excitations in the aforementioned spin-liquid compounds, complementing a well-established neutron scattering method. Irrespective of dimensionality, spin topology, and spin-exchange type, the three materials share several common features in the spectral shape and temperature dependence of magnetic excitations, which can be taken as Raman spectroscopic fingerprints of quantum spin liquids.

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.

Pressure-Tuned Interactions in Frustrated Magnets: Pathway to Quantum Spin Liquids?

Quantum spin liquids are prime examples of strongly entangled phases of matter with unconventional exotic excitations. Here, strong quantum fluctuations prohibit the freezing of the spin system. On the other hand, frustrated magnets, the proper platforms to search for the quantum spin liquid candidates, still show a magnetic ground state in most of the cases. Pressure is an effective tuning parameter of structural properties and electronic correlations. Nevertheless, the ability to influence the magnetic phases should not be forgotten. We review experimental progress in the field of pressure-tuned magnetic interactions in candidate systems. Elaborating on the possibility of tuned quantum phase transitions, we further show that chemical or external pressure is a suitable parameter in these exotic states of matter.

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

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

The specific heat and magnetic properties of two species of spin-1/2 ladders with butterfly-shaped unit blocks

Studies of the structural effects on the thermodynamic properties of two types of Ising-Heisenberg ladders are comprehensively reported. Each structure comprises spin-1/2 particles partitioned into adjoined blocks or cages formed from butterfly-shaped plaquettes and interacting in an Ising manner. We use the transfer-matrix approach to determine the partition functions of these models and numerically investigate their magnetization and specific-heat properties. Both models illustrate all characteristic features of low-temperature magnetization processes and thermodynamics properties such as abrupt variations of the magnetization curves, Schottky-type peak and a double-peak structure of the specific heat. Comparisons between the two ladders reveal some differences in their magnetic and thermodynamic behaviors. For instance, difference in the number of intermediate magnetization plateaus, also difference in the height and temperature-position of the specific heat peaks. We also present that the fluctuations of the specific heat with respect to the magnetic field are in highly accordance with the magnetization plateaus and magnetization jumps. Moreover, we find quite interesting threshold reentrance points within the matrix-plot of the specific heat shown in the (T/J  -  B/J) plane, at which the temperature-position of the Schottky peak alternatively change. Finally, we prove that the reentrance points can be satisfactorily considered as magnetization plateau witnesses even in the high temperatures.

Randomness-Induced Quantum Spin Liquid Behavior in the s=1/2 Random-Bond Heisenberg Antiferromagnet on the Pyrochlore Lattice

We investigate the zero- and finite-temperature properties of the random-bond s=1/2 Heisenberg antiferromagnet on the pyrochlore lattice by the exact diagonalization and the Hams-de Raedt methods. We find that the randomness induces the gapless quantum spin liquid (QSL) state, the random-singlet state. Implications to recent experiments on the mixed-anion pyrochlore-lattice antiferromagnet Lu_{2}Mo_{2}O_{5}N_{2} exhibiting gapless QSL behaviors are discussed.

Thermodynamic, Dynamic, and Transport Properties of Quantum Spin Liquid in Herbertsmithite from an Experimental and Theoretical Point of View

In our review, we focus on the quantum spin liquid (QSL), defining the thermodynamic, transport, and relaxation properties of geometrically frustrated magnet (insulators) represented by herbertsmithite ZnCu 3 ( OH ) 6 Cl 2 . The review mostly deals with an historical perspective of our theoretical contributions on this subject, based on the theory of fermion condensation closely related to the emergence (due to geometrical frustration) of dispersionless parts in the fermionic quasiparticle spectrum, so-called flat bands. QSL is a quantum state of matter having neither magnetic order nor gapped excitations even at zero temperature. QSL along with heavy fermion metals can form a new state of matter induced by the topological fermion condensation quantum phase transition. The observation of QSL in actual materials such as herbertsmithite is of fundamental significance both theoretically and technologically, as it could open a path to the creation of topologically protected states for quantum information processing and quantum computation. It is therefore of great importance to establish the presence of a gapless QSL state in one of the most prospective materials, herbertsmithite. In this respect, the interpretation of current theoretical and experimental studies of herbertsmithite are controversial in their implications. Based on published experimental data augmented by our theoretical analysis, we present evidence for the the existence of a QSL in the geometrically frustrated insulator herbertsmithite ZnCu 3 ( OH ) 6 Cl 2 , providing a strategy for unambiguous identification of such a state in other materials. To clarify the nature of QSL in herbertsmithite, we recommend measurements of heat transport, low-energy inelastic neutron scattering, and optical conductivity σ ¯ in ZnCu 3 ( OH ) 6 Cl 2 crystals subject to an external magnetic field at low temperatures. Our analysis of the behavior of σ ¯ in herbertsmithite justifies this set of measurements, which can provide a conclusive experimental demonstration of the nature of its spinon-composed quantum spin liquid. Theoretical study of the optical conductivity of herbertsmithite allows us to expose the physical mechanisms responsible for its temperature and magnetic field dependence. We also suggest that artificially or spontaneously introducing inhomogeneity at nanoscale into ZnCu 3 ( OH ) 6 Cl 2 can both stabilize its QSL and simplify its chemical preparation, and can provide for tests that elucidate the role of impurities. We make predictions of the results of specified measurements related to the dynamical, thermodynamic, and transport properties in the case of a gapless QSL.

Emergent magnetic order and correlated disorder in formate metal-organic frameworks

Magnetic materials with strong local interactions but lacking long-range order have long been a curiosity of physicists. Probing their magnetic interactions is crucial for understanding the unique properties they can exhibit. Metal-organic frameworks have recently gathered more attention as they can produce more exotic structures, allowing for controlled design of magnetic properties not found in conventional metal-oxide materials. Historically, magnetic diffuse scattering in such materials has been overlooked but has attracted greater attention recently, with advances in techniques. In this study, we investigate the magnetic structure of metal-organic formate frameworks, using heat capacity, magnetic susceptibility and neutron diffraction. In Tb(DCO₂)₃, we observe emergent magnetic order at temperatures below 1.2 K, consisting of two k-vectors. Ho(DCO₂)₃ shows diffuse scattering above 1.6 K, consistent with ferromagnetic chains packed in a frustrated antiferromagnetic triangular lattice, also observed in Tb(DCO₂)₃ above 1.2 K. The other lanthanides show no short- or long-range order down to 1.6 K. The results suggest an Ising-like one-dimensional magnetic order associated with frustration is responsible for the magnetocaloric properties, of some members in this family, improving at higher temperatures. This article is part of the theme issue 'Mineralomimesis: natural and synthetic frameworks in science and technology'.

Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface

The Kitaev model with an applied magnetic field in the [Formula: see text] direction shows two transitions: from a nonabelian gapped quantum spin liquid (QSL) to a gapless QSL at [Formula: see text] and a second transition at a higher field [Formula: see text] to a gapped partially polarized phase, where K is the strength of the Kitaev exchange interaction. We identify the intermediate phase to be a gapless U(1) QSL and determine the spin structure function [Formula: see text] and the Fermi surface [Formula: see text] of the gapless spinons using the density matrix renormalization group (DMRG) method for large honeycomb clusters. Further calculations of static spin-spin correlations, magnetization, spin susceptibility, and finite temperature-specific heat and entropy corroborate the gapped and gapless nature of the different field-dependent phases. In the intermediate phase, the spin-spin correlations decay as a power law with distance, indicative of a gapless phase.

Electron spin resonance on the spin-1/2 triangular magnet NaYbS2

The delafossite structure of NaYbS₂ contains a planar spin-1/2 triangular lattice of Yb³⁺ ions and features a possible realisation of a quantum spin-liquid state. We investigated the Yb³⁺ spin dynamics by electron spin resonance (ESR) in single-crystalline samples of NaYbS₂. Very clear spectra with a well-resolved and large anisotropy could be observed down to the lowest accessible temperature of 2.7 K. In contrast to the ESR properties of other known spin-liquid candidate systems, the resonance seen in NaYbS₂ is accessible at low fields (<1 T) and is narrow enough for accurate characterisation of the relaxation rate as well as the g factor of the Yb³⁺ spins.

Identifying spinon excitations from dynamic structure factor of spin-1/2 Heisenberg antiferromagnet on the Kagome lattice

A spin-[Formula: see text] lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration. So far, the main focus has remained on the ground-state properties; however, the theoretical consensus regarding the magnetic excitations is limited. Here, we study the dynamic spin structure factor (DSSF) of the KAFM by means of the density matrix renormalization group. By comparison with the well-defined magnetically ordered state and the chiral spin liquid sitting nearby in the phase diagram, the KAFM with nearest neighbor interactions shows distinct dynamical responses. The DSSF displays important spectral intensity predominantly in the low-frequency region around the [Formula: see text] point in momentum space and shows a broad spectral distribution in the high-frequency region for momenta along the boundary of the extended Brillouin zone. The excitation continuum identified from momentum- and energy-resolved DSSF signals emergent spinons carrying fractional quantum numbers. These results capture the main observations in the inelastic neutron scattering measurements of herbertsmithite and indicate the spin liquid nature of the ground state. By tracking the DSSF across quantum-phase transition between the chiral spin liquid and the magnetically ordered phase, we identify the condensation of two-spinon bound state driving the quantum-phase transition.

Choreographed entanglement dances: Topological states of quantum matter

It has long been thought that all different phases of matter arise from symmetry breaking. Without symmetry breaking, there would be no pattern, and matter would be featureless. However, it is now clear that for quantum matter at zero temperature, even symmetric disordered liquids can have features, giving rise to topological phases of quantum matter. Some of the topological phases are highly entangled (that is, have topological order), whereas others are weakly entangled (that is, have symmetry-protected trivial order). This Review provides a brief summary of these zero-temperature states of matter and their emergent properties, as well as their importance in unifying some of the most basic concepts in nature.