Chemistry of Quantum Spin Liquids

Spin reorientation and magnetic frustration in Fe32+δGe35-xSix with a kagome lattice broken by crystallographic intergrowth

Fe32+δGe35-xSix was synthesized using solid-state and chemical vapor transport reactions in both powder and single crystalline forms. Single crystal and high-resolution powder X-ray diffraction experiments revealed Fe32+δGe35-xSix to be the third member of the Fe32+δGe35-xEx (E = p-element) family of ternary compounds alongside Fe32+δGe33As2 and Fe32+δGe35-xPx. Fe32+δGe35-xSix features a two-dimensional intergrowth structure of two parent structure types: MgFe6Ge6 and Co2Al5. Similar to the other members, the stabilisation of the intergrowth structure in Fe32+δGe35-xSix occurs as a result of p-element substitution in the MgFe6Ge6-type block. The intergrowth breaks the kagome net of MgFe6Ge6 into individual hexagrams while providing additional layers of geometrically frustrated atomic arrangements. Magnetic measurements showed antiferromagnetic ordering at TN ∼ 150-160 K and spin reorientation below 80-90 K owing to the competition between magnetic interactions in the frustrated magnetic lattice of Fe32+δGe35-xSix.

Kagomé lattice compounds and their related systems

The search for new Kagomé lattice compounds and their related systems has attracted much interest but is still a great challenge, because these compounds usually show unique structural features and various unusual magnetic properties, but an ideal lattice is not easily obtained and some of the magnetic properties are not well understood. In this feature article review, we summarize the works of our research group in recent years, mainly including new types of lattices, structural features, and the magnetic behaviors of such Kagomé related systems. Moreover, current problems and future prospects of this respect are also discussed.

Emergent gauge fields in band insulators

By explicit microscopic construction involving a mapping to a quantum vertex model subject to the "ice rule," we show that an electronically "trivial" band insulator with suitable vibrational (phonon) degrees of freedom can host a "resonating valence-bond" state-a quantum phase with emergent gauge fields. This type of band insulator is identifiable by the existence of emergent gapless "photon" modes and deconfined excitations, the latter of which carry nonquantized mobile charges. We suggest that such phases may exist in the quantum regimes of various nearly ferroelectric materials.

Tuning the Properties of Dodecylpyridinium Metallosurfactants: The Role of Iron-Based Counterions

Metallosurfactants combine the unique soft-matter properties of surfactants with magnetic functionalities of metal ions. The inclusion of iron-based species, in particular, can further boost the functionality of the material, owing to iron's ability to adopt multiple oxidation states and form both high-spin and low-spin complexes. Motivated by this, a series of hybrid inorganic-organic dodecylpyridinium metallosurfactants with iron-containing counterions was developed. It was established that using either divalent or trivalent iron halides in a straightforward synthetic procedure yields C12Py-metallosurfactants with distinct complex counterions: (C12Py)2[Fe2X6O] and (C12Py)[FeX4] (X = Cl or Br), respectively. A combination of techniques-including conductometry, dynamic and electrophoretic light scattering, single-crystal and thermogravimetric analysis, and magnetic measurements-provided in-depth insights into their solution and solid-state properties. The presence of different iron-based counterions significantly influences the crystal structure (interdigitated vs. non-interdigitated bilayers), magnetic properties (paramagnetic vs. nonmagnetic singlet ground state), and self-assembly (vesicles vs. micelles) of the dodecylpyridinium series. To our knowledge, this is the first report on the synthesis and characterization of hybrid organic-inorganic metallosurfactants containing the μ-oxo-hexahalo-diferrate anion.

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

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

Pyrochlore NaYbO2: A Potential Quantum Spin Liquid Candidate

The search for quantum spin liquids (QSL) and chemical doping in such materials to explore superconductivity have continuously attracted intense interest. Here, we report the discovery of a potential QSL candidate, pyrochlore-lattice β-NaYbO2. Colorless and transparent NaYbO2 single crystals, layered α-NaYbO2 (∼250 μm on edge) and octahedral β-NaYbO2 (∼50 μm on edge), were grown for the first time. Synchrotron X-ray single-crystal diffraction unambiguously determined that the newfound β-NaYbO2 belongs to the three-dimensional pyrochlore structure characterized by the R3̅m space group, corroborated by synchrotron X-ray and neutron powder diffraction and pair distribution function. Magnetic measurements revealed no long-range magnetic order or spin glass behavior down to 0.4 K with a low boundary spin frustration factor of 17.5, suggesting a potential QSL ground state. Under high magnetic fields, the potential QSL state was broken and spins order. Our findings reveal that NaYbO2 is a fertile playground for studying novel quantum states.

Spin-Frustrated Metal-Organic Frameworks

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

Structural Modulation and Enhanced Magnetic Ordering in Incommensurate K1-xCrSe2 Crystals

Layered delafossite-type compounds and related transition metal dichalcogenides, characterized by their triangular net structures, serve as prototypical systems for exploring the intricate interplay between crystal structure and magnetic behavior. Herein, we report on the discovery of the compound K1-xCrSe2 (x ≈ 0.13), an incommensurately modulated phase. Single crystals of this compound were grown for the first time using a K/Se self-flux. We find a monoclinic crystal structure with incommensurate modulation that can be rationalized by a 3 + 1-dimensional model. This modulation compensates for the under-stoichiometry of K cations, creating pronounced undulations in the CrSe2 layers. Our anisotropic magnetization measurements reveal that K1-xCrSe2 undergoes a transition to a long-range magnetically ordered state below TN = 133 K, a temperature 1.6 to 3.3 times higher than in earlier reported KCrSe2 compounds. Our findings open new avenues for tuning the magnetic properties of these layered materials through structural modulation.

Stable Mono-Radical and Triplet Diradicals Based on Allylic Radical-Embedded All-Benzenoid Polycyclic Hydrocarbons

High-spin organic radicals are notable for their unique optical, electronic, and magnetic properties, but synthesizing stable high-spin systems is challenging due to their inherent reactivity. This study presents a novel strategy for designing stable high-spin polycyclic hydrocarbons (PHs) by incorporating allylic radical into fused aromatic benzenoid rings. To enhance stability, large steric hindrance groups with a synergistic captodative effect were added to the allylic radical centers. This approach was applied to synthesize derivatives of two open-shell all-benzenoid PHs: benzo[fg]tetracene (1) and dibenzo[fg,lm]heptacene (2). Both compounds exhibited excellent stability, with diradical 2 showing a half-life of up to 17.2 days under ambient conditions. Bond length analysis and theoretical calculations suggest that 1 and 2 predominantly feature Clar's aromatic sextet structures with embedded allylic radicals. Compound 2 was confirmed to have a triplet ground state through DFT calculations and experimental methods, including pulse EPR spectroscopy and SQUID measurements. This work introduces a new design strategy for stable high-spin hydrocarbons, paving the way for future developments in high-spin organic materials.

Frustrated Magnetism and Spin Anisotropy in a Buckled Square Net YbTaO4

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

Experimental Testing of the Theoretically Predicted Magnetic Properties for Kagomé Compounds in the Li-Fe-Ge System

Investigating material properties is essential to assessing their application potential. While computational methods allow for a fast prediction of the material structure and properties, experimental validation is essential to determining the ultimate material potential. Herein, we report the synthesis and experimental magnetic properties of three previously reported Kagome compounds in the Li-Fe-Ge system. LiFe6Ge4, LiFe6Ge5, and LiFe6Ge6 were predicted to have ferromagnetic or antiferromagnetic ground states. The hydride route that replaces the ductile Li metal with salt-like LiH proved to be an excellent alternative for the facile synthesis of the Li-Fe-Ge powders with appreciable purity, permitting the investigation of their bulk magnetic properties. Magnetometry below room temperature and room-temperature 57Fe Mössbauer spectroscopy collectively indicate an antiferromagnetic ground state for the three compounds with ordering temperatures above 300 K, contrary to the prediction of ferromagnetic ground states. Moreover, Mössbauer spectroscopy reveals a magnetization of 1.1-1.3 μB/Fe atom for the Li-Fe-Ge compounds, while higher moments of 1.63-2.90 μB/Fe atom were theoretically predicted. Experimental (in)validation addresses the issue of inaccuracy in determining material properties in silico only and helps to improve the prediction power of the computational models. This work underlines that the contribution of experimentalists continues to be valuable for the accurate determination of structure-property relationships in solid-state materials.

Nitrate-Anion-Induced Formation of a 2D Metal-Organic Framework with an Unconventional Kagomé Lattice Exhibiting Methanol-Mediated Ketone Catalysis

Metal-organic frameworks (MOFs) with kagomé lattice are attractive for their unique physical and chemical properties, but little attention has been paid to their catalytic properties. Herein, we report a 2D MOF based on a phosphonato-amino-carboxylate ligand (NaHL), i. e., [Na0.33Co(L)(CH3OH)2](NO3)0.33 (2), which exhibits an unconventional kagomé lattice. The formation of this kagomé lattice is caused by the selective recognition of the NO3 - anion by the phenolato group of L2- as evidenced by theoretical calculations. Compound 2 can be utilized for the α-methoxymethylation and aminomethylation of aromatic ketones using methanol as a C1 source. Interestingly, compound 2 can be exfoliated in-situ into nanosheets with one-layer thickness under catalytic reaction conditions, which improves the catalytic efficiency. Based on the results of experiments and theoretical calculations, we proposed possible pathways for the catalytic reaction.

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

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

Chemical Design of Spin Frustration to Realize Topological Spin Glasses

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

When van der Waals Met Kagome: A 2D Antimonide with a Vanadium-Kagome Network

2D materials showcase unconventional properties emerging from quantum confinement effects. In this work, a "soft chemical" route allows for the deintercalation of K+ from the layered antimonide KV6Sb6, resulting in the discovery of a new metastable 2D-Kagome antimonide K0.1(1)V6Sb6 with a van der Waals gap of 3.2 Å. The structure of K0.1(1)V6Sb6 was determined via the synergistic techniques, including X-ray pair distribution function analysis, advanced transmission electron microscopy, and density functional theory calculations. The K0.1(1)V6Sb6 compound crystallizes in the monoclinic space group C2/m (a = 9.57(2) Å, b = 5.502(8) Å, c = 10.23(2) Å, β = 97.6(2)°, Z = 2). The [V6Sb6] layers in K0.1(1)V6Sb6 are retained upon deintercalation and closely resemble the layers in the parent compound, yet deintercalation results in a relative shift of the adjacent [V6Sb6] layers. The magnetic properties of the K0.1(1)V6Sb6 phase in the 2-300 K range are comparable to those of KV6Sb6 and another Kagome antimonide KV3Sb5, consistent with nearly temperature-independent paramagnetism. Electronic band structure calculation suggests a nontrivial band topology with flat bands and opening of band crossing afforded by deintercalation. Transport property measurements reveal a metallic nature for K0.1(1)V6Sb6 and a low thermal conductivity of 0.6 W K-1 m-1 at 300 K. Additionally, ion exchange in KV6Sb6 via a solvothermal route leads to a successful partial exchange of K+ with A+ (A = Na, Rb, and Cs). This study highlights the tunability of the layered structure of the KV6Sb6 compound, providing a rich playground for the realization of new 2D materials.

Synthesis, Structures, and Magnetic Investigations of Nickel Phosphates: Ni2(PO4)(OH), Ni7(PO4)3(HPO4)(OH)3, and NaNiPO4 Including Potential Haldane Behavior

Three novel nickel-phosphate structures are reported, Ni2(PO4)(OH) (I), Ni7(PO4)3(HPO4)(OH)3 (II), and NaNiPO4 (III). Each new system was prepared via a high-temperature hydrothermal synthesis at 600-650 °C. All three compounds are built of quasi-one-dimensional (quasi-1-D) Ni2+ containing chains with varying phosphate bridging modes and were characterized by single crystal X-ray diffraction and magnetic susceptibility. All three compounds display very different magnetic behavior. Anisotropic magnetic data is reported for Ni2(PO4)(OH) (I) exhibiting slow antiferromagnetic ordering in the high-temperature regime with substructures that begin to form below 32 K at different field strengths. These characteristics affirm I as being one of the few Haldane-like material candidates. The Ni7(PO4)3(HPO4)(OH)3 (II) material is a member of the unusual ellenbergerite structural family and displays complex inter- and intrachain magnetic interactions while NaNiPO4 (III) shows antiferromagnetic ordering near 18 K. This magnetic behavior is correlated with their structures.

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

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

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

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

Spin-degree manipulation for one-dimensional room-temperature ferromagnetism in a haldane system

The intricate correlation between lattice geometry, topological behavior and charge degrees of freedom plays a key role in determining the physical and chemical properties of a quantum-magnetic system. Herein, we investigate the introduction of the unusual oxidation state as an alternative pathway to modulate the magnetic ground state in the well-known S = 1 Haldane system nickelate Y2BaNiO5 (YBNO). YBNO is topologically reduced to incorporate d9-Ni+ (S = 1/2) in the one-dimensional Haldane chain system. The random distribution of Ni+ for the first time results in the emergence of a one-dimensional ferromagnetic phase with a transition temperature far above room temperature. Theoretical calculations reveal that the antiferromagnetic interplay can evolve into ferromagnetic interactions with the presence of oxygen vacancies, which promotes the formation of ferromagnetic order within one-dimensional nickel chains. The unusual electronic instabilities in the nickel-based Haldane system may offer new possibilities towards unconventional physical and chemical properties from quantum interactions.

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

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

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

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

Heteropentanuclear {Ru(II)Cu(II)4} Kuratowski Complexes Assembled from a Ruthenium(II) Precursor Complex to Study Competing Exchange Interactions in M(II)(ta)2 Networks [ta(-) = 1,2,3-Triazolate]

We report a directed two-step synthesis toward pentanuclear Kuratowski complexes. First, six 5,6-dimethylbenzo[1,2,3]triazole ligands (Me2btaH) are coordinated to a single Ru(II) ion, providing a topologically ideal template for the addition of further metal ions. The synthesis and crystal structures of [RuCu4X4(Me2bta)6] [X = acetylacetonate (acac) and tris(3,5-dimethyl-1-pyrazolyl)borate (Tp*)] are described. Both represent new members of the family of so-called Kuratowski (K3,3) complexes. The coordination units feature triazolato-bridged metal-centered {MM4} tetrahedra, which are known for frustrated magnetic interactions in both complexes and metal-organic frameworks. The novel Ru(II)-centered complexes were synthesized in order to investigate the influence of the presence or absence of a paramagnetic central metal ion in the Kuratowski complex. Superconducting quantum interference device and electron spin resonance measurements demonstrate that small deviations in bond lengths and valence angles can lead to the formation of pairs of magnetic exchange-coupled Cu(II) ions. Which Cu(II) ions pair up can be predicted in Jahn-Teller active compounds by the overlap of the respective orbitals. These data are compared with those gleaned for M(II)(ta)2 (ta = 1,2,3-triazolate) lattices, in which structurally similar {MM4} tetrahedra constitute the secondary building units.

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.

Crystallographic Disorder and Strong Magnetic Anisotropy in Dy3Pt2Sb4.48

We report the crystal growth and characterization of a rare-earth-containing material, Dy3.00(1)Pt2Sb4.48(2). This compound possesses a similar structure to the previously reported Y3Pt4Ge6, but it lacks two layers of Pt atoms. Crystallographic disorder was found in Dy3.00(1)Pt2Sb4.48(2). Additionally, the Dy-Dy framework was found to have both square net and triangular lattices. Dy3.00(1)Pt2Sb4.48(2)8 was determined to be antiferromagnetically ordered around ∼15 K while a competing antiferromagnetic sublattice also exists at lower temperature. Strong magnetic anisotropy was observed, and several metamagnetic transitions were seen in the hysteresis loops. Furthermore, the Curie-Weiss fitting revealed an unusually small effective moment of Dy, which is far below the expected value of Dy3+ (10.65 μB). This material might provide a new platform to study the relationship between crystallographic disorder and magnetism.

Structural approach to charge density waves in low-dimensional systems: electronic instability and chemical bonding

The charge density wave (CDW) instability, usually occurring in low-dimensional metals, has been a topic of interest for longtime. However, some very fundamental aspects of the mechanism remain unclear. Recently, a plethora of new CDW materials, a substantial fraction of which is two-dimensional or even three-dimensional, has been prepared and characterised as bulk and/or single-layers. As a result, the need for revisiting the primary mechanism of the instability, based on the electron-hole instability established more than 50 years ago for quasi-one-dimensional (quasi-1D) conductors, has clearly emerged. In this work, we consider a large number of CDW materials to revisit the main concepts used in understanding the CDW instability, and emphasise the key role of the momentum dependent electron-phonon coupling in linking electronic and structural degrees of freedom. We argue that for quasi-1D systems, earlier weak coupling theories work appropriately and the energy gain due to the CDW and the concomitant periodic lattice distortion (PLD) remains primarily due to a Fermi surface nesting mechanism. However, for materials with higher dimensionality, intermediate and strong coupling regimes are generally at work and the modification of the chemical bonding network by the PLD is at the heart of the instability. We emphasise the need for a microscopic approach blending condensed matter physics concepts and state-of-the-art first-principles calculations with quite fundamental chemical bonding ideas in understanding the CDW phenomenon in these materials.

Robust Spin Liquidity in 2D Metal-Organic Framework Cu3 (HHTP)2 with S=1 /2 Kagome Lattice

On one hand electron or hole doping of quantum spin liquid (QSL) may unlock high-temperature superconductivity and on the other hand it can disrupt the spin liquidity, giving rise to a magnetically ordered ground state. Recently, a 2D MOF, Cu3 (HHTP)2 (HHTP - 2,3,6,7,10,11-hexahydroxytriphenylene), containing Cu(II) S=1 / 2 ${{ 1/2 }}$ frustrated spins in the Kagome lattice is emerging as a promising QSL candidate. Herein, we present an elegant in situ redox-chemistry strategy of anchoring Cu3 (HHTP)2 crystallites onto diamagnetic reduced graphene oxide (rGO) sheets, resulting in the formation of electron-doped Cu3 (HHTP)2 -rGO composite which exhibited a characteristic semiconducting behavior (5 K to 300 K) with high electrical conductivity of 70 S ⋅ m-1 and a carrier density of ~1.1×1018  cm-3 at 300 K. Remarkably, no magnetic transition in the Cu3 (HHTP)2 -rGO composite was observed down to 1.5 K endorsing the robust spin liquidity of the 2D MOF Cu3 (HHTP)2 . Specific heat capacity measurements led to the estimation of the residual entropy values of 28 % and 34 % of the theoretically expected value for the pristine Cu3 (HHTP)2 and Cu3 (HHTP)2 -rGO composite, establishing the presence of strong quantum fluctuations down to 1.5 K (two times smaller than the value of the exchange interaction J).

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

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

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

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

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.

The pressure-stabilized polymorph of indium triiodide

A layered rhombohedral polymorph of indium(III) triiodide is synthesized at high pressure and temperature. The unit cell symmetry and approximate dimensions are determined by single crystal X-ray diffraction. Its R3̄ crystal structure, with a = 7.214 Å, and c = 20.47 Å, is refined by the Rietveld method on powder X-ray diffraction data. The crystal structure is based on InI6 octahedra sharing edges to form honeycomb lattice layers, though with considerable stacking defects. Different from ambient pressure InI3, which has a monoclinic molecular structure and a light-yellow color, high pressure InI3 is layered and has an orange color. The band gaps of both the monoclinic and rhombohedral variants of InI3 are estimated from diffuse reflectance measurements.

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.

Physics-Inspired Quantum Simulation of Resonating Valence Bond States─A Prototypical Template for a Spin-Liquid Ground State

Spin liquids─an emergent, exotic collective phase of matter─have garnered enormous attention in recent years. While experimentally many prospective candidates have been proposed and realized, theoretically modeling real materials that display such behavior may pose serious challenges due to the inherently high correlation content of such phases. Over the last few decades, the second-quantum revolution has been the harbinger of a novel computational paradigm capable of initiating a foundational evolution in computational physics. In this report, we strive to use the power of the latter to study a prototypical model, a spin-1/2-unit cell of a Kagome antiferromagnet. Extended lattices of such unit cells are known to possess a magnetically disordered spin-liquid ground state. We employ robust classical numerical techniques such as the density-matrix renormalization group (DMRG) to identify the nature of the ground state through a matrix-product state (MPS) formulation. We subsequently use the gained insight to construct an auxiliary Hamiltonian with reduced measurables and also design an ansatz that is modular and gate-efficient. With robust error-mitigation strategies, we are able to demonstrate that the said ansatz is capable of accurately representing the target ground state even on a real IBMQ backend within 1% accuracy in energy. Since the protocol is linearly scaling O(n) in the number of unit cells, gate requirements, and the number of measurements, it is straightforwardly extendable to larger Kagome lattices that can pave the way for efficient construction of spin-liquid ground states on a quantum device.

Superconductivity in a breathing kagome metals ROs2 (R = Sc, Y, Lu)

We have successfully synthesized three osmium-based hexagonal Laves compounds ROs2 (R = Sc, Y, Lu), and discussed their physical properties. LeBail refinement of pXRD data confirms that all compounds crystallize in the hexagonal centrosymmetric MgZn2-type structure (P63/mmc, No. 194). The refined lattice parameters are a = b = 5.1791(1) Å and c = 8.4841(2) Å for ScOs2, a = b = 5.2571(3) Å and c = 8.6613(2) Å for LuOs2 and a = b = 5.3067(6) Å and c = 8.7904(1) Å for YOs2. ROs2 Laves phases can be viewed as a stacking of kagome nets interleaved with triangular layers. Temperature-dependent magnetic susceptibility, resistivity and heat capacity measurements confirm bulk superconductivity at critical temperatures, Tc, of 5.36, 4.55, and 3.47 K for ScOs2, YOs2, and LuOs2, respectively. We have shown that all investigated Laves compounds are weakly-coupled type-II superconductors. DFT calculations revealed that the band structure of ROs2 is intricate due to multiple interacting d orbitals of Os and R. Nonetheless, the kagome-derived bands maintain their overall shape, and the Fermi level crosses a number of bands that originate from the kagome flat bands, broadened by interlayer interaction. As a result, ROs2 can be classified as (breathing) kagome metal superconductors.

Kanatzidisite: A Natural Compound with Distinctive van der Waals Heterolayered Architecture

New minerals have long been a source of inspiration for the design and discovery. Many quantum materials, including superconductors, quantum spin liquids, and topological materials, have been unveiled through mineral samples with unusual structure types. In this report, we present kanatzidisite, a new naturally occurring material with formula [BiSbS3]2[Te2] and monoclinic symmetry (space group of P21/m) with lattice parameters a = 4.0021(5) Å, b = 3.9963(5) Å, c = 21.1009(10) Å, and β = 95.392(3)°. The mineral exhibits a unique structure consisting of alternating BiSbS3 double van der Waals layers and distorted [Te] square nets essentially forming an array of parallel zigzag Te chains. Our theoretical calculations suggest that the band structure of kanatzidisite may exhibit topological features characteristic of a Dirac semimetal.

Spin-Frustrated Trisradical Trication of PrismCage

Organic trisradicals featuring threefold symmetry have attracted significant interest because of their unique magnetic properties associated with spin frustration. Herein, we describe the synthesis and characterization of a triangular prism-shaped organic cage for which we have coined the name PrismCage6+ and its trisradical trication─TR3(•+). PrismCage6+ is composed of three 4,4'-bipyridinium dications and two 1,3,5-phenylene units bridged by six methylene groups. In the solid state, PrismCage6+ adopts a highly twisted conformation with close to C3 symmetry as a result of encapsulating one PF6- anion as a guest. PrismCage6+ undergoes stepwise reduction to its mono-, di-, and trisradical cations in MeCN on account of strong electronic communication between its 4,4'-bipyridinium units. TR3(•+), which is obtained by the reduction of PrismCage6+ employing CoCp2, adopts a triangular prism-shaped conformation with close to C2v symmetry in the solid state. Temperature-dependent continuous-wave and nutation-frequency-selective electron paramagnetic resonance spectra of TR3(•+) in frozen N,N-dimethylformamide indicate its doublet ground state. The doublet-quartet energy gap of TR3(•+) is estimated to be -0.08 kcal mol-1, and the critical temperature of spin-state conversion is found to be ca. 50 K, suggesting that it displays pronounced spin frustration at the molecular level. To the best of our knowledge, this example is the first organic radical cage to exhibit spin frustration. The trisradical trication of PrismCage6+ opens up new possibilities for fundamental investigations and potential applications in the fields of both organic cages and spin chemistry.

A Dynamic Triradical: Synthesis, Crystal Structure, and Spin Frustration

Polyradicals, i.e., multispin organic molecules, are playing important roles in radical-based material applications for their spin-spin interaction. A dynamic covalently bonded multispin molecule may endow materials with added function such as memory and switching. However, such a species has yet to be reported. We here report the synthesis, characterization, and crystal structure of a dynamic triradical species. It is generated by the self-assembly of two molecules through a Lewis acid coupled electron transfer. The crystalline species is spin-frustrated without Jahn-Teller distortion at low temperature, while it dissociates back to diamagnetic starting material in solution at high temperature. The reversible process is tracked by variable-temperature NMR, EPR, and UV-vis-NIR spectroscopy. Isolation, property study, and dynamic bonding investigation on such a species lay the foundation for the design of functional polyradicals with potential application as memory or switching devices.

Microstructured layered-kagome BaCo3(VO4)2(OH)2 with variable crystallite size: alternative synthetic route and comparison with nanostructured samples

Microplatelets of the layered-kagome compound BaCo₃(VO₄)₂(OH)₂, which is the Co²⁺ analogue of mineral vesignieite BaCu₃(VO₄)₂(OH)₂, have been prepared with very high yield by hydrothermal reaction using synthetic karpenkoite Co₃V₂O₇(OH)₂·2H₂O as starting reagent. The Rietveld refinement of X-ray diffraction data indicates that Co₃V₂O₇(OH)₂·2H₂O is isostructural with martyite Zn₃V₂O₇(OH)₂·2H₂O. Two single-phased samples of microstructured BaCo₃(VO₄)₂(OH)₂ have been characterized using powder X-ray diffraction, FT-IR and Raman spectroscopies, thermal analyses, scanning electron microscopy, energy-dispersive X-ray spectroscopy and magnetisation measurements. Their crystallite sizes perpendicular to the c-axis are in the range of 92(3) to 146(6) nm and depend on the synthesis conditions. Results have been compared to those previously obtained for quasi-spherical nanoparticles having a crystallite size of the order of 20 nm, to explore the effect of the crystallite size on the properties of BaCo₃(VO₄)₂(OH)₂. This study highlights that the magnetic properties depend on the crystallite sizes only at low temperatures.

Ba4Ni3F14·H2O: a ferrimagnetic compound with a staircase kagomé lattice

A new crystalline fluoride Ba₄Ni₃F₁₄·H₂O was found to exhibit a rare S = 1 staircase kagomé lattice built by Ni²⁺ ions. Magnetic measurements indicate a ferrimagnetic transition at ∼28 K, while 1/3 plateau can be observed from the magnetization curve. We suggest that the hydrogen-bond interactions of O-H⋯F pathways may play an important role for magnetic properties of the system.

A Triply Negatively Charged Nanographene Bilayer with Spin Frustration

We report on the largest open-shell graphenic bilayer and also the first example of triply negatively charged radical π-dimer. Upon three-electron reduction, bilayer nanographene fragment molecule (C₉₆ H₂₄ Ar₆ )₂ (Ar=2,6-dimethylphenyl) (1₂ ) was transformed to a triply negatively charged species 1₂ ^3.- , which has been characterized by single-crystal X-ray diffraction, electron paramagnetic resonance (EPR) spectroscopy and magnetic properties on a superconducting quantum interference device (SQUID). 1₂ ^3.- features a 96-center-3-electron (96c/3e) pancake bond with a doublet ground state, which can be thermally excited to a quartet state. It consists of 34 π-fused rings with 96 conjugated sp² carbon atoms. Spin frustration is observed with the frustration parameter f>31.8 at low temperatures in 1₂ ^3.- , which indicates graphene upon reduction doping may behave as a quantum spin liquid.

Ground-State Spin Dynamics in d1 Kagome-Lattice Titanium Fluorides

Many quantum magnetic materials suffer from structural imperfections. The effects of structural disorder on bulk properties are difficult to assess systematically from a chemical perspective due to the complexities of chemical synthesis. The recently reported S = 1/2 kagome lattice antiferromagnet, (CH₃NH₃)₂NaTi₃F₁₂, 1-Ti, with highly symmetric kagome layers and disordered interlayer methylammonium cations, shows no magnetic ordering down to 0.1 K. To study the impact of structural disorder in the titanium fluoride kagome compounds, (CH₃NH₃)₂KTi₃F₁₂, 2-Ti, was prepared. It presents no detectable structural disorder and only a small degree of distortion of the kagome lattice. The methylammonium disorder model of 1-Ti and order in 2-Ti were confirmed by atomic-resolution transmission electron microscopy. The antiferromagnetic interactions and band structures of both compounds were calculated based on spin-polarized density functional theory and support the magnetic structure analysis. Three spin-glass-like (SGL) transitions were observed in 2-Ti at 0.5, 1.4, and 2.3 K, while a single SGL transition can be observed in 1-Ti at 0.8 K. The absolute values of the Curie-Weiss temperatures of both 1-Ti (-139.5(7) K) and 2-Ti (-83.5(7) K) are larger than the SGL transition temperatures, which is indicative of geometrically frustrated spin glass (GFSG) states. All the SGL transitions are quenched with an applied field >0.1 T, which indicates novel magnetic phases emerge under small applied magnetic fields. The well-defined structure and the lack of structural disorder in 2-Ti suggest that 2-Ti is an ideal model compound for studying GFSG states and the potential transitions between spin liquid and GFSG states.

Anomalously field-susceptible spin clusters emerging in the electric-dipole liquid candidate κ-(ET)2Hg(SCN)2Br

Mutual interactions in many-body systems bring about various exotic phases, among which liquid-like states failing to order due to frustration are of keen interest. The organic system with an anisotropic triangular lattice of molecular dimers, κ-(ET)₂Hg(SCN)₂Br, has been suggested to host a dipole liquid arising from intradimer charge-imbalance instability, possibly offering an unprecedented stage for the spin degrees of freedom. Here, we show that an extraordinary unordered/unfrozen spin state having soft matter-like spatiotemporal characteristics emerges in this system. ¹H nuclear magnetic resonance (NMR) spectra and magnetization measurements indicate that gigantic, staggered moments are nonlinearly and inhomogeneously induced by a magnetic field, whereas the moments vanish in the zero-field limit. The analysis of the NMR relaxation rate signifies that the moments fluctuate at a characteristic frequency slowing down to below megahertz at low temperatures. The inhomogeneity, local correlation, and slow dynamics indicative of middle-scale dynamical correlation length of several nanometers suggest novel frustration-driven spin clusterization.

Ln2 (SeO3 )2 (SO4 )(H2 O)2 (Ln=Sm, Dy, Yb): A Mixed-Ligand Pathway to New Lanthanide(III) Multifunctional Materials Featuring Nonlinear Optical and Magnetic Anisotropy Properties

Bottom-up assembly of optically nonlinear and magnetically anisotropic lanthanide materials involving precisely placed spin carriers and optimized metal-ligand coordination offers a potential route to developing electronic architectures for coherent radiation generation and spin-based technologies, but the chemical design historically has been extremely hard to achieve. To address this, we developed a worthwhile avenue for creating new noncentrosymmetric chiral Ln3+ materials Ln2 (SeO3 )2 (SO4 )(H2 O)2 (Ln=Sm, Dy, Yb) by mixed-ligand design. The materials exhibit phase-matching nonlinear optical responses, elucidating the feasibility of the heteroanionic strategy. Ln2 (SeO3 )2 (SO4 )(H2 O)2 displays paramagnetic property with strong magnetic anisotropy facilitated by large spin-orbit coupling. This study demonstrates a new chemical pathway for creating previously unknown polar chiral magnets with multiple functionalities.

Uncovering the Kagome Ferromagnet within a Family of Metal-Organic Frameworks

Kagome networks of ferromagnetically or antiferromagnetically coupled magnetic moments represent important models in the pursuit of a diverse array of novel quantum and topological states of matter. Here, we explore a family of Cu²⁺-containing metal-organic frameworks (MOFs) bearing kagome layers pillared by ditopic organic linkers with the general formula Cu₃(CO₃)₂(x)₃·2ClO₄ (MOF-x), where x is 1,2-bis(4-pyridyl)ethane (bpe), 1,2-bis(4-pyridyl)ethylene (bpy), or 4,4'-azopyridine (azpy). Despite more than a decade of investigation, the nature of the magnetic exchange interactions in these materials remained unclear, meaning that whether the underlying magnetic model is that of an kagome ferromagnet or antiferromagnet is unknown. Using single-crystal X-ray diffraction, we have developed a chemically intuitive crystal structure for this family of materials. Then, through a combination of magnetic susceptibility, powder neutron diffraction, and muon-spin spectroscopy measurements, we show that the magnetic ground state of this family consists of ferromagnetic kagome layers that are coupled antiferromagnetically via their extended organic pillaring linkers.

Structural Diversity in Oxoiridates with 1D IrnO3(n+1) Chain Fragments and Flat Bands

A previously unreported series of hexagonal-perovskite-based Rb-oxoiridates, Rb₅Ir₂O₉, Rb₇Ir₃O₁₂, and Rb₁₂Ir₇O₂₄, have been synthesized and structurally analyzed via N₂-protected single-crystal X-ray diffraction (SC-XRD). These materials exhibit different 1D Ir_nO_3(n+1) chain fragments along their c axes. IrO₆ octahedra and RbO_x (x = 6, 8, and 10) polyhedra are their basic building blocks. The IrO₆ octahedra are linked via face-sharing, forming Ir₂O₉ dimers, Ir₃O₁₂ trimers, and Ir₇O₂₄ heptamers. The nonmagnetic RbO_x (x = 6, 8, and 10) polyhedra serve as both bridging units and spacers. Temperature-dependent SC-XRD shows all three to display positive thermal expansion and rules out structural transitions from their triangular symmetries down to 100 K. Density functional theory results suggest semiconducting-like behavior for the title compounds. The flatness of the electronic bands and our structural analysis are of potential interest for understanding and designing 1D quantum materials.

LiYbSe2: Frustrated Magnetism in the Pyrochlore Lattice

Three-dimensionally (3D) frustrated magnets generally exist in the magnetic diamond and pyrochlore lattices, in which quantum fluctuations suppress magnetic orders and generate highly entangled ground states. LiYbSe₂ in a previously unreported pyrochlore lattice was discovered from LiCl flux growth. Distinct from the quantum spin liquid (QSL) candidate NaYbSe₂ hosting a perfect triangular lattice of Yb³⁺, LiYbSe₂ crystallizes in the cubic pyrochlore structure with space group Fd3m (No. 227). The Yb³⁺ ions in LiYbSe₂ are arranged on a network of corner-sharing tetrahedra, which is particularly susceptible to geometrical frustration. According to our temperature-dependent magnetic susceptibility measurements, the dominant antiferromagnetic interaction in LiYbSe₂ is expected to appear around 8 K. However, no long-range magnetic order is detected in thermomagnetic measurements above 70 mK. Specific heat measurements also show magnetic correlations shifting with applied magnetic field with a degree of missing entropy that may be related to the slight mixture of Yb³⁺ on the Li site. Such magnetic frustration of Yb³⁺ is rare in pyrochlore structures. Thus, LiYbSe₂ shows promise in intrinsically realizing disordered quantum states like QSL in pyrochlore structures.

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.