Chemistry of Quantum Spin Liquids

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.

Structural, Thermodynamic, and Transport Properties of the Small-Gap Two-Dimensional Metal-Organic Kagomé Materials Cu3(hexaiminobenzene)2 and Ni3(hexaiminobenzene)2

Metal-organic frameworks (MOFs) provide exceptional chemical tunability and have recently been demonstrated to exhibit electrical conductivity and related functional electronic properties. The kagomé lattice is a fruitful source of novel physical states of matter, including the quantum spin liquid (in insulators) and Dirac fermions (in metals). Small-bandgap kagomé materials have the potential to bridge quantum spin liquid states and exhibit phenomena such as superconductivity but remain exceptionally rare. Here we report a structural, thermodynamic, and transport study of the two-dimensional kagomé metal-organic frameworks Ni₃(HIB)₂ and Cu₃(HIB)₂ (HIB = hexaiminobenzene). Magnetization measurements yield Curie constants of 0.989 emu K (mol Ni)^-1 Oe^-1 and 0.371 emu K (mol Cu)^-1 Oe^-1, respectively, close to the values expected for ideal S = 1 Ni²⁺ and S = ¹/₂ Cu²⁺. Weiss temperatures of -10.6 and -14.3 K indicate net weak mean field antiferromagnetic interactions between ions. Electrical transport measurements reveal that both materials are semiconducting, with gaps (E_g) of 22.2 and 103 meV, respectively. Specific heat measurements reveal a large T-linear contribution γ of 148(4) mJ mol-fu^-1 K^-2 in Ni₃(HIB)₂ with only a gradual upturn below ∼5 K and no evidence of a phase transition to an ordered state down to 0.1 K. Cu₃(HIB)₂ also lacks evidence of a phase transition above 0.1 K, with a substantial, field-dependent, magnetic contribution below ∼5 K. Despite them being superficially in agreement with the expectations of magnetic frustration and spin liquid physics, we ascribe these observations to the stacking faults found from a detailed analysis of synchrotron X-ray diffraction data. At the same time, our results demonstrate that these MOFs exhibit localized magnetism with simultaneous proximity to a metallic state, thus opening up opportunities to explore the connection between the insulating and metallic ground states of kagomé materials in a highly tunable chemical platform.

Site-Selective d10/d0 Substitution in an S = 1/2 Spin Ladder Ba2CuTe1-xWxO6 (0 ≤ x ≤ 0.3)

Isovalent nonmagnetic d10 and d0 B″ cations have proven to be a powerful tool for tuning the magnetic interactions between magnetic B' cations in A2B'B″O6 double perovskites. Tuning is facilitated by the changes in orbital hybridization that favor different superexchange pathways. This can produce alternative magnetic structures when B″ is d10 or d0. Furthermore, the competition generated by introducing mixtures of d10 and d0 cations can drive the material into the realms of exotic quantum magnetism. Here, Te6+ d10 was substituted by W6+ d0 in the hexagonal perovskite Ba2CuTeO6, which possesses a spin ladder geometry of Cu2+ cations, creating a Ba2CuTe1-xWxO6 solid solution (x = 0-0.3). We find W6+ is almost exclusively substituted for Te6+ on the corner-sharing site within the spin ladder, in preference to the face-sharing site between ladders. The site-selective doping directly tunes the intraladder, Jrung and Jleg, interactions. Modeling the magnetic susceptibility data shows the d0 orbitals modify the relative intraladder interaction strength (Jrung/Jleg) so the system changes from a spin ladder to isolated spin chains as W6+ increases. This further demonstrates the utility of d10 and d0 dopants as a tool for tuning magnetic interactions in a wide range of perovskites and perovskite-derived structures.

A cationic sulfur-hydrocarbon triradical with an excited quartet state

The triptycene-bridged tris(thianthrene) compound 1 was designed and synthesized. Three-electron oxidation of 1 by NO[Al(OC(CF₃)₃)₄], followed by crystallization at two different temperatures resulted in the triradical trication salts 2a and 2b respectively, which feature different crystal packing patterns. The triradical trications in 2a and 2b both feature a doublet ground state which can be thermally populated to a quartet state, representing the first examples of cationic main-group triradicals.

Honeycomb-Structure RuI3 , A New Quantum Material Related to α-RuCl3

The layered honeycomb lattice material α-RuCl₃ has emerged as a prime candidate for displaying the Kitaev quantum spin liquid state, and as such has attracted much research interest. Here a new layered honeycomb lattice polymorph of RuI₃ , a material that is strongly chemically and structurally related to α-RuCl₃ is described_. The material is synthesized at moderately elevated pressures and is stable under ambient conditions. Preliminary characterization reveals that it is a metallic conductor, with the absence of long-range magnetic order down to 0.35 K and an unusually large T-linear contribution to the heat capacity. It is proposed that this phase, with a layered honeycomb lattice and strong spin-orbit coupling, provides a new route for the characterization of quantum materials.

Enhancement of Photoresponse on Narrow-Bandgap Mott Insulator α-RuCl3 via Intercalation

Charge doping to Mott insulators is critical to realize high-temperature superconductivity, quantum spin liquid state, and Majorana fermion, which would contribute to quantum computation. Mott insulators also have a great potential for optoelectronic applications; however, they showed insufficient photoresponse in previous reports. To enhance the photoresponse of Mott insulators, charge doping is a promising strategy since it leads to effective modification of electronic structure near the Fermi level. Intercalation, which is the ion insertion into the van der Waals gap of layered materials, is an effective charge-doping method without defect generation. Herein, we showed significant enhancement of optoelectronic properties of a layered Mott insulator, α-RuCl₃, through electron doping by organic cation intercalation. The electron-doping results in substantial electronic structure change, leading to the bandgap shrinkage from 1.2 eV to 0.7 eV. Due to localized excessive electrons in RuCl₃, distinct density of states is generated in the valence band, leading to the optical absorption change rather than metallic transition even in substantial doping concentration. The stable near-infrared photodetector using electronic modulated RuCl₃ showed 50 times higher photoresponsivity and 3 times faster response time compared to those of pristine RuCl₃, which contributes to overcoming the disadvantage of a Mott insulator as a promising optoelectronic device and expanding the material libraries.

Unraveling the Electrical and Magnetic Properties of Layered Conductive Metal-Organic Framework With Atomic Precision

This paper describes structural elucidation of a layered conductive metal-organic framework (MOF) material Cu₃ (C₆ O₆ )₂ by microcrystal electron diffraction with sub-angstrom precision. This insight enables the first identification of an unusual π-stacking interaction in a layered MOF material characterized by an extremely short (2.73 Å) close packing of the ligand arising from pancake bonding and ordered water clusters within pores. Band structure analysis suggests semiconductive properties of the MOF, which are likely related to the localized nature of pancake bonds and the formation of a singlet dimer of the ligand. The spin of Cu^II within the Kagomé arrangement dominates the paramagnetism of the MOF, leading to strong geometrical magnetic frustration.

Ferromagnetic Cr4PtGa17: A Half-Heusler-Type Compound with a Breathing Pyrochlore Lattice

We describe the crystal structure and elementary magnetic properties of a previously unreported ternary intermetallic compound, Cr₄PtGa₁₇, which crystallizes in a rhombohedral unit cell in the noncentrosymmetric space group R3m. The crystal structure is closely related to those of XYZ half-Heusler compounds, where X, Y, and Z are reported to be single elements only, occupying three different face-centered-cubic sublattices. The new material, Cr₄PtGa₁₇, can be most straightforwardly illustrated by writing the formula as (PtGa₂)(Cr₄Ga₁₄)Ga (X = PtGa₂, Y = Cr₄Ga₁₄, Z = Ga); that is, the X and Y sites are occupied by clusters instead of single elements. The magnetic Cr occupies a breathing pyrochlore lattice. Ferromagnetic ordering is found below T_C ∼ 61 K, by both neutron diffraction and magnetometer studies, with a small, saturated moment of ∼0.25 μ_B/Cr observed at 2 K, making Cr₄PtGa₁₇ the first ferromagnetically ordered material with a breathing pyrochlore lattice. A magnetoresistance of ∼140% was observed at 2 K. DFT calculations suggest that the material has a nearly half-metallic electronic structure. The new material, Cr₄PtGa₁₇, the first realization of both a half-Heusler-type structure and a breathing pyrochlore lattice, might pave a new way to achieve novel types of half-Heusler compounds.

3D supramolecular chiral crystal structures of radical anion salts of (−)-NDI-Δ and possible magnetic phase diagrams

Supramolecular chiral crystals of radical anion salts of a triangular chiral electron acceptor, (−)-naphthalene diimide (NDI)-Δ, were electrochemically grown in propylene carbonate electrolyte solutions in the presence of cyclic multidentate ligands.