Possible valence-bond condensation in the frustrated cluster magnet LiZn2Mo3O8

Low-Temperature Glassy Behavior of Sr2Ni3(C2O4)3(OH)4·3H2O with Frustrated Spin Hexamers

In this paper, we studied the synthesis, crystal structure, magnetism, and memory effect of a spin hexamer compound Sr2Ni3(C2O4)3(OH)4·3H2O. The basic magnetic unit of this compound is a ringed spin hexamer (Ni6 cluster). These Ni6 clusters are connected by an oxalate group, constituting a two-dimensional framework along the ab plane. With decreasing temperature, three anomalies are detected in susceptibility curves, corresponding to the formation of short-range spin correlation around 42.5 K, the onset of an antiferromagnetic ordering at 21.4 K, and a reentrant cluster spin-glass state below 12 K. A strong spin frustration is demonstrated with a frustrated factor f ∼ 11. The dominant exchange interactions are J1/kB = -17.1 K and J2/kB = -81.1 K, evaluated by exact diagonalization analysis with an isolated Ni6 cluster model. A nonequilibrium dynamics study of magnetic memory effect indicates the evolution of several intermediate metastable states.

Quasimolecular J_{tet}=3/2 Moments in the Cluster Mott Insulator GaTa_{4}Se_{8}

Quasimolecular orbitals in cluster Mott insulators provide a route to tailor exchange interactions, which may yield novel quantum phases of matter. We demonstrate the cluster Mott character of the lacunar spinel GaTa_{4}Se_{8} using resonant inelastic x-ray scattering (RIXS) at the Ta L_{3} edge. Electrons are fully delocalized over Ta_{4} tetrahedra, forming quasimolecular J_{tet}=3/2 moments. The modulation of the RIXS intensity as function of the transferred momentum q allows us to determine the cluster wave function, which depends on competing intracluster hopping terms that mix states with different character. This mixed wave function is decisive for the macroscopic properties since it affects intercluster hopping and exchange interactions and furthermore renormalizes the effective spin-orbit coupling constant. The versatile wave function, tunable via intracluster hopping, opens a new perspective on the large family of lacunar spinels and cluster Mott insulators in general.

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.

Magnetic molecular orbitals in MnSi

A large body of knowledge about magnetism is attained from models of interacting spins, which usually reside on magnetic ions. Proposals beyond the ionic picture are uncommon and seldom verified by direct observations in conjunction with microscopic theory. Here, using inelastic neutron scattering to study the itinerant near-ferromagnet MnSi, we find that the system's fundamental magnetic units are interconnected, extended molecular orbitals consisting of three Mn atoms each rather than individual Mn atoms. This result is further corroborated by magnetic Wannier orbitals obtained by ab initio calculations. It contrasts the ionic picture with a concrete example and presents an unexplored regime of the spin waves where the wavelength is comparable to the spatial extent of the molecular orbitals. Our discovery brings important insights into not only the magnetism of MnSi but also a broad range of magnetic quantum materials where structural symmetry, electron itinerancy, and correlations act in concert.

As-Se Pentagonal Linkers to Induce Chirality and Polarity in Mixed-Valent Fe-Se Tetrahedral Chains Resulting in Hidden Magnetic Ordering

A novel mixed-valent hybrid chiral and polar compound, Fe₇As₃Se₁₂(en)₆(H₂O), has been synthesized by a single-step solvothermal method. The crystal structure consists of 1D [Fe₅Se₉] chains connected via [As₃Se₂]-Se pentagonal linkers and charge-balancing interstitial [Fe(en)₃]²⁺ complexes (en = ethylenediamine). Neutron powder diffraction verified that interstitial water molecules participate in the crystal packing. Magnetic polarizability of the produced compound was confirmed by X-ray magnetic circular dichroism (XMCD) spectroscopy. X-ray absorption spectroscopy (XAS) and ⁵⁷Fe Mössbauer spectroscopy showed the presence of mixed-valent Fe²⁺/Fe³⁺ in the Fe-Se chains. Magnetic susceptibility measurements reveal strong antiferromagnetic nearest neighbor interactions within the chains with no apparent magnetic ordering down to 2 K. Hidden short-range magnetic ordering below 70 K was found by ⁵⁷Fe Mössbauer spectroscopy, showing that a fraction of the Fe³⁺/Fe²⁺ in the chains are magnetically ordered. Nevertheless, complete magnetic ordering is not achieved even at 6 K. Analysis of XAS spectra demonstrates that the fraction of Fe³⁺ in the chain increases with decreasing temperature. Computational analysis points out several competing ferrimagnetic ordered models within a single chain. This competition, together with variation in the Fe oxidation state and additional weak intrachain interactions, is hypothesized to prevent long-range magnetic ordering.

Identification of a metastable uranium metal–organic framework isomer through non-equilibrium synthesis

Since the structure of supramolecular isomers determines their performance, rational synthesis of a specific isomer hinges on understanding the energetic relationships between isomeric possibilities. To this end, we have systematically interrogated a pair of uranium-based metal–organic framework topological isomers both synthetically and through density functional theory (DFT) energetic calculations. Although synthetic and energetic data initially appeared to mismatch, we assigned this phenomenon to the appearance of a metastable isomer, driven by levers defined by Le Châtelier's principle. Identifying the relationship between structure and energetics in this study reveals how non-equilibrium synthetic conditions can be used as a strategy to target metastable MOFs. Additionally, this study demonstrates how defined MOF design rules may enable access to products within the energetic phase space which are more complex than conventional binary (e.g., kinetic vs. thermodynamic) products.

Identifying the relationship between structure and energetics in a uranium MOF isomer system reveals how non-equilibrium synthetic conditions can be used as a strategy to target metastable MOFs.

The missing MIL-101(Mn): geometrically guided synthesis and topologically correlated valence states

Through a geometrically guided approach, i.e. with the aid of pyridyl modulators, the long-sought MIL-101(Mn) structure is finally achieved, which features emergent topologically correlated mixed-valence states that are apt for enzymatic catalysis.

From (S = 1) Spin Hexamer to Spin Tetradecamer by CuO Interstitials in A2Cu3O(CuO)x(SO4)3 (A = alkali)

(Na,K)₂Cu₃O(SO₄)₃ compounds form structural chains of Cu₆ hexameric units with nominal S = 1 spins due to the interplay between inner strong antiferromagnetic and ferromagnetic exchanges. We show here that the lattice relaxation after the replacement of alkali by larger Rb and Cs ones is accompanied by the insertion of neutral CuO species into (Rb,Cs)₂Cu₃O(CuO)_x(SO₄)₃ phases. Structurally, interstitial CuO links the next two Cu₆ units in longer Cu₁₄ tetradecameric ones. For A = Cs (x = 0.5), the cationic ordering is perfect inside a double-cell superstructure. Magnetically, the original Cu₁₄ units consist of frustrated fragments of an S = ¹/₂ spin ladder, with ferromagnetic rung-like but antiferromagnetic leg-like and next-nearest neighbor couplings. It returns S = 1 Cu₁₄ spin clusters, effective around 100 K. Our density functional theory calculations and susceptibility fits also show that at low temperatures they interact in two-dimensional lattices, despite the existence of short inter-Cu-Cu distances between the next two clusters along pseudo-one-dimensional chains.

A high dimensional oxysulfide built from large iron-based clusters with partial charge-ordering

Herein we report the original Ba₁₀Fe_7.75Zn_5.25S₁₈Si₃O₁₂ oxysulfide which crystallizes in a new structural type. Contrary to the usual oxychalcogenides, it crystallizes with a non-centrosymmetric 3D spatial network structure built from large magnetic clusters consisting of twelve (Fe^2+/3+/Zn)S₃O tetrahedra decorating a central Fe²⁺S₆ octahedron and exhibiting a spin glass state.

Emergent Moments and Random Singlet Physics in a Majorana Spin Liquid

We exhibit an exactly solvable example of a SU(2) symmetric Majorana spin liquid phase, in which quenched disorder leads to random-singlet phenomenology of emergent magnetic moments. More precisely, we argue that a strong-disorder fixed point controls the low temperature susceptibility χ(T) of an exactly solvable S=1/2 model on the decorated honeycomb lattice with vacancy and/or bond disorder, leading to χ(T)=C/T+DT^{α(T)-1}, where α(T)→0 slowly as the temperature T→0. The first term is a Curie tail that represents the emergent response of vacancy-induced spin textures spread over many unit cells: it is an intrinsic feature of the site-diluted system, rather than an extraneous effect arising from isolated free spins. The second term, common to both vacancy and bond disorder [with different α(T) in the two cases] is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P).

Survival of itinerant excitations and quantum spin state transitions in YbMgGaO4 with chemical disorder

A recent focus of quantum spin liquid (QSL) studies is how disorder/randomness in a QSL candidate affects its true magnetic ground state. The ultimate question is whether the QSL survives disorder or the disorder leads to a “spin-liquid-like” state, such as the proposed random-singlet (RS) state. Since disorder is a standard feature of most QSL candidates, this question represents a major challenge for QSL candidates. YbMgGaO₄, a triangular lattice antiferromagnet with effective spin-1/2 Yb³⁺ions, is an ideal system to address this question, since it shows no long-range magnetic ordering with Mg/Ga site disorder. Despite the intensive study, it remains unresolved as to whether YbMgGaO₄ is a QSL or in the RS state. Here, through ultralow-temperature thermal conductivity and magnetic torque measurements, plus specific heat and DC magnetization data, we observed a residual κ₀/T term and series of quantum spin state transitions in the zero temperature limit for YbMgGaO₄. These observations strongly suggest that a QSL state with itinerant excitations and quantum spin fluctuations survives disorder in YbMgGaO₄.

It remains an open question as to whether the quantum spin liquid state survives material disorder, or is replaced by some spin-liquid like state. Here, Rao et al succeed in resolving a resolving a κ₀/T residual in the thermal conductivity of YbMgGaO₄ strongly suggesting the survival of the quantum spin liquid state.

Hybrid electrons in the trimerized GaV4O8

Mixed-valent transition-metal compounds display complex structural, electronic and magnetic properties, which often intricately coexist. Here, we report the new ternary oxide GaV₄O₈, a structural sibling of skyrmion-hosting lacunar spinels. GaV₄O₈ contains a vanadium trimer and an original spin-orbital-charge texture that forms upon the structural phase transition at T_S = 68 K followed by the magnetic transition at T_N = 35 K. The texture arises from the coexistence of orbital molecules on the vanadium trimers and localized electrons on the remaining vanadium atoms. Such hybrid electrons create opportunities for novel types of spin, charge, and orbital order in mixed-valent transition-metal compounds.

A pentanuclear {Co5} cluster motif forming a capped breathing kagomé lattice

A new pentanuclear {Co5} cluster motif is found to have a D3h oblate trigonal bipyramidal geometry, which is extended into a 3D triangle network, forming a unique capped breathing kagomé lattice. Magnetic results confirmed a paramagnetism down to 2 K, accompanying the disappearance of two-thirds of the spin moment at low-temperature and the appearance of a 1/5 magnetization plateau.

Chemistry of Quantum Spin Liquids

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

Orbital Effects in Solids: Basics, Recent Progress, and Opportunities

The properties of transition metal compounds are largely determined by nontrivial interplay of different degrees of freedom: charge, spin, lattice, and also orbital ones. Especially rich and interesting effects occur in systems with orbital degeneracy. For example, they result in the famous Jahn-Teller effect, leading to a plethora of consequences for static and dynamic properties, including nontrivial quantum effects. In the present review, we discuss the main phenomena in the physics of such systems, paying central attention to the novel manifestations of those. After shortly summarizing the basic phenomena and their descriptions, we concentrate on several specific directions in this field. One of them is the reduction of effective dimensionality in many systems with orbital degrees of freedom due to the directional character of orbitals, with the concomitant appearance of some instabilities that lead in particular to the formation of dimers, trimers, and similar clusters in a material. The properties of such cluster systems, which are largely determined by their orbital structure, are discussed in detail, and many specific examples of those in different materials are presented. Another big field that has acquired special significance relatively recently is the role of the relativistic spin-orbit interaction. The mutual influence of this interaction and the more traditional Jahn-Teller physics is treated in detail in the second part of the review. In discussing all of these questions, special attention is paid to novel quantum effects.

Multimodal Structure Solution with 19F NMR Crystallography of Spin Singlet Molybdenum Oxyfluorides

Complex crystal structures with subtle atomic-scale details are now routinely solved using complementary tools such as X-ray and/or neutron scattering combined with electron diffraction and imaging. Identifying unambiguous atomic models for oxyfluorides, needed for materials design and structure-property control, is often still a considerable challenge despite their advantageous optical responses and applications in energy storage systems. In this work, NMR crystallography and single-crystal X-ray diffraction are combined for the complete structure solution of three new compounds featuring a rare triangular early transition metal oxyfluoride cluster, [Mo₃O₄F₉]^5-. After framework identification by single-crystal X-ray diffraction, 1D and 2D solid-state ¹⁹F NMR spectroscopy supported by ab initio calculations are used to solve the structures of K₅[Mo₃O₄F₉]·3H₂O (1), K₅[Mo₃O₄F₉]·2H₂O (2), and K₁₆[Mo₃O₄F₉]₂[TiF₆]₃·2H₂O (3) and to assign the nine distinct fluorine sites in the oxyfluoride clusters. Furthermore, ¹⁹F NMR identifies selective fluorine dynamics in K₁₆[Mo₃O₄F₉]₂[TiF₆]₃·2H₂O. These dual scattering and spectroscopy methods are used to demonstrate the generality and sensitivity of ¹⁹F shielding to small changes in bond length, on the order of 0.01 Å or less, even in the presence of hydrogen bonding, metal-metal bonding, and electrostatic interactions. Starting from the structure models, the nature of chemical bonding in the molybdates is explained by molecular orbital theory and electronic structure calculations. The average Mo-Mo distance of 2.505 Å and diamagnetism in 1, 2, and 3 are attributed to a metal-metal bond order of unity along with a 1a²1e⁴ electronic ground state configuration for the [Mo₃O₄F₉]^5- cluster, leading to a rare trimeric spin singlet involving d² Mo⁴⁺ ions. The approach to structure solution and bonding analysis is a powerful strategy for understanding the structures and chemical properties of complex fluorides and oxyfluorides.

LiZn2V3O8: a new geometrically frustrated cluster spin-glass

We have investigated the structural and magnetic properties of a new cubic spinel LiZn₂V₃O₈ (LZVO) through x-ray diffraction, dc and ac susceptibility, magnetic relaxation, aging, memory effect, heat capacity and ⁷Li nuclear magnetic resonance (NMR) measurements. A Curie-Weiss fit of the dc susceptibility [Formula: see text]([Formula: see text]) yields a Curie-Weiss temperature [Formula: see text] K. This suggests strong antiferromagnetic (AFM) interactions among the magnetic vanadium ions. The dc and ac susceptibility data indicate the spin-glass behavior below a freezing temperature T _f [Formula: see text] 3 K. The frequency dependence of the T _f is characterized by the Vogel-Fulcher law and critical dynamic scaling behavior or power law. From both fitting, we obtained the value of the characteristic angular frequency [Formula: see text] [Formula: see text] 3.56 [Formula: see text] 10⁶ Hz, the dynamic exponent [Formula: see text] [Formula: see text] 2.65, and the critical time constant [Formula: see text] [Formula: see text] 1.82 [Formula: see text] 10^-6 s, which falls in the conventional range for typical cluster spin-glass (CSG) systems. The value of relative shift in freezing temperature [Formula: see text] [Formula: see text] 0.039 supports a CSG ground states. We also found aging phenomena and memory effects in LZVO. The asymmetric response of the magnetic relaxation below T _f supports the hierarchical model. Heat capacity data show no long-range or short-range ordering down to 2 K. Only about 25% magnetic entropy change [Formula: see text] signifies the presence of strong frustration in the system. The ⁷Li NMR spectra show a shift and broadening with decreasing temperature. The spin-lattice and spin-spin relaxation rates show anomalies due to spin freezing around 3 K as the bulk magnetization.

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

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

Nonpolar-to-Polar Trimerization Transitions in the S = 1 Kagomé Magnet Na2Ti3Cl8

Kagomé lattice magnets have emerged as a versatile platform on which to discover and explore the underlying physics of quantum-spin liquids and related states of matter, although experimental examples of ideal kagomé lattices remain rare. Here we report that Na₂Ti₃Cl₈ is an ideal realization of an insulating S = 1 kagomé magnet. This material undergoes a discrete two-step trimerization upon cooling, transforming from a centrosymmetric, paramagnetic high-temperature (HT) R3m phase to noncentrosymmetric, polar, and trimerized intermediate- (IT) and low-temperature (LT) R3m phases via two successive first-order phase transitions. Symmetry mode decomposition analysis shows that trimerization requires activation of the proper polar order parameter Γ₂^- and that this mode becomes active at the HT → IT phase transition. The magnitude of this order parameter approximately doubles at the IT → LT transition, with possible activation of a second polar mode, corresponding to Na₂ and Ti₃Cl₈ displacing layers toward each other, at the IT → LT transition. Specific heat measurements reveal comparable changes in entropy between the LT → IT transition, 18.6(1.0) J (mol of f.u.)^-1 K^-1, and the IT → LT transition, 16.8(1.0) J (mol of f.u.)^-1 K^-1, demonstrating loss of the magnetic degrees of freedom and constraining possible models for the magnetic and electronic structures of the IT and LT phases. Thus, Na₂Ti₃Cl₈ demonstrates a novel mechanism to obtain polar structures driven by geometrically frustrated lattices and metal-metal bonding and highlights the rich physics arising from kagomé lattice materials.

Tunable Magnetic Transition to a Singlet Ground State in a 2D van der Waals Layered Trimerized Kagomé Magnet

Incorporating magnetism into two-dimensional (2D) van der Waals (vdW) heterostructures is crucial for the development of functional electronic and magnetic devices. Here, we show that Nb₃X₈ (X = Cl, Br) is a family of 2D layered trimerized kagomé magnets that are paramagnetic at high temperatures and undergo a first-order phase transition on cooling to a singlet magnetic state. X-ray diffraction shows that a rearrangement of the vdW stacking accompanies the magnetic transition, with high- and low-temperature phases consistent with scanning transmission electron microscopy images of the end members α-Nb₃Cl₈ and β-Nb₃Br₈. The temperature of this transition is systematically varied across the solid solution Nb₃Cl_8-xBr_x (x = 0-8), with x = 6 having transitions near room temperature. The solid solution also varies the optical properties, which are further modulated by the phase transition. As such, they provide a platform on which to understand and exploit the interplay between dimensionality, magnetism, and optoelectronic behavior in vdW materials.

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

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

Progress toward Solid State Synthesis by Design

Ages of history are defined by the underlying materials that promoted human development: stone, bronze, and iron ages. Since the middle of the last century, humanity has lived in a silicon age, where the development of the transistor ushered in new technologies previously thought inconceivable. But as technology has advanced, so have the requirements for new materials to sustain increasing physical demands. The field of solid state chemistry is dedicated to the discovery of new materials and phenomena, and though most materials discoveries in history have been through serendipity rather than careful reaction design, the last few decades have seen an increase in the number of materials discovered through a consideration of chemical reaction kinetics and thermodynamics. Materials by design have changed the way solid state chemists approach the synthesis of possible materials with interesting and useful properties. Unlike other chemistry subfields such as organic chemistry and biochemistry, solid state chemistry does not currently benefit from a toolbox of reactions that can allow for the synthesis of any arbitrary material. The diversity and complexity of the solid state phase space likely inhibits chemists from ever having such a toolbox. However, a thorough understanding of the various synthetic techniques involved in the synthesis of stable and metastable solids may be realized through an understanding of the reaction kinetics and thermodynamics. In the Account, we review the common synthesis techniques involved in the formation of metastable materials and break down their underlying chemistry to the simplest reaction mechanisms involved. The synthesis reactions of most metastable materials can be understood through these three reaction driving parameters, which include the exploitation of Le Chatelier's principle, thermo-kinetic reaction coupling, and lowering the activation energy of formation of the metastable product, and we identify several materials whose syntheses are described either by one or a combination of these driving parameters. We identify what exists at the frontier of materials discovery by design, including novel applications of supercritical fluids for tuning between "gas" and "solvent"-like environments. While conventional solvation requires changes in either the temperature or composition of the system, supercritical fluid solvation requires only changes in the fluid density, which opens up the possibilities for the synthesis of new materials. Most importantly, however, we look toward the future of materials synthesis by design and see that it must be a collaborative one. At present, chemists design materials using knowledge about chemical structure and reactivity but often target specific materials with very specific properties. In contrast, computational chemists perform calculations on millions of different elemental combinations and find many candidates of possible materials with interesting properties, though most of these are not realizable synthetically due to limitations in reactivity, kinetics, or thermodynamics. Synthetic harmony can be achieved through active collaboration and communication between these two subfields of chemistry, such that new calculations can incorporate complete knowledge about reaction kinetics and thermodynamics, and new syntheses target computationally predicted materials derived from an understanding of mapped reaction landscapes.

Scaling and data collapse from local moments in frustrated disordered quantum spin systems

Recently measurements on various spin–1/2 quantum magnets such as H₃LiIr₂O₆, LiZn₂Mo₃O₈, ZnCu₃(OH)₆Cl₂ and 1T-TaS₂—all described by magnetic frustration and quenched disorder but with no other common relation—nevertheless showed apparently universal scaling features at low temperature. In particular the heat capacity C[H, T] in temperature T and magnetic field H exhibits T/H data collapse reminiscent of scaling near a critical point. Here we propose a theory for this scaling collapse based on an emergent random-singlet regime extended to include spin-orbit coupling and antisymmetric Dzyaloshinskii-Moriya (DM) interactions. We derive the scaling C[H, T]/T ~ H^−γF_q[T/H] with F_q[x] = x^q at small x, with q ∈ {0, 1, 2} an integer exponent whose value depends on spatial symmetries. The agreement with experiments indicates that a fraction of spins form random valence bonds and that these are surrounded by a quantum paramagnetic phase. We also discuss distinct scaling for magnetization with a q-dependent subdominant term enforced by Maxwell’s relations.

There are many proposals for new forms of quantum matter in frustrated magnets but in practice disorder prevents the realisation of theoretically-tractable idealised models. Kimchi et al. show that recently observed scaling behavior common to several disordered quantum magnets can be understood as the emergence of a universal random-singlet regime.

Tunable Quantum Spin Liquidity in the 1/6th-Filled Breathing Kagome Lattice

We present measurements on a series of materials, Li_{2}In_{1-x}Sc_{x}Mo_{3}O_{8}, that can be described as a 1/6th-filled breathing kagome lattice. Substituting Sc for In generates chemical pressure which alters the breathing parameter nonmonotonically. Muon spin rotation experiments show that this chemical pressure tunes the system from antiferromagnetic long range order to a quantum spin liquid phase. A strong correlation with the breathing parameter implies that it is the dominant parameter controlling the level of magnetic frustration, with increased kagome symmetry generating the quantum spin liquid phase. Magnetic susceptibility measurements suggest that this is related to distinct types of charge order induced by changes in lattice symmetry, in line with the theory of Chen et al. [Phys. Rev. B 93, 245134 (2016)PRBMDO2469-995010.1103/PhysRevB.93.245134]. The specific heat for samples at intermediate Sc concentration, which have the minimum breathing parameter, show consistency with the predicted U(1) quantum spin liquid.

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

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

Nearest-neighbour resonating valence bonds in YbMgGaO4

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

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

Interacting nanoscale magnetic superatom cluster arrays in molybdenum oxide bronzes

In this study, we examine several reduced ternary molybdates in the family of yellow rare earth molybdenum bronzes produced by electrochemical synthesis with composition LnMo₁₆O₄₄. These compounds contain an array of electrically isolated but magnetically interacting multi-atom clusters with composition Mo₈O₃₆. These arrayed superatom clusters support a single hole shared among the eight molybdenum atoms in the unit, corresponding to a net spin moment of 1μ_B, and exhibit magnetic exchange between the units via the MoO₄ tetrahedra (containing Mo⁶⁺ ions) and the LnO₈ cubes (containing Ln³⁺ ions). The findings presented here expand on the physics of the unusual collective properties of multi-atom clusters and extend the discussion of such assemblages to the rich structural chemistry of molybdenum bronzes.

Synthesis and magnetic properties of two isostructural fluorophosphates BaMPO4F (M = Cu, Co) with a tunnel structure

Two fluorophosphates, BaMPO₄F (M = Cu, Co), have been synthesized by a conventional hydrothermal method, and they crystallize in the orthorhombic system with the space group P2₁2₁2₁, exhibiting a tunnel structure built by distorted MO₄F square-pyramids and PO₄ tetrahedra. The magnetic behaviors of the two compounds are investigated by means of magnetic susceptibility, magnetization, and heat capacity measurements. The results indicate that BaCuPO₄F exhibits a paramagnetic behavior down to 2 K, while BaCoPO₄F undergoes long-range antiferromagnetic ordering at 11.3 K and short-range magnetic ordering at ∼22 K.

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

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

Covalent bonds against magnetism in transition metal compounds

Magnetism in transition metal compounds is usually considered starting from a description of isolated ions, as exact as possible, and treating their (exchange) interaction at a later stage. We show that this standard approach may break down in many cases, especially in 4d and 5d compounds. We argue that there is an important intersite effect-an orbital-selective formation of covalent metal-metal bonds that leads to an "exclusion" of corresponding electrons from the magnetic subsystem, and thus strongly affects magnetic properties of the system. This effect is especially prominent for noninteger electron number, when it results in suppression of the famous double exchange, the main mechanism of ferromagnetism in transition metal compounds. We study this mechanism analytically and numerically and show that it explains magnetic properties of not only several 4d-5d materials, including Nb2O2F3 and Ba5AlIr2O11, but can also be operative in 3d transition metal oxides, e.g., in CrO2 under pressure. We also discuss the role of spin-orbit coupling on the competition between covalency and magnetism. Our results demonstrate that strong intersite coupling may invalidate the standard single-site starting point for considering magnetism, and can lead to a qualitatively new behavior.

Spin dynamics in Na(4-x)Ir₃O₈ (x = 0.3 and 0.7) investigated by ²³Na NMR and μSR

We report (23)Na nuclear magnetic resonance (NMR) and zero-field (ZF) and longitudinal-field (LF) muon spin relaxation (μSR) measurements of the depleted hyperkagome compounds Na(4-x)Ir3O8 (x  =  0.3 and 0.7), which undergo an insulator-semimetal transition as a function of x. The (23)Na spin-lattice relaxation rates, T1(-1), follow a T(2.5) power law behavior at accessible temperatures of T  =  120-350 K. A substantial temperature dependence of T1(-1) indicates the presence of gapped excitations at elevated temperatures through the transition to a semimetallic phase. ZF-μSR results reveal that hole-doping leads to a melting of quasi-static order to a dynamically fluctuating state. The very slow muon depolarization rate which varies hardly with temperature indicates that spins are close to an itinerant limit in the largest doping x  =  0.7. The dynamic relaxation rates extracted from the LF-μSR spectra show a three-dimensional diffusive transport. Our combined NMR and μSR results suggest the occurrence of intriguing spin and charge excitations across the insulator-semimetal transition.

Direct assignment of molecular vibrations via normal mode analysis of the neutron dynamic pair distribution function technique

For over a century, vibrational spectroscopy has enhanced the study of materials. Yet, assignment of particular molecular motions to vibrational excitations has relied on indirect methods. Here, we demonstrate that applying group theoretical methods to the dynamic pair distribution function analysis of neutron scattering data provides direct access to the individual atomic displacements responsible for these excitations. Applied to the molecule-based frustrated magnet with a potential magnetic valence-bond state, LiZn2Mo3O8, this approach allows direct assignment of the constrained rotational mode of Mo3O13 clusters and internal modes of MoO6 polyhedra. We anticipate that coupling this well known data analysis technique with dynamic pair distribution function analysis will have broad application in connecting structural dynamics to physical properties in a wide range of molecular and solid state systems.

Coulomb Liquid Phases of Bosonic Cluster Mott Insulators on a Pyrochlore Lattice

Employing large-scale quantum Monte Carlo simulations, we reveal the full phase diagram of the extended Hubbard model of hard-core bosons on the pyrochlore lattice with partial fillings. When the intersite repulsion is dominant, the system is in a cluster Mott insulator phase with an integer number of bosons localized inside the tetrahedral units of the pyrochlore lattice. We show that the full phase diagram contains three cluster Mott insulator phases with 1/4, 1/2, and 3/4 boson fillings, respectively. We further demonstrate that all three cluster Mott insulators are Coulomb liquid phases and its low-energy property is described by the emergent compact U(1) quantum electrodynamics. In addition to measuring the specific heat and entropy of the cluster Mott insulators, we investigate the correlation function of the emergent electric field and verify it is consistent with the compact U(1) quantum electrodynamics description. Our result sheds light on the magnetic properties of various pyrochlore systems, as well as the charge physics of the cluster magnets.

Synthesis, structure and magnetic properties of hydroxychlorides A3Cu3(OH)Cl8 (A = Cs, Rb) with isolated tricopper

A₃Cu₃(OH)Cl₈ (A = Cs, Rb) features an isolated triangular building unit of [Cu₃(OH)Cl₈]³⁻, displaying ferromagnetic coupling via the Cu(2)–Cl(5)–Cu(3) route.

Fractionalized charge excitations in a spin liquid on partially filled pyrochlore lattices

We study the Mott transition from a metal to cluster Mott insulators in the 1/4- and 1/8-filled pyrochlore lattice systems [corrected]. It is shown that such Mott transitions can arise due to charge localization in clusters or in tetrahedron units, driven by the nearest-neighbor repulsive interaction. The resulting cluster Mott insulator is a quantum spin liquid with a spinon Fermi surface, but at the same time a novel fractionalized charge liquid with charge excitations carrying half the electron charge. There exist two emergent U(1) gauge fields or "photons" that mediate interactions between spinons and charge excitations, and between fractionalized charge excitations themselves, respectively. In particular, it is suggested that the emergent photons associated with the fractionalized charge excitations can be measured in x-ray scattering experiments. Various other experimental signatures of the exotic cluster Mott insulator are discussed in light of candidate materials with partially filled bands on the pyrochlore lattice.

Candidate quantum spin liquid due to dimensional reduction of a two-dimensional honeycomb lattice

As with quantum spin liquids based on two-dimensional triangular and kagome lattices, the two-dimensional honeycomb lattice with either a strong spin-orbital coupling or a frustrating second-nearest-neighbor coupling is expected to be a source of candidate quantum spin liquids. An ammonium salt [(C₃H₇)₃NH]₂[Cu₂(C₂O₄)₃](H₂O)_2.2 containing hexagonal layers of Cu²⁺ was obtained from solution. No structural transition or long-range magnetic ordering was observed from 290 K to 2 K from single crystal X-ray diffraction, specific heat and susceptibility measurements. The anionic layers are separated by sheets of ammonium and H₂O with distance of 3.5 Å and no significant interaction between anionic layers. The two-dimensional honeycomb lattice is constructed from Jahn-Teller distorted Cu²⁺ and oxalate anions, showing a strong antiferromagnetic interaction between S = 1/2 metal atoms with θ = −120 (1) K. Orbital analysis of the Cu²⁺ interactions through the oxalate-bridges suggests a stripe mode pattern of coupling with weak ferromagnetic interaction along the b axis, and strong antiferromagnetic interaction along the a axis. Analysis of the magnetic susceptibility shows that it is dominated by a quasi-one-dimensional contribution with spin chains that are at least as well isolated as those of well-known quasi-one-dimensional spin liquids.

Molecular quantum magnetism in LiZn2Mo3O8

Inelastic neutron scattering at low temperatures T≤30  K from a powder of LiZn2Mo3O8 demonstrates this triangular-lattice antiferromagnet hosts collective magnetic excitations from spin-1/2 Mo3O13 molecules. Apparently gapless (Δ<0.2  meV) and extending at least up to 2.5 meV, the low-energy magnetic scattering cross section is surprisingly broad in momentum space and involves one-third of the spins present above 100 K. The data are compatible with the presence of valence bonds involving nearest-neighbor and next-nearest-neighbor spins forming a disordered or dynamic state.

Ultrasound-assisted fabrication of a biocompatible magnetic hydroxyapatite

This work describes the fabrication and characterization of a biocompatible magnetic hydroxyapatite (HA) using an ultrasound-assisted co-precipitation method. X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR), and transmission electron microscopy (TEM) were used to characterize the structure and chemical composition of the produced samples. The M-H loops of synthesized materials were traced using a vibrating sample magnetometer (VSM) and the biocompatibility was evaluated by cell culture and MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide) assay. Furthermore, in vivo histopathological examinations were used to evaluate the potential toxicological effects of Fe₃O₄-HA composites on kidney of SD rats injected intraperitoneally with Fe₃O₄-HA particles. The results showed that magnetic iron oxide particles first replace OH ions of HA, which are parallel to the c axis, and then enter the HA crystal lattice which produces changes in the crystal surface of HA. Chemical bond interaction was observed between PO₄³⁻ groups of HA and iron ions of Fe₃O₄. The saturation magnetization (MS ) of Fe₃O₄-HA composites was 46.36 emu/g obtained from VSM data. Cell culture and MTT assays indicated that HA could affect the growth and proliferation of HEK-293 cells. This Fe₃O₄-HA composite produced no negative effects on cell morphology, viability, and proliferation and exhibited remarkable biocompatibility. Moreover, no inflammatory cell infiltration was observed in kidney histopathology slices. Therefore, this study succeeds to develop a Fe₃O₄-HA composite as a prospective biomagnetic material for future applications.

Emergent honeycomb lattice in LiZn2Mo3O8

We introduce the idea of emergent lattices, where a simple lattice decouples into two weakly coupled lattices as a way to stabilize spin liquids. In LiZn2Mo3O8, the disappearance of 2/3 of the spins at low temperatures suggests that its triangular lattice decouples into an emergent honeycomb lattice weakly coupled to the remaining spins, and we suggest several ways to test this proposal. We show that these orphan spins act to stabilize the spin liquid in the J1-J2 honeycomb model and also discuss a possible 3D analogue, Ba2MoYO6 that may form a "depleted fcc lattice."