Molecular quantum magnetism in LiZn2Mo3O8

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.

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.

VERDI: VERsatile DIffractometer with wide-angle polarization analysis for magnetic structure studies in powders and single crystals

The VERsatile DIffractometer will set a new standard for a world-class magnetic diffractometer with versatility for both powder and single crystal samples and capability for wide-angle polarization analysis. The instrument will utilize a large single-frame bandwidth and will offer high-resolution at low momentum transfers and excellent signal-to-noise ratio. A horizontal elliptical mirror concept with interchangeable guide pieces will provide high flexibility in beam divergence to allow for a high-resolution powder mode, a high-intensity single crystal mode, and a polarized beam option. A major science focus will be quantum materials that exhibit emergent properties arising from collective effects in condensed matter. The unique use of polarized neutrons to isolate the magnetic signature will provide optimal experimental input to state-of-the-art modeling approaches to access detailed insight into local magnetic ordering.

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.

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.

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.

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.

Quantum Magnetic Properties in Perovskite with Anderson Localized Artificial Spin-1/2

Quantum magnetic properties in a geometrically frustrated lattice of spin-1/2 magnet, such as quantum spin liquid or solid and the associated spin fractionalization, are considered key in developing a new phase of matter. The feasibility of observing the quantum magnetic properties, usually found in geometrically frustrated lattice of spin-1/2 magnet, in a perovskite material with controlled disorder is demonstrated. It is found that the controlled chemical disorder, due to the chemical substitution of Ru ions by Co-ions, in a simple perovskite CaRuO3 creates a random prototype configuration of artificial spin-1/2 that forms dimer pairs between the nearest and further away ions. The localization of the Co impurity in the Ru matrix is analyzed using the Anderson localization formulation. The dimers of artificial spin-1/2, due to the localization of Co impurities, exhibit singlet-to-triplet excitation at low temperature without any ordered spin correlation. The localized gapped excitation evolves into a gapless quasi-continuum as dimer pairs break and create freely fluctuating fractionalized spins at high temperature. Together, these properties hint at a new quantum magnetic state with strong resemblance to the resonance valence bond system.

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.

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.

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.

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.