Magnetic Ground States of the Rare-Earth Tripod Kagome Lattice Mg_{2}RE_{3}Sb_{3}O_{14} (RE=Gd,Dy,Er)

Low-temperature behaviors of the dipolar magnet Dy3Sb3Zn2O14with a strongly site-mixing disordered kagome lattice

Interesting behaviors may emerge in the magnetic frustrated materials with significant site-mixing disorder. We present the results of the structural, magnetic susceptibility, and specific heat measurements of Dy3Sb3Zn2O14with ∼20%Dy/Zn site-mixing disorder, which results in either a diluted 2D triangular lattice, or an intermediate structure between the kagome and pyrochlore lattice. In addition to the sharp anomaly of the temperature dependence of specific heat atT∼0.35 K, which was attributed to the emergent charge order state for the sample with less disorder, a broad peak atT∼1.5 K, and a small hump belowT∼0.1 K are observed. The measured temperature dependence of specific heat and the Monte Carlo simulation suggest that the magnetic frustration persists despite of a strong site-mixing disorder.

Exceptional Magnetocaloric Responses in a Gadolinium Silicate with Strongly Correlated Spin Disorder for Sub-Kelvin Magnetic Cooling

The development of magnetocaloric materials with a significantly enhanced volumetric cooling capability is highly desirable for the application of adiabatic demagnetization refrigerators in confined spatial environments. Here, the thermodynamic characteristics of a magnetically frustrated spin-7/2 Gd9.33[SiO4]6O2 is presented, which exhibits strongly correlated spin disorder below ≈1.5 K. A quantitative model is proposed to describe the magnetization results by incorporating nearest-neighbor Heisenberg antiferromagnetic and dipolar interactions. Remarkably, the recorded magnetocaloric responses are unprecedentedly large and applicable below 1.0 K. It is proposed that the S = 7/2 spin liquids serve as versatile platforms for investigating high-performance magnetocaloric materials in the sub-kelvin regime, particularly those exhibiting a superior cooling power per unit volume.

Magnetic and Magnetocaloric Properties of the A2LnSbO6 Lanthanide Oxides on the Frustrated fcc Lattice

Frustrated lanthanide oxides are promising candidates for cryogen-free magnetic refrigeration due to their suppressed ordering temperatures and high magnetic moments. While much attention has been paid to the garnet and pyrochlore lattices, the magnetocaloric effect in frustrated face-centered cubic (fcc) lattices remains relatively unexplored. We previously showed that the frustrated fcc double perovskite Ba₂GdSbO₆ is a top-performing magnetocaloric material (per mol Gd) because of its small nearest-neighbor interaction between spins. Here we investigate different tuning parameters to maximize the magnetocaloric effect in the family of fcc lanthanide oxides, A₂LnSbO₆ (A = {Ba²⁺, Sr²⁺} and Ln = {Nd³⁺, Tb³⁺, Gd³⁺, Ho³⁺, Dy³⁺, Er³⁺}), including chemical pressure via the A site cation and the magnetic ground state via the lanthanide ion. Bulk magnetic measurements indicate a possible trend between magnetic short-range fluctuations and the field-temperature phase space of the magnetocaloric effect, determined by whether an ion is a Kramers or a non-Kramers ion. We report for the first time on the synthesis and magnetic characterization of the Ca₂LnSbO₆ series with tunable site disorder that can be used to control the deviations from Curie-Weiss behavior. Taken together, these results suggest fcc lanthanide oxides as tunable systems for magnetocaloric design.

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.

Single-Ion Behavior in New 2-D and 3-D Gadolinium 4f7 Materials: CsGd(SO4)2 and Cs[Gd(H2O)3(SO4)2]·H2O

The recent creation of 4f⁷ gadolinium materials has enabled vital studies of the free-ion properties of the Gd(III) cations. While the ⁸ S ground state in a trivalent Gd compound is, in principle, isotropic, it has been demonstrated that there is a residual orbital angular momentum affected by the crystal field and structural distortion in certain systems. By exploiting the atomistic control innate to material growth, we address a fundamental question of how the isotropic nature of Gd(III) is preserved in different dimensionalities of crystal structures. To achieve this, we designed two new trivalent Gd materials possessing two structurally distinct features, a 2-D CsGd(SO₄)₂ and a 3-D Cs[Gd(H₂O)₃(SO₄)₂]·H₂O. The tunability of the structural dimension is facilitated by O-H---O hydrogen bonds. The structural divergence between the two compounds allows us to investigate each material individually and make a comparison between them regarding their physical properties as a function of lattice dimension. Our results demonstrate that structural dimensions have a negligible effect on the single-ion behavior of the materials. Magnetization measurements for the Gd(III) complexes yielded paramagnetic states with the isotropic spin-only nature. Specific heat data suggest that there is a lack of magnetic phase transition down to T = 1.8 K, and coupled lattice vibrations in the materials are attributable to strong covalent bonding characters of the (SO₄)^2- and H₂O ligands. This work offers a pathway for retaining the single-ion property of Gd(III) while constructing the large spin magnetic moment S = 7/2 in large-scale extended frameworks.

Frustration in a generalized kagomé Ising antiferromagnet: Exact results

We obtain the exact ground-state phase diagram of a generalized kagomé antiferromagnet with both pair and triplet interactions, J_{2} and J_{3}, respectively, in the presence of a magnetic field h appropriately tuned. We find that when the pair interaction J_{2}<0 dominates, the ground state is geometrically frustrated; on the other hand, the ground state is disordered but not frustrated when the triplet interaction J_{3} dominates, the boundaries between the two cases being at J_{3}=±J_{2}. The exact ground-state crossover lines between the two distinct types of disorder remain identifiable crossover curves at finite temperatures. In the frustrated domain, the ground state of the three-parameter model is identical to the ground state of the prototype one-parameter (J_{2}<0) model of geometrical frustration. Towards further understanding the frustration domain of the three-parameter model, a closed-form approximation (exact at zero temperature) determines solutions on a two-parameter subspace for induced magnetization and parallel magnetic susceptibility at finite fields h and temperatures T, the inverse susceptibility showing a Curie-Weiss behavior. We argue that the existence of an exact T=0 threshold magnetic field, below which the magnetization remains zero, indicates the existence of a gapped spectrum attributable to the presence of the triplet interaction J_{3}.

Cation Regulation to Investigate the Chalcogenide Borate RE6Nb2MgSB8O26 (RE = La-Nd) Family

Chalcogenide borates have been developed and are considered an attractive system due to their favorable physical properties such as magnetism and nonlinear optical effects. Here, isostructural RE₆Nb₂MgSB₈O₂₆ (RE = La-Nd) compounds in the title family have been obtained through cation regulation in rare-earth and VB group metals. This family crystalizes in the centrosymmetric P3̅ space group and features 3D frameworks formed by {[Mg(NbB₄O₁₃)₂]^16-}_∞ polyanionic layers and QRE₆ octahedra. The structural chemistry was characterized and theoretical calculations were performed to understand the structural merit of this family. In addition, RE₆Nb₂MgSB₈O₂₆ possess the largest band gaps among known rare-earth chalcogenide borates, and they all show antiferromagnetic-like behaviors.

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.

Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho3Mg2Sb3O14

A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod-kagome lattice material Ho3Mg2Sb3O14 unites an icelike magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho3+ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition at T * ≈ 0.32 K to a remarkable state with three peculiarities: a concurrent recovery of magnetic entropy associated with the strongly coupled electronic and nuclear degrees of freedom; a fragmentation of the spin into periodic and icelike components; and persistent inelastic magnetic excitations down to T ≈ 0.12 K . These observations deviate from expectations of classical spin fragmentation on a kagome lattice, but can be understood within a model of dipolar kagome ice under a homogeneous transverse magnetic field, which we survey with exact diagonalization on small clusters and mean-field calculations. In Ho3Mg2Sb3O14, hyperfine interactions dramatically alter the single-ion and collective properties, and suppress possible quantum correlations, rendering the fragmentation with predominantly single-ion quantum fluctuations. Our results highlight the crucial role played by hyperfine interactions in frustrated quantum magnets and motivate further investigations of the role of quantum fluctuations on partially ordered magnetic states.

Realization of the kagome spin ice state in a frustrated intermetallic compound

Spin ices are exotic phases of matter characterized by frustrated spins obeying local "ice rules," in analogy with the electric dipoles in water ice. In two dimensions, one can similarly define ice rules for in-plane Ising-like spins arranged on a kagome lattice. These ice rules require each triangle plaquette to have a single monopole and can lead to different types of orders and excitations. Using experimental and theoretical approaches including magnetometry, thermodynamic measurements, neutron scattering, and Monte Carlo simulations, we establish HoAgGe as a crystalline (i.e., nonartificial) system that realizes the kagome spin ice state. The system features a variety of partially and fully ordered states and a sequence of field-induced phases at low temperatures, all consistent with the kagome ice rule.

Frustrated Magnetism in Triangular Lattice TlYbS2 Crystals Grown via Molten Flux

The triangular lattice compound TlYbS₂ was prepared as large single crystals via a molten flux growth technique using sodium chloride. Anisotropic magnetic susceptibility measurements down to 0.4 K indicate a complete absence of long-range magnetic order. Despite this lack of long-range order, short-range antiferromagnetic interactions are evidenced through broad transitions, suggesting frustrated behavior. Variable magnetic field measurements reveal metamagnetic behavior at temperatures ≤2 K. Complex low temperature field-tunable magnetic behavior, in addition to no observable long-range order down to 0.4 K, suggest that TlYbS₂ is a frustrated magnet and a possible quantum spin liquid candidate.

Homogeneous reduced moment in a gapful scalar chiral kagome antiferromagnet

We present a quantitative experimental investigation of the scalar chiral magnetic order with in Nd3Sb3Mg2O14. Static magnetization reveals a net ferromagnetic ground state, and inelastic neutron scattering from the hyperfine coupled nuclear spin reveals a local ordered moment of 1.76(6) μ B , just 61(2)% of the saturated moment size. The experiments exclude static disorder as the source of the reduced moment. A 38(1) μ eV gap in the magnetic excitation spectrum inferred from heat capacity rules out thermal fluctuations and suggests a multipolar explanation for the moment reduction. We compare Nd3Sb3Mg2O14 to Nd pyrochlores and show that Nd2Zr2O7 is in a spin fragmented state using nuclear Schottky heat capacity.

Emergent order in the kagome Ising magnet Dy3Mg2Sb3O14

The Ising model—in which degrees of freedom (spins) are binary valued (up/down)—is a cornerstone of statistical physics that shows rich behaviour when spins occupy a highly frustrated lattice such as kagome. Here we show that the layered Ising magnet Dy₃Mg₂Sb₃O₁₄ hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scattering and bulk thermomagnetic measurements reveal a phase transition at ∼0.3 K from a disordered spin-ice-like regime to an emergent charge ordered state, in which emergent magnetic charge degrees of freedom exhibit three-dimensional order while spins remain partially disordered. Monte Carlo simulations show that an interplay of inter-layer interactions, spin canting and chemical disorder stabilizes this state. Our results establish Dy₃Mg₂Sb₃O₁₄ as a tuneable system to study interacting emergent charges arising from kagome Ising frustration.

Frustration in lattices of interacting spins can lead to rich and exotic physics, such as fractionalized excitations and emergent order. Here, the authors demonstrate a low-temperature transition from a disordered spin-ice-like phase to an emergent charge ordered phase in the bulk kagome Ising magnet Dy₃Mg₂Sb₃O₁₄.