Universal geometric frustration in pyrochlores

Low-temperature properties of magnetically frustrated rare-earth zirconatesA2Zr2O7

Rare-earthA2Zr2O7zirconates have attracted considerable attention of the scientific community for their complex magnetic, electronic and material properties applicable in modern technologies. The light rare-earth members of the series, crystallising in the pyrochlore variant of cubic crystal structure, have been studied in detail. The heavierA2Zr2O7compounds have been investigated mainly from the material properties viewpoint, focussing on their thermal properties and stability at high temperature and pressure. Low-temperature studies were mostly missing until recently. We present the low-temperature magnetic and thermodynamic properties ofA2Zr2O7withA= Y, La, Nd, Eu, Gd, Tb, Dy, Ho, Tm, Yb, and Lu, well covering the whole series, newly synthesised by high-temperature sintering and melting methods. X-ray diffraction reveals and confirms the ordered pyrochlore structure in the light members, the disordered cubic structure of the defect-fluorite type inA2Zr2O7withA= Y, Gd-Yb, and finally the lower symmetry rhombohedral structure in the end-member Lu2Zr2O7. The specific heat of the investigated compounds is dominated by a low-temperature anomaly associated with magnetic ordering: long-range in light rare-earth zirconates; and short-range in heavier members. The effective magnetic moment in the studied compounds, determined by fitting the magnetisation data to the Curie-Weiss formula, is in good agreement with the expected value of theA3+free ion. The magnetic properties have been revealed to be strongly influenced by the geometric frustration of the magnetic moments of both the pyrochlore structure, as well as the face centred cubic lattice created by the cations of the defect-fluorite structure, but connected also to intrinsic atomic disorder. The experimental results are discussed in the framework of previous studies onA2Zr2O7zirconates, as well as otherA2B2O7compounds.

An A2 B2 O7 -Type High-Entropy Oxide for Efficient Photoelectrochemical Photodetector with Excellent Long-Term Stability

Optoelectronics with excellent long-term stability is meaningful for practical applications. Herein, for the first time, an A2 B2 O7 type high-entropy oxide of (La0.2 Ce0.2 Nd0.2 Gd0.2 Bi0.2 )2 Ti2 O7 (ATO) is synthesized and applied for photoelectrochemical photodetection. The lattice distortion, highly dispersed metal composition, and exposed active sites of ATO are beneficial for the fast separation and transmission of photogenerated electron/hole pairs, endowing ATO-based devices with good photodetection performance. Both the density functional theory calculations and the nondegenerate transient absorption spectroscopy demonstrate the good optoelectronic properties of ATO. The systematic experimental studies reveal the tunable photodetection capability of ATO-based photodetector (PD) in the visible region. A photocurrent of 772.00 nA cm-2 and a responsivity of 4.02 µA W-1 can be achieved as the PD in 1.0 m KOH with the bias potential of 0.6 V. Importantly, the robust and reproducible ON/OFF signals of the PD can be verified and there is only ≈5.00% attenuation in photocurrent even after 6 months, revealing the great potential of high- entropy oxides for practical applications.

Emerging natural and tailored perovskite-type mixed oxides–based catalysts for CO2 conversions

The rapid economic and societal development have led to unprecedented energy demand and consumption resulting in the harmful emission of pollutants. Hence, the conversion of greenhouse gases into valuable chemicals and fuels has become an urgent challenge for the scientific community. In recent decades, perovskite-type mixed oxide-based catalysts have attracted significant attention as efficient CO2 conversion catalysts due to the characteristics of both reversible oxygen storage capacity and stable structure compared to traditional oxide-supported catalysts. In this review, we hand over a comprehensive overview of the research for CO2 conversion by these emerging perovskite-type mixed oxide-based catalysts. Three main CO2 conversions, namely reverse water gas shift reaction, CO2 methanation, and CO2 reforming of methane have been introduced over perovskite-type mixed oxide-based catalysts and their reaction mechanisms. Different approaches for promoting activity and resisting carbon deposition have also been discussed, involving increased oxygen vacancies, enhanced dispersion of active metal, and fine-tuning strong metal-support interactions. Finally, the current challenges are mooted, and we have proposed future research prospects in this field to inspire more sensational breakthroughs in the material and environment fields.

Structural Distortion-Modulated Magnetic and Dielectric Properties in Nonstoichiometric Yb2-xTi2O7-δ Pyrochlore

Rare-earth titanate pyrochlores have attracted considerable attention for their unique magnetic frustration. Among those compounds, Yb₂Ti₂O₇, a candidate for quantum spin ice, has been extensively studied in its magnetic ground state. However, works on its dielectric property and structure-property relationship lag far more behind. Here, by preparing and investigating nonstoichiometric Yb_2-xTi₂O_7-δ (x = 0-0.15) ceramics, we demonstrate that the samples with x ≤ 0.05 maintain a single-pyrochlore phase, but the nonstoichiometry arouses significant structural distortion and increased oxygen vacancy. As a result, the ferromagnetism, indicated by a positive Curie-Weiss temperature, decreases almost linearly with increasing x value. Remarkably composition-dependent low-temperature dielectric relaxations have been observed. In addition, through introducing nonstoichiometry, the relaxor degree of dielectric behavior is enhanced, and the dielectric curve shows an altered shape. The origin of this dielectric relaxation is attributed to the increased structural distortion reflected by the changed bond length/angle, since there is no phase transition in 90-300 K. Our work gives a comprehensive view on the structural, magnetic, and dielectric properties of Yb₂Ti₂O₇, which is instructive for further work on pyrochlores.

Strategies and Considerations for Least-Squares Analysis of Total Scattering Data

The process of least-squares analysis has been applied for decades in the field of crystallography. Here, we discuss the application of this process to total scattering data, primarily in the combination of least-squares Rietveld refinements and fitting of the atomic pair distribution function (PDF). While these two approaches use the same framework, the interpretation of results from least-squares fitting of PDF data should be done with caution through carefully constructed analysis approaches. We provide strategies and considerations for applying least-squares analysis to total scattering data, combining both crystallographic Rietveld and fitting of PDF data, given in context with recent examples from the literature. This perspective is aimed to be an accessible document for those new to the total scattering approach, as well as a reflective framework for the total scattering expert.

Persistent Structure and Frustrated Magnetism in High Entropy Rare-Earth Zirconates

The configurational complexity and distinct local atomic environments of high entropy oxides remain largely unexplored, leaving structure-property relationships and the hypothesis that the family offers rich tunability for applications ambiguous. This work investigates the influence of cation size and materials synthesis in determining the resulting structure and magnetic properties of a family of high entropy rare-earth zirconates (HEREZs, nominal composition RE₂ Zr₂ O₇ with RE = rare-earth element combinations including Eu, Gd, Tb, Dy, Ho, La, or Sc). The structural characterization of the series is examined through synchrotron X-ray diffraction and pair distribution function analysis, and electron microscopy, demonstrating average defect-fluorite structures with considerable local disorder, in all samples. The surface morphology and particle sizes are found to vary significantly with preparation method, with irregular micron-sized particles formed by high temperature sintering routes, spherical nanoparticles resulting from chemical co-precipitation methods, and porous nanoparticle agglomerates resulting from polymer steric entrapment synthesis. In agreement with the disordered cation distribution found across all samples, magnetic measurements indicate that all synthesized HEREZs show frustrated magnetic behavior, as seen in a number of single-component RE₂ Zr₂ O₇ pyrochlore oxides. These findings advance the understanding of the local structure of high entropy oxides and demonstrate strategies for designing nanostructured morphologies in the class.

Probing Multiscale Disorder in Pyrochlore and Related Complex Oxides in the Transmission Electron Microscope: A Review

Transmission electron microscopy (TEM), and its counterpart, scanning TEM (STEM), are powerful materials characterization tools capable of probing crystal structure, composition, charge distribution, electronic structure, and bonding down to the atomic scale. Recent (S)TEM instrumentation developments such as electron beam aberration-correction as well as faster and more efficient signal detection systems have given rise to new and more powerful experimental methods, some of which (e.g., 4D-STEM, spectrum-imaging, in situ/operando (S)TEM)) facilitate the capture of high-dimensional datasets that contain spatially-resolved structural, spectroscopic, time- and/or stimulus-dependent information across the sub-angstrom to several micrometer length scale. Thus, through the variety of analysis methods available in the modern (S)TEM and its continual development towards high-dimensional data capture, it is well-suited to the challenge of characterizing isometric mixed-metal oxides such as pyrochlores, fluorites, and other complex oxides that reside on a continuum of chemical and spatial ordering. In this review, we present a suite of imaging and diffraction (S)TEM techniques that are uniquely suited to probe the many types, length-scales, and degrees of disorder in complex oxides, with a focus on disorder common to pyrochlores, fluorites and the expansive library of intermediate structures they may adopt. The application of these techniques to various complex oxides will be reviewed to demonstrate their capabilities and limitations in resolving the continuum of structural and chemical ordering in these systems.

Decoding ionic conductivity and reordering in cation-disordered pyrochlores

The ordered structure A₂B₂O₆O' in pyrochlores engenders twin rows of inequivalent anion sublattices each centred on alternating cations. While it is known that cation antisite disorder augments the ionic conductivity by several orders of magnitude, the local cation environment around the anions and the dynamic anion reordering during the cation disordering are not well-elucidated. Using atomistic simulations on Gd₂Zr₂O₇, we first show that the anions engage in concerted hops to the neighbouring tetrahedral sites mostly along with the 〈1 0 0〉 direction while completely avoiding the octahedral sites. While the initially vacant 8a sites start accommodating oxygen ions with increasing cation disorder, they show noticeable reluctance even at significant levels of disorder. We have also tracked both the distribution of available oxygen sites following random cation disorder, which is dependent only on cation disordering, and the probability of occupation of these sites. Interestingly, the available oxygen sites show a non-monotonic dependence on the number of B ions in the nearest neighbouring shell while the occupation probability of all the available oxygen sites increases monotonically. A tetrahedral oxygen site thus has a better probability of being occupied when it has a greater number of second neighbour B ions. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Magnetic ordering in the Ising antiferromagnetic pyrochlore Nd2ScNbO7

The question of structural disorder and its effects on magnetism is relevant to a number of spin liquid candidate materials. Although commonly thought of as a route to spin glass behaviour, here we describe a system in which the structural disorder results in long-range antiferromagnetic order due to local symmetry breaking. Nd₂ScNbO₇is shown to have a dispersionless gapped excitation observed in other neodymium pyrochlores belowT_N= 0.37 K through polarized and inelastic neutron scattering. However the dispersing spin waves are not observed. This excited mode is shown to occur in only 14(2)% of the neodymium ions through spectroscopy and is consistent with total scattering measurements as well as the magnitude of the dynamic moment 0.26(2)μ_B. The remaining magnetic species order completely into the all-in all-out Ising antiferromagnetic structure. This can be seen as a result of local symmetry breaking due disordered Sc⁺³and Nb⁺⁵ions about theA-site. From this work, it has been established thatB-site disorder restores the dipole-like behaviour of the Nd⁺³ions compared to the Nd₂B₂O₇parent series.

Spin-ice physics in cadmium cyanide

Spin-ices are frustrated magnets that support a particularly rich variety of emergent physics. Typically, it is the interplay of magnetic dipole interactions, spin anisotropy, and geometric frustration on the pyrochlore lattice that drives spin-ice formation. The relevant physics occurs at temperatures commensurate with the magnetic interaction strength, which for most systems is 1-5 K. Here, we show that non-magnetic cadmium cyanide, Cd(CN)2, exhibits analogous behaviour to magnetic spin-ices, but does so on a temperature scale that is nearly two orders of magnitude greater. The electric dipole moments of cyanide ions in Cd(CN)2 assume the role of magnetic pseudospins, with the difference in energy scale reflecting the increased strength of electric vs magnetic dipolar interactions. As a result, spin-ice physics influences the structural behaviour of Cd(CN)2 even at room temperature.

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.

Discovery and Single Crystal Growth of High Entropy Pyrochlores

A family of high entropy oxides with the formula Mg₂Ta₃Ln₃O₁₄ (Ln = La, Pr, Nd, Sm, Eu, Gd) has been discovered and synthesized. Single crystals, 5 mm OD × 2.5 cm, for Ln = Nd have been grown using the laser optical floating zone technique. Crystal orientations are confirmed by Laue diffraction, and structure solutions were obtained via single crystal X-ray diffraction. The structure is found to be a partially disordered pyrochlore, space group Fd-3m, fractional chemical formula (Mg_0.25Nd_0.75)₂(Mg_0.25Ta_0.75)₂O₇. Magnetization measurements indicate ordinary paramagnetic behavior in all compounds down to T = 2 K, except in the Eu variant which possesses Van Vleck paramagnetism. Specific heat measurements for Ln = Nd shows no phase transitions between T = 300 and 2 K. We demonstrate the ability to prepare magnetically disordered materials by substitution of Mg with Ni, Mn, and Co, demonstrating the flexibility of this family in accommodating defects. The stabilization of these compounds could be due to the entropy gain associated with defects, showcasing a "materials by design" approach by using disorder to stabilize novel magnetic and optical materials. Our work also demonstrates the feasibility of preparing high entropy oxides in single crystalline form.

Chemically directed structure evolution for crystal structure prediction

The chemically directed structure evolution method uses chemical models to quantify the environment of atoms and vacancy sites in a crystal structure with that information used to inform how to modify the structure for crystal structure prediction.

Elusive Valence Transition in Mixed-Valence Sesquioxide Cs4O6

Cs₄O₆ is a mixed-valence molecular oxide with a cubic structure, comprising valency-delocalized O₂^4/3- units and with properties highly sensitive to cooling protocols. Here we use neutron powder diffraction to authenticate that, while upon deep quenching the cubic phase is kinetically arrested down to cryogenic temperatures, ultraslow cooling results in an incomplete structural transition to a contracted tetragonal phase. Two dioxygen anions in a 1:2 ratio are identified, providing evidence that the transition is accompanied by charge and orbital order and stabilizes a Robin-Day Class II mixed-valence state, comprising O₂^2- and O₂^- anions. The phenomenology of the phase change is consistent with that of a martensitic transition. The response of the low-temperature phase assemblage to heating is complex, involving a series of successive interconversions between the coexisting phases. Notably, a broad interconversion plateau is present near 260 K, signifying reentrant kinetic arrest of the tetragonal phase upon heating because of the combined effects of increased steric hindrance for molecular rotation and melting of charge and orbital order. The geometrically frustrated pyrochlore lattice adopted by the paramagnetic S = ¹/₂ O₂^- units provides an intimate link between the crystal and magnetic properties of charge-ordered Cs₄O₆, naturally accounting for the absence of magnetic order.

Role of defects in determining the magnetic ground state of ytterbium titanate

Pyrochlore systems are ideally suited to the exploration of geometrical frustration in three dimensions, and their rich phenomenology encompasses topological order and fractional excitations. Classical spin ices provide the first context in which it is possible to control emergent magnetic monopoles, and anisotropic exchange leads to even richer behaviour associated with large quantum fluctuations. Whether the magnetic ground state of Yb₂Ti₂O₇ is a quantum spin liquid or a ferromagnetic phase induced by a Higgs transition appears to be sample dependent. Here we have determined the role of structural defects on the magnetic ground state via the diffuse scattering of neutrons. We find that oxygen vacancies stabilise the spin liquid phase and the stuffing of Ti sites by Yb suppresses it. Samples in which the oxygen vacancies have been eliminated by annealing in oxygen exhibit a transition to a ferromagnetic phase, and this is the true magnetic ground state.

Exploring the role of structural defect is essential to understand the exotic quantum spin phenoma in rare earth pyrochlores. Here the authors show oxygen vacancies can stabilise the spin liquid phase and reveal the ferromagnetic ground state when oxygen vacancies are eliminated in Yb₂Ti₂O₇.