Orbital Dimer Model for the Spin-Glass State in Y_{2}Mo_{2}O_{7}

Torsional flexibility in zinc-benzenedicarboxylate metal-organic frameworks

We explore the role and nature of torsional flexibility of carboxylate-benzene links in the structural chemistry of metal-organic frameworks (MOFs) based on Zn and benzenedicarboxlyate (bdc) linkers. A particular motivation is to understand the extent to which such flexibility is important in stabilising the unusual topologically aperiodic phase known as TRUMOF-1. We compare the torsion angle distributions of TRUMOF-1 models with those for crystalline Zn/1,3-bdc MOFs, including a number of new materials whose structures we report here. We find that both periodic and aperiodic Zn/1,3-bdc MOFs sample a similar range of torsion angles, and hence the formation of TRUMOF-1 does not require any additional flexibility beyond that already evident in chemically-related crystalline phases. Comparison with Zn/1,4-bdc MOFs does show, however, that the lower symmetry of the 1,3-bdc linker allows access to a broader range of torsion angles, reflecting a greater flexibility of this linker.

Truchet-tile structure of a topologically aperiodic metal-organic framework

When tiles decorated to lower their symmetry are joined together, they can form aperiodic and labyrinthine patterns. Such Truchet tilings offer an efficient mechanism of visual data storage related to that used in barcodes and QR codes. We show that the crystalline metal-organic framework [OZn₄][1,3-benzenedicarboxylate]₃ (TRUMOF-1) is an atomic-scale realization of a complex three-dimensional Truchet tiling. Its crystal structure consists of a periodically arranged assembly of identical zinc-containing clusters connected uniformly in a well-defined but disordered fashion to give a topologically aperiodic microporous network. We suggest that this unusual structure emerges as a consequence of geometric frustration in the chemical building units from which it is assembled.

Eminuscent phase in frustrated magnets: a challenge to quantum spin liquids

A geometrically frustrated (GF) magnet consists of localised magnetic moments, spins, whose orientation cannot be arranged to simultaneously minimise their interaction energies. Such materials may host novel fascinating phases of matter, such as fluid-like states called quantum spin-liquids. GF magnets have, like all solid-state systems, randomly located impurities whose magnetic moments may “freeze” at low temperatures, making the system enter a spin-glass state. We analyse the available data for spin-glass transitions in GF materials and find a surprising trend: the glass-transition temperature grows with decreasing impurity concentration and reaches a finite value in the impurity-free limit at a previously unidentified, “hidden”, energy scale. We propose a scenario in which the interplay of interactions and entropy leads to a crossover in the permeability of the medium that assists glass freezing at low temperatures. This low-temperature, “eminuscent”, phase may obscure or even destroy the widely-sought spin-liquid states in rather clean systems.

A spin-glass forms in frustrated magnetic systems when at low temperatures impurity sites “freeze” into a random spin configuration. Here, by looking back at previous experimental results, Syzranov and Ramirez show that the glass-transition temperature grows with decreasing impurity concentration.

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.

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.

Designing disorder into crystalline materials

Crystals are a state of matter characterized by periodic order. Yet, crystalline materials can harbour disorder in many guises, such as non-repeating variations in composition, atom displacements, bonding arrangements, molecular orientations, conformations, charge states, orbital occupancies or magnetic structure. Disorder can sometimes be random but, more usually, it is correlated. Frontier research into disordered crystals now seeks to control and exploit the unusual patterns that persist within these correlated disordered states in order to access functional responses inaccessible to conventional crystals. In this Review, we survey the core design principles that guide targeted control over correlated disorder. We show how these principles - often informed by long-studied statistical mechanical models - can be applied across an unexpectedly broad range of materials, including organics, supramolecular assemblies, oxide ceramics and metal-organic frameworks. We conclude with a forward-looking discussion of the exciting link between disorder and function in responsive media, thermoelectrics and topological phases.

Role of spin-glass behavior in the formation of exotic magnetic states in GdB6

Randomness and frustration are believed to be two crucial criteria for the formation of spin glass state. However, the spin freezing occurs in some well-ordered crystals below the related temperature T_f due to the instability of each spin state, which induces the variation of either magnetic moment value or exchange energy. Here we explore the new mechanism of the in-site originated disorder in antiferromagnets Gd_0.73La_0.27B₆ and GdB₆, which is caused by the random mutual shifts of Gd³⁺ spins from the centrally symmetrical positions in the regular cubic lattice. The universal scaling of ESR linewidth temperature dependencies to the power law ΔH(T) ~ ((T − T_D)/T_D)^α with α = − 1.1 ± 0.05 in the paramagnetic phase of both compounds demonstrates the identity of the origin of magnetic randomness. In Gd_0.73La_0.27B₆ the resulting random spin configurations freeze at T_f ≈ 10.5 K where the maximum of magnetization is observed. Below T_f the splitting of ZFC and FC magnetization curves takes place as well as the magnetic state depends on the antecedent sample history. In the case of GdB₆ the coherent displacement of Gd ions compete with these random shifts forming an antiferromagnetic (AFM) phase at T_N = 15.5 K, which prevails over the spin freezing at T_f ≈ 13 K, expected from the ESR data. The observation of the hysteresis of the ESR spectrum in the AFM phase suggests that its properties may be determined by the competition of two types of AFM orders, which results in formation of stable magnetic domains with nonequivalent positions of AFM Gd pairs at T < 10 K.

Spin-Orbital Glass Transition in a Model of a Frustrated Pyrochlore Magnet without Quenched Disorder

We show theoretically that spin and orbital degrees of freedom in the pyrochlore oxide Y_{2}Mo_{2}O_{7}, which is free of quenched disorder, can exhibit a simultaneous glass transition, working as dynamical disorder for each other. The interplay of spins and orbitals is mediated by the Jahn-Teller lattice distortion that selects the choice of orbitals, which then generates variant spin exchange interactions ranging from ferromagnetic to antiferromagnetic ones. Our Monte Carlo simulations detect the power-law divergence of the relaxation times and the negative divergence of both the magnetic and dielectric nonlinear susceptibilities, resolving the long-standing puzzle on the origin of the disorder-free spin glass.

First-principles studies of spin-orbital physics in pyrochlore oxides

The pyrochlore oxides [Formula: see text]O₇ exhibit a complex interplay between geometrical frustration, electronic correlations, and spin-orbit coupling (SOC), due to the lattice structure and active charge, spin, and orbital degrees of freedom. Understanding the properties of these materials is a theoretical challenge, because their intricate nature depends on material-specific details and quantum many-body effects. Here we review our recent studies based on first-principles calculations and quantum many-body theories for 4d and 5d pyrochlore oxides with B  =  Mo, Os, and Ir. In these studies, the SOC and local electron correlations are treated within the local density approximation (LDA)  +  U and LDA  +  dynamical mean-field theory formalisms. We also discuss the technical aspects of these calculations.

Local orbital degeneracy lifting as a precursor to an orbital-selective Peierls transition

Fundamental electronic principles underlying all transition metal compounds are the symmetry and filling of the d-electron orbitals and the influence of this filling on structural configurations and responses. Here we use a sensitive local structural technique, x-ray atomic pair distribution function analysis, to reveal the presence of fluctuating local-structural distortions at high temperature in one such compound, CuIr₂S₄. We show that this hitherto overlooked fluctuating symmetry-lowering is electronic in origin and will modify the energy-level spectrum and electronic and magnetic properties. The explanation is a local, fluctuating, orbital-degeneracy-lifted state. The natural extension of our result would be that this phenomenon is likely to be widespread amongst diverse classes of partially filled nominally degenerate d-electron systems, with potentially broad implications for our understanding of their properties.

A common feature of many transition metal materials is global symmetry breaking at low temperatures. Here the authors show that such materials are characterized by fluctuating symmetry-lowering distortions that exist pre-formed in higher temperature phases with greater average symmetry.

Giant Magnetoelastic-Coupling Driven Spin-Lattice Liquid State in Molybdate Pyrochlores

We propose the idea of a spin-lattice liquid, in which spin and lattice degrees of freedom are strongly coupled and remain disordered and fluctuating down to low temperatures. We show that such a state arises naturally from a microscopic analysis of a class of molybdate pyrochlore compounds, and is driven by a giant magnetoelastic effect. Finally, we argue that this could explain some of the experimental features of Y_{2}Mo_{2}O_{7}.

Ultrafast calculation of diffuse scattering from atomistic models

Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering instruments can rapidly measure large volumes of diffuse-scattering data. Unfortunately, current algorithms for atomistic diffuse-scattering calculations are too slow to model large data sets completely, because the fast Fourier transform (FFT) algorithm has long been considered unsuitable for such calculations [Butler & Welberry (1992). J. Appl. Cryst. 25, 391-399]. Here, a new approach is presented for ultrafast calculation of atomistic diffuse-scattering patterns. It is shown that the FFT can actually be used to perform such calculations rapidly, and that a fast method based on sampling theory can be used to reduce high-frequency noise in the calculations. These algorithms are benchmarked using realistic examples of compositional, magnetic and displacive disorder. They accelerate the calculations by a factor of at least 10², making refinement of atomistic models to large diffuse-scattering volumes practical.

μSR study of spin freezing and persistent spin dynamics in NaCaNi2F7

A new pyrochlore compound, NaCaNi₂F₇, was recently synthesized and has a single magnetic site with spin-1 Ni²⁺ . We present zero field and longitudinal field muon spin rotation (μSR) measurements on this pyrochlore. Density functional theory calculations show that the most likely muon site is located between two fluorine ions, but off-centre. A characteristic F-μ-F muon spin polarization function is observed at high temperatures where Ni spin fluctuations are sufficiently rapid. The Ni²⁺ spins undergo spin freezing into a disordered ground state below 4 K, with a characteristic internal field strength of 140 G. Persistent Ni spin dynamics are present to our lowest temperatures (75 mK), a feature characteristic of many geometrically frustrated magnetic systems.

Universal geometric frustration in pyrochlores

Materials with the pyrochlore/fluorite structure have diverse technological applications, from magnetism to nuclear waste disposal. Here we report the observation of structural instability present in the pyrochlores A₂Zr₂O₆Oʹ (A = Pr, La) and Yb₂Ti₂O₆Oʹ, that exists despite ideal stoichiometry, ideal cation-ordering, the absence of lone pair effects, and a lack of magnetic order. Though these materials appear to have good long-range order, local structure probes find displacements, of the order of 0.01 nm, within the pyrochlore framework. The pattern of displacements of the A₂Oʹ sublattice mimics the entropically-driven fluxional motions characteristic of and well-known in the silica mineral β-cristobalite. The universality of such displacements within the pyrochlore structure adds to the known structural diversity and explains the extreme sensitivity to composition found in quantum spin ices and the lack of ferroelectric behavior in pyrochlores.

The family of pyrochlore complex oxides includes many materials of fundamental or practical interest, such as spin ices and dielectrics. Trump et al. show that flexibility of the pyrochlores’ structure leads to local displacements that explain some of their unusual physical properties.

Negative Hydration Expansion in ZrW_{2}O_{8}: Microscopic Mechanism, Spaghetti Dynamics, and Negative Thermal Expansion

We use a combination of x-ray diffraction, total scattering, and quantum mechanical calculations to determine the mechanism responsible for hydration-driven contraction in ZrW_{2}O_{8}. The inclusion of H_{2}O molecules within the ZrW_{2}O_{8} network drives the concerted formation of new W─O bonds to give one-dimensional (─W─O─)_{n} strings. The topology of the ZrW_{2}O_{8} network is such that there is no unique choice for the string trajectories: the same local changes in coordination can propagate with a large number of different periodicities. Consequently, ZrW_{2}O_{8}·H_{2}O is heavily disordered, with each configuration of strings forming a dense aperiodic "spaghetti." This new connectivity contracts the unit cell via large shifts in the Zr and W atom positions. Fluctuations of the undistorted parent structure towards this spaghetti phase emerge as the key negative thermal expansion (NTE) phonon modes in ZrW_{2}O_{8} itself. The large relative density of NTE phonon modes in ZrW_{2}O_{8} actually reflects the degeneracy of volume-contracting spaghetti excitations, itself a function of the particular topology of this remarkable material.

Spin-Orbit Dimers and Noncollinear Phases in d^{1} Cubic Double Perovskites

We formulate and study a spin-orbital model for a family of cubic double perovskites with d^{1} ions occupying a frustrated fcc sublattice. A variational approach and a complementary analytical analysis reveal a rich variety of phases emerging from the interplay of Hund's rule and spin-orbit coupling. The phase digram includes noncollinear ordered states, with or without a net moment, and, remarkably, a large window of a nonmagnetic disordered spin-orbit dimer phase. The present theory uncovers the physical origin of the unusual amorphous valence bond state experimentally suggested for Ba_{2}BMoO_{6} (B=Y, Lu) and predicts possible ordered patterns in Ba_{2}BOsO_{6} (B=Na, Li) compounds.