Local Sn Dipolar-Character Displacements behind the Low Thermal Conductivity in SnSe Thermoelectric.

The local atomic structure of SnSe was characterized across its orthorhombic-to-orthorhombic structural phase transition using x-ray pair distribution function analysis. Substantial Sn displacements with a dipolar character persist in the high-symmetry high-temperature phase, albeit with a symmetry different from that of the ordered displacements below the transition. The analysis implies that the transition is neither order-disorder nor displacive but rather a complex crossover. Robust ferrocoupled SnSe intralayer distortions suggest a ferroelectriclike instability as the driving force. These local symmetry-lowering Sn displacements are likely integral to the ultralow lattice thermal conductivity mechanism in SnSe.

Dual Orbital Degeneracy Lifting in a Strongly Correlated Electron System.

The local structure of NaTiSi_{2}O_{6} is examined across its Ti-dimerization orbital-assisted Peierls transition at 210 K. An atomic pair distribution function approach evidences local symmetry breaking preexisting far above the transition. The analysis unravels that, on warming, the dimers evolve into a short range orbital degeneracy lifted (ODL) state of dual orbital character, persisting up to at least 490 K. The ODL state is correlated over the length scale spanning ∼6 sites of the Ti zigzag chains. Results imply that the ODL phenomenology extends to strongly correlated electron systems.

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.

Magnetism in semiconducting molybdenum dichalcogenides.

Transition metal dichalcogenides (TMDs) are interesting for understanding the fundamental physics of two-dimensional (2D) materials as well as for applications to many emerging technologies, including spin electronics. Here, we report the discovery of long-range magnetic order below T M = 40 and 100 K in bulk semiconducting TMDs 2H-MoTe2 and 2H-MoSe2, respectively, by means of muon spin rotation (µSR), scanning tunneling microscopy (STM), and density functional theory (DFT) calculations. The µSR measurements show the presence of large and homogeneous internal magnetic fields at low temperatures in both compounds indicative of long-range magnetic order. DFT calculations show that this magnetism is promoted by the presence of defects in the crystal. The STM measurements show that the vast majority of defects in these materials are metal vacancies and chalcogen-metal antisites, which are randomly distributed in the lattice at the subpercent level. DFT indicates that the antisite defects are magnetic with a magnetic moment in the range of 0.9 to 2.8 µB. Further, we find that the magnetic order stabilized in 2H-MoTe2 and 2H-MoSe2 is highly sensitive to hydrostatic pressure. These observations establish 2H-MoTe2 and 2H-MoSe2 as a new class of magnetic semiconductors and open a path to studying the interplay of 2D physics and magnetism in these interesting semiconductors.

Author Correction: Signatures of the topological s+- superconducting order parameter in the type-II Weyl semimetal T d -MoTe2.

The original version of this article omitted the following from the Acknowledgements: "CAM and AL were supported by the NSF MRSEC program through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). Additionally, this research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under 'Contract No. DE-AC02-05CH11231'." This has now been corrected in both the PDF and HTML versions of the article.

Signatures of the topological s +- superconducting order parameter in the type-II Weyl semimetal T d-MoTe2.

In its orthorhombic T d polymorph, MoTe2 is a type-II Weyl semimetal, where the Weyl fermions emerge at the boundary between electron and hole pockets. Non-saturating magnetoresistance and superconductivity were also observed in T d-MoTe2. Understanding the superconductivity in T d-MoTe2, which was proposed to be topologically non-trivial, is of eminent interest. Here, we report high-pressure muon-spin rotation experiments probing the temperature-dependent magnetic penetration depth in T d-MoTe2. A substantial increase of the superfluid density and a linear scaling with the superconducting critical temperature T c is observed under pressure. Moreover, the superconducting order parameter in T d-MoTe2 is determined to have 2-gap s-wave symmetry. We also exclude time-reversal symmetry breaking in the superconducting state with zero-field µSR experiments. Considering the strong suppression of T c in MoTe2 by disorder, we suggest that topologically non-trivial s +- state is more likely to be realized in MoTe2 than the topologically trivial s ++ state.

Algorithm for systematic peak extraction from atomic pair distribution functions.

The study presents an algorithm, ParSCAPE, for model-independent extraction of peak positions and intensities from atomic pair distribution functions (PDFs). It provides a statistically motivated method for determining parsimony of extracted peak models using the information-theoretic Akaike information criterion (AIC) applied to plausible models generated within an iterative framework of clustering and chi-square fitting. All parameters the algorithm uses are in principle known or estimable from experiment, though careful judgment must be applied when estimating the PDF baseline of nanostructured materials. ParSCAPE has been implemented in the Python program SrMise. Algorithm performance is examined on synchrotron X-ray PDFs of 16 bulk crystals and two nanoparticles using AIC-based multimodeling techniques, and particularly the impact of experimental uncertainties on extracted models. It is quite resistant to misidentification of spurious peaks coming from noise and termination effects, even in the absence of a constraining structural model. Structure solution from automatically extracted peaks using the Liga algorithm is demonstrated for 14 crystals and for C60. Special attention is given to the information content of the PDF, theory and practice of the AIC, as well as the algorithm's limitations.

Synthesis and characterization of two-dimensional Nb4C3 (MXene).

We report on the synthesis of a phase-pure, 2-dimensional transition metal carbide Nb4C3, produced by immersing Nb4AlC3 powders in hydrofluoric acid. The structure of this, only second MXene with formula M4X3, was investigated with pair distribution function analysis. The resistivity of a cold-pressed disc was 0.0046 Ω m, rendering this MXene one of the most conductive to date.

Local vibrations and negative thermal expansion in ZrW2O8.

We present an x-ray pair distribution function (XPDF) analysis and extended x-ray absorption fine structure (EXAFS) data for ZrW2O8 (10-500 K) with a focus on the stiffness of the Zr-O-W linkage. The XPDF is highly sensitive to W-Zr and W-W correlations, but much less so to O-O or W-O correlations. The Zr-W peak in the XPDF data has a weak temperature dependence and, hence, this linkage is relatively stiff and does not permit bending of the Zr-O-W link. We propose that the low energy vibrational modes that lead to negative thermal expansion involve correlated rotations of ZrO6 octahedra that produce large <111> translations of the WO4 tetrahedra, rather than a transverse motion of O atoms that imply a flexible Zr-O-W linkage.

Cu(Ir1 - xCrx)2S4: a model system for studying nanoscale phase coexistence at the metal-insulator transition.

Increasingly, nanoscale phase coexistence and hidden broken symmetry states are being found in the vicinity of metal-insulator transitions (MIT), for example, in high temperature superconductors, heavy fermion and colossal magnetoresistive materials, but their importance and possible role in the MIT and related emergent behaviors is not understood. Despite their ubiquity, they are hard to study because they produce weak diffuse signals in most measurements. Here we propose Cu(Ir1 - xCrx)2S4 as a model system, where robust local structural signals lead to key new insights. We demonstrate a hitherto unobserved coexistence of an Ir(4+) charge-localized dimer phase and Cr-ferromagnetism. The resulting phase diagram that takes into account the short range dimer order is highly reminiscent of a generic MIT phase diagram similar to the cuprates. We suggest that the presence of quenched strain from dopant ions acts as an arbiter deciding between the competing ground states.

Detailed mapping of the local Ir4+ dimers through the metal-insulator transitions of CuIr2S4 thiospinel by X-ray atomic pair distribution function measurements.

The evolution of the short-range structural signature of the Ir4+ dimer state in CuIr2S4 thiospinel has been studied across the metal-insulator phase transitions as the metallic state is induced by temperature, Cr doping, and x-ray fluence. An atomic pair distribution function (PDF) approach reveals that there are no local dimers that survive into the metallic phase when this is invoked by temperature and doping. The PDF shows Ir4+ dimers when they exist, regardless of whether or not they are long-range ordered. At 100 K, exposure to a 98 keV x-ray beam melts the long-range dimer order within a few seconds, though the local dimers remain intact. This shows that the metallic state accessed on warming and doping is qualitatively different from the state obtained under x-ray irradiation.

The Liga algorithm for ab initio determination of nanostructure.

Computational techniques for nanostructure determination of substances that resist standard crystallographic methods are often laborious processes starting from initial guess solutions not derived from experimental data. The Liga algorithm can create nanostructures using only lists of lengths or distances between atom pairs, providing an experimental basis for starting structures. These distance lists may be extracted from a variety of experimental probes and we illustrate the procedure with distances determined from the pair distribution function. Candidate subclusters that are a subset of a structure's atoms compete based on adherence to the length list. Atoms are added to well performing candidates and removed from poor ones, until a complete structure with sufficient agreement to the length list emerges. The Liga algorithm is shown to reliably recreate Lennard-Jones clusters from ideal length lists and the C60 structure from neutron-scattering data. The correct fullerene structure was obtained with experimental data which missed several distances and had loosened constraints on distance multiplicity. This suggests that the Liga algorithm may have robust applicability for a wide range of nanostructures even in the absence of ideal data.

Quadrupolar ordering in LaMnO3 revealed from scattering data and geometric modeling.

Many strongly correlated materials display quadrupolar (Jahn-Teller) distortion of the local octahedral structural units. It is common for these distortions to be observed by probes of local structure but absent in the crystallographic average structure. The ordering of these quadrupoles is important in determining the properties of manganites and cuprates, and the nature of the disorder in these structures has been an unsolved problem. We combine high resolution scattering data and novel geometrical modeling techniques to obtain a detailed picture of the local atomic structure, and also to extract the quadrupolar order parameter associated with the distorted octahedra. We show that in LaMnO3, quadrupoles undergo a strong first-order phase transition at 730 K, but with nonzero order parameter remaining in the high-temperature phase.

Understanding the insulating phase in colossal magnetoresistance manganites: shortening of the Jahn-Teller long-bond across the phase diagram of La1-xCaxMnO3.

The detailed evolution of the magnitude of the local Jahn-Teller (JT) distortion in La(1-x)Ca(x)MnO3 is obtained across the phase diagram for 0< or =x< or =0.5 from high-quality neutron diffraction data using the atomic pair distribution function method. A local JT distortion is observed in the insulating phase for all Ca concentrations studied. However, in contrast with earlier local structure studies, its magnitude is not constant, but decreases continuously with increasing Ca content. This observation is at odds with a simple small-polaron picture for the insulating state.

Quantum correction to the pair distribution function.

We report a numerical technique that allows the quantum effects of zero-point motion to be incorporated into Pair Distribution Functions calculated classically for molecules using Monte Carlo or Molecular Dynamics simulations. We establish the basis for this approximation using a diatomic molecule described by a Morse potential. The correction should significantly improve the agreement between modeled and experimental data, and facilitate conclusions about inter- and intra-molecular motion and flexibility. We describe a similar approach to obtain the energy and the specific heat.

PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals.

PDFfit2 is a program as well as a library for real-space refinement of crystal structures. It is capable of fitting a theoretical three-dimensional (3D) structure to atomic pair distribution function data and is ideal for nanoscale investigations. The fit system accounts for lattice constants, atomic positions and anisotropic atomic displacement parameters, correlated atomic motion, and experimental factors that may affect the data. The atomic positions and thermal coefficients can be constrained to follow the symmetry requirements of an arbitrary space group. The PDFfit2 engine is written in C++ and is accessible via Python, allowing it to inter-operate with other Python programs. PDFgui is a graphical interface built on the PDFfit2 engine. PDFgui organizes fits and simplifies many data analysis tasks, such as configuring and plotting multiple fits. PDFfit2 and PDFgui are freely available via the Internet.

Geometric simulation of perovskite frameworks with Jahn-Teller distortions: applications to the cubic manganites.

A new approach is presented for modeling perovskite frameworks with disordered Jahn-Teller (JT) distortions and has been applied to study the elastic response of the LaMnO3 structure to defects in the JT ordering. Surprisingly, antiphase domain boundary defects in the pattern of ordered JT octahedra, along the [110] and [110] bonding directions, are found to produce 1D stripe patterns rotated 45 degrees along a* directions, similar to stripe structures observed in these systems. Geometric simulation is shown to be an efficient and powerful approach for finding relaxed atomic structures in the presence of disorder in networks of corner-shared JT-distorted octahedra such as the perovskites. Geometric modeling rapidly relaxes large supercells (thousands of octahedra) while preserving the local coordination chemistry, and shows great promise for studying these complex systems.

Local atomic structure and discommensurations in the charge density wave of CeTe3.

The local structure of in the incommensurate charge density wave (IC-CDW) state has been obtained using atomic pair distribution function analysis of x-ray diffraction data. Local atomic distortions in the Te nets due to the CDW are larger than observed crystallographically, resulting in distinct short and long Te-Te bonds. Observation of different distortion amplitudes in the local and average structures is explained by the discommensurated nature of the CDW, since the pair distribution function is sensitive to the local displacements within the commensurate regions, whereas the crystallographic result averages over many discommensurated domains. The result is supported by STM data. This is the first quantitative local structural study within the commensurate domains in an IC-CDW system.

Ab initio determination of solid-state nanostructure.

Advances in materials science and molecular biology followed rapidly from the ability to characterize atomic structure using single crystals. Structure determination is more difficult if single crystals are not available. Many complex inorganic materials that are of interest in nanotechnology have no periodic long-range order and so their structures cannot be solved using crystallographic methods. Here we demonstrate that ab initio structure solution of these nanostructured materials is feasible using diffraction data in combination with distance geometry methods. Precise, sub-ångström resolution distance data are experimentally available from the atomic pair distribution function (PDF). Current PDF analysis consists of structure refinement from reasonable initial structure guesses and it is not clear, a priori, that sufficient information exists in the PDF to obtain a unique structural solution. Here we present and validate two algorithms for structure reconstruction from precise unassigned interatomic distances for a range of clusters. We then apply the algorithms to find a unique, ab initio, structural solution for C60 from PDF data alone. This opens the door to sub-ångström resolution structure solution of nanomaterials, even when crystallographic methods fail.

Orbital correlations in the pseudocubic O and rhombohedral R phases of LaMnO3.

The local and intermediate structure of stoichiometric LaMnO3 has been studied in the pseudocubic and rhombohedral phases at high temperatures (300-1150 K). Neutron powder diffraction data were collected and a combined Rietveld and high real space resolution atomic pair distribution function analysis was carried out. The nature of the Jahn-Teller (JT) transition around 750 K is confirmed to be orbital order to disorder. In the high-temperature orthorhombic (O) and rhombohedral (R) phases, the MnO6 octahedra are still fully distorted locally. More importantly, the intermediate structure suggests the presence of local ordered clusters of diameter approximately 16 A ( approximately 4 MnO6 octahedra) implying strong nearest-neighbor JT antiferrodistortive coupling. These clusters persist well above the JT transition temperature even into the high-temperature R phase.