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Symmetry-adapted distortion modes provide a natural way of describing distorted structures derived from higher-symmetry parent phases. Structural refinements using symmetry-mode amplitudes as fit variables have been used for at least ten years in Rietveld refinements of the average crystal structure from diffraction data; more recently, this approach has also been used for investigations of the local structure using real-space pair distribution function (PDF) data. Here, the value of performing symmetry-mode fits to PDF data is further demonstrated through the successful application of this method to two topical materials: TiSe 2 , where a subtle but long-range structural distortion driven by the formation of a charge-density wave is detected, and MnTe, where a large but highly localized structural distortion is characterized in terms of symmetry-lowering displacements of the Te atoms. The analysis is performed using fully open-source code within the DiffPy framework via two packages developed for this work: isopydistort , which provides a scriptable interface to the ISODISTORT web application for group theoretical calculations, and isopytools , which converts the ISODISTORT output into a DiffPy -compatible format for subsequent fitting and analysis. These developments expand the potential impact of symmetry-adapted PDF analysis by enabling high-throughput analysis and removing the need for any commercial software. 

Abstract Topological semimetals with symmetry-protected band crossings have emerged as a rich landscape to explore intriguing electronic phenomena. Nonsymmorphic symmetries in particular have been shown to play an important role in protecting the crossings along a line (rather than a point) in momentum space. Here we report experimental and theoretical evidence for Dirac nodal line crossings along the Brillouin zone boundaries in PtPb 4 , arising from the nonsymmorphic symmetry of its crystal structure. Interestingly, while the nodal lines would remain gapless in the absence of spin–orbit coupling (SOC), the SOC, in this case, plays a detrimental role to topology by lifting the band degeneracy everywhere except at a set of isolated points. Nevertheless, the nodal line is observed to have a bandwidth much smaller than that found in density functional theory (DFT). Our findings reveal PtPb 4 to be a material system with narrow crossings approximately protected by nonsymmorphic crystalline symmetries. 

New phases of matter emerge at the edge of magnetic instabilities, which can occur in materials with moments that are localized, itinerant or intermediate between these extremes. In local moment systems, such as heavy fermions, the magnetism can be tuned towards a zero-temperature transition at a quantum critical point (QCP) via pressure, chemical doping, and, rarely, magnetic field. By contrast, in itinerant moment systems, QCPs are more rare, and they are induced by pressure or doping; there are no known examples of field induced transitions. This means that no universal behaviour has been established across the whole itinerant-to-local moment range—a substantial gap in our knowledge of quantum criticality. Here we report an itinerant antiferromagnet, Ti₃Cu₄, that can be tuned to a QCP by a small magnetic field. We see signatures of quantum criticality and the associated non-Fermi liquid behaviour in thermodynamic and transport measurements, while band structure calculations point to an orbital-selective, spin density wave ground state, a consequence of the square net structural motif in Ti₃Cu₄. Ti₃Cu₄thus provides a platform for the comparison and generalisation of quantum critical behaviour across the whole spectrum of magnetism.

 

Transition metal oxides of the 4dand 5dblock have recently become the targets of materials discovery, largely due to their strong spin–orbit coupling that can generate exotic magnetic and electronic states. Here, we report the high-pressure synthesis of Lu₂Rh₂O₇, a new cubic pyrochlore oxide based on 4d⁵Rh⁴⁺, and characterizations via thermodynamic, electrical transport, and muon spin relaxation measurements. Magnetic susceptibility measurements reveal a large temperature-independent Pauli paramagnetic contribution, while heat capacity shows an enhanced Sommerfeld coefficient,γ = 21.8(1) mJ/mol-Rh K². Muon spin relaxation measurements confirm that Lu₂Rh₂O₇remains paramagnetic down to 2 K. Taken in combination, these three measurements suggest that Lu₂Rh₂O₇is a correlated paramagnetic metal with a Wilson ratio ofR_W = 2.5. However, electric transport measurements present a striking contradiction as the resistivity of Lu₂Rh₂O₇is observed to monotonically increase with decreasing temperature, indicative of a nonmetallic state. Furthermore, although the magnitude of the resistivity is that of a semiconductor, the temperature dependence does not obey any conventional form. Thus, we propose that Lu₂Rh₂O₇may belong to the same novel class of non-Fermi liquids as the nonmetallic metal FeCrAs.