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Abstract While ∼30% of materials are reported to be topological, topological insulators are rare. Magnetic topological insulators (MTI) are even harder to find. Identifying crystallographic features that can host the coexistence of a topological insulating phase with magnetic order is vital for finding intrinsic MTI materials. Thus far, most materials that are investigated for the determination of an MTI are some combination of known topological insulators with a magnetic ion such as MnBi₂Te₄. Motivated by the recent success of EuIn₂As₂, the role of chemical pressure on topologically trivial insulator is investigated, Eu₅In₂Sb₆via Ga substitution. Eu₅Ga₂Sb₆is predicted to be topological but is synthetically difficult to stabilize. The intermediate compositions between Eu₅In₂Sb₆and Eu₅Ga₂Sb₆are observed through theoretical works to explore a topological phase transition and band inversion mechanism. The band inversion mechanism is attributed to changes in Eu–Sb hybridization as Ga is substituted for In due to chemical pressure. Eu₅In_4/3Ga_2/3Sb₆is also synthesized, the highest Ga concentration in Eu₅In_2‐xGa_xSb₆, and report the thermodynamic, magnetic, transport, and Hall properties. Overall, the work paints a picture of a possible MTI via band engineering and explains why Eu‐based Zintl compounds are suitable for the co‐existence of magnetism and topology. 

Flat bands that do not merely arise from weak interactions can produce exotic physical properties, such as superconductivity or correlated many-body effects. The quantum metric can differentiate whether flat bands will result in correlated physics or are merely dangling bonds. A potential avenue for achieving correlated flat bands involves leveraging geometrical constraints within specific lattice structures, such as the kagome lattice; however, materials are often more complex. In these cases, quantum geometry becomes a powerful indicator of the nature of bands with small dispersions. We present a simple, soft-chemical processing route to access a flat band with an extended quantum metric below the Fermi level. By oxidizing Ni-kagome material Cs₂Ni₃S₄to CsNi₃S₄, we see a two orders of magnitude drop in the room temperature resistance. However, CsNi₃S₄is still insulating, with no evidence of a phase transition. Using experimental data, density functional theory calculations, and symmetry analysis, our results suggest the emergence of a correlated insulating state of unknown origin. 

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. 

Magnetic topological semimetals allow for an effective control of the topological electronic states by tuning the spin configuration. Among them, Weyl nodal line semimetals are thought to have the greatest tunability, yet they are the least studied experimentally due to the scarcity of material candidates. Here, using a combination of angle-resolved photoemission spectroscopy and quantum oscillation measurements, together with density functional theory calculations, we identify the square-net compound EuGa₄as a magnetic Weyl nodal ring semimetal, in which the line nodes form closed rings near the Fermi level. The Weyl nodal ring states show distinct Landau quantization with clear spin splitting upon application of a magnetic field. At 2 K in a field of 14 T, the transverse magnetoresistance of EuGa₄exceeds 200,000%, which is more than two orders of magnitude larger than that of other known magnetic topological semimetals. Our theoretical model suggests that the non-saturating magnetoresistance up to 40 T arises as a consequence of the nodal ring state. 

Abstract The Dicke model describes the cooperative interaction of an ensemble of two-level atoms with a single-mode photonic field and exhibits a quantum phase transition as a function of light–matter coupling strength. Extending this model by incorporating short-range atom–atom interactions makes the problem intractable but is expected to produce new physical phenomena and phases. Here, we simulate such an extended Dicke model using a crystal of ErFeO₃, where the role of atoms (photons) is played by Er³⁺spins (Fe³⁺magnons). Through terahertz spectroscopy and magnetocaloric effect measurements as a function of temperature and magnetic field, we demonstrated the existence of a novel atomically ordered phase in addition to the superradiant and normal phases that are expected from the standard Dicke model. Further, we elucidated the nature of the phase boundaries in the temperature–magnetic-field phase diagram, identifying both first-order and second-order phase transitions. These results lay the foundation for studying multiatomic quantum optics models using well-characterized many-body solid-state systems. 

Abstract 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.