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Two-dimensional (2D) kagome lattice metals are interesting because their corner sharing triangle structure enables a wide array of electronic and magnetic phenomena. Recently, post-growth annealing is shown to both suppress charge density wave (CDW) order and establish long-range CDW with the ability to cycle between states repeatedly in the kagome antiferromagnet FeGe. Here we perform transport, neutron scattering, scanning transmission electron microscopy (STEM), and muon spin rotation (μSR) experiments to unveil the microscopic mechanism of the annealing process and its impact on magneto-transport, CDW, and magnetism in FeGe. Annealing at 560 °C creates uniformly distributed Ge vacancies, preventing the formation of Ge-Ge dimers and thus CDW, while 320 °C annealing concentrates vacancies into stoichiometric FeGe regions with long-range CDW. The presence of CDW order greatly affects the anomalous Hall effect, incommensurate magnetic order, and spin-lattice coupling in FeGe, placing FeGe as the only kagome lattice material with tunable CDW and magnetic order. 

Abstract Magnetic order in most materials occurs when magnetic ions with finite moments arrange in a particular pattern below the ordering temperature. Intriguingly, if the crystal electric field (CEF) effect results in a spin-singlet ground state, a magnetic order can still occur due to the exchange interactions between neighboring ions admixing the excited CEF levels. The magnetic excitations in such a state are spin excitons generally dispersionless in reciprocal space. Here we use neutron scattering to study stoichiometric Ni 2 Mo 3 O 8 , where Ni 2+ ions form a bipartite honeycomb lattice comprised of two triangular lattices, with ions subject to the tetrahedral and octahedral crystalline environment, respectively. We find that in both types of ions, the CEF excitations have nonmagnetic singlet ground states, yet the material has magnetic order. Furthermore, CEF spin excitons from the tetrahedral sites form a dispersive diffusive pattern around the Brillouin zone boundary, likely due to spin entanglement and geometric frustrations. 

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.