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Polycrystalline IrGe 4 was synthesized by annealing elements at 800 °C for 240 h, and the composition was confirmed by energy-dispersive X-ray spectroscopy. IrGe 4 adopts a chiral crystal structure (space group P 3 1 21) instead of a polar crystal structure ( P 3 1 ), which was corroborated by the convergent-beam electron diffraction and Rietveld refinements using synchrotron powder X-ray diffraction data. The crystal structure features layers of IrGe 8 polyhedra along the b axis, and the layers are connected by edge- and corner-sharing. Each layer consists of corner-shared [Ir 3 Ge 20 ] trimers, which are formed by three IrGe 8 polyhedra connected by edge-sharing. Temperature-dependent resistivity indicates metallic behavior. The magnetoresistance increases with increasing applied magnetic field, and the nonsaturating magnetoresistance reaches 11.5% at 9 T and 10 K. The Hall resistivity suggests that holes are the majority carrier type, with a carrier concentration of 4.02 × 10 21 cm -3 at 300 K. Electronic band structures calculated by density functional theory reveal a Weyl point with a chiral charge of +3 above the Fermi level.

Cu 2 TSiS 4 (T = Mn and Fe) polycrystalline and single-crystal materials were prepared with high-temperature solid-state and chemical vapor transport methods, respectively. The polar crystal structure (space group Pmn 2 1 ) consists of chains of corner-sharing and distorted CuS 4 , Mn/FeS 4 , and SiS 4 tetrahedra, which is confirmed by Rietveld refinement using neutron powder diffraction data, X-ray single-crystal refinement, electron diffraction, energy-dispersive X-ray spectroscopy, and second harmonic generation (SHG) techniques. Magnetic measurements indicate that both compounds order antiferromagnetically at 8 and 14 K, respectively, which is supported by the temperature-dependent (100-2 K) neutron powder diffraction data. Additional magnetic reflections observed at 2 K can be modeled by magnetic propagation vectors k = (1/2,0,1/2) and k = (1/2,1/2,1/2) for Cu 2 MnSiS 4 and Cu 2 FeSiS 4 , respectively. The refined antiferromagnetic structure reveals that the Mn/Fe spins are canted away from the ac plane by about 14°, with the total magnetic moments of Mn and Fe being 4.1(1) and 2.9(1) μ B , respectively. Both compounds exhibit an SHG response with relatively modest second-order nonlinear susceptibilities. Density functional theory calculations are used to describe the electronic band structures.

Polycrystalline LiMo 8 O 10 was prepared in a sealed Mo crucible at 1380 °C for 48 h using the conventional high-temperature solid-state method. The polar tetragonal crystal structure (space group I 4 1 md ) is confirmed based on the Rietveld refinement of powder neutron diffraction and 7 Li/ 6 Li solid-state NMR. The crystal structure features infinite chains of Mo 4 O 5 (i.e., Mo 2 Mo 4/2 O 6/2 O 6/3 ) as a repeat unit containing edge-sharing Mo 6 octahedra with strong Mo-Mo metal bonding along the chain. X-ray absorption near-edge spectroscopy of the Mo-L 3 edge is consistent with the formal Mo valence/configuration. Magnetic measurements reveal that LiMo 8 O 10 is paramagnetic down to 1.8 K. Temperature-dependent resistivity [ρ(T)] measurement indicates a semiconducting behavior that can be fitted with Mott's variable range hopping conduction mechanism in the temperature range of 215 and 45 K. The ρ(T) curve exhibits an exponential increase below 5 K with a large ratio of ρ 1.8 /ρ 300 = 435. LiMo 8 O 10 shows a negative field-dependent magnetoresistance between 2 and 25 K. Heat capacity measurement fitted with the modified Debye model yields the Debye temperature of 365 K.

A polycrystalline iridate Li 8 IrO 6 material was prepared via heating Li 2 O and IrO 2 starting materials in a sealed quartz tube at 650 °C for 48 h. The structure was determined from Rietveld refinement of room-temperature powder neutron diffraction data. Li 8 IrO 6 adopts the nonpolar space group R 3̅ with Li atoms occupying the tetrahedral and octahedral sites, which is supported by the electron diffraction and solid-state 7 Li NMR. This results in a crystal structure consisting of LiO 4 tetrahedral layers alternating with mixed IrO 6 and LiO 6 octahedral layers along the crystallographic c -axis. The +4 oxidation state of Ir 4+ was confirmed by near-edge X-ray absorption spectroscopy. An in situ synchrotron X-ray diffraction study of Li 8 IrO 6 indicates that the sample is stable up to 1000 °C and exhibits no structural transitions. Magnetic measurements suggest long-range antiferromagnetic ordering with a Néel temperature ( T N ) of 4 K, which is corroborated by heat capacity measurements. The localized effective moment μ eff (Ir) = 1.73 μ B and insulating character indicate that Li 8 IrO 6 is a correlated insulator. First-principles calculations support the nonpolar crystal structure and reveal the insulating behavior both in paramagnetic and antiferromagnetic states.