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Single pair of type-III Weyl points half-metals: BaNiIO$_6$ as an example

The realization of Weyl systems with the minimum nonzero number of Weyl points (WPs) and full spin polarization remains challenging in topology physics and spintronic. In this study, for the first time, we used first-principle calculations and symmetry analysis to demonstrate that BaNiIO$_6$, a dynamically and thermodynamically stable half-metallic material, hosts fully spin-polarized single-pair WPs (SP-WPs) with a charge number ($\cal{C}$) of $\pm$2 and a type-\uppercase\expandafter{\romannumeral3} band dispersion around the Fermi level. Moreover, the fully spin-polarized SP-WPs induce double-helicoid Fermi arcs on the (10$\overline{1}$0) surface. The half-metallic state and the spin-polarized SP-WPs are robust to uniform strains (from -10\% to +8\%) and on-site Hubbard-Coulomb interactions (from 0 eV to 6 eV). When +9 % or +10 % uniform strain is applied to the BaNiIO$_6$ system, it hosts six additional type-\uppercase\expandafter{\romannumeral2} WPs with $\lvert{\cal{C}}\rvert=1$ in the three-dimensional Brillouin zone in addition to the two type-\uppercase\expandafter{\romannumeral3} WPs with $\lvert{\cal{C}}\rvert=2$. We hope that this study will motivate future research into SP-WPs half-metals.