  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.
