Fully spin-polarized hourglass charge-three Weyl points and sextuple-helicoid surface arcs in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>P</mml:mi><mml:msub><mml:mn>6</mml:mn><mml:mn>3</mml:mn></mml:msub><mml:mn>22</mml:mn></mml:mrow></mml:math>-type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>BaNiIO</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:math>

Magnetic topological materials exhibiting unique topological quantum physics due to the combination of spintronics and topology have aroused the interest of researchers. We propose $P{6}_{3}22$-type ${\mathrm{BaNiIO}}_{6}$---a dynamically stable material with two fully spin-polarized hourglass charge-three (C-3) Weyl points (WPs) and six fully spin-polarized charge-one (C-1) WPs around the Fermi level---with the help of first-principles calculations and symmetry analysis. C-3 WPs have been theoretically proposed for more than a decade. However, they have only been reported in nonmagnetic phonon systems rather than in magnetic electronic systems. $P{6}_{3}22$-type ${\mathrm{BaNiIO}}_{6}$ shows 100% spin polarization and belongs to the group of half-metals due to the metallic states and the semiconducting states for the bands in spin-up and spin-down directions, respectively. The half-metallic state and the spin-polarized C-3 and C-1 WPs are robust to uniform strains (from $\ensuremath{-}5$ to 5%) and on-site Hubbard-Coulomb interactions (from 0 to 6 eV). Furthermore, unique surface arcs connected the projections of two spin-polarized C-3 WPs and six spin-polarized C-1 WPs, leading to fully spin-polarized sextuple-helicoid surface arcs on the (001) surface of $P{6}_{3}22$-type ${\mathrm{BaNiIO}}_{6}$. Undoubtedly, $P{6}_{3}22$-type ${\mathrm{BaNiIO}}_{6}$, with fully spin-polarized C-3 and C-1 WPs and fully spin-polarized sextuple-helicoid surface arcs, is a promising candidate for applications in spintronic and topological physics.

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