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We continue the study of $U(1)$ vortices with cholesteric vacuum structure. Anew class of solutions is found which represent global vortices of the internalspin field. These spin vortices are characterized by a non-vanishing angulardependence at spatial infinity, or winding. We show that despite thetopological $\mathbb{Z}_2$ behavior of $SO(3)$ windings, the topological chargeof the spin vortices is of the $\mathbb{Z}$ type in the cholesteric. We findthese solutions numerically and discuss the properties derived from their lowenergy effective field theory in $1+1$ dimensions.

Spin vortices in the Abelian-Higgs model with cholesteric vacuum structure