  Twisting in bilayers introduces structural chirality with two enantiomers,
i.e., left- and right-hand bilayers, depending on the oriented twist angle. The
interplay between this global chirality and additional degrees of freedom, such
as magnetic ordering and the local octahedral chirality arising from the
geometry of the bonds, can yield striking phenomena. In this work, we focus on
collinear antiferromagnetic CrI$_3$ twisted homo-bilayers, which are
characterized by a staggered octahedral chirality in each monolayer. Using
symmetry analysis, density functional theory and tight-binding model
calculations we show that layers twisting can lower the structural and magnetic
point-group symmetries, thus activating pyroelectricity and the magneto-optical
Kerr effect, which would otherwise be absent in untwisted antiferromagnetic
homo-bilayers. Interestingly, both electric polarization and Kerr angle are
controllable by the twist angle and their sign is reversed when switching from
left- to right-twisted bilayers. We further unveil the occurrence of
unconventional vortices with spin textures that alternate opposite chiralities
in momentum space. These findings demonstrate that the interplay between
twisting and octahedral chirality in magnetic bilayers and related van der
Waals heterostructures represents an extraordinary resource for tailoring their
physical properties for spintronic and optoelectronic applications.
