  In magnetic insulators, the sense of rotation of the magnetization is
associated with novel phases of matter and exotic transport phenomena. Aimed to
find new sources of chiral magnetism rooted in intrinsic fields and geometry,
twisted square bilayers of magnetic dipoles with easy plane anisotropy are
studied. For no twist, each lattice settles in the zig-zag magnetic state and
orders antiferromagnetically to the other layer. The moire patterns that result
from the mutual rotation of the two square lattices influence such zig-zag
order, giving rise to several phases that depict non-collinear magnetic
textures with chiral motifs that break both time and inversion symmetry. For
certain moire angles, helical and toroidal magnetic orders arise. Changing the
vertical distance between layers can further manipulate these novel phases. It
is shown that the dipolar interlayer interaction induces an emergent
twist-dependent chiral magnetic field orthogonal to the direction of the
zig-zag chains, which is responsible for the internal torques conjugated to the
toroidal orders.
