  We demonstrate the spontaneous reversal of spin chirality in a single crystal
sample of the intermetallic magnet EuAl$_4$. We solve the nanoscopic nature of
each of the four magnetically phases of EuAl$_4$ using resonant magnetic x-ray
scattering, and demonstrate all four phases order with single-k incommensurate
magnetic modulation vectors. Below 15.4 K the system forms a spin density
modulated spin structure where the spins are orientated in the ab plane
perpendicular to the orientation of the magnetic propagation vector. Below 13.2
K a second spin density wave orders with moments aligned parallel to the
c-axis, such that the two spin density wave orders coexist. Below 12.2 K a
magnetic helix of a single chirality is stabilised across the entire sample.
Below 10 K the chirality of the magnetic helix reverses, and the sample remains
a single chiral domain. Concomitant with the establishment of the helical
magnetic ordering is the lowering of the crystal symmetry to monoclinic, as
evidenced the formation of uniaxial charge and spin strip domains. A group
theoretical analysis demonstrates that below 12.2 K the symmetry lowers to
polar monoclinic, which is necessary to explain the observed asymmetry in the
chiral states of the magnetic helix and the spin chiral reversal. We find that
in every magnetically ordered phase of EuAl4 the in-plane moment is
perpendicular to the orientation of the magnetic propagation vector, which we
demonstrate is favoured by magnetic dipolar interactions.
