  Neutron diffraction on the centrosymmetric square-net magnet EuGa$_2$Al$_2$
reveals multiple incommensurate magnetic states (AFM1,2,3) in zero field. In
applied field, a new magnetic phase (A) is identified from magnetization and
transport measurements, bounded by two of the $\mu_0H$~=~0 incommensurate
magnetic phases (AFM1,helical and AFM3, cycloidal) with different moment
orientations. Moreover, magneto-transport measurements indicate the presence of
a topological Hall effect, with maximum values centered in the A phase.
Together, these results render EuGa$_2$Al$_2$ a material with non-coplanar or
topological spin texture in applied field. X-ray diffraction reveals an
out-of-plane (OOP) charge density wave (CDW) below $T_{CDW} \sim$ 50 K while
the magnetic propagation vector lies in plane below $T_N$ = 19.5 K. Together
these data point to a new route to realizing in-plane non-collinear spin
textures through an OOP CDW. In turn, these non-collinear spin textures may be
unstable against the formation of topological spin textures in an applied
field.
