  Magnetic helices and skyrmions in noncentrosymmetric magnets are
representative examples of chiral spin textures in solids. Their spin swirling
direction, often termed as the magnetic helicity and defined as either
left-handed or right-handed, is uniquely determined by the
Dzyaloshinskii-Moriya interaction (DMI) in fixed chirality host crystals. Thus
far, there have been relatively few investigations of the DMI in metallic
magnets as compared with insulating counterparts. Here, we focus on the
metallic magnets Co$_{8-x}$Fe$_x$Zn$_8$Mn$_4$ (0 $\leq$ $x$ $\leq$ 4.5) with a
$\beta$-Mn-type chiral structure and find that as $x$ varies under a fixed
crystal chirality, a reversal of magnetic helicity occurs at $x_\mathrm{c}$
$\sim$ 2.7. This experimental result is supported by a theory based on
first-principles electronic structure calculations, demonstrating the DMI to
depend critically on the electron band filling. Thus by composition tuning our
work shows the sign change of the DMI with respect to a fixed crystal chirality
to be a universal feature of metallic chiral magnets.
