  We report low-temperature powder X-ray and neutron diffraction studies on
breathing pyrochlore magnets Cu$M$Cr$_{4}$S$_{8}$ ($M$ = Al, Ga), which undergo
a magnetic transition at $T_{\rm N} \approx$ 21 and 31 K for {$M$ = Al and Ga,
respectively. X-ray diffraction reveals that the magnetic transition
accompanies a structural transition from cubic $F{\overline 4}3m$ to polar
orthorhombic $Imm2$ symmetry for both the compounds, with larger distortion
observed for $M$ = Ga at low temperatures. Neutron diffraction reveals
incommensurate magnetic modulation ${\mathbf Q} = (q_{\rm IC}, 0.5, 0)$ in the
orthorhombic setting, where $q_{\rm IC} \approx$ 0.39 and 0.31 for $M$ = Al and
Ga, respectively. Our magnetic-structure analysis suggests cycloid-type
magnetic order but not proper-screw type for both the compounds. We find strong
correlation between the local spin configuration and Cr-Cr bond lengths,
indicating that the spin-lattice coupling as well as the magnetic frustration
play an important role in determining the ground state. Cu$M$Cr$_{4}$S$_{8}$
potentially offers a platform to explore magnetoelectric effects arising from
the helimagnet driven electric polarity.
