Spin-lattice-coupled helical magnetic order in breathing pyrochlore magnets, CuAlCr${}_4$S${}_8$ and CuGaCr${}_4$S${}_8$

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 $T_{\mathrm{N}}\approx$ 21 and 31 K for {$M$ = Al and Ga, respectively. X-ray diffraction reveals that the magnetic transition accompanies a structural transition from cubic $F\bar{4}3m$ 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 $\mathbf{Q}=(q_{\mathrm{I}\mathrm{C}},0.5,0)$ in the orthorhombic setting, where $q_{\mathrm{I}\mathrm{C}}\approx$ 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.