Polarity vs Chirality: Functionality from competing magneto-structural instabilities

We report a phenomenological magneto-structural model based on competing free-energy terms that couple either polar or chiral distortions in cubic quadruple perovskites, depending on the global direction of magnetic moments. The model naturally explains why some compounds in this material system host magnetically-induced ferroelectricity at low temperature, while others such as CaMn${}_3$(Cr${}_3$Mn)O${}_{12}$, which we characterise experimentally, do not. Importantly, our results suggest a new approach towards developing an applied multiferroic functionality, and can be generalised to other multi-sublattice systems where the magnetic interaction between sublattices is prohibited by spatial inversion.