Symmetry based approaches to discovering new improper ferroelectrics / multiferroics

The area of improper ferroelectrics and potentially multiferroics has recently received significant attention do the prediction that a combination of a$^{-}$a$^{-}$c$^{+}$ tilting and layered ordering of the A site cations along [001]$_{\mathrm{perov}}$ in perovskite ABX$_{3}$ systems, leads to non-centrosymmetric structures which are predicted to have significant switchable polarisations. Here we elaborate a superspace description of cation ordering in tilted perovskites that allows the prediction of the symmetry of arbitrary cation ordered superlattices, along \textless 100\textgreater $_{\mathrm{perov}}$, \textless 110\textgreater $_{\mathrm{perov}}$ and \textless 111\textgreater $_{\mathrm{perov}}$ and ordering of both A and B cations, of the various tilted perovskites, which also rationalizes the observed domain structures. This approach is expaned to include magnetic symmetry and the potential for finding other suitable structural distortions in different systems will be discussed.