  The presence of a switchable spontaneous electric polarization makes
ferroelectrics ideal candidates for the use in many applications such as memory
and sensors devices. Since known ferroelectrics are rather limited, finding new
ferroelectric (FE) materials has become a flourishing field. One promising
route is to design the so-called hybrid improper ferroelectricity. However, the
previous approach based on the Landau theory is not easily adopted to the
systems that are unrelated to the Pbnm perovskite structure. To this end, we
develop a general design rule that is applicable to any systems. By combining
this rule with density functional theory calculations, we identify previously
unrecognized classes of FE materials. It shows that the R-3c perovskite
structure can become FE by substituting half of the B-site cations. ZnSrO2 with
a non-perovskite layered structure can also be FE through the anion
substitution. Moreover, our approach can be used to design new multiferroics as
illustrated in the case of fluorine substituted LaMnO3.
