  Hyperferroelectrics are receiving a growing interest thanks to their unique
property to retain a spontaneous polarization even in presence of a
depolarizing field. Nevertheless, general microscopic mechanisms driving
hyperferroelectricity, which is ascribed to the softening of a polar $LO$ mode,
are still missing. Here, by means of phonons calculations and force constants
analysis in two class of hyperferroelectrics, the ABO$_3$-LiNbO3-type systems
and the prototypical hexagonal-ABC systems, we unveiled common features in the
dynamical properties of a hyperferroelectric behind such $LO$ instability:
negative or vanishing on-site force constant associated to the cation driving
the $LO$ polar distortion, and destabilizing cation-anion interactions, both
induced by short-range forces. We also predict possible enhancement of the
hyperferroelectric properties by applying an external positive pressure;
pressure strengthens the destabilizing short-range interactions. Particularly,
the increase in the mode effective charges associated to the unstable $LO$ mode
under pressure suggests an eventual enhancement of the $D$=0 polarization under
compressive strain.
