Why is it that titanates and zirconates can achieve such remarkably large dielectric constants? These perovskites have ions that can move substantially as the structure switches from cubic to tetragonal. The transition occurs at the Curie Temperature above which there is no net polarization (all is random) but below which we observe net polarization.
This leads to ferroelectric domains.
Piezoelectrics are materials where you can apply a stress and produce an electric polarization as a result. This is an example of a multiferroic.
Copyright image attribution:
https://en.wikipedia.org/wiki/Piezoelectricity#/media/File:Perovskite.svg
Created: 5 August 2010, Pinin - Own work, Perovskite structure of PZT