We demonstrate theoretically how, by imposing epitaxial strain in a ferroelectric perovskite, it is possible to achieve a dynamical control of phonon propagation by means of external electric fields, which yields a giant electrophononic response, i.e. the dependence of the lattice thermal conductivity on external electric fields. Specifically, we study the strain-induced manipulation of the lattice structure and analyze its interplay with the electrophononic response. We show that tensile biaxial strain can drive the system to a regime where the electrical polarization can be effortlessly rotated and thus yield giant electrophononic responses that are at least one order of magnitude larger than in the unstrained system. These results derive directly from the almost divergent behavior of the electrical susceptibility at those critical strains that drive the polarization on the verge of a spontaneous rotation.
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