Rotational instability of the electric polarization and divergence of the shear elastic compliance

The rotational instability of the electric polarization $\mathbf{P}$ during phase transformations between ferroelectric phases is of great practical interest, since it may be accompanied by extremely large values of the piezoelectric coefficient, and a divergence of the coupled shear compliance contributes to such enhancements. In the literature, this has been explicitly calculated in the framework of the Landau theory and discussed with specific numerical simulations involving tetragonal, orthorhombic, and rhombohedral ferroelectric phases. When monoclinic phases are involved, such an approach is practically impossible, and an approximated treatment has been proposed, based on the observation that in those cases there are shear strains almost linearly coupled to the transverse component of $\mathbf{P}$, implying a divergence of the Curie-Weiss type in the associated compliances. Here the argument is extended to the general case of transitions whose major effect is a rotation of the polarization, and the limits of its validity are discussed. As experimental verification, the elastic response of ${\mathrm{BaTiO}}₃$ is measured and analyzed, together with those of other ferroelectric perovskites available in the literature, such as KNN.