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Relaxor-based ferroelectrics are prized for their giant electromechanical coupling and have revolutionized sensor and ultrasound applications. A long-standing challenge for piezoelectric materials has been to understand how these ultrahigh electromechanical responses occur when the polar atomic displacements underlying the response are partially broken into polar nanoregions (PNRs) in relaxor-based ferroelectrics. Given the complex inhomogeneous nanostructure of these materials, it has generally been assumed that this enhanced response must involve complicated interactions. By using neutron scattering measurements of lattice dynamics and local structure, we show that the vibrational modes of the PNRs enable giant coupling by softening the underlying macrodomain polarization rotations in relaxor-based ferroelectric PMN-xPT {(1 - x)[Pb(Mg1/3Nb2/3)O3] - xPbTiO3} (x = 30%). The mechanism involves the collective motion of the PNRs with transverse acoustic phonons and results in two hybrid modes, one softer and one stiffer than the bare acoustic phonon. The softer mode is the origin of macroscopic shear softening. Furthermore, a PNR mode and a component of the local structure align in an electric field; this further enhances shear softening, revealing a way to tune the ultrahigh piezoelectric response by engineering elastic shear softening.

Magneto-optical imaging was used to visualize the inhomogeneous penetration of magnetic flux into polycrystalline TlBa2Ca2Cu3Ox films with high critical current densities, to reconstruct the local two-dimensional supercurrent flow patterns and to correlate inhomogeneities in this flow with the local crystallographic misorientation. The films have almost perfect c-axis alignment and considerable local a- and b-axis texture because the grains tend to form colonies with only slightly misaligned a and b axes. Current flows freely over these low-angle grain boundaries but is strongly reduced at intermittent colony boundaries of high misorientation. The local (<10-micrometer scale) critical current density Jc varies widely, being up to 10 times as great as the transport Jc (scale of approximately 1 millimeter), which itself varies by a factor of about 5 in different sections of the film. The combined experiments show that the magnitude of the transport Jc is largely determined by a few high-angle boundaries.