Atomic mapping of periodic dipole waves in ferroelectric oxide

A dipole wave is composed of head-to-tail connected electric dipoles in the form of sine function. Potential applications in information carrying, transporting, and processing are expected, and logic circuits based on nonlinear wave interaction are promising for dipole waves. Although similar spin waves are well known in ferromagnetic materials for their roles in some physical essence, electric dipole wave behavior and even its existence in ferroelectric materials are still elusive. Here, we observe the atomic morphology of large-scale dipole waves in PbTiO₃/SrTiO₃ superlattice mediated by tensile epitaxial strains on scandate substrates. The dipole waves can be expressed in the formula of y = Asin (2πx/L) + y ₀, where the wave amplitude (A) and wavelength (L) correspond to 1.5 and 6.6 nm, respectively. This study suggests that by engineering strain at the nanoscale, it should be possible to fabricate unknown polar textures, which could facilitate the development of nanoscale ferroelectric devices.