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) + y0, 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.

FEATURES OF WEAKLY NONLINEAR WAVE INTERACTION

Regular and stochastic dynamics of three wave interaction and dynamics of cascades of such three wave processes were investigated. It was shown that matrix elements of wave interaction are inversely proportional to square of frequency of LF wave participating in three wave interaction. It was shown, that thresholds of arising of regimes with dynamics chaos are proportional to cube of LF wave. By numerical methods dynamics of cascades of interacting waves was investigated in detail.