Solitons in thin-film ferroelectric material

Abstract

Through the Landau-Ginzburg-Devonshire mean field theory, the equation governing the behavior of the polarization field in ferroelectric material is derived. Ferroelectric material is subjected to a standing electric field which inhibits remanent polarization and facilitates the access to the instantaneous polarization. Some transformations turn the equation into a well-known ordinary differential equation. As a result, dark soliton and cnoidal waves, which have not yet been observed in ferroelectrics, are obtained. Also, a bright soliton is found. It exists in a given range of temperatures and has an amplitude and a width which vary inversely with temperature.

Harvesting microwave energy using pyroelectricity of nanostructured graphene/zirconium-doped hafnium oxide ferroelectric heterostructures

“…The positive-sign voltage transient pulse is attributed to the rising time of the microwave pulse when the temperature is increasing, whereas the small negative-sign voltage transient pulse reflects the progressive decrease of the temperature during the remaining duration of the microwave pulse. It is worth noticing that the shape of the transient pulses can be fitted with a sech 2 function: this originates from solitons that are described by nonlinear equations and that are typical for thin film ferroelectrics [30]. 16…”

“…The measurements were performed at 1.6 GHz, with an input power of 0 dBm, V D = 0 V, and V G = −5 V. The arbitrary-level input square wave (50 μs duration) is superimposed for reference as well. At the beginning of the AM microwave pulse, the HfZrO thin film absorbs the microwave power, whose main effect is the generation of transient voltages, since the temperature increases and decreases due to the subμs switching of the ferroelectric domains (figure 9 shape of the transient pulses can be fitted with a sech 2 function: this originates from solitons that are described by nonlinear equations and that are typical for thin film ferroelectrics [30].…”

Soliton phenomena in the process of the functioning of the heart

“…It can be concluded that we are dealing with the second center that creates the structure of the image of the world and is responsible for the psychophysical development of man, health and disease. In current biology and psychology, there is no room for solitons and spin functions that quantum physics deals with [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63].…”

Dynamical features and sensitivity visualization of thin-film Polarisation equation

“…Mathematical equations that model the dynamics of a wave traveling through the substance under investigation are frequently developed while studying these materials. Scalar and vector short pulse equations have been obtained for optical fibers [3,4], ferrites [2,5], and thin-film ferroelectric materials [6], as well as onedimensional and two-dimensional equations for each of these materials. Since their solutions are more expressive in describing the dynamics of waves in the material of interest, the topic of these equations' integrability is raised once they are available.…”

“…The Hirota bilinear method, Kudryashov's method, the first integral approach, the sub-equation technique, the simple hyperbolic function ansatzes, the hyperbolic tangent methods, etc are some examples of mathematical tools that are more direct in providing analytical expressions of the solution to nonlinear equations [9][10][11][12][13][14][15][16]. When considering the idealized model of a one-dimensional array of N identical ferroelectric domains, a nonlinear equation's solution has been derived in [6] for thin-film ferroelectric materials [6,17]. An equation for the nonlinear polarization evolution in thin-film materials has been developed while considering the Landau-Ginzburg-Devonshire mean-field theory.…”