The ferroelectric materials such as lithium niobate and lithium tantalate show a non-linear hysteresis behaviour, which may be explained by dynamical system analysis. The behaviour of these ferroelectrics are usually explained by domains and the domain wall movements. So, the spatial variation of the domain wall was studied previously in order to see its effect on domain wall width in the context of Landau-Ginzburg functional. In the present work, both temporal and spatial variations of polarization are considered and by using Euler-Lagrange dynamical equation of motion, a Klein-Gordon equation is derived by taking the ferroelectrics as a Hamiltonian system. An interaction has been considered between the nearest neighbour domains, which are stacked sideways in a parallel array with uniform polarization. This interaction term is associated with the spatial term and when this interaction is assumed zero, the spatial term vanishes giving rise to a Duffing oscillator differential equation, which can be also studied by a dynamic system analysis.
Keywords: Klein-Gordon, Ferroelectrics, Spatial-Temporal Variation, Critical field for Soliton Motion.
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After spatial and temporal variation on domain wall and domain respectively, Klein-Gordon approach is adopted here to take cre of both spatial and temporal variation of polarization, eventually to find up to what critical field the soliton motion prevails in our system of ferroelectrics.
(J. Phys.: Condensed Matter, 18 (2006) 4093)
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