Dynamical systems analysis for polarization in ferroelectrics

A. K. Bandyopadhyay, P. C. Ray, Venkatraman Gopalan

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

The nonlinear hysteresis behavior in ferroelectric materials, such as lithium tantalate and lithium niobate, may be explained by dynamical systems analysis. In a previous work, the polarization "domain wall width" was studied in terms of only spatial variation and eventually critical values of polarization were determined to derive the stability zone in the context of Landau-Ginzburg free energy functional. In the present work, the temporal dynamics of the domains themselves are considered by taking the time variation through Euler-Lagrange dynamical equation of motion, which gives rise to a Duffing oscillator differential equation as a governing equation. From this nonlinear Duffing oscillator equation, three cases are studied theoretically: First, with no electric field with and without any damping; secondly, taking the external field as static with damping; and finally, taking an oscillatory electric field with damping. After giving perturbation at the coercive field, the eigenvalues deduced through a Jacobian transformation of the perturbed matrix show interesting cases of stability and instability of polarization for different values of electric field. The possibility of chaos at high oscillatory electric field is also briefly explored merely as a limiting case in terms of the Lyapunov exponents spectrum in our particular ferroelectric system.

Original languageEnglish (US)
Article number114106
JournalJournal of Applied Physics
Volume100
Issue number11
DOIs
StatePublished - Dec 1 2006

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systems analysis
dynamical systems
electric fields
damping
polarization
lithium niobates
oscillators
ferroelectric materials
domain wall
chaos
equations of motion
differential equations
eigenvalues
free energy
hysteresis
exponents
perturbation
matrices

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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title = "Dynamical systems analysis for polarization in ferroelectrics",
abstract = "The nonlinear hysteresis behavior in ferroelectric materials, such as lithium tantalate and lithium niobate, may be explained by dynamical systems analysis. In a previous work, the polarization {"}domain wall width{"} was studied in terms of only spatial variation and eventually critical values of polarization were determined to derive the stability zone in the context of Landau-Ginzburg free energy functional. In the present work, the temporal dynamics of the domains themselves are considered by taking the time variation through Euler-Lagrange dynamical equation of motion, which gives rise to a Duffing oscillator differential equation as a governing equation. From this nonlinear Duffing oscillator equation, three cases are studied theoretically: First, with no electric field with and without any damping; secondly, taking the external field as static with damping; and finally, taking an oscillatory electric field with damping. After giving perturbation at the coercive field, the eigenvalues deduced through a Jacobian transformation of the perturbed matrix show interesting cases of stability and instability of polarization for different values of electric field. The possibility of chaos at high oscillatory electric field is also briefly explored merely as a limiting case in terms of the Lyapunov exponents spectrum in our particular ferroelectric system.",
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Dynamical systems analysis for polarization in ferroelectrics. / Bandyopadhyay, A. K.; Ray, P. C.; Gopalan, Venkatraman.

In: Journal of Applied Physics, Vol. 100, No. 11, 114106, 01.12.2006.

Research output: Contribution to journalArticle

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AB - The nonlinear hysteresis behavior in ferroelectric materials, such as lithium tantalate and lithium niobate, may be explained by dynamical systems analysis. In a previous work, the polarization "domain wall width" was studied in terms of only spatial variation and eventually critical values of polarization were determined to derive the stability zone in the context of Landau-Ginzburg free energy functional. In the present work, the temporal dynamics of the domains themselves are considered by taking the time variation through Euler-Lagrange dynamical equation of motion, which gives rise to a Duffing oscillator differential equation as a governing equation. From this nonlinear Duffing oscillator equation, three cases are studied theoretically: First, with no electric field with and without any damping; secondly, taking the external field as static with damping; and finally, taking an oscillatory electric field with damping. After giving perturbation at the coercive field, the eigenvalues deduced through a Jacobian transformation of the perturbed matrix show interesting cases of stability and instability of polarization for different values of electric field. The possibility of chaos at high oscillatory electric field is also briefly explored merely as a limiting case in terms of the Lyapunov exponents spectrum in our particular ferroelectric system.

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