TY - JOUR

T1 - Dynamical systems analysis for polarization in ferroelectrics

AU - Bandyopadhyay, A. K.

AU - Ray, P. C.

AU - Gopalan, Venkatraman

N1 - Funding Information:
The authors would like to thank Professor E. Klotins, Institute of Solid State Physics (Latvia), for an interesting discussion on Duffing oscillator equation. One of the authors (V.G.) would like to acknowledge support from the National Science Foundation (Grant Nos. DMR-0122638, DMR-0507146, DMR-0512165, DMR-0349632, and DMR-0103354), and NSF-MRSEC center at Penn State (DMR-0213623).

PY - 2006

Y1 - 2006

N2 - 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.

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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U2 - 10.1063/1.2388124

DO - 10.1063/1.2388124

M3 - Article

AN - SCOPUS:33845763444

SN - 0021-8979

VL - 100

JO - Journal of Applied Physics

JF - Journal of Applied Physics

IS - 11

M1 - 114106

ER -