Dynamical systems analysis for polarization in ferroelectrics

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.