Nonlinear Dynamics of Domain-Wall Propagation in Epitaxial Ferroelectric Thin Films

We investigated the ferroelectric domain-wall propagation in epitaxial $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_3$ thin film over a wide temperature range (3–300 K). We measured the domain-wall velocity under various electric fields and found that the velocity data is strongly nonlinear with electric fields, especially at low temperature. We found that, as one of surface growth issues, our domain-wall velocity data from ferroelectric epitaxial film could be classified into the creep, depinning, and flow regimes due to competition between disorder and elasticity. The measured values of velocity and dynamical exponents indicate that the ferroelectric domain walls in the epitaxial films are fractal and pinned by a disorder-induced local field.

Figure 1

(a) A schematic diagram of domain-wall propagation in disordered medium. Elastic forces come from the curvature of domain wall, and defects work as strong pinning sites. (b) Theoretical prediction on the domain-wall velocity $v$ vs electric field $E$ in system governed by competition between disorder and elasticity effects. $E_{C0}$ represents a threshold $E$.

Figure 2

(a) $P\mathrm{\text{−}}E$ hysteresis loops at different $T$. (b) Time-dependent normalized switched polarization, $\Delta p(t)$, behaviors (solid symbols) from switching current and (open symbols) from PFM measurements. The solid lines show the fitting results using the KAI model. (c) Scanned images of $t$-dependent domain growth at $E=0.3\mathrm{MV}/\mathrm{cm}$. (d) Plot of $1/t_0$ vs $v$. This relationship is linear, suggesting that $1/t_0$ from switching current studies can be used to parameterize $v$.

Figure 3

$\Delta p(t)$ obtained via switching current measurements under various $E$ values at (a) 300 and (b) 3 K. The solid lines show the fitting results using the KAI model.

Figure 4

(a) (Solid symbols) $T$ dependent curves of $1/t_0$ vs $E$. The dotted and solid lines are guidelines for eye. (b) $\log (t_0)$ vs $1/E$ curves. The linear fitting indicates a dynamic exponent $\mu \sim 1$. The inset shows that $U{E}_{C0}/k_B$ is nearly independent of $T$. (c) Plot of $\log (1/t_0)$ vs $\log (E-E_{C0})$ with the $E_{C0}\sim 1\mathrm{MV}/\mathrm{cm}$. From the slope of the plot, we found a velocity exponent $\theta \sim 0.7$.