Domain Dynamics under Ultrafast Electric-Field Pulses

Exploring the dynamic responses of a material is of importance to both understanding its fundamental physics at high frequencies and potential device applications. Here we develop a phase-field model for predicting the dynamics of ferroelectric materials and study the dynamic responses of ferroelectric domains and domain walls subjected to an ultrafast electric-field pulse. We discover a transition of domain evolution mechanisms from pure domain growth at a relatively low field to combined nucleation and growth of domains at a high field. We derive analytical models for the two regimes which allow us to extract the effective mass and damping coefficient of ferroelectric domain walls. The exhibition of two regimes for the ferroelectric domain dynamics at low and high electric fields is expected to be a general phenomenon that would appear for ferroic domains under other ultrafast stimuli. The present Letter also offers a general framework for studying domain dynamics and obtaining fundamental properties of domain walls and thus for manipulating the dynamic functionalities of ferroelectric materials.

Figure 1

(a) Schematic of a ${\mathrm{BaTiO}}_3$ crystal with $a\text{−}c$ domains subjected to an ultrafast electric-field pulse. (b) Evolution of (first panel) the polarization change of each domain as well as (second panel) the displacement and (third panel) the velocity of the sideways motion of the $a\text{−}c$ domain wall, under an electric-field pulse $E=1\mathrm{MV}/\mathrm{m}$ with duration indicated by the yellow region. (c) Evolution of the polarization profile across an $a\text{−}c$ domain wall.

Figure 2

(a) Volume fraction of switched $a$ domains under low fields as a function of pulse duration, from both the phase-field model and the analytical model. (b) Velocity of the sideways motion of the $a\text{−}c$ domain wall under static low fields. (c) (Dots) field dependence of the saturation domain wall velocity and fittings to (dashed line) $v_0^{\mathrm{DW}}\propto E$ for $E\le 1\mathrm{MV}/\mathrm{m}$ and (dash-dotted line) $v_0^{\mathrm{DW}}\propto E^{1.3}$ for $E>1\mathrm{MV}/\mathrm{m}$. (d) (Squares) effective mass and (circles) damping coefficient of the domain wall. The gray dotted lines in (c) and (d) indicate $E=1\mathrm{MV}/\mathrm{m}$ where a change in the field dependence of $v_0^{\mathrm{DW}}$ and ${\alpha }^{\mathrm{DW}}$ occurs.

Figure 3

(a) Volume fraction of switched $a$ domains under high fields as a function of pulse duration, from both the phase-field model and the analytical model. (b) Evolution of the average polarization in the original $a$ domains under electric-field pulses with $E=20\mathrm{MV}/\mathrm{m}$ and different durations. (c) Initial domain structure and final domain structures after applying electric-field pulses with $E=20\mathrm{MV}/\mathrm{m}$ and different durations. (d) Electric field strength—pulse duration stability diagram of the $a\text{−}c$ domains. The red and blue dashed lines are guides to the eyes, following $E{T}_E=0.015\mathrm{V}\mathrm{s}/\mathrm{m}$ and $E{T}_E=0.29\mathrm{V}\mathrm{s}/\mathrm{m}$, respectively.