Nature of Dynamical Coupling between Polarization and Strain in Nanoscale Ferroelectrics from First Principles

A first-principle-based technique is used to investigate dynamical coupling between polarization and picosecond time-scale strain pulses in ferroelectric nanolayers. Two different dynamical mechanisms are found. The first mechanism concerns homogeneous dipole patterns, is governed by the ultrafast soft-mode dynamics, mostly consists in the modification of the dipoles’ magnitude, and leads to a polarization only weakly changing and following the strain pulse via an “usual” coupling law. On the other hand, the second mechanism occurs in highly inhomogeneous dipole patterns, is characterized by a large change in polarization and by a time delay between polarization and strain, and is governed by the “slower breathing” of dipolar inhomogeneities. This second mechanism provides a successful explanation of puzzling experimental data.

Figure 1

Tetragonality [panel (a)] and average dipole moment [panels (b)–(d)], with respect to their equilibrium values, as a function of time for three different simulated dynamical strain pulses and in experiment. Lines show our predictions while the symbols represent the measurements of Ref. [11]. Simulation data in panels (b), (c), and (d) correspond to PZT thin films exhibiting the pattern I, pattern III with a nanobubble volume of $5.3{\mathrm{nm}}^3$ and pattern IV with a nanobubble volume of $59.7{\mathrm{nm}}^3$, respectively.

Figure 2

Snapshots at different times of a ($x$, $y$) cross section of the dipole pattern in a PZT film initially possessing low-density nanobubbles (pattern III). This cross section corresponds to the most inner (001) $B$ plane, and the $x$ and $y$ axis lie along the [100] and [010] directions, respectively. Red (respectively, blue) areas show areas with dipoles pointing up (respectively, down) along the $z$ direction. These data correspond to the intermediate strain pulse [dashed lines in Figs. 1a, 1c], and an initial nanobubble volume of $5.3{\mathrm{nm}}^3$.

Figure 3

Same as Fig. 2 but for pattern IV (high-density nanobubbles) with an initial nanobubble volume of $59.7{\mathrm{nm}}^3$.