Coupled Ultrafast Lattice and Polarization Dynamics in Ferroelectric Nanolayers

We report the first analysis of the polarization and lattice dynamics in a metal/ferroelectric/metal nanolayer system by femtosecond x-ray diffraction. Two Bragg reflections provide information on the coupled dynamics of the two relevant phonon modes for ferroelectricity in perovskites, the tetragonal distortion and the soft mode. Optical excitation of the ${\mathrm{SrRuO}}_3$ metal layers generates giant stress ($>1\mathrm{GPa}$) compressing the ${\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_3$ layers by up to 2%. The resulting change of tetragonality reaches a maximum after 1.3 ps. As a result, the ferroelectric polarization $P$ is reduced by up to 100% with a slight delay that is due to the anharmonic coupling of the two modes.

Figure 1

(a) Tetragonal strain $\eta =c/a$ and ferroelectric ion displacements ${\xi }_{\mathrm{Ti}/\mathrm{Zr}\mathrm{\text{−}}\mathrm{O}}$ and ${\xi }_{\mathrm{Pb}\mathrm{\text{−}}\mathrm{O}}$ in the unit cell of PZT. (b) TEM image of a thinned PZT/SRO SL. (c) Schematic anharmonic potential energy surface as a function of $\eta$ and ${\xi }_{\mathrm{Pb}\mathrm{\text{−}}\mathrm{Ti}}$ (contour plot). The minimum of the potential lies on the white line [equilibrium ${\xi }_{\mathrm{Pb}\mathrm{\text{−}}\mathrm{Ti}}(\eta )={\xi }_{\mathrm{Pb}\mathrm{\text{−}}\mathrm{O}}-{\xi }_{\mathrm{Ti}/\mathrm{Zr}\mathrm{\text{−}}\mathrm{O}}$, Eq. (1)]. The initial values (${\eta }_0$, ${\xi }_0$) and the critical tetragonality ${\eta }_C$ for which ${\xi }_{\mathrm{Pb}\mathrm{\text{−}}\mathrm{Ti}}=0$ are indicated. (d) Contour plot of the calculated change of the $(0056)$ reflectivity as a function of the tetragonality $\eta$ and the relative ion displacement $\xi /{\xi }_0$. Black line: trajectory derived from Fig. 2b with red dots indicating selected time delays. (e) Calculated reflectivity change of $(0055)$ as a function of $\eta$ and $\xi$.

Figure 2

(a) Measured (green line) and simulated (thick black line) stationary x-ray reflectivity of the PZT/SRO SL as a function of the Bragg angle $\Theta$. Substrate peak at 23.3°. (b) Transient change of the $(0056)$ (blue circles) and $(0055)$ (red squares) reflectivities for a pump fluence of $5\mathrm{mJ}/{\mathrm{cm}}^2$. (c) Derived transient change of the tetragonality $\eta (t)$ (blue circles) and soft mode elongation ${\xi }_{\mathrm{Pb}\mathrm{\text{−}}\mathrm{Ti}}$ (red squares), equivalent to the trajectories in Figs. 1d, 1e. Solid symbols are reproduced as dots in Figs. 1d, 1e. (d) Oscillatory $(0056)$ signal with a 2 ps period on a longer time scale. (e) Fluence dependence of the peak reflectivity change of the $(0056)$ reflection around $t\approx 1.5\mathrm{ps}$. The solid line indicates the calculated reflectivity change according to a linear fluence dependence of the tetragonality with a $\xi$ given by Eq. (1). For the highest fluence ($15\mathrm{mJ}/{\mathrm{cm}}^2$) $\Delta R_{\max }/R_0=3$ which implies that $P$ approaches zero [red region in lower left corner of Fig. 1d].

Figure 3

Relative angular shift of the $(0056)$ Bragg reflection for an excitation fluence of $5\mathrm{mJ}/{\mathrm{cm}}^2$. Right ordinate scale: corresponding change of the SL period.