Strain propagation in nanolayered perovskites probed by ultrafast x-ray diffraction

Strain propagation in a perovskite heterostructure grown on a ${\mathrm{SrTiO}}_3$ (STO) substrate is studied by ultrafast x-ray diffraction. Femtosecond displacive phonon excitation in a ${\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_3∕{\mathrm{SrRuO}}_3$ (PZT/SRO) film launches acoustic strain waves propagating into the STO substrate. We demonstrate a two-step time evolution of diffracted x-ray intensity which originates from different interfering contributions to the (004) Bragg peak of the STO substrate. Analysis by dynamical x-ray diffraction theory gives the absolute strain $\mathrm{\Delta }a∕a_0$ in a wide range of optical pump fluences. Ultrafast transient strain as small as $\mathrm{\Delta }a∕a_0=2\times {10}^{-5}$ is determined in this way.

Figure 1

(Color online) (a) Pump-probe setup for ultrafast x-ray diffraction. Pump pulses at $400\mathrm{nm}$ are generated by frequency doubling $7\%$ of the output power of a Ti:sapphire laser system, delivering $45\mathrm{fs}$ pulses with $5\mathrm{mJ}$ energy. The major part of the laser output is focused onto a copper tape target to generate ultrashort hard x-ray pulses via laser-plasma interaction. (b) CCD camera image of the (004) Bragg peak of the STO substrate. The two components are due to diffraction of copper $K_{\alpha 1}$ and $K_{\alpha 2}$ radiation. The pump area indicates the excited region on the sample as projected on the CCD camera image. (c) TEM cross section of a PZT/SRO heterostructure sample with a $250\mathrm{nm}$ thick PZT film grown on STO substrate.

Figure 2

(Color online) Measured angle-integrated diffraction intensity of the (004) reflection of STO for different pump fluences of (a) $1.6\mathrm{mJ}∕{\mathrm{cm}}^2$, (b) $=0.74\mathrm{mJ}∕{\mathrm{cm}}^2$ and (c) =$0.43\mathrm{mJ}∕{\mathrm{cm}}^2$. Solid circles represent the measured data points and the lines are guides to the eye. The reflectivity change $\mathrm{\Delta }R∕R_0$ is plotted as a function of the delay time between $400\mathrm{nm}$ pump and x-ray probe pulses. (d) Measured strain amplitude (circles) versus excitation fluence together with linear fit.

Figure 3

(Color online) (a) Schematic of the strain wave in the STO substrate for three time delays after impulsive excitation of stress in the PZT/SRO layers. (b) Calculated reflectivity change $\mathrm{\Delta }R∕R_0$ of the (004) reflection of STO normalized to the strain amplitude $\mathrm{\Delta }a∕a_0$ as a function of the position of the strain wave [leading edges of the wave in (a) indicated by dashed lines] for different strain amplitudes as indicated. For $\mathrm{\Delta }a∕a_0=1.25\times {10}^{-4}$ the signal grows in two steps (thick red line). (c), (d) Schematic of lattice planes in the unstrained and strained STO crystal. (d) shows an accumulated lattice displacement of one full lattice-plane distance, i.e., 1/4 of the lattice constant $a_0$.

Figure 4

(Color online) (a) Reflectivity of the (004) reflection of the STO substrate as a function of the diffraction angle $\Theta$ calculated without (solid black) and with (red dotted) a strain wave. A convolution with the angular resolution of the experiment results in the dashed lines. (b) Calculated extinction length of the (004) reflection as a function of $\Theta$.