Ultrafast light-induced shear strain probed by time-resolved x-ray diffraction: Multiferroic ${\mathrm{BiFeO}}_3$ as a case study

Enabling the light control of complex systems on ultrashort timescales gives rise to rich physics with promising applications. Although crucial, the quantitative determination of both the longitudinal and the shear photoinduced strains still remains challenging. Here, by scrutinizing asymmetric Bragg peaks pairs $(\pm h01)$ in ${\mathrm{BiFeO}}_3$ using picosecond time-resolved x-ray diffraction experiments, we simultaneously determine the longitudinal and shear strains. Importantly, we reveal a difference in the dynamical response of the longitudinal strain with respect to the shear one due to an interplay of quasilongitudinal and quasitransverse acoustic modes, well reproduced by our model. Finally, we show that the relative amplitude of those strains can be explained only if both thermal and nonthermal processes contribute to the acoustic phonon photogeneration process.

Figure 1

(a) Three-dimensional view of the BFO pseudocubic unit cell with displacement vector associated with the longitudinal and shear photoinduced strains (orange and green arrows). The black arrow is the ${\mathrm{BiFeO}}_3$ ferroelectric polarization pointing along the ${\left[111\right]}_c$ direction. (b) Side view of the ${\mathrm{BiFeO}}_3$ pseudocubic unit cell before and after the laser excitation showing the in-plane and out-of-plane motions. (c) Transient optical reflectivity signal of the BFO single crystal measured with 400-nm pump and 800-nm probe beams. The red line shows the acoustic phonon signal once the base line has been subtracted. The inset shows the fast Fourier transform with the quasilongitudinal and quasitransverse acoustic phonon modes.

Figure 2

(a) Scheme of the time-resolved x-ray diffraction in the grazing incidence geometry. (b) Reciprocal space imaging of the ${\left(101\right)}_c$ and ${(-101)}_c$ Bragg diffraction peaks at equilibrium. The positions ($\gamma ,\delta$) of the ${\left(101\right)}_c$ and ${(-101)}_c$ Bragg diffraction peaks are $(26.{1874}^{\circ },26.{0802}^{\circ })$ and ($26.{0367}^{\circ },25.{6879}^{\circ }$), respectively, with a camera resolution of $8.64\times {10}^{-3}{}^{\circ }/\mathrm{pixel}$. (c) Differential reciprocal space imaging of the ${\left(101\right)}_c$ and ${(-101)}_c$ Bragg diffraction peaks at a time delay of 200 ps and at a fluence of $3{\mathrm{mJ}\mathrm{cm}}^{-2}$.

Figure 3

(a) Time dependence of the relative variation of the interplanar distance for the ${\left(101\right)}_c$ and ${(-101)}_c$ planes. (b) Same as (a) but for the ${\left(201\right)}_c$ and ${(-201)}_c$ planes. (c) Comparison of the experimentally determined photoinduced longitudinal $\langle {\eta }_L\rangle \left(t\right)$ and shear strains $\langle {\eta }_S\rangle \left(t\right)$ calculated from Eq. (2) (symbols) with the ones (lines) deduced from Eqs. (3) and (4) based on the theory of acoustic waves propagation and x-ray scattering. The horizontal dashed lines represent the estimated maximum strain coming from the laser-induced heating effect [thermoelastic effect (TE), see the text]. (d) Sketch of the time-dependent shape of the unit cell (from a cubic to a trapezoidal form) related to the spatial separation of the in-plane and out-of-plane strain components of the QLA and QTA modes.