Fig. 6. Light-induced longitudinal and shear strains.

(A and B) Time evolution of the longitudinal [η_L (A)] and shear [η_T (B)] strains extracted from the 403_m/40${\overline{3}}_{\mathrm{m}}$ and 530_m/5$\overline{3}{0}_{\mathrm{m}}$ Bragg reflections. The color filling [orange and green in (A) and (B)] and the small sketches in (A) and (B) indicate the unit cell distortions. The purple dashed line shows the approximate arrival time of the out-of-plane strain pulse to the BiFeO₃-substrate interface. (C) Simulation of the spatial dependence of the longitudinal strain in the sample at 30 ps after ultrashort laser pulse excitation. The profile shows the compressive front (green) and the tensile tail (orange) of the strain pulse propagating at the speed of sound. These opposite strain components lead to the two diffraction peaks as shown in (D) and Fig. 5B. (D) Left: Sketch of the light-induced strain components (longitudinal-L and shear-T) within the BiFeO₃ film illustrating the compressive front and tensile tail of the L and T strain pulses. Right: The 403_m and $40{\overline{3}}_{\mathrm{m}}$ Bragg peaks at 10-ps time delay. The different shifts of the two Bragg peaks are related to the L and T strain contributions. Note that the shear strain component has an opposite contribution for 403_m and $40{\overline{3}}_{\mathrm{m}}$ consistently with Eq. 1. (E) Temporal and spatial dependence of the light-induced strain in BiFeO₃ thin film and its effect on the ferroelectric polarization. The longitudinal and shear strains travel at velocities v_L and v_T, respectively, distort the unit cell and the local unit-cell ferroelectric polarization direction (small purple arrows) as a function of the time delay. The uniform macroscopic ferroelectric polarization before laser excitation is shown by the large purple arrow (sketch I).