Ultrafast light-induced shear strain probed by time-resolved X-ray diffraction: the model multiferroic BiFeO$_3$ as a case study

Enabling the light-control of complex systems on ultra-short timescales gives rise to rich physics with promising applications. While crucial, the quantitative determination of both the longitudinal and shear photo-induced strains still remains challenging. Here, by scrutinizing asymmetric Bragg peaks pairs $(pm h01)$ using picosecond time-resolved X-ray diffraction experiments in BiFeO$_3$, we simultaneously determine the longitudinal and shear strains. The relative amplitude of those strains can be explained only if both thermal and non-thermal processes contribute to the acoustic phonon photogeneration process. Importantly, we also reveal a difference of the dynamical response of the longitudinal strain with respect to the shear one due to an interplay of quasi-longitudinal and quasi-transverse acoustic modes, well reproduced by our model.