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Advancements of high-power laser sources in the THz frequency range have opened up opportunities for coherent intense excitation of infrared(IR)-active phonons in crystalline materials. The nonlinear phononics mechanism utilizes anharmonic coupling between driven IR-active modes and other lattice modes to induce changes in crystal structure and functional properties on picosecond timescales. Recent experimental and theoretical works have noted the potential for phonon-induced strains on these short time scales [npj Quantum Mater. 5, 95 (2020) , PRL 129, 167401 (2022)]. A natural way to measure the response of the lattice due to these THz pulses is by employing X-ray diffraction to observe changes to the position and intensities of Bragg peaks.

We show, using theory and first-principle calculations, that these lattice anharmonicities are responsible for the expansion of the c-axis in a biaxially strained thin film of LaAlO₃ via a phonon-strain coupling. Our theoretical modeling agrees well with the  experimental x-ray diffraction results both in time-scales and unusual signals in the fourier transform.