Three-mode-interactions in the anharmonic phononic coupling process

Nonlinear phononic coupling is a modern way to manipulate material structure, accessing non-equilibrium state beyond those in the static phase diagram. Presently, most studies focus on a single displacive excitation of a Raman mode that couples to the coherently laser-excited IR mode. However, in principle all the symmetry-allowed Raman modes could be excited simultaneously. When the excited modes strongly interact with each other, the dynamics of the original targeted Raman mode should be different. We demonstrate quantitatively these differences by extending the phonon equations-of-motion to include the IR-Raman-Raman interaction. The displacive amplitude of the targeted Raman mode saturates as the light intensity continues to increase. The energy transfers to the two Raman modes and beating is observed. With first-principles density functional theory calculations, we investigate the three-mode-coupling in the titanate YTiO₃ as an example to predict a new magnetic phase not found in the thermodynamic phase diagram.