Giant intrinsic nonlinear phonon-magnon coupling in the antiferromagnet CoF$_2$

The observation of strongly coupled lattice and spin dynamics in altermagnet CoF$_2$ is reported. On the background of the expected spin-phonon interaction leading to renormalization of all phonons at the Neel temperature an additional strong coupling between one-magnon excitation and the lowest frequency Raman-active phonon of B1g symmetry was observed and manifested an anomaly in its energy, full width, and intensity at temperature T*=23 K precisely where the frequency of the phonon becomes exactly twice the frequency of the magnon. We assigned this effect to unique magnon-phonon coupling in the form of a two-magnons-one-phonon interaction. The consistent experimental data clearly demonstrate that there is an intrinsic coupling that does not require coherent excitation.