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The interaction between lattice and spins is at the heart of an extremelyintriguing ultrafast dynamics in magnetic materials. In this work we formulatea general non-equilibrium theory that disentangles the complex interplaybetween them in a THz laser-excited antiferromagnetic insulator. The theoryprovides a quantitative description of the transient energy flow between thespin and lattice sub-systems, subject to magnon-phonon and phonon-phononscatterings, giving rise to finite life-times of the quasiparticles and to theequilibration time of the system. We predict a novel kind of scattering processwhere two magnons of opposite polarizations decay into a phonon, previouslyomitted in the literature. The theory is combined with first-principlecalculations and then applied to simulate a realistic dynamics of NiO. The mainrelaxation channels and hot spots in the reciprocal space, giving the strongestcontribution to the energy transfer between phonons and magnons are identified.The diverse interaction strengths lead to distinct coupled dynamics of thelattice and spin systems and subsequently to different equilibrationtimescales.

Microscopic Theory of Ultrafast Out-of-Equilibrium Dynamics in Magnetic Insulators. Unraveling the Magnon-Phonon Coupling