Magnon-phonon interaction and the underlying role of the Pauli exclusion principle

The magnon-phonon interaction is receiving growing attention due to its key role in spin caloritronics and the emerging field of acoustic spintronics. At resonance, this magnetoelastic forms magnon polarons, which underpin exotic phenomena such as magnonic heat currents phononic spin, but mostly investigated using mesoscopic spin-lattice models. Motivated integrate into first-principles many-body electronic structure theory, we set out derive exchange contribution, subtler than spin-orbit Schwinger functional derivatives. To avoid having solve famous Hedin-Baym equations self-consistently, phonons are treated perturbations structure. A formalism based on imposing a crossing-symmetric electron-electron developed order treat charge equal footing respect Pauli exclusion principle. Due conservation, first enters second through magnon-magnon interaction, renormalizes magnons. We show by iteration that contains ``screened $T$ matrix'' term an arguably more important which, local-spin limit, enables phonon emission absorption amplitudes, predicted phenomenological These terms are, respectively, screened collective four-point $\mathcal{W}$---a analog Hedin's $W$. Proof-of-principle results presented at varying temperatures for isotropic spectrum three dimensions presence flat optical branch.