Magnon-phonon coupling from a crossing symmetric screened interaction

Abstract

The magnon-phonon coupling has received growing attention in recent years due to its central role in spin caloritronics and the emerging field of acoustic spintronics. At resonance, this magnetoelastic interaction drives the formation of magnon polarons, which underpin exotic phenomena such as magnonic heat currents and phononic spin, but has with a few recent exceptions only been investigated using mesoscopic spin-lattice models. Motivated to integrate the magnon-phonon coupling into first-principle many-body electronic structure theory, we set up to derive the non-relativistic exchange-contribution, which is more subtle than the spin-orbit contribution, using Schwinger's method of functional derivatives. To avoid having to solve the famous Hedin-Baym equations self-consistently, the phonons are treated as a perturbation to the electronic structure. A formalism is developed around the idea of imposing crossing symmetry on the interaction, in order to treat charge and spin on equal footing. By an iterative scheme, we find that the spin-flip component of the ${\mathit collective}$ four-point interaction, $\mathcal{V}$, which is used to calculate the magnon spectrum, contains a first-order "screened T matrix" part and an arguably more important second-order part, which in the limit of local spins describes the same processes of phonon emission and absorption as obtained from phenomenological magnetoelastic models. Here, the "order" refers to the ${\mathit screened}$ ${\mathit collective}$ four-point interaction, $\mathcal{W}$ - the crossing-symmetric analog of Hedin's $W$. Proof-of-principle model calculations are performed at varying temperatures for the isotropic magnon spectrum in three dimensions in the presence of a flat optical phonon branch.