Phonon-induced renormalization of exchange interactions in metallic two-dimensional magnets

TL;DR

This paper develops a theory showing how electron-phonon interactions in metallic 2D magnets can weaken exchange interactions, soften magnon modes, and reduce Curie temperature, with implications for tunable magnetic properties.

Contribution

The paper introduces a theoretical framework to quantify phonon-induced renormalization of exchange interactions in metallic 2D magnets, applied to Fe$_3$GeTe$_2$.

Findings

Exchange interactions decrease with temperature due to electron-phonon coupling.

Magnon modes soften, leading to a ~10% reduction in Curie temperature.

Effect is more pronounced with stronger electron-phonon coupling or non-equilibrium phonon distributions.

Abstract

The presence of spin-polarized charge carriers in metallic magnets provides a mechanism for spin-lattice interactions mediated by electron-phonon coupling. Here, we present a theory of this mechanism used to estimate its effect on the exchange interactions in 2D magnets. Starting from a square lattice model at half filling, we show that the presence of electron-phonon coupling with equilibrium phonon distribution leads to a notable suppression of exchange interactions with temperature. We then apply our approach to the prototypical 2D metallic ferromagnet, Fe$_3$GeTe$_2$, with moderate electron-phonon coupling. We find that the exchange interactions undergo a renormalization, leading to a softening of the magnon modes, and suppression of the Curie temperature by $\sim$10\%. We expect that this effect can be further enhanced in systems with strong electron-phonon coupling, as well as for non-equilibrium distribution of phonons induced by strong laser fields or charge currents.