Magnon-phonon interactions from first principles

Abstract

Modeling spin-wave (magnon) dynamics in novel materials is important to advance spintronics and spin-based quantum technologies. The interactions between magnons and lattice vibrations (phonons) limit the length scale for magnon transport. However, quantifying these interactions remains challenging. Here we show many-body calculations of magnon-phonon (mag-ph) coupling based on the ab initio Bethe-Salpeter equation. We derive expressions for mag-ph coupling matrices and compute them in 2D ferromagnets, focusing on hydrogenated graphene and monolayer CrI3. Our analysis shows that electron-phonon (e-ph) and mag-ph interactions differ significantly, where modes with weak e-ph coupling can exhibit strong mag-ph coupling (and vice versa), and reveals which phonon modes couple more strongly with magnons. In both materials studied here, the inelastic magnon relaxation time is found to decrease abruptly above the threshold for emission of strongly coupled phonons, thereby defining a low-energy window for efficient magnon transport. By averaging in this window, we compute the temperature-dependent magnon mean-free path, a key figure of merit for spintronics, entirely from first principles. The theory and computational tools shown in this work enable studies of magnon interactions, scattering, and dynamics in generic materials, advancing the design of magnetic systems and magnon- and spin-based devices.

Figures (4)

• Figure 1: Magnon dispersions in (a) H-MLG and (b) monolayer CrI3, computed with the finite-momentum magnon BSE. Results from the Heisenberg model with up to third nearest-neighbor exchange couplings and experimental data from Ref. Lebing2018 are shown for comparison.
• Figure 2: (a) The mag-ph interaction viewed as a superposition of electron- (red) and hole-phonon (blue) scattering processes between initial and final magnon states, shown as ovals. (b) Phonon dispersion in H-MLG and CrI3 overlaid with a color map of average mag-ph and $e$-ph coupling strengths for each phonon mode, $|\mathcal{G}_{\nu}(\mathbf{q})|$ and $|g_{\nu}(\mathbf{q})|$, respectively. The mag-ph coupling in CrI$_3$ is an average of acoustic and optical magnons at $\mathbf{Q}=0$. The blue lines show the magnon dispersions in both materials. (c) Phonon modes with the largest mag-ph coupling in H-MLG and CrI3.
• Figure 3: Brillouin-zone maps of average mag-ph coupling strengths, $\overline{G}_{n\textbf{Q}} (\textbf{q})$ defined in the text, plotted as a function of phonon momentum $\mathbf{q}$. Results are shown for H-MLG (top) and CrI3 (bottom), for acoustic magnons with momenta ${\mathbf{Q}=\Gamma,K,M}$ in respective panels from left to right.
• Figure 4: (a) Magnon dispersions with color-coded mag-ph relaxation times at 20 K. The dashed lines indicate the energy of the phonon with the strongest mag-ph couplin in each material. (b) Mag-ph relaxation times as a function of temperature. In each plot, the orange lines are averages over short-lived magnon states, while the blue lines are averages over long-lived magnon states, as explained in the text. (c) Average mean free paths $\overline{L}(T)$ in H-MLG (left) and CrI3 (right), obtained by taking a thermal average of the magnon mode-dependent mean free paths.