Spin-dependent quasiparticle lifetimes in altermagnets

TL;DR

This work addresses how many-body interactions modify spin-split electronic bands in altermagnets by computing electron self-energies from couplings to magnons, phonons, and magnetoelastic modes on a 2D Lieb-lattice model. Using Migdal theory and a full bosonic spectrum (phonons, magnons, and hybrid magnetoelastic modes), it reveals a strong, spin-dependent lifetime asymmetry near the Fermi surface driven by magnon scattering, while phonons contribute weaker broadening; magnetoelastic coupling largely mirrors the magnon case. Crucially, the intrinsic spin-splitting remains spectroscopically resolvable in the presence of these many-body effects, with temperature enhancing broadening and reducing visibility. The results provide microscopic criteria for ARPES interpretation in altermagnets and offer guidance for experiments probing spin dynamics and spin-dependent transport in spin-split materials.

Abstract

We investigate many-body effects on the spin-split electron bands in altermagnets by computing the electron self-energy arising from interactions with magnons, phonons, and hybridized magnon-phonon modes. These interactions lead to band broadening, which can obscure the intrinsic spin-splitting in spectroscopic measurements. We consider a $d$-wave Lieb lattice altermagnet as a representative example. Our results reveal that the spin-splitting remains spectroscopically resolvable and provide theoretical estimates of lifetime effects relevant for experimental detection. For electron-magnon coupling, we find a distinct difference between spectral function broadening for up and down spins close to the Fermi surface, which is not present in the case of electron-phonon coupling. We relate it to the spin splitting of the magnon modes in altermagnets. The results, including magneto-elastic coupling, are very similar to the pure magnon case. This provides insights into quasiparticle dynamics in altermagnets and contributes to the broader understanding of many-body interactions in spin-split systems. By including the temperature dependence of the self-energies, we also quantify how thermal fluctuations influence the broadening of the electronic states.

Figures (7)

• Figure 1: Lieb lattice where the red, blue, and yellow sites have spin-up, spin-down, and no net spin, respectively. The black dashed square marks the unit cell, and the arrows indicate different electron hoppings up to third nearest neighbor hopping.
• Figure 2: The bands of the electrons and the three different bosons we are considering along a path in the Brillouin zone between high-symmetry points, where numerical parameters are given in Tab. \ref{['tab:Parameters']}. (a) The electron bands, (b) the magnon bands, (c) the phonon bands, and (d) the magnon-phonon hybridized bands. The colors in (d) give how magnon- and phonon-like the magnetoelastic modes are [see \ref{['eq:Def of c_n']}], where blue means completely phonon-like and red is completely magnon-like.
• Figure 3: The sunset Feynman diagram, where straight lines represent electrons, and wavy lines represent bosons. The couplings and all relevant quantum numbers are also labeled.
• Figure 4: The real and imaginary parts of the electron self-energy for scattering of electrons off three different bosonic modes: phonons (yellow line), magnons (red line), and magnetoelastic modes (blue dashed line). The first and second rows show the zero-temperature limit ($T=1$ mK), whereas the third and fourth rows show the case with $T=20$ K. The first and third rows show results when the external electron has spin down, while the second and fourth rows show results for electrons with spin up. $\textbf{k}_{\mathrm{F}\downarrow}$ lies on the FS of spin-down electrons along the X-$\Gamma$ line. The values of the other parameters that are used are given in Tab. \ref{['tab:Parameters']}.
• Figure 5: The spectral function as function of both $\textbf{k}$ along the x-axis and $\omega$ along the y-axis. The values of $\textbf{k}$ follow a path in the BZ between high-symmetry points. The dashed blue (green) lines indicate the original bands for spin-down (up) electrons. We consider the case $T=20$ K in all of the plots and (a) spin-down electrons interacting with phonons, (b) spin-up electrons interacting with phonons, (c) the sum of these, (d) spin-down electrons interacting with magnons, (e) spin-up electrons interacting with magnons, and (f) the sum of these. For the rest of the parameters used, see Tab. \ref{['tab:Parameters']}.