- Editors' Suggestion
- Letter
Magnon spectrum of altermagnets beyond linear spin wave theory: Magnon-magnon interactions via time-dependent matrix product states versus atomistic spin dynamics
Phys. Rev. B 111, L020407 – Published 15 January, 2025
DOI: https://doi.org/10.1103/PhysRevB.111.L020407
Abstract
The energy-momentum dispersion of magnons, as collective low-energy excitations of a magnetic material, is routinely computed from an effective quantum spin Hamiltonian but simplified via linearized Holstein-Primakoff transformations to describe noninteracting magnons. The dispersion produced by such linear spin wave theory (LSWT) is then plotted as “sharp bands” of infinitely long-lived quasiparticles. However, magnons are prone to many-body interactions with other quasiparticles—such as electrons, phonons, and other magnons—which can lead to shifting (i.e., band renormalization) and broadening of the sharp bands as a signature of a finite quasiparticle lifetime. The magnon-magnon interactions can be particularly important in antiferromagnets, and, therefore, possibly in newly classified altermagnets sharing many features of collinear antiferromagnets. Here, we employ nonperturbative quantum many-body calculations via time-dependent matrix product states (TDMPSs) to obtain the magnon spectral function for a altermagnet whose effective quantum spin Hamiltonian is put onto a four-leg cylinder. Its upper band is shifted away from the upper sharp band of LSWT, as well as broadened, which is explained as the consequence of hybridization of the latter with the three-magnon continuum. This implies that two-magnon Raman scattering spectra cannot be computed from LSWT bands, which offers a litmus test for the relevance of magnon-magnon interactions. Finally, we employ atomistic spin dynamics (ASD) simulations based on the classical Landau-Lifshitz-Gilbert (LLG) equation to obtain the magnon spectrum at finite temperature and/or at a fraction of the cost of TDMPS calculations. Despite including magnon-magnon interactions via the nonlinearity of the LLG equation, ASD simulations cannot match the TDMPS-computed magnon spectrum, thereby signaling nonclassical effects harbored by antiferromagnets and altermagnets.
