Magnon spectrum of altermagnets: Time-dependent matrix product states vs.linearized Holstein-Primakoff calculations unravelling spontaneous magnon decay*

The energy-momentum dispersion of magnons, as collective low-energy excitations of magnetic

material, is often computed from an effective quantum spin Hamiltonian but simplified via linear

spin wave theory (LSWT) transformations to describe noninteracting magnons. Their dispersion

is then plotted as “sharp bands” signifying infinitely long-lived quasiparticles. However, magnons

are prone to many-body interactions with other quasiparticles—such as electrons, phonons or other

magnons—which can lead to their spontaneous decay, i.e., shifting and broadening of sharp bands as

the signature of finite quasiparticle lifetime. The magnon-magnon interactions can be particularly

important in antiferromagnets, and, therefore, also in newly classified altermagnets sharing many

features of collinear antiferromagnets. Here, we employ nonperturbative quantum many-body cal-

culations, via numerically (quasi)exact time-dependent matrix product states (TDMPS), to obtain

magnon spectral function of a 4-leg altermagnetic cylinder. The extracted bands are broadened

and overlap with sharp bands of LSWT theory only at the edges/center of the Brillouin zone. No-

ticeable deviating otherwise. Artificially making exchange interactions within two sublattices closer

in value forces TDMPS- and LSWT-computed spactra to overlap, thereby unraveling the property

of effective spin Hamiltonian that causes failure of LSWT approach. Such features translate into

the difference between their respective density of states, which could be tested by Raman spec-

troscopy. Finally, we employ Landau-Lifshitz-Gilbert (LLG) equation-based classical atomistic spin

dynamics (ASD) simulations to obtain magnon spectrum at finite temperature. Despite includ-

ing magnon-magnon interactions via nonlinearity of LLG equation, ASD simulations cannot fully

match the TDMPS-computed magnon spectrum due to nonclassical effects harbored by antiferro-

and altermagnets