Nonlinear Spin-Wave Theory in Altermagnets: Spontaneous Magnon Decays from Nonrelativistic Band Splitting

Collinear magnets include ferromagnets, antiferromagnets, and the recently discovered altermagnets [1]. Altermagnets have attracted attention due to their unique nonrelativistic spin splitting in electronic and magnonic bands [2], showing potential for spintronic applications. In insulating altermagnets, magnons are the primary spin carriers, unaffected by Landau damping. However, quantum fluctuations may induce spontaneous magnon decays [3]. This raises the key question: How stable are magnons in altermagnets?

We show that in altermagnets, the higher-in-energy magnon branch is generally unstable. Using a 2D Heisenberg model with d-wave spin splitting, we apply a nonlinear spin-wave expansion to calculate the renormalized spectrum and magnon lifetimes. Our results reveal how the splitting opens decay channels for the higher-energy magnon branch, which vanish as the splitting reduces to zero, recovering a stable antiferromagnetic spectrum. We compare these perturbative results to nonperturbative time-evolution calculations based on matrix product states.

[1] Šmejkal, Sinova, Jungwirth, Phys. Rev. X 12, 031042 (2022); Phys. Rev. X 12, 040501 (2022)

[2] Šmejkal et al., Phys. Rev. Lett. 131, 256703 (2023)

[3] Zhitomirsky, Chernyshev, Rev. Mod. Phys. 85, 219 (2013)