Spontaneous magnon decays from nonrelativistic time-reversal symmetry breaking in altermagnets

TL;DR

This paper demonstrates that altermagnets, a new class of collinear magnets with nonrelativistic time-reversal symmetry breaking, exhibit spontaneous magnon decays, challenging the traditional stability dichotomy in quantum magnets.

Contribution

It reveals that even in nonrelativistic collinear systems, band splitting in altermagnets induces magnon decay, expanding understanding of quasiparticle stability in magnetic materials.

Findings

Weak band splitting enables magnon decay in altermagnets.

D-wave altermagnets show a stable region at the Brillouin zone center.

Altermagnets exhibit a quasiparticle stability trichotomy.

Abstract

Quasiparticles are central to condensed matter physics, but their stability can be undermined by quantum many-body interactions. Magnons, quasiparticles in quantum magnets, are particularly intriguing because their properties are governed by both real and spin space. While crystal symmetries may be low, spin interactions often remain approximately isotropic, limiting spontaneous magnon decay. Textbook wisdom holds that collinear Heisenberg magnets follow a dichotomy: ferromagnets host stable magnons, while antiferromagnetic magnons may decay depending on dispersion curvature. Up to now, relativistic spin-orbit coupling and noncollinear order that connect spin space to real space, were shown to introduce more complex magnon instability mechanisms. Here, we show that even in nonrelativistic isotropic collinear systems, this conventional dichotomy is disrupted in altermagnets. Altermagnets, a newly identified class of collinear magnets, exhibit compensated spin order with nonrelativistic time-reversal symmetry breaking and even-parity band splitting. Using kinematic analysis, nonlinear spin-wave theory, and quantum simulations, we reveal that even weak band splitting opens a decay phase space, driving quasiparticle breakdown. Additionally, d-wave altermagnets form a rare ``island of stability'' at the Brillouin zone center. Our findings establish a quasiparticle stability trichotomy in collinear Heisenberg magnets and position altermagnets as a promising platform for unconventional spin dynamics.