Nonrelativistic magnon chiral splitting in altermagnets has garnered significant recent attention. In this Letter, we demonstrate that nonlinear three-wave mixing—where magnons split or coalesce—extends this phenomenon into unprecedented relativistic regimes. Employing a bilayer antiferromagnet with Dzyaloshinskii-Moriya interactions, we identify three distinct classes of chiral splitting, each dictated by specific symmetries, such as $C_{4}T$, ${\sigma }_{v}T$, or their combination. This reveals a novel bosonic mechanism for symmetry-protected chiral splitting, capitalizing on the unique ability of magnons to violate particle-number conservation, a feature absent in low-energy fermionic systems. Our findings pave the way for engineering altermagnetic splitting, with potential applications in advanced magnonic devices and deeper insights into magnon dynamics in complex magnetic systems.

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• Magnons
• Spintronics
• Altermagnets
• Many-body techniques