The magnons in altermagnets exhibit chiral splitting even in the absence of spin-orbit coupling and external magnetic fields. Typically, this chiral splitting behavior can be well described by alternating isotropic spin exchanges (ISEs) near the zero temperature. However, its finite-temperature dynamics, particularly when incorporating spin-orbit coupling, remains elusive. In this Letter, we reveal that, when including magnon-magnon interactions, long-range anisotropic spin exchanges (ASE) of altermagnets can effectively induce chiral splitting of magnons at finite temperatures. Crucially, the ASE-induced chiral splitting competes with that arising from ISE, leading to a pronounced temperature-dependent modulation. Moreover, this competition is intimately coupled to quantum spin fluctuations, and can reverse the spin current driven by the band splitting as temperature increases. Our work uncovers the intrinsic competition governing collective spin excitations in altermagnets, providing insights into their finite-temperature dynamical behavior.

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• Magnetic interactions
• Magnons
• Spin dynamics
• Altermagnets
• Hartree-Fock methods
• Linear spin wave theory
• Mean field theory