We study the magnon spectrum of $\alpha$-MnTe by utilizing the density functional perturbation theory. In contrast to conventional antiferromagnets, the spectra of chiral magnons in $\alpha$-MnTe are found to coincide in four nodal planes, possess the same peak energy but different peak intensities at the Brillouin zone boundaries, and completely diverge elsewhere, which indicates the magnon chiral splitting. Symmetry analysis from electronic states reveals that the inversion symmetry breaking or half-cell translation breaking leads to the magnon bands' splitting in altermagnets. We also verify the $g$-wave magnetism in MnTe from first principles. Our findings provide direct microscopic insights into collective spin excitations in altermagnets.

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• Electronic structure
• Magnons
• Spin dynamics
• Spin-orbit coupling
• First-principles calculations