Altermagnets represent a recently identified class of magnetic materials that combine features of both ferromagnets and antiferromagnets. While they have compensated magnetic order, as in antiferromagnets, they exhibit time-reversal broken and spin-polarized bands as in ferromagnets, leading to unconventional spin excitations. Although the electronic properties of altermagnets have been intensively studied, revealing spin-split band structure, the same is not true for their magnonic excitations. One altermagnetic material of great recent interest is CrSb that has a metallic character with perfectly compensated Ising spins below a Néel temperature $T_N\approx 735\mathrm{K}$. The magnon dispersion relations in CrSb have been recently measured by inelastic neutron scattering (INS) techniques over various directions of the Brillouin zone (BZ), revealing a chiral magnon splitting for wave vectors along a low-symmetry direction. Here we present an analytical quantum spin-wave theory for CrSb considering five exchange interactions and a uniaxial magnetic anisotropy that gives analytical expressions for the magnon dispersion relations for wave vectors along main BZ axes. These expressions give simple equations relating the interaction parameters with the values of the measured magnon energies at some symmetry points of the Brillouin zone. Within the uncertainties, the calculated parameters agree well with the ones obtained by fitting the theory to the whole INS data for CrSb.

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• Magnetic interactions
• Magnetic order
• Magnetism
• Magnetization dynamics