Magnons in Metallic Altermagnetic $\text{KV}_2\text{Se}_2\text{O}$
We investigate the spin excitation in altermagnetic vanadium oxyselenides, focusing on the metallic quasi-two-dimensional compound $\text{KV}_2\text{Se}_2\text{O}$. Using a fermionic Hamiltonian derived from ab initio calculations, we compute the transverse spin susceptibilities within the random phase approximation and extract the magnon dispersion relation. We show that the altermagnetic symmetry leads to characteristic degeneracies and directional splittings in both the electronic bands and the magnon spectra along high-symmetry paths of the Brillouin zone. The metallic $\text{KV}_2\text{Se}_2\text{O}$ exhibits finite magnon linewidths arising from the coupling to the particle-hole continuum. Furthermore, by fixing the magnitude of the wave vector and varying its in-plane direction, we uncover a pronounced angular dependence of the magnon energies and lifetimes, with complementary damping behavior between the two magnon branches. Upon including spin-orbit coupling, the system exhibits an out-of-plane easy c-axis anisotropy, which opens a magnon gap of approximately 6 meV at the $Γ$-point, possibly rendering the magnetic order stable at room temperature. Our results demonstrate that altermagnetism controls not only the dispersion but also the anisotropic decay of spin excitations, highlighting altermagnetic metals as promising platforms for directionally selective magnon transport.