Abstract
The magnetic properties of two-dimensional altermagnets can be obtained from a square lattice Heisenberg model with antiferromagetic nearest neighbor interaction and two types of next-nearest neighbor interactions arranged in a checkerboard pattern. Using nonlinear spin-wave theory we calculate for this model the corrections to the renormalized magnon spectrum and the staggered magnetization to first order in the inverse spin quantum number 1/S. We also show that to order 1/S² the ground state energy is not sensitive to the component of the interaction which is responsible for altermagnetism. At the Γ-point the 1/S-correction to the magnon dispersion vanishes so that quantum fluctuations do not induce a gap in the magnon spectrum of altermagnets, as expected by Goldstone's theorem. We extract the leading 1/S-corrections to the spin-wave velocity and the effective mass characterizing the curvature of the magnon dispersion in altermagnets.