Quantum fluctuations in two-dimensional altermagnets

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 $1/S^2$ the ground state energy is not sensitive to the component of the interaction which is responsible for altermagnetism. At the $\Gamma$-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.