Instability of Antiferromagnetic Magnons in Strong Fields

We predict that spin waves in an ordered quantum antiferromagnet in a strong magnetic field become unstable with respect to spontaneous two-magnon decays. At zero temperature, the instability occurs between the threshold field $H^{*}$ and the saturation field $H_c$. As an example, we investigate the high-field dynamics of a Heisenberg antiferromagnet on a square lattice and show that the single-magnon branch of the spectrum disappears in most of the Brillouin zone.