Magnon lifetime in the easy-plane antiferromagnets

Considering a prototypical 2D easy-plane antiferromagnet on a square lattice in which gapped excitations coexist with acoustic spin waves, we find that random disorder induces a relaxation of the gapped magnon with the rate that greatly exceed the effect of conventional magnon-magnon scattering. Anomalous disorder-induced $T$-dependence of the energy gap of the optical magnon and of the scattering rate of the acoustic magnon are also discussed. These can be readily probed by the high-resolution neutron-resonance spin-echo technique. Implications for other systems are discussed and comparison with the available experimental data is presented.