Role of dimensionality in spontaneous magnon decay: Easy-plane ferromagnet

We calculate the magnon lifetime in an easy-plane ferromagnet on a tetragonal lattice in a transverse magnetic field. At zero temperature magnons are unstable with respect to spontaneous decay into two other magnons. Varying the ratio of intrachain to interchain exchanges in this model, we consider the effect of dimensionality on spontaneous magnon decay. The strongest magnon damping is found in the quasi-one-dimensional case for momenta near the Brillouin zone boundary. The sign of a weak interchain coupling has little effect on the magnon decay rate. The obtained theoretical results suggest the possibility of an experimental observation of spontaneous magnon decay in a quasi-one-dimensional ferromagnet CsNiF₃. We also find an interesting enhancement of the magnon decay rate for a three-dimensional ferromagnet. The effect is present only for the nearest-neighbor model and is related to an effective dimensionality reduction in the two-magnon continuum.