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

We calculate magnon lifetime in an easy-plane ferromagnet on a tetragonal lattice in transverse magnetic field. At zero temperature magnons are unstable with respect to spontaneous decay into two other magnons. Varying 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 a little effect on the magnon decay rate. The obtained theoretical results suggest possibility of experimental observation of spontaneous magnon decay in a quasi-one-dimensional ferromagnet CsNiF$_3$. 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 effective dimensionality reduction in the two-magnon continuum.