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

TL;DR

This paper investigates how the dimensionality of an easy-plane ferromagnet influences spontaneous magnon decay, revealing the strongest damping in quasi-one-dimensional systems and potential experimental observation in CsNiF3.

Contribution

It provides a detailed theoretical analysis of magnon decay rates across different dimensional regimes in an easy-plane ferromagnet, highlighting the role of interchain coupling.

Findings

Maximum magnon damping occurs in quasi-one-dimensional systems.

Weak interchain coupling minimally affects magnon decay rates.

Enhanced decay rates are predicted for three-dimensional ferromagnets due to effective dimensionality reduction.

Abstract

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.