Longitudinal magnons in large-$S$ easy-axis magnets

TL;DR

This paper investigates longitudinal magnons in large-spin easy-axis magnets, deriving an effective model and comparing multiple theoretical approaches to understand their dynamics and decay properties.

Contribution

It introduces a simplified effective spin-1/2 model for longitudinal magnons in large-$S$ magnets and compares various theoretical methods to analyze their behavior.

Findings

Effective spin-1/2 model describes magnon dynamics.

Multiboson spin-wave theory predicts magnon decay rates.

Spectral evolution from strong to weak anisotropy is characterized.

Abstract

Longitudinal magnons are a distinct type of multipolar excitations in magnetic materials with large spins $S\ge 1$ and strong easy-axis anisotropy. These excitations have angular momentum $S^z = \pm 2S$ and can be viewed as a propagating full spin reversal. We study longitudinal magnons for the nearest-neighbor Heisenberg ferromagnet and antiferromagnet on a square lattice with large single-ion anisotropy. In the strong-coupling limit, we derive an effective spin-1/2 model including two leading contributions in $J/D$. The effective model provides a simple description of the longitudinal magnon dynamics. For $S=1$, we compare results from several theoretical approaches that include the effective spin-1/2 model, the linked-cluster expansion, the multiboson spin-wave theory, and, for a ferromagnet, an exact two-particle solution. Among these approaches, the multiboson spin-wave theory provides the decay rate of longitudinal magnons and describes evolution of the excitation spectra from strong to weak anisotropy.