Longitudinal magnons in large- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>S</mml:mi> </mml:math> easy-axis magnets

Longitudinal magnons are a distinct type of multipolar excitations in magnetic materials with large spins $S\ensuremath{\ge}1$ and strong easy-axis anisotropy. These excitations have angular momentum ${S}^{z}=\ifmmode\pm\else\textpm\fi{}2S$ 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.