Longitudinal magnetic excitations in classical spin systems

Using spin dynamics simulations we predict the splitting of the longitudinal spin wave peak in all antiferromagnets with single site anisotropy into two peaks separated by twice the energy gap at the Brillouin zone center. This phenomenon has yet to be observed experimentally but can be easily investigated through neutron scattering experiments on MnF$_2$ and FeF$_2$. We have also determined that for all classical Heisenberg models the longitudinal propagative excitations are entirely multiple spin-wave in nature.