Longitudinal modes in quasi-one-dimensional antiferromagnets

Neutron-scattering data on ${\mathrm{CsNiCl}}_3$, a quasi-one-dimensional spin-one antiferromagnet, exhibit an anomalous mode. It was later proposed, based on a Landau-Ginsburg model, that this should be viewed as a longitudinal fluctuation of the sublattice magnetization. This theory is elaborated in more detail here and compared with experimental data on ${\mathrm{CsNiCl}}_3$ and ${\mathrm{RbNiCl}}_3$. In particular, we give explicitly a renormalization-group argument for the existence of such modes in Néel-ordered antiferromagnets which are nearly disordered by quantum fluctuations, due to quasi-one-dimensionality or other effects. We then discuss the non-Néel case of a stacked triangular lattice such as ${\mathrm{CsNiCl}}_3$ where longitudinal and transverse modes mix. In this case the quantum disorder transition is driven first order by fluctuations and the longitudinal mode always has a finite width. Effects of a magnetic field on the magnon spectrum are calculated both in conventional spin-wave theory and in the Landau-Ginsburg model and are compared with experimental data on ${\mathrm{CsNiCl}}_3$. This model is compared with an alternative Lagrangian-based one that was proposed recently.