A theory of magnetic excitations formulated within the framework of the Lagrange equations of motion is used to study spin waves in stacked triangular antiferromagnets. As a consequence of geometrical frustration, a longitudinal mode parasitically coupled to transverse excitations is predicted. The model demonstrates good agreement with inelastic neutron scattering data for spin-1 ${\mathrm{CsNiCl}}_3$ and ${\mathrm{RbNiCl}}_3$, as well as spin-5/2 ${\mathrm{CsMnI}}_3$, in contrast with results based on the Haldane conjecture and with standard spin-wave theory. This formalism has general relevance to all frustrated spin systems.

• Received 26 July 1991

DOI:https://doi.org/10.1103/PhysRevLett.68.1042