Rotons in triangular lattice antiferromagnet

Elementary excitations above magnetically ordered state: spin waves (magnons). Harmonic approximation = non-interacting spin waves: good for collinear antiferromagnets because interaction-induced corrections appear only in 1/S² order of the perturbative 1/S expansion only.

Non-collinear (spiral) antiferromagnet: triple vertices (like a⁺aa) describing decay of magnon into two appear already in 1/S^1/2 order. Hence expect much stronger 1/S effect.

We find significant renormalization of spin waves at 1/S level, including shallow local minima at the mid-points of BZ faces (points B and F). Most importantly - pronounced flat region with very weak dispersion (green area in right figure). Also find finite lifetime inside the shaded star-like area of the Brillouin zone (left figure).

Flat spin-wave dispersion in a triangular antiferromagnet, O.A. Starykh, A.V. Chubukov, and A.G. Abanov, Phys. Rev. B 74, 180403 (2006).

Closely related works: W. Zheng, J. O. Fjaerestad, R. R. P. Singh, R. H. McKenzie, and R. Coldea, Phys. Rev. Lett. 96, 057201 (2006) and Phys. Rev. B 74, 224420 (2006); A. L. Chernyshev and M. E. Zhitomirsky, Phys. Rev. Lett. 97, 207202 (2006); N. Perkins and W. Brenig, Phys. Rev. B 77, 174412 (2008).