Degenerate helimagnetic states, lines of soft modes and absence of long-range order in three dimensions

The triangular and hexagonal classical Heisenberg model with suitable competing intraplane interactions have infinitely many ground states having inequivalent helical order of different pitch Q. The spin wave energy vanishes along a line in k space, the locus of the Q vectors. Helimagnetic long-range order is destroyed at finite temperature also in three dimensions. The existence of a new phase is suggested: an isotropic helimagnet that leads to a characteristic ring scattering. The effect of quantum corrections and of easy plane anisotropy is also considered.