  Instability of the excitation spectrum of an ordered noncollinear Heisenberg
antiferromagnet (AF) with respect to spontaneous two-magnon decays is
investigated. We use a spin-1/2 AF on a triangular lattice as an example and
examine the characteristic long- and short wave-length features of its
zero-temperature spectrum within the 1/S-approximation. The kinematic
conditions are shown to be crucial for the existence of decays and for overall
properties of the spectrum. The XXZ and the J-J' generalizations of the model,
as well as the role of higher-order corrections are discussed.
