  Incommensurate spiral order is a common occurrence in frustrated magnetic
insulators. Typically, all magnetic moments rotate uniformly, through the same
wavevector. However the honeycomb iridates family Li2IrO3 shows an
incommensurate order where spirals on neighboring sublattices are
counter-rotating, giving each moment a different local environment.
Theoretically describing its spin dynamics has remained a challenge: the Kitaev
interactions proposed to stabilize this state, which arise from strong
spin-orbit effects, induce magnon umklapp scattering processes in spin-wave
theory. Here we propose an approach via a (Klein) duality transformation into a
conventional spiral of a frustrated Heisenberg model, allowing a direct
derivation of the dynamical structure factor. We analyze both Kitaev and
Dzyaloshinskii-Moriya based models, both of which can stabilize counterrotating
spirals, but with different spin dynamics, and we propose experimental tests to
identify the origin of counterrotation.
