Spin dynamics of counterrotating Kitaev spirals via duality

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 ${\mathrm{Li}}₂{\mathrm{IrO}}₃$ shows an incommensurate order where spirals on neighboring sublattices are counterrotating, 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.