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We study the dynamics of topological defects of a frustrated spin systemdisplaying spiral order. As a starting point we consider the SO(3) nonlinearsigma model to describe long-wavelength fluctuations around the noncollinearspiral state. Besides the usual spin-wave magnetic excitations, the modelallows for topologically non-trivial static solutions of the equations ofmotion, associated with the change of chirality (clockwise or counterclockwise)of the spiral. We consider two types of these topological defects, singlevortices and vortex-antivortex pairs, and quantize the corresponding solutionsby generalizing the semiclassical approach to a non-Abelian field theory. Theuse of the collective coordinates allows us to represent the defect as aparticle coupled to a bath of harmonic oscillators, which can be integrated outemploying the Feynman-Vernon path-integral formalism. The resulting effectiveaction for the defect indicates that its motion is damped due to the scatteringby the magnons. We derive a general expression for the damping coefficient ofthe defect, and evaluate its temperature dependence in both cases, for a singlevortex and for a vortex-antivortex pair. Finally, we consider an application ofthe model for cuprates, where a spiral state has been argued to be realized inthe spin-glass regime. By assuming that the defect motion contributes to thedissipative dynamics of the charges, we can compare our results with themeasured inverse mobility in a wide range of temperature. The relatively goodagreement between our calculations and the experiments confirms the possiblerelevance of an incommensurate spiral order for lightly doped cuprates.Comment: 22 pages, 7 figures, final published versio

Dissipative dynamics of topological defects in frustrated Heisenberg spin systems