Dissipative dynamics of topological defects in frustrated Heisenberg spin systems

TL;DR

This paper investigates the dissipative dynamics of topological defects in frustrated Heisenberg spin systems with spiral order, using a nonlinear sigma model and path-integral methods, and relates findings to experimental data in cuprates.

Contribution

It introduces a semiclassical quantization of non-Abelian topological defects and derives their damping behavior, connecting theoretical models with experimental observations in cuprate materials.

Findings

Damping of defects is temperature-dependent and quantifiable.

The model's predictions align with experimental inverse mobility data.

Spiral order may be relevant in the spin-glass regime of cuprates.

Abstract

We study the dynamics of topological defects of a frustrated spin system displaying spiral order. As a starting point we consider the SO(3) nonlinear sigma model to describe long-wavelength fluctuations around the noncollinear spiral state. Besides the usual spin-wave magnetic excitations, the model allows for topologically non-trivial static solutions of the equations of motion, associated with the change of chirality (clockwise or counterclockwise) of the spiral. We consider two types of these topological defects, single vortices and vortex-antivortex pairs, and quantize the corresponding solutions by generalizing the semiclassical approach to a non-Abelian field theory. The use of the collective coordinates allows us to represent the defect as a particle coupled to a bath of harmonic oscillators, which can be integrated out employing the Feynman-Vernon path-integral formalism. The resulting effective action for the defect indicates that its motion is damped due to the scattering by the magnons. We derive a general expression for the damping coefficient of the defect, and evaluate its temperature dependence in both cases, for a single vortex and for a vortex-antivortex pair. Finally, we consider an application of the model for cuprates, where a spiral state has been argued to be realized in the spin-glass regime. By assuming that the defect motion contributes to the dissipative dynamics of the charges, we can compare our results with the measured inverse mobility in a wide range of temperature. The relatively good agreement between our calculations and the experiments confirms the possible relevance of an incommensurate spiral order for lightly doped cuprates.