Dissipative dynamics of topological defects in frustrated Heisenberg spin systems

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.

Quantum criticality in photorefractive optics: Vortices in laser beams and antiferromagnets

“…Early papers which found and explored the spin-glass phase in a very similar model are [39,40,47,49]. The main difference is that the papers cited consider the spiral (non-collinear) spin order.…”

“…These works are all inspired by the cuprate materials, the most celebrated brand of high-temperature superconductors. While [40,47] explore in detail the transport properties, we have no pretension neither to provide a realistic model of cuprates nor to explore in detail all the properties of the spin-glass phase. We are content to see that the PR system of Z vortices reproduces the phase structure of a certain kind of dirty Heisenberg antiferromagnets (with O(3) spins and Z 2 "vortices"), besides the more obvious connection to systems which directly reproduce the Z vortices in multicomponent U (1) systems like multicomponent Bose-Einstein condensates and type-1.5 superconductors.…”

“…The authors of previous works on this model [40,47,48,58] were motivated mainly by the ubiquitous problem of understanding the pseudogap phase in cuprate superconductors. The applicability of the model to this particular problem is still an open question -it may well be that cuprate physics goes far beyond.…”

“…Just as in the disorder-free case, we are particularly interested in possible spin-glass phenomena in doped insulating O(3) antiferromagnets [39,40,[47][48][49] and in the last section we will discuss also the spin-glass phase in such systems.…”

“…When coupled to a charge density wave (speaking about the usual, U (1) electromagnetic charge) and a superconducting order parameter, it becomes a toy model of cuprate materials (one variant is given in [58]). In the light of what we know today, the ability of this model to realistically describe the cuprate physics is quite questionable; but even so it is an interesting magnetic system on its own, and it was already found in [39,47] to exhibit a spin-glass phase, though in a slightly different variant (in particular, with spiral instead of collinear ordering).…”