Dynamics of Vortices in Two-Dimensional Magnets

TL;DR

This paper reviews the dynamics of vortices in two-dimensional magnetic materials, exploring their types, equations of motion, effects of thermal fluctuations, noise, and experimental observations of vortex behavior.

Contribution

It provides a comprehensive analysis of vortex dynamics, including stochastic equations of motion, noise effects, and experimental validation in 2D magnetic systems.

Findings

Planar vortices exhibit Newtonian dynamics with strong discreteness effects.

Non-planar vortices have non-Newtonian, smooth trajectories.

Experimental observations confirm vortex-related peaks in spin correlation spectra.

Abstract

Theories, simulations and experiments on vortex dynamics in quasi-two-dimensional magnetic materials are reviewed. These materials can be modelled by the classical two-dimensional anisotropic Heisenberg model with XY (easy-plane) symmetry. There are two types of vortices, characterized by their polarization (a second topological charge in addition to the vorticity): Planar vortices have Newtonian dynamics (even-order equations of motion) and exhibit strong discreteness effects, while non-planar vortices have non-Newtonian dynamics (odd-order equations of motion) and smooth trajectories. The influence of thermal fluctuations on single vortices is investigated. Different types of noise and damping are discussed and implemented into the microscopic equations which yields stochastic equations of motion for the vortices. The solutions of the these equations are compared with Langevin dynamics simulations. Moreover, noise-induced transitions between opposite polarizations of a vortex are investigated. For temperatures above the Kosterlitz-Thouless vortex-antivortex unbinding transition, a phenomenological theory, namely the vortex gas approach, yields central peaks in the dynamic form factors for the spin correlations. Such peaks are observed both in combined Monte Carlo- and Spin Dynamics-Simulations and in inelastic neutron scattering experiments. However, the assumption of ballistic vortex motion appears questionable.