Spinwave damping in the two-dimensional ferromagnetic XY model

TL;DR

This paper investigates how spinwaves dampen in a two-dimensional ferromagnetic XY model, calculating damping rates and analyzing their effects on the dynamic structure function through advanced theoretical and simulation methods.

Contribution

It introduces a detailed calculation of spinwave damping rates using diagrammatic techniques and extends the memory function formalism to include these effects in the XY model.

Findings

Non-divergent spinwave peaks with a background intensity that increases with temperature.

Finite-size systems exhibit multiple weak peaks related to system size and wavevector.

Results are consistent with classical Monte Carlo and Spin-Dynamics simulations.

Abstract

The effect of damping of spinwaves in a two-dimensional classical ferromagnetic XY model is considered. The damping rate $\Gamma_{q}$ is calculated using the leading diagrams due to the quartic-order deviations from the harmonic spin Hamiltonian. The resulting four-dimensional integrals are evaluated by extending the techniques developed by Gilat and others for spectral density types of integrals. $\Gamma_{q}$ is included into the memory function formalism due to Reiter and Solander, and Menezes, to determine the dynamic structure function $S(q,\omega)$. For the infinite sized system, the memory function approach is found to give non-divergent spinwave peaks, and a smooth nonzero background intensity (``plateau'' or distributed intensity) for the whole range of frequencies below the spinwave peak. The background amplitude relative to the spinwave peak rises with temperature, and eventually becomes higher than the spinwave peak, where it appears as a central peak. For finite-sized systems, there are multiple sequences of weak peaks on both sides of the spinwave peaks whose number and positions depend on the system size and wavevector in integer units of $2\pi/L$. These dynamical finite size effects are explained in the memory function analysis as due to either spinwave difference processes below the spinwave peak or sum processes above the spinwave peak. These features are also found in classical Monte Carlo -- Spin-Dynamics simulations.