Thermal conductivity of a classical one dimensional spin-phonon system

TL;DR

This paper studies how different phonon interactions affect heat transport in a classical spin chain, revealing conditions that lead to divergent, diffusive, or ballistic thermal conductivity.

Contribution

It provides a comprehensive analysis of the impact of harmonic, anharmonic, and substrate couplings on thermal conductivity in a classical spin-phonon system.

Findings

Coupling to acoustic phonons causes diverging thermal conductivity.

Adding a substrate induces diffusive behavior.

Anharmonic potentials without substrate result in diffusive or ballistic transport.

Abstract

We investigate the thermal conductivity of the classical Heisenberg spin chain coupled to a variety of phonon systems using a Green-Kubo approach as well as coupling to heat reservoirs. The decay of energy current correlations is power law or exponential, depending on the type of (an)harmonicity of the phonon system and the presence of a substrate. In particular, we find that coupling the spin system to displacements with an acoustic type harmonic inter-site potential leads to a diverging thermal conductivity. Adding a substrate, harmonic or periodic such as sine-Gordon, drives the system to diffusive behavior. With anharmonic potential without a substrate the generic transport is diffusive even for the integrable Toda potential, while for the FPU chain is ballistic.