Thermal Conductivity of Square Ice

TL;DR

This study explores how emergent magnetic monopoles influence thermal conductivity in square ice, revealing monopole diffusion as a key energy transport mechanism and its temperature dependence.

Contribution

It provides the first detailed computational analysis of thermal conductivity in square ice, linking monopole dynamics to heat transport and discussing implications for three-dimensional spin ice.

Findings

Thermal conductivity computed via two methods shows consistent results.

Magnetic monopole diffusion governs energy transport in square ice.

Thermal diffusivity vanishes at zero temperature due to monopole subdiffusion.

Abstract

We investigate thermal transport in square ice, a two-dimensional analogue of spin ice, exploring the role played by emergent magnetic monopoles in transporting energy. Using kinetic Monte Carlo simulations based on energy preserving extensions of single-spin-flip dynamics, we explicitly compute the (longitudinal) thermal conductivity, $\kappa$, over a broad range of temperatures. We use two methods to determine $\kappa$: a measurement of the energy current between thermal baths at the boundaries, and the Green-Kubo formula, yielding quantitatively consistent values for the thermal conductivity. We interpret these results in terms of transport of energy by diffusion of magnetic monopoles. We relate the thermal diffusivity, $\kappa/C$ where $C$ is the heat capacity, to the diffusion constant of an isolated monopole, showing that the subdiffusive monopole implies $\kappa/C$ vanishes at zero temperature. Finally, we discuss the implications of these results for thermal transport in three-dimensional spin ice, in spin ice materials such as Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$, and outline some open questions for thermal transport in highly frustrated magnets.