Thermal conductivity of square ice
Abstract
We investigate thermal transport in square ice, a twodimensional analog of spin ice, exploring the role played by emergent magnetic monopoles in transporting energy. Using kinetic Monte Carlo simulations based on energypreserving extensions of singlespinflip dynamics, we explicitly compute the (longitudinal) thermal conductivity κ over a broad range of temperatures. We use two methods to determine κ : a measurement of the energy current between thermal baths at the boundaries, and the GreenKubo 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 κ /C , where C is the heat capacity, to the diffusion constant of an isolated monopole, showing that the subdiffusive motion of the monopole implies κ /C vanishes at zero temperature. Finally, we discuss the implications of these results for thermal transport in threedimensional spin ice, in spinice 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.
 Publication:

Physical Review B
 Pub Date:
 March 2022
 DOI:
 10.1103/PhysRevB.105.104405
 arXiv:
 arXiv:2111.14872
 Bibcode:
 2022PhRvB.105j4405S
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Statistical Mechanics
 EPrint:
 18 pages, 8 figures