Thermal Hall conductivity from semiclassical spin dynamics simulations: implementation and applications to chiral ferromagnets and Kitaev magnets

TL;DR

This paper develops a semiclassical spin dynamics simulation method to compute thermal Hall conductivity in magnetic systems, demonstrating its effectiveness on chiral ferromagnets and Kitaev magnets, capturing complex interactions beyond simple models.

Contribution

It introduces a practical semiclassical simulation framework for thermal Hall transport, extending previous approaches to include real-time energy current correlations and energy magnetization calculations.

Findings

Efficiently computes thermal Hall conductivity in complex magnetic models.

Captures effects beyond intrinsic non-interacting approximations.

Provides benchmarks for experimental comparisons in non-linear regimes.

Abstract

We investigate thermal Hall transport in magnetic systems, using semiclassical spin dynamics simulations. Building on a linear response framework, we discuss the intricacies of computing the thermal Hall conductivity from real-time energy current correlations and the energy magnetization. We then apply this methodology to two models: a square-lattice chiral magnet with in-plane Dzyaloshinskii-Moriya interaction, and the antiferromagnetic Kitaev model in a field. Our results demonstrate the efficiency of semiclassical spin dynamics to study thermal Hall transport capturing quantitative effects beyond the simple intrinsic non-interacting approximation. They can serve as a benchmark for comparison with experiments in regimes where non-linearities from magnon-magnon interactions and strong thermal fluctuations play a crucial role.