Energy Magnetization and Thermal Hall Effect

TL;DR

This paper develops a systematic framework for calculating magnetizations and thermal transport coefficients in magnetic systems, addressing divergences in traditional methods and confirming the Wiedemann-Franz law in anomalous Hall systems.

Contribution

It introduces general formulae for energy magnetization and corrects thermal Hall conductivity calculations, improving upon existing approaches.

Findings

Magnetization corrections eliminate unphysical divergences.

Corrected thermal Hall conductivity obeys Wiedemann-Franz law.

Provides a unified approach for magnetic and thermal transport analysis.

Abstract

We obtain a set of general formulae for determining magnetizations, including the usual electromagnetic magnetization as well as the gravitomagnetic energy magnetization. The magnetization corrections to the thermal transport coefficients are explicitly demonstrated. Our theory provides a systematic approach for properly evaluating the thermal transport coefficients of magnetic systems, eliminating the unphysical divergence from the direct application of the Kubo formula. For an anomalous Hall system, the corrected thermal Hall conductivity obeys the Wiedemann-Franz law.