The inverse thermal spin-orbit torque and the relation of the Dzyaloshinskii-Moriya interaction to ground-state energy currents

TL;DR

This paper derives a formalism to calculate heat currents generated by magnetization dynamics in materials with spin-orbit interaction, revealing the role of Dzyaloshinskii-Moriya interaction and predicting strong heat currents in fast domain walls.

Contribution

It introduces a method to separate heat currents from energy currents in systems with DMI, linking DMI coefficients to energy currents and providing ab-initio predictions for Mn/W(001) bilayers.

Findings

DMI contributes to energy currents driven by magnetization dynamics.

A formal relation between DMI energy current and DMI coefficient is established.

Fast domain walls generate significant inverse thermal spin-orbit torque heat currents.

Abstract

Using the Kubo linear-response formalism we derive expressions to calculate the heat current generated by magnetization dynamics in magnets with broken inversion symmetry and spin-orbit interaction (SOI). The effect of producing heat currents by magnetization dynamics constitutes the Onsager reciprocal of the thermal spin-orbit torque (TSOT), i.e., the generation of torques on the magnetization due to temperature gradients. We find that the energy current driven by magnetization dynamics contains a contribution from the Dzyaloshinskii-Moriya interaction (DMI), which needs to be subtracted from the Kubo linear response of the energy current in order to extract the heat current. We show that the expressions of the DMI coefficient can be derived elegantly from the DMI energy current. Guided by formal analogies between the Berry phase theory of DMI on the one hand and the modern theory of orbital magnetization on the other hand we are led to an interpretation of the latter in terms of energy currents as well. Based on \textit{ab-initio} calculations we investigate the heat current driven by magnetization dynamics in Mn/W(001) magnetic bilayers. We predict that fast domain walls drive strong ITSOT heat currents.