Microscopic calculation of thermally-induced spin-transfer torques

TL;DR

This paper presents a microscopic calculation of thermally-induced spin-transfer torques in conducting ferromagnets, revealing the importance of subtracting equilibrium components to obtain correct Mott-like formulas.

Contribution

It introduces a method to calculate thermal spin-transfer torques microscopically using a fictitious gravitational field and clarifies how to handle divergences for accurate results.

Findings

Derived a Mott-like formula for dissipative spin-transfer torque.

Identified the necessity of subtracting equilibrium components in calculations.

Suggested that coupling to entropy could simplify the approach.

Abstract

Spin-transfer torques induced by temperature gradients in conducting ferromagnets are calculated microscopically for smooth magnetization textures. Temperature gradients are treated a la Luttinger by introducing a fictitious gravitational field that couples to the energy density. The thermal torque coefficients obtained by the Kubo formula contain divergences caused by equilibrium components that should be subtracted before applying the Einstein-Luttinger relation. Only by following this procedure a familiar Mott-like formula is obtained for the dissipative spin-transfer torque. The result indicates that a fictitious field coupled to the entropy rather than energy would solve the issue from the outset.