Landau-Lifshitz theory of the magnon-drag thermopower

TL;DR

This paper develops a theoretical framework using the Landau-Lifshitz equation to analyze magnon-drag thermopower in metallic ferromagnets, revealing how magnetic dynamics influence electron transport under temperature gradients.

Contribution

It introduces a stochastic Landau-Lifshitz model to quantify the magnonic contributions to thermopower, highlighting the roles of adiabatic and dissipative forces and their dependence on damping parameters.

Findings

The adiabatic Berry-phase force pushes electrons toward the hot side.

Dissipative correction drags electrons toward the cold side.

The ratio of these forces depends on damping coefficients  and .

Abstract

Metallic ferromagnets subjected to a temperature gradient exhibit a magnonic drag of the electric current. We address this problem by solving a stochastic Landau-Lifshitz equation to calculate the magnon-drag thermopower. The long-wavelength magnetic dynamics result in two contributions to the electromotive force acting on electrons: (1) An adiabatic Berry-phase force related to the solid angle subtended by the magnetic precession and (2) a dissipative correction thereof, which is rooted microscopically in the spin-dephasing scattering. The first contribution results in a net force pushing the electrons towards the hot side, while the second contribution drags electrons towards the cold side, i.e., in the direction of the magnonic drift. The ratio between the two forces is proportional to the ratio between the Gilbert damping coefficient $\alpha$ and the coefficient $\beta$ parametrizing the dissipative contribution to the electromotive force.