Variational principle for magnetisation dynamics in a temperature gradient

TL;DR

This paper uses a variational principle within extended irreversible thermodynamics to generalize the Landau-Lifshitz equation, revealing how temperature gradients influence magnetic damping and confirming the Magnetic Seebeck effect.

Contribution

It introduces a variational approach to derive a generalized Landau-Lifshitz equation accounting for temperature gradients in ferromagnets.

Findings

Temperature gradient induces a magnetic induction field.

The magnetic induction field modulates damping depending on wave-vector orientation.

Quantitative estimate of the Magnetic Seebeck effect strength is provided.

Abstract

By applying a variational principle on a magnetic system within the framework of extended irreversible thermodynamics, we find that the presence of a temperature gradient in a ferromagnet leads to a generalisation of the Landau-Lifshitz equation with an additional magnetic induction field proportional to the temperature gradient. This field modulates the damping of the magnetic excitation. It can increase or decrease the damping, depending on the orientation of the magnetisation wave-vector with respect to the temperature gradient. This variational approach confirms the existence of the Magnetic Seebeck effect which was derived from thermodynamics and provides a quantitative estimate of the strength of this effect.