Origin of intrinsic Gilbert damping

TL;DR

This paper derives the Gilbert damping term from first principles using a non-relativistic expansion of the Dirac equation, linking it to spin-orbit coupling and electromagnetic fields.

Contribution

It provides a fundamental derivation of the Gilbert damping from quantum mechanics, clarifying its physical origin.

Findings

Gilbert damping arises from spin-orbit coupling effects.

The derivation connects damping to electromagnetic field variations.

First-principles approach enhances understanding of magnetization relaxation.

Abstract

The damping of magnetization, represented by the rate at which it relaxes to equilibrium, is successfully modeled as a phenomenological extension in the Landau-Lifschitz-Gilbert equation. This is the damping torque term known as Gilbert damping and its direction is given by the vector product of the magnetization and its time derivative. Here we derive the Gilbert term from first principles by a non-relativistic expansion of the Dirac equation. We find that the Gilbert term arises when one calculates the time evolution of the spin observable in the presence of the full spin-orbital coupling terms, while recognizing the relationship between the curl of the electric field and the time varying magnetic induction.