On the Energy Dissipation in the Landau-Lifshitz-Gilbert Equation

TL;DR

This paper analyzes how energy dissipation and resonance properties in ferromagnetic nanomagnets depend on local energy landscape curvature within the Landau-Lifshitz-Gilbert framework, especially near bifurcation points.

Contribution

It systematically investigates the influence of local curvature on FMR frequency, damping, and quality factor, highlighting limitations of common approximations near bifurcations.

Findings

FMR frequency and damping depend on the energy landscape curvature.

The quality factor approximation Q ≈ 1/2α fails near bifurcation points.

FMR decay time behavior changes near bifurcations.

Abstract

The dynamics of magnetization near a stable equilibrium in ferromagnetic nanomagnets are examined within the Landau--Lifshitz--Gilbert (LLG) framework. For a small angle precession, the dependence of ferromagnetic resonance (FMR) frequency, the damping constant and the resulting quality factor $Q$ of the resonance on the local curvature around the free-energy minimum is systematically analyzed. Special attention is devoted to the behavior of the FMR decay time in the vicinity of bifurcation points, where the number of metastable energy minima changes and the commonly used approximation for the quality factor $Q\simeq 1/2\alpha$ (where $\alpha$ denotes the Gilbert damping) fails.