Stochastic dynamics of magnetization in a ferromagnetic nanoparticle out of equilibrium

TL;DR

This paper models the stochastic behavior of magnetization in a ferromagnetic nanoparticle out of equilibrium, using the stochastic Landau-Lifshitz-Gilbert equation to analyze magnetic susceptibility under bias and temperature variations.

Contribution

It introduces a framework for describing magnetization dynamics in nanoparticles connected to electrodes, incorporating electron exchange effects and stochastic modeling.

Findings

Magnetization exhibits Brownian motion driven by electron exchange.

The stochastic Landau-Lifshitz-Gilbert equation effectively describes out-of-equilibrium dynamics.

Calculated magnetic susceptibility relevant for ferromagnetic resonance experiments.

Abstract

We consider a small metallic particle (quantum dot) where ferromagnetism arises as a consequence of Stoner instability. When the particle is connected to electrodes, exchange of electrons between the particle and the electrodes leads to a temperature- and bias-driven Brownian motion of the direction of the particle magnetization. Under certain conditions this Brownian motion is described by the stochastic Landau-Lifshitz-Gilbert equation. As an example of its application, we calculate the frequency-dependent magnetic susceptibility of the particle in a constant external magnetic field, which is relevant for ferromagnetic resonance measurements.