Dynamics of single-domain magnetic particles at elevated temperatures

TL;DR

This paper derives a stochastic differential equation for single-domain magnetic particles that captures temperature-dependent dynamics, including diffusion behaviors in ferromagnetic and paramagnetic states, validated by simulations.

Contribution

It introduces a comprehensive stochastic macrospin model that describes magnetic particle dynamics across all temperatures, extending existing deterministic theories.

Findings

Diffusion is angular and increases linearly with temperature before saturating at T_c.

Diffusion in macrospin magnitude increases sharply near T_c.

Model agrees well with atomistic simulations across temperature regimes.

Abstract

A stochastic differential equation that describes the dynamics of single-domain magnetic particles at any temperature is derived using a classical formalism. The deterministic terms recover existing theory and the stochastic process takes the form of a mean-reverting random walk. In the ferromagnetic state diffusion is predominantly angular and the relevant diffusion coefficient increases linearly with temperature before saturating at the Curie point ($T_c$). Diffusion in the macrospin magnitude, while vanishingly small at room temperature, increases sharply as the system approaches $T_c$. Beyond $T_c$, in the paramagnetic state, diffusion becomes isotropic and independent of temperature. The stochastic macrospin model agrees well with atomistic simulations.