"Stochastic Modeling of Coercivity " - A Measure of Non-equilibrium State

TL;DR

This paper develops a stochastic model combining Gilbert, Fokker-Planck, and Kramer's theories to explain coercivity behavior in magnetic nanoparticles, accounting for measurement time and non-equilibrium states.

Contribution

It introduces a comprehensive stochastic framework that integrates multiple theoretical approaches to analyze coercivity in magnetic nanoparticles, including measurement time effects.

Findings

Coercivity peaks at a specific particle size due to single domain behavior.

The model explains the decrease in coercivity beyond a critical size.

Measurement time significantly influences coercivity measurements.

Abstract

A typical coercivity versus particle size curve for magnetic nanoparticles has been explained by using the Gilbert equation followed by the corresponding Fokker Plank equation. Kramer's treatment has been employed to explain the increase in coercivity in the single domain region. The single to multi-domain transformation has been assumed to explain the decrease in coercive field beyond a certain particle size. The justification for using Langevin theory of paramagnetism (including anisotropy energy) to fit the M vs H curve is discussed. The super-symmetric Hamiltonian approach is used to find out the relaxation time for the spins (making an angle greater than $90^0$ with applied field) at domain wall. The main advantage of our technique is that we can easily take into account the time of measurement as we usually do in realistic measurement.