# Energy barriers in three-dimensional micromagnetic models and the physics of thermo-viscous magnetization in multidomain particles

## TL;DR

This paper presents a micromagnetic model and a new computational method to analyze viscous remanent magnetization in particle ensembles, explaining stability and acquisition dynamics in paleomagnetic studies.

## Contribution

It introduces a fast relaxation algorithm combining nudged elastic band and action minimization to compute energy barriers in micromagnetic particles.

## Key findings

- Identified 60 local energy minima and calculated all energy barriers between them.
- Estimated energy barriers in weak external fields for VRM transition matrices.
- Demonstrated that VRM acquisition can overshoot and occur faster than decay in PSD particles.

## Abstract

A first principle micromagnetic and statistical calculation of viscous remanent magnetization (VRM) in an ensemble of cubic magnetite pseudo single-domain particles is presented. This is achieved by developing a fast relaxation algorithm for finding optimal transition paths between micromagnetic local energy minima. It combines a nudged elastic band technique with action minimization. Initial paths are obtained by repetitive minimizations of modified energy functions. For a cubic pseudo-single domain particle, 60 different local energy minima are identified and all optimal energy barriers between them are numerically calculated for zero external field. The results allow to estimate also the energy barriers in in weak external fields which are necessary to construct the time dependent transition matrices which describe the continuous homogeneous Markov processes of VRM acquisition and decay. By spherical averaging the remanence acquisition in an isotropic PSD ensemble was calculated over all time scales. The modelled particle ensemble shows a physically meaningful overshooting during VRM acquisition. The results also explain why VRM acquisition in PSD particles can occur much faster than VRM decay and therefore can explain for findings of extremely stable VRM in some paleomagnetic studies.