Stochastic ferrimagnetic Landau-Lifshitz-Bloch equation for finite magnetic structures

TL;DR

This paper introduces a stochastic, coarse-grained Landau-Lifshitz-Bloch model for finite-sized ferrimagnetic nanoparticles, accurately capturing temperature effects and magnetization dynamics efficiently compared to atomistic simulations.

Contribution

The authors derive a stochastic ferrimagnetic LLB equation incorporating temperature-dependent susceptibilities and an intergrain exchange field, enabling fast, accurate modeling of finite ferrimagnetic structures.

Findings

Model accurately simulates 5x10 nm² ferrimagnetic particles.

Trajectories agree with atomistic LLG simulations.

The simplified model matches detailed atomistic results.

Abstract

Precise modeling of the magnetization dynamics of nanoparticles with finite size effects at fast varying temperatures is a computationally challenging task. Based on the Landau-Lifshitz-Bloch (LLB) equation we derive a coarse grained model for disordered ferrimagnets, which is both fast and accurate. First, we incorporate stochastic fluctuations to the existing ferrimagnetic LLB equation. Further, we derive a thermodynamic expression for the temperature dependent susceptibilities, which is essential to model finite size effects. Together with the zero field equilibrium magnetization the susceptibilities are used in the stochastic ferrimagnetic LLB to simulate a $5\times10$ nm$^2$ ferrimagnetic GdFeCo particle with 70 % FeCo and 30 % Gd under various external applied fields and heat pulses. The obtained trajectories agree well with those of an atomistic model, which solves the stochastic Landau-Lifshitz-Gilbert equation for each atom. Additionally, we derive an expression for the intergrain exchange field which couple the ferromagnetic sublattices of a ferrimagnet. A comparison of the magnetization dynamics obtained from this simpler model with those of the ferrimagnetic LLB equation shows a perfect agreement.