Dynamic approach for micromagnetics close to the Curie temperature

TL;DR

This paper demonstrates that the Landau-Lifshitz-Bloch equation more accurately models magnetization dynamics near the Curie temperature than the traditional Landau-Lifshitz-Gilbert equation, accounting for variable magnetization magnitude and enhanced damping.

Contribution

The study introduces the Landau-Lifshitz-Bloch equation as a superior alternative to LLG for high-temperature micromagnetic simulations, incorporating effects of critical phenomena.

Findings

Conventional micromagnetism fails near the Curie temperature.

Enhanced damping observed approaching the Curie temperature.

Magnetization magnitude varies over time at elevated temperatures.

Abstract

In conventional micromagnetism magnetic domain configurations are calculated based on a continuum theory for the magnetization which is assumed to be of constant length in time and space. Dynamics is usually described with the Landau-Lifshitz-Gilbert (LLG) equation the stochastic variant of which includes finite temperatures. Using simulation techniques with atomistic resolution we show that this conventional micromagnetic approach fails for higher temperatures since we find two effects which cannot be described in terms of the LLG equation: i) an enhanced damping when approaching the Curie temperature and, ii) a magnetization magnitude that is not constant in time. We show, however, that both of these effects are naturally described by the Landau-Lifshitz-Bloch equation which links the LLG equation with the theory of critical phenomena and turns out to be a more realistic equation for magnetization dynamics at elevated temperatures.