Influence of grain size and exchange interaction on the LLB modeling procedure

TL;DR

This paper investigates how grain size and exchange interactions affect the modeling of magnetization dynamics using the LLB equation, demonstrating that scaling material functions with Curie temperature suffices for accurate predictions.

Contribution

The study shows that temperature-dependent material functions can be scaled with Curie temperature changes, avoiding recalculations for different grain sizes and exchange constants.

Findings

Material functions scale with Curie temperature for size and exchange variations.

Negligible errors for volume changes up to ±40% and exchange variations up to ±10%.

Switching probabilities remain consistent when scaling functions.

Abstract

Reliably predicting bit-error rates in realistic heat-assisted magnetic recording simulations is a challenging task. Integrating the Landau-Lifshitz-Bloch (LLB) equation can reduce the computational effort to determine the magnetization dynamics in the vicinity of the Curie temperature. If one aims that these dynamics coincide with trajectories calculated from the atomistic Landau-Lifshitz-Gilbert equation, one has to carefully model required temperature dependent material functions such as the zero-field equilibrium magnetization as well as the parallel and normal susceptibilities. We present an extensive study on how these functions depend on grain size and exchange interactions. We show that, if the size or the exchange constant of a reference grain is modified, the material functions can be scaled, according to the changed Curie temperature, yielding negligible errors. This is shown to be valid for volume changes of up to $\pm 40$ % and variations of the exchange constant of up to $\pm10$ %. Besides the temperature dependent material curves, computed switching probabilities also agree well with probabilities separately determined for each system. Our study suggest that there is no need to recalculate the required LLB input functions for each particle. Within the presented limits it is sufficient to scale them to the Curie temperature of the altered system.