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

Abstract

Reliably predicting bit-error rates in realistic heat-assisted magnetic recording simulations is a challenging task. Integrating the Landau-Lifshitz-Bloch (LLB) equation, within a coarse graining approach, can reduce the computational effort to determine the magnetization dynamics in the vicinity of the Curie temperature, compared to solving the atomistic Landau-Lifshitz-Gilbert equation. If the aim is that the dynamics of both approaches coincide, temperature dependent material functions, such as the zero-field equilibrium magnetization as well as the parallel and normal susceptibilities, must be modeled carefully in order to use them as input in the LLB equation. 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 ±40% and variations of the exchange constant of up to ±10%. Besides the temperature dependent material curves, computed switching probabilities also agree well with probabilities separately determined for each system. Our study suggests 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.