Modeling of hysteresis in magnetic multidomains

In this paper, the analysis of multi-domain nanostructures is made by means of numerical approaches. The Landau–Lifshitz–Gilbert LLG equation is used to compute the magnetic hysteresis loops for different alternate scalar polarizations. The data computed are then used to identify the parameters of a phenomenological model, based on the extension of the Preisach model in 2-D. The identification in this case is the evaluation of the size and the position of the hysterons in the H-plane. Each hysteron is associated to a domain of the nanostructure and the assembly of hysterons reproduces with satisfactory accuracy the hysteretic behavior of the nanostructure computed by the LLG equation with an extremely reduced computational time. Some possible relationships between the magnetization nanostructure and the parameters of the hysteron are suggested. These relationship should be used for a “blind” prediction of the magnetization state of much larger magnetic structures, whose computation using the LLG equation is not possible in practice due to the enormous computational time, supposing that magnetic structures with the same aspect ratio exhibit a similar distribution of magnetic domains. The theory is applied here to an example of Permalloy nanostructure.