Scaling Magnetic Systems

It is often very useful to be able to take an existing magnetic design and scale it up or down in size without having to expend large computational resource recalculating a new solution. If a suitable scaling rule can be found, the dimensionality of the design space can be reduced by at least one and the computational effort reduced-possibly by a large factor. This paper explores scaling rules that can be applied to electromagnetic systems in general and, in particular, to magnetic systems modeled by the Landau-Lifshitz-Gilbert and/or the Arrhenius-Néel formulations. Simple scaling rules are found to exist for various situations. These generally involve scaling not only the physical dimensions but also the time-scale and electrical and magnetic properties of the materials. There is one scaling scenario that preserves the energies of all the elements in the system. This “constant-energy´ scaling is very relevant to superparamagnetic systems since all the energy barriers remain fixed. Modern magnetic recording media is approaching the superparamagnetic limit.