Numerical Simulations of Ferromagnetic Materials

In this article, we give a glimpse on our last works in simulation of ferromagnetism phenomena. The main problems encountered in this type of computation are the demagnetization field and the microwave susceptibility computations. Difficulties for the demagnetization field come principally form the fact that the operator is nonlocal and the discretized operator gives a full matrix, we will focus here on the periodic case ; the microwave susceptibility computation requests the resolution of many ill-conditionned linear systems. Résumé. Dans cet article, nous présentons des travaux récents concernant la simulation de phénomènes ferromagnétiques. Les principaux problèmes rencontrés sont le calcul du champ démagnétisant et de la susceptibilité. En ce qui concerne le calcul du champ démagnétisant, il s’agit de discrétiser un opérateur non-local. Nous nous concentrerons sur le cas périodique. Quant à la susceptibilité, il s’agit ici de résoudre plusieurs systèmes linéaires mal conditionn és. Mathematics Subject Classification. 35Q60,65Z05. Introduction Ferromagnetic materials are of high importance for applications, they are used, for example, in nano electronic, telephony or magnetic data recording. All these applications needs the creation of expensive samples whose have long time processes f built. Then, in order to optimize these objects, if becomes necessary to be able to simulate the behavior of magnetic objects before their effective conception. When simulations of static and dynamic sates are acquired, the comparison with experiments is a crucial point. It is solved by computing the microwave susceptibility the magnetic objects. In this article, we will remind quickly the notion microwave susceptibility. The model used in this article for ferromagnetism is the micromagnetism, introduced by W.-F. Brown in 60’. This model, based upon a thermodynamic analysis of the ferromagnetism phenomena, can be modelized using a static approach or a dynamic approach. In fact, at least formally, the time asymptotic solutions of the dynamical approach are local minimizers of the energy used in the static approach. In a first part we will give a quick reminder of the micromagnetism problem (see also [2,4,5]). In a second part we will recall the principles of the dynamic simulation [6, 9] and of the magnetostatic computation in the nonperiodic and periodic case [3,7]. The last part will be dedicated to the microwave susceptibility computations [8] and particularly to the strategy adopted to treat the ill-conditionning of the systems to solve for each frequence.