Extracting Individual Properties from Global Behaviour: First-order Reversal Curve Method Applied to Magnetic Nanowire Arrays

The behaviour of a group cannot be simply reduced to the sum of the behaviour of individuals (Le Bon, 1895). Examples abound in nature: school of fish or swarms of insect act like a single individual, but with emergent properties, i.e. properties which none of the individuals in the group possess, but which appear when these individuals are grouped into a system. A key element characterising a crowd is that the individuals should know that they are part of an ensemble (Le Bon, 1895). In other words, there must be interactions between them, on a short or long range. Otherwise they only constitute a system of several isolated individuals without emergent properties. Whatever the system, it is usually much easier to access its global behaviour, compared to the behaviour of individuals and their method of communication. However, the understanding of the global behaviour, in order to be able to control it subsequently, necessarily requires the knowledge of individual behaviour and of their interactions. According to these criteria, the magnetic behaviour of structures composed of magnetic entities embedded in a non-magnetic matrix must be considered as a crowd: entities "talking" to each other via exchange or dipolar interactions depending upon the distance that separates them. Therefore, the behaviour of the global (or collective) structure may differ from that of the local (or individual) entities. This difference will be accentuated in the presence of non-uniformity (geometric, structural, etc.) of the entities. To access the magnetostatic properties of a system (coercivity, remanence, interactions, etc.), one usually uses a magnetometer to measure the major hysteresis curve. It is possible to use the same experimental setup to obtain the local magnetostatic properties of the system, by measuring multiple minor hysteresis curves, called first-order reversal curves (FORC) (Mayergoyz, 1985). This technique can be particularly efficient and powerful in the case of highly interacting systems, like ferromagnetic nanowire arrays (Fig. 1). The large dipolar interaction field between the wires, associated with small interwire distance, strongly affects the overall array behaviour. Array properties (high anisotropy, resonance frequency in the gigahertz, etc.) make them promising candidates for high frequency devices (Saib et al., 2005), highdensity magnetic memories (Almawlawi et al., 1991; Ross, 2001) and sensors (Lindeberg &