LLG relaxation

For problems where we are only interested in a static metastable magnetisation state -- i.e. those for which we do not need to know the coercive field value or indeed need the hysteresis loop -- these can be simply ``relaxed''. Relaxing the system involves defining some initial magnetisation configuration, usually homogeneous or random, and then allowing the system to iterate over the Landau-Lifshitz-Gilbert equation until the rate of change of magnetisation is below a certain threshold. The configuration, complete with any domains and states in which it might prefer to exist, can be observed and then the magnetic microstructure can be analysed. This should, of course, be repeated several times to verify that the remanent magnetisation states are consistent. Figure 2.9 shows the relaxation states of a 100nm $\times$ 100nm $\times$ 20nm supermalloy (79% nickel, 17% iron and 4% molybdenum) nanomagnet from our computations; virtually identical results can be seen in the paper by Cowburn (2000).

Figure 2.9: Cutplane showing the relaxed magnetisation from an edge-aligned initial state (left) and a diagonally-aligned initial state (right)