Micromagnetic simulation of size effects on the properties of ferromagnetic materials

Magnetic materials exhibit strikingly different performances at different length scales, especially when their sizes reach nanometer scale, such as ultra-thin films, at which their magnetic properties vary dramatically with the change in material length scale. In order to demonstrate such peculiar behaviour, a numerical simulation was carried out using a carefully devised model, in which the Landau-Lifshitz-Gilbert equation governs the evolution of magnetization. The simulation results clearly showed that there was a critical length at which the coercivity reached a maximum value. In addition, when the length scale was sufficiently small, for example, when it was comparable to or smaller than the exchange length, the phenomenon of coercivity almost vanished and the material was in the so-called superparamagnetic state. The effect of an external stress field on magnetic domain pattern was also taken into account in the present study. The former can affect the latter due to the coupling of the magnetization and elastic fields.