Nanomagnetism

An overview is presented of the methods used to describe the behaviour of ferromagnetic materials on small spatial scales. Methods based on energy minimisation (micromagnetics) are discussed. It is shown that these methods naturally identify a characteristic length (exchange length) that controls the insurgence of phenomena that are inherent to nanomagnetism. It is then shown how the previous methods can be extended to dynamical conditions by introducing the Landau-Lifshitz equation for magnetization dynamics. The characteristic time, field, and energy scales associated with this description are discussed. Finally, the extension of dynamical methods to the description of spin-transfer-driven magnetization dynamics is discussed. It is shown that in this case one can take important advantage of the equivalence between the dynamics of interest and general aspects of nonlinear dynamical system theory. This equivalence permits one to identify properties of the dynamics that are particularly robust in nature because they are the consequence of general geometrical and topological constraints that the magnetization state space imposes on the dynamics.