Numerical Simulations of Nano-Scale Magnetization Dynamics

The discovery of the giant magnetoresistance (Baibich et al., 1988) attracted much scientific interest to the magnetization dynamics at the nano-scale, which eventually led to the formation of a new field – spintronics – aiming to join the conventional charge transfer electronics with spin-related phenomena. The characteristics of spintronic devices (Žutic, Fabian & Das, 2004) are very attractive, including extremely small size (nanometer scale), fast response time and high operating frequencies (on the GHz domain), high sensitivity and vast spectrum of possible applications ranging from magnetic memories (based on magnetization reversal) to microwave generators (involving steady magnetization precession) (Kiselev et al., 2003). The design of these devices, together with the resolution of many problems required for full harvest of spin transport effects in traditional silicon-based semiconductor electronics, is greatly aided by theoretical studies and numerical simulations. For these, one should use adequate models describing magnetization dynamics at the desired scale. If we go down to atomic level, the modelling from first-principles is obligatory. Despite a huge progress in this field (and significant improvement of the computational power of modern equipment), these calculations are far from being real-time and can embrace only a limited amount of particles. Increasing the size of the computational cell to several nanometers, it is possible to introduce the micromagnetic modelling technique, for which every ferromagnetic particle is characterized by an average magnetic moment M. These moments can interact with each other by short and long range forces due to exchange coupling and dipole-dipole interactions. The evolution of the individual particle is governed by the Landau-Lifshitz-Gilbert (LLG) equation – a semi-classical approximation allowing to represent the time evolution of the magnetization vector M depending on applied magnetic fields and spin-polarized currents passing through the particle. Micromagnetics is a rapidly-developing field allowing tackling many serious problems (Fidler & Schrefl, 2000; Berkov & Gorn, 2006). It is far simpler to implement in comparison