An Introduction to Micromagnetics in the Dynamic Regime

Abstract

This first review introduces the equations of magnetization dynamics, starting from the basic equations of quantum mechanics. The macrospin model is then considered, i.e. a model in which no spatial variation of magnetization is allowed for. General expressions for the frequencies and decrement rates of small magnetization oscillations are established. Within the macrospin model, the different behaviors of magnetization submitted to pulsed fields are investigated for a set of typical parameters. The existence of ballistic trajectories (the no-ringing case) is established. The first part ends with a description of magnetization dynamics based on a Lagrangian formalism. The second part deals with nonuniform magnetization distributions. After recalling the relevant equations for the dynamics of these structures, several results of numerical simulations in the case of submicron size rectangular Permalloy platelets are shown and discussed. The relevance of precessional motion for fast switching characteristics is emphasized. The concept of an apparent damping constant, derived from the temporal evolution of average quantities, is introduced. This apparent damping constant is always larger than the microscopic one. A procedure that checks the accuracy of the time integration of the Landau-Lifshitz-Gilbert equation is described, in which the microscopic damping constant is systematically recalculated. Following an initial quasi-coherent rotation of the magnetization, simulation results reveal the development of large amplitude magnetization waves, which bear some analogy to the spin waves that exist in such confined structures.