Ph.D. Thesis

Nonlinear Magnetization Dynamics in Thin-films and Nanoparticles

In chapter 1 the micromagnetic model and the Landau-Lifshitz-Gilbert (LLG) equation are introduced to describe magnetization phenomena in ferromagnetic bodies. First, an approach in terms of the free energy associated with the magnetic body is presented to derive the static equilibrium conditions for magnetization vector field. Then, the dynamic effects due to the gyromagnetic precession are introduced. Both Landau-Lifshitz and Landau-Lifshitz-Gilbert equation are presented. Phenomenological Gilbert damping is analyzed in terms of Rayleigh dissipation function.

In chapter 2 the study of magnetization dynamics in uniformly magnetized particles is addressed. In particular, first the static Stoner-Wohlfarth model and then magnetization switching processes are analyzed. In addition, novel analytical techniques to study magnetization dynamics under circularly polarized external fields and magnetization dynamics driven by spin-polarized currents are introduced and deeply discussed. In this respect, it is shown how some behaviors indeed observed in experiments, can be explained in terms of bifurcations of fixed points and limit cycles of the LLG dynamical system.

As a further step, in chapter 3, the assumption of magnetization spatial uniformity is removed and the problem of studying thin-films reversal processes of technological interest is addressed. In this respect, as preliminary step, the issue of the computation of magnetostatic fields, which is still the bottleneck of micromagnetic simulations, is illustrated together with the mostly used methods at this time. Then, a comparison of damping and precessional switching processes in thin-films is performed, showing that fast precessional switching can be considered spatially quasi-uniform and, therefore, its crucial aspects can be analyzed by means of uniform mode theory discussed in chapter 2. Finally, a uniform mode analysis is applied to the fast switching of granular tilted media which represents one of the most promising solutions for high density magnetic storage in future hard disks.

In chapter 4, the problem of the geometrical integration of LLG equation is considered. In particular, the mid-point rule time-stepping is applied to the LLG equation. In fact, it is shown that the fundamental properties of magnetization dynamics, embedded in the continuous model, are reproduced by the mid-point discretized LLG equation regardless of the time step. In addition, since the resulting numerical scheme is implicit, special and reasonably fast quasi-Newton technique is developed to solve the nonlinear system of equations arising at each time step. The proposed mid-point technique is validated on the micromagnetic standard problem no. 4 whichconcerns with thin-films reversal processes. Finally, numerical results and computational cost are discussed.