2.4.1 Critical parameters for magnetization switching

Before starting to analyze specific kinds of switching processes, it is convenient to indicate what we mean with critical parameters. In this respect, let us refer to the case of switching with external magnetic fields. Generally, at time instant $t=0$, a field pulse is applied to realize switching. Referring for sake of simplicity to a rectangular pulse (see Fig. 2.5), we can say that our critical parameters are:

Figure 2.5: Design parameters for external field pulse amplitude.

• Applied field direction.
• Minimum field pulse amplitude $h_c$ to obtain successful switching.
• Minimum field pulse duration $T_p$ to obtain successful switching.
• Switching time, namely the time instant $T_s$ at which magnetization is approximately in the reversed orientation.

Generally, given an applied field direction, the critical pulse amplitude $h_c$ can be found as a function of material parameters $K_1,M_s$ and shape parameters $N_x,N_y,N_z$ (or equivalently coefficients $D_x,D_y,D_z$). Then, the time $T_p$, as well as the time instant $T_s$, will be a function of the field amplitude $h_c$. Next we report some recent results present in literature regarding two different ways to achieve magnetization switching: the so-called ``damping switching'' and ``precessional switching''. We refer to the derivations worked out in Refs. [26,27] for the former and in Refs. [28,35] for the latter. These results are very important since in chapter 3 we will demonstrate that some of them can be used to predict the values of control parameters in micromagnetic (non-uniform) simulations of switching processes for thin-films having spatial dimensions of technological interest.