3.2 Comparison between Damping and Precessional switching in magnetic thin-films

We have seen in section 2.4.2 that traditionally, magnetization reversal in thin films is realized by applying a sufficiently large magnetic field almost antiparallel to the initial magnetization state and that the resulting reversal dynamics is driven by dissipative processes. This kind of switching is referred to as damping switching in literature [26,27].

Figure 3.2: Sketch of the thin-film geometry.

Nevertheless, as seen in section 2.4.3, the possibility of using precessional motion of magnetization to realize the switching of thin films and particles has been recently investigated [34,37,68]. In this kind of switching, referred to as precessional switching [28], the in-plane external field is approximately orthogonal to the initial magnetization state and produces a torque that drives precessional motion of magnetization; this results in a faster and less energy-consuming magnetization dynamics. Magnetization reversal is realized by switching the external field off precisely when precession has brought the magnetization state close to its reversed orientation. Therefore, the applied field pulse duration has to be carefully chosen, while in damping switching there is no such need. Although it is generally desired that thin films and nanoelements in magnetic storage devices are in almost uniform magnetization states, both conventional switching and precessional switching are nonuniform dynamic processes. Here, we investigate the switching process of a permalloy magnetic rectangular thin-film: the thickness is $c=5$ nm, the major and mean edge length are respectively $a=500$ nm and $b=250$ nm (see Fig. 3.2). The thin-film medium has a uniaxial magneto-crystalline anisotropy whose easy axis is along the x-axis (long axis), the uniaxial anisotropy constant is $K_1=2\times10^3$ J/m$^3$, the exchange stiffness constant is $A=1.3\times 10^{-11}$ J/m, the saturation magnetization $M_s\approx795$ kA/m (such that $\mu_0 M_s=1$ T) and the damping constant is $\alpha =0.02$; the exchange length of the material, defined by Eq. 1.92, is

$$l_ =\sqrt{\frac{2A}{\mu_0M_s^2}}=5.7160 \quad.$$ (3.19)

We assume that magnetization dynamics of the thin-film is described by the Landau-Lifshitz-Gilbert equation (1.83), namely:

$$\frac{\partial \textbf{M}}{\partial t} =-\gamma \textbf{M}\times\... ...ac{\alpha}{M_s} \textbf{M}\times\frac{\partial \textbf{M}}{\partial t} \quad,$$ (3.20)

where $\textbf{H}_{\text{eff}}$ is the effective field defined by Eq. (1.68)

$$\textbf{H}_{\text{eff}}\left(\textbf{M}(\cdot)\right) = {\mathbf{H}_\text{m}} +\mathbf{H}_{\text{exc}}+\mathbf{H}_{\text{an}}+\mathbf{H}_a \quad,$$ (3.21)

Figure 3.3: (a) Conventional (damping) switching process. (b) Precessional switching process.

which includes the applied field $\mathbf{H}_a$, the exchange field $\mathbf{H}_$exc, the anisotropy field $\mathbf{H}_$an and the magnetostatic (demagnetizing) field $\mathbf{H}_m$, as seen in section 1.2.2. In micromagnetic simulations, the numerical time integration of Eq. (3.20) is performed by using a backward differentiation formula [69]; the spatial discretization is done using the finite element method [52] with a mesh consisted of tetrahedrons; the mesh is finer near the corners of the thin-film (mesh edge length $=5$ nm$<l_$exc) where a stronger accuracy is required for the computation of magnetostatic field. The hybrid finite element boundary element method [70], discussed in section 3.1.2, is used to solve the magnetostatic problem. All the numerical simulations that we will present in this section have been performed with the parallel code MAGPAR [73] developed by W. Scholz at Vienna University of Technology [80]. First, we perform micromagnetic simulations of conventional (damping) and precessional switching process for the thin-film. Initially, the thin-film is saturated along the $y$ direction and then relaxed, by switching the external field off, to the remanent C-state (see Fig. 3.4, on the right), which is one of the equilibrium configurations really observed in experiments on magnetic thin-films^3.2. At time $t=0$ the external field is applied, respectively antiparallel and orthogonal to the easy axis, as sketched in figure 3.3. We compare two aspects of the switching processes: the switching speed and the uniformity of the magnetization during the reversal process.

Figure 3.4: Numerical results. Remanent states of magnetic thin-film. (left) S-state. (right) C-state.