3.2.2 Spatial Magnetization uniformity

As far as the uniformity of magnetization is concerned, we consider a very simple indicator $u(t)$, given by the sum of the square values of the average magnetization components

$$u(t)=<m_x(t)>^2+<m_y(t)>^2+<m_z(t)>^2 \quad,$$ (3.23)

where the symbol $<\cdot>$ means spatial average. The indicator $u(t)$ is useful to check the spatial uniformity of magnetization as function of time, that is, during the reversal process. The results are reported in Fig. 3.6.

Figure: Numerical results. Plot of the uniformity indicator $u$ vs time in the interval $(0,t_0)$ for damping (right) and precessional switching (left). The external field is $H_a=19.51$ kA/m.

One can easily observe that precessional switching is a quasi-uniform process, because the sum of the square values of the average magnetization components remain almost constant during time and close to unity, whereas for damping switching it decreases rapidly towards zero, showing the occurring of domain nucleation and domain wall motion. In fact, the spatial behavior of magnetization vector field, at given time instants, is depicted in Fig. 3.7 for the case of damping switching. One can clearly observe that the nucleated domains at the ends of the thin-film enlarge during time, giving rise to the so-called head-to-head configuration involving the motion of two domain walls. At the end of the process the two walls collapse and determine again a quasi-uniform configuration with average orientation in the opposite direction to the initial one. In this way the switching is realized. The spatial behavior of magnetization is reported in Fig. 3.8 for the case of precessional switching. One can clearly observe that rather than domain wall motion, coherent rotation can be observed, that is, the magnetization rotates almost at the unison, driven by the magnetic torque produced by the applied field. This kind of motion recalls the term ``quasi-ballistic'' used in Ref. [68] to describe precessional switching.

Figure: Numerical results. Screenshots of magnetization vector field during reversal for damping switching. The external field is $H_a=19.51$ kA/m.

Figure: Numerical results. Screenshots of magnetization vector field during reversal for precessional switching. The external field is $H_a=19.51$ kA/m.

Thus we can conclude that for precessional switching, in our case of thin-film medium, one can reasonably apply the uniform mode theory to predict the duration of the external field pulse, which is necessary to achieve successful switching, as described in section 2.4.3.