Mechanism of magnetization reversal

Magnetization reversal refers to the switching of magnetization between its initial and final remanent states under the influence of an externally applied magnetic field. To study the magnetization reversal we employ in situ MOKE (see Sec. 2.4.1) since the direction of the applied field can be varied more easily in MOKE compared to SQUID magnetometry.

The switching behavior was studied as a function of the angle of the in-plane applied field, θ_H measured with respect to the [332] axis. Figure 3.19(a) shows a set of MOKE loops for a 26-nm-thick Fe film. From SQUID magnetometry (not shown), the sample is well-known to exhibit a dominant four-fold magnetic anisotropy with a weak UMA. In fact, the anisotropy ratio r as determined from the fitting of the SQUID magnetization curves is about 0.6. Thus the easy axes are in the neighborhood of45^◦/135^◦in Fig. 3.19(a) (see Fig. 3.15). However, the anisotropy is not resolved in Fig. 3.19(a), since the sample is not completely saturated in all directions due to the low field available in our MOKE

Figure 3.20: (a) Plot of the coercive field, H_c as a function of the in-plane direction, θ_H of the applied field for the sample presented in Fig. 3.19(a) with uniaxial ratio r = 0.6.

(b) The simulated coercive fields as a function of θ_H for a uniaxial ratio r = 0.6 and 2K₁/M_s = 440Oe (see text).

set-up. Nevertheless, several important observations can be made from this figure:

1. The magnetization curve along the[332]and[110]axes exhibits one reversible jump, which we call a one-jump switching process.

2. The magnetization curve along [031] and some other intermediate directions shows two irreversible jumps, which we call a two-jump switching process.

3. The coercive field along [332] is larger compared to that along [110].

The angular dependence of the reversal process can be more clearly seen in Fig. 3.20(a), where the first and second coercive fields are plotted as a function of the in-plane direc-tion of the magnetic field, θ_H. As indicated, the behavior is distinguished into two regions depending on the two-jump (hatched) and one-jump (unhatched) switching process. The first coercive field Hc1 increases until 15^◦ and then decreases until 90^◦ with a symmetric behavior on the other side, i.e., between 90 to 180^◦. The second coercive field H_c2 ex-hibits a rapid increase from 15 to 90^◦ in the two-jump switching region and also has a symmetrical behavior.

The origin of the two-jump switching We are aware of two different kinds of expla-nation in literature for the two-jump switching in magnetic thin films. A first explaexpla-nation has been discussed in connection with Fe/GaAs system by Dabooet al.[3, 138] using the simple Stoner-Wohlfarth (SW) formulation. In this model, one can expect a two-jump switching depending on the exact values of θ_H and r. Using the SWM, Daboo et al.

obtained a qualitative agreement with the experiment though the exact value of the co-ercive field was not reproduced. The other explanation has been discussed in connection with ultrathin Fe films on Ag by Cowburn et al. [139, 140] by considering the domain

Figure 3.21: The evolution of local minima in the anisotropic energy of the Fe(113)-plane with the applied magnetic field for a uniaxial ratio of r = 0.6. The one-jump and two-jump switching process are demonstrated for (a) θH = 0^◦ and (b) θH = 45^◦. Here, 0^◦ indicates the [332] direction.

processes. Cowburn et al. assumed that depending on the field orientation, reversal can proceed either via a one-jump mechanism, (by the sweeping of 180^◦ domain walls) which results in a classic square hysteresis loop, or by a two-jump mechanism, (by the sweeping of 90^◦ domain walls) which results in a more unusual hysteresis loop with two irreversible transitions. By using the experimentally determined pinning energy, they obtain a quan-titative agreement of the switching field. In the following the simple SW formulation, will be shown sufficient to describe the experimental observations of Fig. 3.19(a).

First, we will provide some experimental evidence to show that the explanation of Cowburn et al. cannot be applied to our films. Their films also exhibit a dominant four-fold magnetic anisotropy with a small non-vanishing UMA. However, the easy axis of UMA in their case coincides with the bulk easy axes h100i, whereas in our samples the easy axis is along a non-easy axis of bulk Fe. The small UMA in our samples shifts the easy axes from the h031i axes towards the h332i axes. Thus the possible four domains are not perpendicular to each other. This could provide an unfavorable condition for the sweeping of 90^◦ domain walls. This is indeed the case in the experiment: the angular dependence of the second coercive field shows one maximum in our samples compared to two maxima in Fig. 6 of Ref [139]. Hence, the explanation of Cowburn et al. cannot be applied to the sample shown in Fig. 3.19(a).

However, it is possible to understand the experimental switching behavior of Fig. 3.19 and Fig. 3.20 by using the SWM. Figure 3.21 demonstrates how one-jump and two-jump

switching can arise from a calculation using the SW formulation by simply considering the anisotropy present in the sample. The figure shows the anisotropic anergy of the Fe(113) film [see Eq. (3.4)] for the magnetic field applied at an angle of 0and 45^◦, measured with respect to the [332] direction. The reversal process starts off with the magnetization sit-ting in the negative saturation energy minimum with an orientation close to the applied field direction as indicated by the solid circle (the so-called SW particle). At zero field, the magnetization switches to one of the nearest local minima as shown in the next plot.

As the field reverses this minimum becomes shallower and eventually disappears. At this point the magnetization undergoes an irreversible jump and falls into a different energy minimum. In the one-jump switching process (θ_H= 0^◦), this second minimum is the pos-itive saturation energy minimum, and the magnetization remains in this minimum as the applied field is swept towards the positive saturation. However, for a two-jump switching process (θ_H= 45^◦), a third intermediate energy minimum exists once the positive satura-tion minimum disappears, with the result that the magnetizasatura-tion falls into this minimum causing the first jump. However, as the field is further reversed, this intermediate min-imum also disappears and magnetization eventually ends up in the positive saturation energy minimum. Thus by following the local minimum we can calculate the hysteresis loops. These calculations, as shown in Fig. 3.19(b), indicate that the reversal process can proceed either by one or two jumps depending on the exact values of θ_H andr, and are in agreement with experiment. A clear qualitative agreement with experiment can be seen and the above mentioned three observations are well reproduced in the simulation. The angular dependence of the coercive fields also exhibits qualitatively similar behavior as shown in Fig. 3.20. However, the switching fields exhibit a large quantitative disagree-ment. The experimental switching field is smaller compared to that of the simulation, which was also observed for Fe/GaAs(001) system [3, 138]. As also discussed before, we attribute this difference to the detailed magnetic microstructure of the film which is not accounted for in the simple SWM.

Detailed thickness dependent calculations show good agrement with the experiment similar to that in Ref [138]. One-jump switching is predicted for dominant UMA, which agrees well with experiment. Two-jump switching is predicted only for r <1, depending on the orientation of the in-plane field. However, in some thicker films, we observe a two-jump switching when calculation predicts a one-two-jump switching. This was also reported by Daboo et al [138]. They ascribe the phenomena to a “non-ideal" two-jump switching process governed by the magnetic microstructure of the sample.