## 3 Results
### Helicity-Dependent All Optical Switching (HD-AOS)
#### 3.1.2 Helicity-Dependent All Optical Switching with Magnetic Circular Dichroism  
In the previous subsection, we have verified that a realistic numerical framework considering the laser heating and the IFE can reproduce the experimental observations of the HD-AOS. Now, we study if the MCD can lead by itself to optical magnetization switching, using the proper combinations of initial magnetization and helicity. After an adequate choice of the fluence and MCD parameters, we plot the snapshots of the magnetization under the same train of pulses as used for the previous IFE analysis. The corresponding results for the four different combinations of the initial magnetic state (\(\overset{\rightarrow}{m}\uparrow\) or \(\overset{\rightarrow}{m}\downarrow\)) and the laser pulse helicity (\(\sigma^{+}\) or \(\sigma^{-}\)) are shown in Figure 5. Note that in this section the micromagnetic results do not take into account the IFE, and only the MCD is evaluated. Figure 5: Magnetization snapshots after several pulses under the influence of the MCD. Results are shown for right-handed (\(\sigma^{+}\)) (**a**) and (**c**) and left-handed (\(\sigma^{-}\) ) (**b**) and (**d**) circular polarization of the laser beam, and initial magnetic states pointing up (\(\overset{\rightarrow}{m}\uparrow\) ) (**a**) and (**b**) or down (\(\overset{\rightarrow}{m}\downarrow\) ) (**c**) and (**d**). The fluence and the MCD absorption rate are \(F~{}=~{}0.5\) J/m\({}^{2}\) and MCD = 10% respectively. A video of these HD-AOS is provided as Supplementary Material (video S1). The results presented in Figure 5 (where the MCD is set on, and the IFE is off) are similar to the ones presented in Figure 2 (where the IFE was set on, and the MCD off). Therefore, the analysis suggests that it is still possible to obtain qualitatively similar final states by IFE and MCD. However, some discrepancies between the final states obtained by IFE and MCD were noticed. If the MCD were the main mechanism of the HD-AOS processes in the evaluated samples, the switching seems to be less clear than in the IFE scenario, with higher noise in the central part under the laser beam. In any case, the MCD seems to be also a valid mechanism that can describe the AOS observations. This is even clearer if we consider the phase diagram where we vary the fluence and the MCD absorption rate. The corresponding MCD phase diagram is shown in Figure 6a. Considering the MCD as the only responsible mechanism for the HD-AOS, the final states are similar to those of IFE, with regions that present no inversion (Figure 6b), central inverted domains (Figure 6c) and central multi-domain states, with (Figure 6d) or without (Figure 6e) the surrounding inverted ring. The main difference with respect to the IFE scenario is the small area that corresponds to the central inversion, which appears only over a fluence threshold of about \(F~{}=~{}0.5\,\mathrm{J/m^{2}}\) independently on the MCD rate. We confirmed that such abrupt transition at \(F~{}=~{}0.5\,\mathrm{J/m^{2}}\) occurs when the central part of the sample overcomes \(T_{C}\) during each laser pulse. In this case, the inversion mechanism is probabilistic: non inverted domains absorb more energy, and as the local temperature decreases again under \(T_{C}\) once the laser pulse is turned off, they may magnetize randomly either up or down. As the regions magnetized down absorb less power from the laser beam, they present less probability of another demagnetization than those with already up magnetization. Additionally, the external part of the sample that remains magnetized up produces a dipolar field that aids to the remagnetization in the down configuration. For higher fluences (\(F>0.5\,\mathrm{J/m^{2}}\)) the thermal noise increases, and the region where temperature passes through \(T_{C}\) presents a random multi-domain magnetization. The external region, with lower temperature, and therefore smaller thermal noise, presents an inverted region, leading to similar states as those obtained from the IFE scenario.