## 3 Results
### Helicity-Dependent All Optical Switching (HD-AOS)
#### 3.1.1 Helicity-Dependent All Optical Switching with Inverse Faraday Effect
According to our results, we find transitions passing through non inversion (Figure 3b), single domain central switching (Figure 3c), multi-domain state surrounded by a ring (Figure 3c), and fully demagnetized state (Figure 3e), which reproduces the experimental results as a function of fluence for a given \(B_{MO}^{0}\). Therefore, our model could provide a realistic determination of the magnitude of \(\overset{\rightarrow}{B}_{MO}\) by direct comparison to experimental measurements. On the other hand, each laser pulse is usually applied every millisecond (ms) in experimental setups. With such a repetition rate (1 pulse per ms), it is possible to obtain images of the magnetic state after several ms. However, due to the limitation of the computing time, it is not possible to simulate such pulse repetition rates. Nevertheless, we also performed simulations changing the time between consecutive laser pulses (\(\Delta t_{L}\)) from 0.5 ns to 12 ns. For very fast repetition rates (\(\Delta t_{L}<\) 5 ns), the sample is not cooled down to 300 K after each pulse, but after five pulses, there is no more heat accumulation and the substrate extracts all the energy of the following pulses. This small substrate temperature increase does not change substantially the quantitative behavior. The results confirm that the phase diagram (Figure 3a) does not qualitatively depend on the separation between pulses. As expected, the inverted area increases as the separation time between consecutive pulses decreases, and it converges with the number of laser pulses (Figure 4a,b). Although the experiments show results for a very high number of pulses and pulse separation of several ms that cannot be simulated due to computing restrictions, our micromagnetic studies are still valid for comparison. Figure 4: (**a**) Inverted area (\(S_{int}\)) normalized to the area of the laser spot (\(S_{Laser}\ =\ \pi r_{0}^{2}\) with \(r_{0}\ =\ d_{0}/2\) being the FWHM laser radius) as a function of the number of pulses for several of the separation time between consecutive pulses (\(\Delta t_{L}\) ). (**b**) Normalized inverted area (\(S_{int}/S_{Laser}\) ) as a function of separation time (\(\Delta t_{L}\) ) between consecutive laser pulses. (**c**) Normalized inverted area (\(S_{int}/S_{Laser}\) ) as a function of the normalized delay time between the magneto-optical field and the laser duration (\(\tau_{d}/\tau_{L}\) ) for two different values of \(B_{MO}^{0}\). (**d**) Normalized inverted area (\(S_{int}/S_{Laser}\) ) as a function of the \(B_{MO}^{0}\) when the magneto-optical field and the laser duration are the same (\(\tau_{d}\ =\ 0\) ). Another IFE parameter which cannot be experimentally measured is the temporal delay (\(\tau_{d}\)) of the magneto-optical field \(\overset{\rightarrow}{B}_{MO}\) with respect to the laser pulse (see the temporal profile of the laser pulse Equation (1) and the corresponding one of \(\overset{\rightarrow}{B}_{MO}\) in Equation (10)). The theory of the IFE predicts the existence of the transient induced magneto-optic field, but its duration remains essentially unknown. However, the role of such delay can be easily evaluated in our numerical framework. To check the influence of the delay, we carried out simulations changing \(\tau_{d}\), and even assuming that the duration of the \(\overset{\rightarrow}{B}_{MO}\) is the same that the one of the laser pulse (\(\tau_{d}~{}=~{}0\)). As shown in Figure 4c, we verify that it is still possible to achieve HD-AOS in the absence of delay if the \(\overset{\rightarrow}{B}_{MO}\) reaches high enough values. We can conclude that although the quantitative values of the phase diagram presented in Figure 3 may differ depending on pulse duration (\(\tau_{L}\)), number of applied pulses and the delay of \(\overset{\rightarrow}{B}_{MO}\) (\(\tau_{d}\)), this IFE scenario predicts the existence of a fluence dependence of the switching and the appearance of four magnetic configurations which are usually found in the experimental literature (see, for example, Figure 1d or Figure 3b of Ref.