## 3 Results
### Helicity-Dependent All Optical Switching (HD-AOS)
#### 3.1.1 Helicity-Dependent All Optical Switching with Inverse Faraday Effect  
We firstly evaluate if the IFE can reproduce the experimental observation for the different combinations of helicity and initial state of the sample. Therefore, here, the MCD is not taken into account and the results are obtained by assuming that the IFE is the only helicity-dependent phenomenon. Figure 2 shows transient magnetization snapshots of a sample with \(\ell\ =\ 12\) um submitted to a train of 25 laser pulses with \(\tau_{L}\ =\ 200\) fs. The IFE generates an effective magneto-optical field with \(B_{MO,MAX}\ =\ 5\) T, which has a delay of \(\tau_{d}\ =\ 400\) fs with respect to the laser power. The laser \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \(M_{S}\) (\(\frac{\mathrm{kA}}{\mathrm{m}}\)) & \(k_{a}\)(\(\frac{\mathrm{M}}{\mathrm{m}^{3}}\)) & \(A_{ex}\)(\(\frac{\mathrm{p}}{\mathrm{m}}\)) & \(D\)(\(\frac{m}{\mathrm{m}^{3}}\)) & \(K_{e}\)(\(\frac{W}{\mathrm{m}\cdot\mathrm{k}}\)) & \(\gamma_{e}\)(\(\frac{\mathrm{J}}{\mathrm{m}^{3}\mathrm{K}^{2}}\)) & \(C_{L}\)(\(\frac{\mathrm{M}}{\mathrm{m}^{3}\mathrm{K}}\)) & \(g_{e}\)(\(\frac{W}{\mathrm{m}^{3}\mathrm{K}}\)) & \(T_{C}\)(K) & \(\tau_{subs}\)(ns) \\ \hline
1.1 & 1.25 & 15 & 2.25 & 91 & 930 & 3.7 & \(6\times 10^{17}\) & 550 & 0.9 \\ \hline \end{tabular}
\end{table} 
Table 1: Micromagnetic and thermal parameters employed in the simulations. fluence is \(F~{}=~{}0.55\,\mathrm{J/m^{2}}\). It can be seen that after 25 pulses only the laser with helicity that creates a transient magneto-optic field (\(\overset{\rightarrow}{B}_{MO}\)) pointing in the opposite direction to the initial state, produces the local switching of the magnetization. This happens for \(\left(\overset{\rightarrow}{m}\uparrow,\sigma^{-}\right)\) (Figure 2b) and for \(\left(\overset{\rightarrow}{m}\downarrow,\sigma^{+}\right)\) (Figure 2c). No local switching is achieved for the rest of combinations \(\left(\overset{\rightarrow}{m}\uparrow,\sigma^{+}\right)\) or \(\left(\overset{\rightarrow}{m}\downarrow,\sigma^{-}\right)\)), where the final state is the same as the initial one (see last snapshots in Figure 2a,d). These results are in accordance with those published in [8], where a very large number of laser pulses were required to promote the HD-AOS. According to these micromagnetic results, the IFE is revealed as a possible cause of the AOS, qualitatively reproducing the experimental observations. Although the IFE scenario seems to be consistent with observations, the magnitude of the magneto-optical effective field (\(B_{MO}^{0}\)) or its delay with respect to the laser pulse (\(\tau_{d}\)) are difficult (if possible) to determine by experimental means. However, our numerical formalism allows us to evaluate the magnetization dynamics under laser pulses with both \(B_{MO}^{0}\) and \(\tau_{d}\) as being free input parameters. As the main uncertainty is in the value of \(B_{MO}^{0}\), which is essentially unknown in experimental setups, we have studied the HD-AOS dependence on \(F\) and \(B_{MO}^{0}\) under series of laser pulses with fixed delay (\(\tau_{d}~{}=~{}400~{}f\)s). The micromagnetic results are summarized in Figure 3, where the initial state is up \(\left(\overset{\rightarrow}{m}\uparrow\right)\) and the helicity is left-handed (\(\sigma^{-}\)), the one which generates a field \(\overset{\rightarrow}{B}_{MO}\propto-\overset{\rightarrow}{u}_{z}\) pointing in the opposite direction to the initial magnetic state, and consequently promotes the switching depending on \(F\) and \(B_{MO}^{0}\). Figure 2: Snapshots of the magnetization after different laser pulses for different combination of the initial state (\(\overset{\rightarrow}{m}\uparrow,\overset{\rightarrow}{m}\downarrow\)) corresponding to (**a**,**b**) and (**c**,**d**) respectively and laser helicities (\(\sigma^{+},\sigma^{-}\) ) corresponding to (**a**–**c**) and (**b**–**d**) respectively under the influence of the IFE (\(F~{}=~{}0.55\,\mathrm{J/m^{2}}\), \(B_{MO}^{0}~{}=~{}5\,\mathrm{T}\) ).