## 4 Conclusions  
We presented a micromagnetic model based on the LLB equation and the 2 TM which also takes into account the IFE and MCD phenomena and allows us to evaluate their real scope in different helicity-dependent all-optical processes. Numerical simulations suggest that helicity-dependent all-optical switching (HD-AOS) in ferromagnetic systems with high PMA can be qualitatively consistent with both IFE and MCD scenarios, which both indicate that the final magnetic state depends on the laser helicity and the initial magnetic state. However, some discrepancies between IFE and MCD results were evidenced. In the IFE scenario, the magnitude of the magneto-optical field needed to promote a single reversed domain decreases as the laser fluence increases. On the contrary, there is a minimum fluence to promote the switching which is independent on the energy absorption rate in the MCD scenario. We also detected a size expansion of the reversed domain with the number laser pulses in the IFE scenario. This expansion is not present when the HD-AOS processes are evaluated in the framework of the MCD scenario. Although the final magnetic states presented in the MCD phase diagram seem to be similar to the ones in the IFE diagram, the numerically required MCD absorption rates (MCD-10%) appears to be significantly higher than the ones expected from experiments (MCD-1%). The role of the IFE and the MCD has been also evaluated to describe the helicity-dependent DW motion (HD-DWM). In this case, only IFE results are consistent with experimental observations, where the DW is only displaced from its initial location for the correct combination of the relative laser spot location and helicity. On the contrary, the MCD hardly affects the DW position for any of the two circular polarizations of the laser pulses. Indeed, MCD results for both laser helicities (circular polarization) are similar to the ones obtained for linear polarization, where the only effect of the laser pulse is the generation of thermal gradients, which were not sufficient to promote any DW motion in the present analysis. Based on these results, we conclude that the IFE has a dominant role over the MCD to describe the helicity-dependent all-optical manipulation of magnetization in ferromagnetic thin films with perpendicular anisotropy. We believe that our methods can be useful in the next future when estimating the value of some parameters, as the ones related with inverse Faraday effect, which remain essentially unknown nowadays. Figure 8: Initial and final snapshots of the magnetization of a sample with down and up domains separated by a domain wall. The final magnetic state is obtained after 100 laser pulses of \(\tau_{L}~{}=~{}200\) ps. A MCD absorption rate of 10% is considered for both circular polarizations (top (\(\sigma^{-}\) ) and bottom (\(\sigma^{+}\) ) graphs). The case of linear polarization (MCD = 0) is depicted in bottom graphs. Red dotted circles indicate the location of the laser beam. The in-plane sample size is 1.5 \(\upmu\)m \(\times\) 1.5 \(\upmu\)m and the center of laser spot is displaced 192 nm to the left (**a**) or to the right (**b**) of the DW. **Supplementary Materials:** The following are available online at [[http://www.mdpi.com/2076-3417/10/4/1307/s1](http://www.mdpi.com/2076-3417/10/4/1307/s1)]([http://www.mdpi.com/2076-3417/10/4/1307/s1](http://www.mdpi.com/2076-3417/10/4/1307/s1)), **Video S1:** Comparison of temporal magnetization evolution of the HD-AOS for the IFE and the MCD scenarios under 25 laser pulses. Up and down initial states and right-handed and left-handed circular polarization are evaluated in both cases. **Video S2:** Comparison of the HD-DWM for the IFE and the MCD scenarios. Right-handed and left-handed circular polarization, and two different locations of the laser spot (either at the left side or the right side of the down-up DW) are presented for both IFE and MCD simulations. **Author Contributions:** [PERSON] and [PERSON] proposed and coordinated the research project.