## 1 Introduction
For instance, it is expected that a region with down magnetization (\(\overset{\rightarrow}{m}\ \downarrow\)) submitted to a laser pulse with right-handed helicity (\(\sigma^{+}\ =\ +1\)) absorbs more energy than the same region with opposite magnetization (\(\overset{\rightarrow}{m}\ \uparrow\)), and vice versa for the opposite laser helicity (\(\sigma^{-}\ =\ -1\)). If the laser is linearly polarized (\(\sigma^{0}\ =\ 0\)), the absorption energy rate is the same for both up and down magnetic states. Therefore, a given helicity promotes the magnetization reversal whereas the other supports the initial state of the magnetization. Although some numerical studies have been performed to describe the role of the MCD in ferrimagnetic samples [17], no realistic numerical simulations based on MCD have been presented for ferromagnetic materials. Some theoretical trials have been presented in the past trying to describe the switching of the magnetization in these AOS processes. Those approaches include atomistic simulations [24] or solving the magnetic three temperatures model (M3 TM) coupled to a simplified dynamical equation [1; 25; 26]. However, a realistic evaluation of the role of the IFE and the MCD has not been carried yet. One of main reasons for the lack of such a realistic description is due to numerical limitations. Indeed, as the samples used for AOS are large, with sizes of hundreds of \(\upmu\)m\({}^{2}\), solving the full micromagnetic problem is a complicated task. Moreover, the involved time scales in these processes also differ over a wide range, going from the femtosecond scale of the laser pulses, the picosecond scale of the temperature evolution, and nanosecond scale for the magnetization dynamics and temperature dissipation to the substrate. Additionally, the temperature even exceeds the Curie temperature (\(T_{C}\)), and consequently, LLB equation must be numerically solved. This requires small time stepping, which makes the numerical problem even more time-consuming. To date, there has been no full micromagnetic simulator that takes into account all the physics involved in extended samples and consequently, a realistic description of available HD-AOS experiments is still missing. Therefore, it has not been possible to realistically elucidate the real role of the IFE and the MCD in helicity-dependent all-optical switching or domain wall motion processes, which is precisely the aim of the present work. Here, we present a full micromagnetic formalism based on a model that couples the laser heating, described by the two temperatures model (2 TM) [3, 12], to the magnetization dynamics governed by the stochastic LLB Equation [12, 27], which includes the transient magnetic field caused by the IFE and/or the different energy absorption rates due to the MCD. Our analysis reveals the scope of both effects in two different helicity-dependent experiments: switching and domain wall motion. Thus paper is structured into the following sections: in Section 2, we introduce the theoretical framework we have developed to model helicity-dependent all-optical processes. Section 3 presents our numerical results for the two mentioned problems. Section 3.1 analyzes the Helicity-Dependent All-Optical Switching (HD-AOS), where starting from a uniformly magnetic state, the switching by circular polarized laser pulses is evaluated. In Section 3.2, we studied the Helicity-Dependent Domain Wall Motion (HD-DWM). In both subsections, the role of the IFE or the MCD is studied in a separated manner, and the analysis allows us to check under which conditions these phenomena describe the experimental observations. The conclusions are exposed in Section 4.