## 2 Micromagnetic Model
Some experiments suggest that the energy absorption rate of a PMA ferromagnetic sample depends on the its magnetic state (up \(\overrightarrow{m}\)\(\uparrow\) or down \(\overrightarrow{m}\)\(\downarrow\)), and its energy absorption rate may be different for right (RC, \(\sigma^{+}\)) and left (LC, \(\sigma^{-}\)) circular polarizations [10]. To model the MCD we consider that the up state (\(\overrightarrow{m}\)\(\uparrow\)) absorbs more power from the laser pulse for the left-handed polarization than for the right-handed circular polarizations. The opposite happens for the down state (\(\overrightarrow{m}\)\(\downarrow\)). We characterize this different absorption rate by the MCD coefficient, defined as [17]  
\[\mathrm{MCD}(\%)~{}=~{}\frac{A_{LC}-A_{RC}}{A_{LP}}\times 100 \tag{11}\]  
where \(A_{i}\) with \(i:LC,RC,~{}LP\) are dimensionless parameters representing the absorption rate for left-handed circular (\(\sigma^{-}\)), right-handed circular (\(\sigma^{+}\)) and linear polarizations of the laser pulse respectively. MCD is included in Equation (2) by the coefficient \(\eta\)(\(\overrightarrow{m},\sigma\)), which accounts the different absorption rates depending on the laser polarization and the magnetic state. Typically, MCD is a function of frequency obtained by ellipsometry measurements that leads to MCD(\(\%\)) values of some units [17; 36]. In our micromagnetic model, as \(\overrightarrow{m}\)(\(\overrightarrow{r},t\)) is a continuous function of position and time, we assume a linear dependence with the out-of-plane component (\(m_{z}\)) as follows:  
\[\eta\)(\(\overrightarrow{m},\sigma\)) = \(A_{LP}[1-\sigma^{\pm}~{}m_{z}~{}\mathrm{MCD}(\%)] \tag{12}\]  
where \(\sigma^{\pm}~{}=~{}\pm 1\). The function \(\eta\)(\(\overrightarrow{m},\sigma\)) represents the variation of power absorption from the circularly polarized laser relative to the absorption for the linearly polarized laser pulse (\(A_{LP}\)). For example, a region with \(m_{z}~{}=~{}+1\) has a minimum absorption for right-handed (\(\sigma^{+}\)) pulses (\(\eta\)(\(+1,\sigma^{+}\)) = \(A_{LP}[1-\mathrm{MCD}(\%)]\)), and a maximum absorption for left-handed (\(\sigma^{-}\)) pulses (\(\eta\)(\(+1,\sigma^{-}\)) = \(A_{LP}[1+\mathrm{MCD}(\%)]\)). The absorption rate is linear with \(m_{z}\), which varies from \(-1\) to \(+1\). In the present work, we simulate a Pt/Co bilayer on top of a Silicon wafer. A square-shape thin film Co layer of side \(\ell\) and thickness \(t_{FM}\) with high PMA is submitted to a train of laser pulses of full width at half power of \(d_{0}~{}=~{}\ell/2\). For the simulations, we adopted typical thermal and micromagnetic parameters for a Pt/Co bilayer. These inputs are collected in Table 1. \(\ell\) was varied from \(1.5~{}\upmu\)m to \(12~{}\upmu\)m to check the dependence with the size of the laser beam. Disorder was taken into account in the form of grains, with a random a variation of the easy-axis direction of the PMA of \(\pm 3^{0}\) from grain to grain, being \(15~{}\mathrm{nm}\) the characteristic grain size [37]. The Co layer was discretized using a finite difference scheme. The in-plane size of the computational cells is \(\Delta x\ =\ \Delta y\ =\ 3\) nm, while \(\Delta z\ =\ 0.8\) nm coincides with the thickness of the Co layer (\(t_{FM}\)). Micromagnetic simulations, solving Equations (2) and (3) simultaneously, were performed by using a Heun integration scheme with an adaptive time step: during each laser pulse, which is \(\tau_{L}\ =\ 200\) fs long, the time step was set to \(\Delta t\ =\ 1\) fs. Once each laser pulse is turned off, the time step was enlarged to \(\Delta t\ =\ 25\) fs to speed up the computations. Several tests were performed with reduced cell sizes and time steps to ensure the numerical validity of the presented results.