## 2 Micromagnetic Model
The LLB Equation (3) also includes stochastic terms \(\overrightarrow{H}_{th}\) and \(\overrightarrow{H}_{th}\) to account for stochastic fluctuations due to the thermal noise [27]. The first one (\(\overrightarrow{H}_{th}\)) is a random thermal field orthogonal to the local magnetization, whereas the second one (\(\overrightarrow{H}_{th}\)) describes the longitudinal noise, parallel to the local magnetization. Their statistical properties are summarized by  
\[ \begin{array}{c}H_{i}^{\bot}(t)~{}=~{}0\\ H_{i}^{\bot}(\overrightarrow{r},t)H_{j}^{\bot}(\overrightarrow{r}^{\prime},t^ {\prime})~{}=~{}\frac{2k_{B}T(\pi_{(}\pm\alpha_{1})\mu_{0})}{\gamma_{0}^{ \ast}\gamma_{0}^{\ast}\
abla_{x}^{2}}\delta_{ij}\delta(t-t^{\prime})\delta( \overrightarrow{r}-\overrightarrow{r}^{\prime})\\ H_{i}^{\|}(t)~{}=~{}0\\ H_{i}^{\|}(\overrightarrow{r},t)H_{j}^{\|}(\overrightarrow{r}^{\prime},t^ {\prime})~{}=~{}\frac{2\gamma_{0}^{\ast}T_{2}\delta_{ij}}{\Lambda_{0}^{\ast }\
abla_{x}^{2}}\delta_{ij}\delta(t-t^{\prime})\delta(\overrightarrow{r}- \overrightarrow{r}^{\prime})\\ H_{i}^{\bot}(\overrightarrow{r},t)H_{j}^{\|}(\overrightarrow{r}^{\prime},t^ {\prime})~{}=~{}0\end{array}  \tag{8}\]  
In these expressions, the notation \(\cdots\) indicates the average over different stochastic realizations of the noise, and the sub-indexes are the Cartesian components, \(i,j:x,y,z\). \(V\) is the volume of the computational cell (see [32] for details). By solving Equations (2) and (3) we can obtain the dynamical behavior of the magnetization as a function of temperature in a self-consistent way. However, some other phenomena need to be considered when circularly polarized laser pulses are applied. IFE or MCD are taken into account in the micromagnetic formalism as follows:  
(a) _Inverse Faraday Effect_ (IFE). The generation of a magnetic field from a circularly polarized laser beam has been demonstrated experimentally [33] by measuring the amplitude of magnetic precession under different helicities. Theoretically, the IFE [34] predicts the existence of an optically induced magnetic field which can be described as  
\[\overrightarrow{B}_{MO}\Big{(}\overrightarrow{r},t\Big{)}~{}=~{}\mu_{0} \overrightarrow{H}_{MO}\Big{(}\overrightarrow{r},t\Big{)}~{}=~{}(\alpha^{ \pm})B_{MO}^{0}~{}f_{MO}\Big{(}\overrightarrow{r},t\Big{)}\overrightarrow{u} _{z} \tag{9}\]where \(B^{0}_{MO}\) determines the maximum value of the \(\overrightarrow{B}_{MO}\)(\(\overrightarrow{r},t\)), which occurs at \(t~{}=~{}t_{0}\) in the center of the laser spot. This field points along the out-of-plane direction (\(\overrightarrow{u}_{z}\)) and its sense, either positive or negative, is imposed by the helicity of the laser helicity: \(\sigma^{+}~{}=~{}+1\) for right-handed (RC), and \(\sigma^{-}~{}=~{}-1\) for left-handed (LC) circular polarizations. The space-temporal dependence of the magneto-optical field is described by the function \(f_{MO}\)(\(\overrightarrow{r},t\)):  
\[f_{MO}\)(\(\overrightarrow{r},t\)) = \left\{ \begin{array}{ll}\exp\biggl{[}-\frac{r^{2}}{d_{0}^{2}/(4 \ln 2)}\biggr{]}\exp\biggl{[}-\frac{(t-t_{0})^{2}}{\tau_{L}^{2}/(4\ln 2)} \biggr{]},&\qquad t<t_{0}\\ \\ \exp\biggl{[}-\frac{r^{2}}{d_{0}^{2}/(4\ln 2)}\biggr{]}\exp\biggl{[}-\frac{(t-t_{0}) ^{2}}{(\tau_{L}+\tau_{d})^{2}/(4\ln 2)}\biggr{]},&\qquad t>t_{0}\end{array} \right. \tag{10}\]  
with \(\tau_{d}\) accounts for the possible delay of the magneto-optical field decay with respect to the power of laser pulse [3; 35]. According to the theoretical description of the IFE, the magnitude \(B^{0}_{MO}\) should be related to the laser fluence \(F\) and that IFE susceptibility \(\chi_{IFE}\). However, as it is difficult to infer \(\chi_{IFE}\) from first principles or measure it from experimental means, in the present study, we assume that \(F\) and \(B^{0}_{MO}\) are independent parameters. (b) _Magnetic circular Dichroism_ (MCD).