## 2 Micromagnetic Model
In this case, the dynamics of the normalized magnetization is given by the equation [29]:  
\[\frac{d\overrightarrow{m}\left(\overrightarrow{r},t\right)}{dt}\ =\ -\gamma_{0}^{ \prime}\overrightarrow{m}\times\overrightarrow{H}_{eff}\ -\ \gamma_{0}^{\prime}\frac{\alpha_{\parallel}}{m^{2}}\left[ \overrightarrow{m}\ \times\left(\overrightarrow{m}\ \times\left(\overrightarrow{H}_{eff}+ \overrightarrow{H}_{th}^{\perp}\right)\right)\right]\ +\ \gamma_{0}^{\prime}\frac{\alpha_{ \parallel}}{m^{2}}\left(\overrightarrow{m}\cdot\overrightarrow{H}_{eff} \right)\overrightarrow{m}\ +\ \overrightarrow{H}_{th}^{\parallel} \tag{3}\]  
where \(\overrightarrow{m}\left(\overrightarrow{r},t\right)=\ \overrightarrow{M}\left( \overrightarrow{r},t\right)/M_{\mathrm{s}}^{0}\) is the normalized magnetization with \(M_{\mathrm{s}}^{0}\) the saturation magnetization at \(T\ =\ 0\) K. In the following we denote \(m\ =\ m(T)\equiv\left|\overrightarrow{m}\right|\), as the magnitude of \(\overrightarrow{m}\) depends on the local temperature because its equilibrium magnitude, \(m_{e}(T)\), is temperature-dependent.\(\gamma_{0}^{\prime}\ =\ \gamma_{0}/\left(1+\alpha^{2}\right)\) with \(\gamma_{0}\) being the gyromagnetic ratio and \(\alpha\) is the Gilbert damping. \(\alpha_{\parallel}\) and \(\alpha_{\perp}\) are the longitudinal and transverse damping parameters given by  
\[ \begin{array}{ll}\alpha_{\parallel}\ =\ \alpha\left(\frac{2T}{3T_{C}}\right) \alpha_{\perp}\ =\ \alpha\left(1-\frac{T}{3T_{C}}\right)&T<T_{c}\\ \alpha_{\parallel}\ =\ \alpha_{\perp}=\alpha\left(\frac{2T}{3T_{C}}\right)&T>T_{c} \end{array}  \tag{4}\]  
Figure 1: (**a**) Schematic of the Pt/Co thin film and the laser setup. (**b**) Time dependence of electron (red line) and lattice (blue line) temperatures obtained from the 2 TM model for two laser pulses. (**c**) Detail of the temperature evolution during the time interval when the laser pulse is present, showing the differences between both electrons (red) and lattice (blue). The green line represents the normalized laser pulse power for comparison. (**d**) Temporal evolution of the averaged out-of-plane component of the magnetization (\(m_{z}\)) showing the ultrafast reduction due to the heating generated by the laser pulses. The effective field \(\overrightarrow{H}_{eff}\) in Equation (3) includes all the conventional micromagnetic interactions plus the magneto-optical field due to the IFE (\(\overrightarrow{H}_{MO}~{}=~{}\overrightarrow{B}_{MO}/\mu_{0}\)) that will be described later. Namely,  
\[\overrightarrow{H}_{eff}~{}=~{}\overrightarrow{H}_{exch}+\overrightarrow{H}_{ DM}~{}\rightarrow\overrightarrow{H}_{dmg}+\overrightarrow{H}_{ani}+ \overrightarrow{H}_{m}+\overrightarrow{H}_{MO} \tag{5}\]  
where \(\overrightarrow{H}_{exch}\) is the exchange contribution, \(\overrightarrow{H}_{DM}\) is the DMI interaction, \(\overrightarrow{H}_{dmg}\) is the demagnetizing field, and \(\overrightarrow{H}_{ani}\) is the magnetic anisotropy. Further details on these contributions of the effective field can be found in [30]. \(\overrightarrow{H}_{m}\) represents the internal field in the LLB Equation (3), which is given by  
\[\overrightarrow{H}_{m}~{}=~{}\left\{ \begin{array}{cc}\frac{1}{2\chi_{1}} \Big{(}1-\frac{m^{2}}{m_{e}^{2}}\Big{)}\overrightarrow{m},&T<T_{C}\\ \\ -\frac{1}{\chi_{1}}\Big{(}1+\frac{3}{5}\frac{T_{C}m^{2}}{(T-T_{C})}\Big{)} \overrightarrow{m},&T>T_{C}\end{array} \right. \tag{6}\]  
where \(\chi_{1}\) is the longitudinal susceptibility,  
\[\chi_{1}~{}=~{}\left( \begin{array}{c}\frac{\partial m_{e}}{\partial H_{ext} }\end{array} \right)_{H_{ext}\to 0}~{}=~{}\frac{\frac{\mu_{0}\mu_{B}}{k_{B}T}B^{ \prime}(x)}{\Big{(}1-\frac{T_{C}}{T}B^{\prime}(x)\Big{)}} \tag{7}\]  
where \(B^{\prime}(x)~{}=~{}\frac{\partial B(x)}{\partial x}\) with \(B(x)\) being the Brillouin function with \(x~{}=~{}\frac{T_{C}}{T}m_{e}\)[31], \(k_{B}\) the Boltzmann constant, and \(\mu_{B}\) the Bohr magneton. \(\overrightarrow{H}_{m}\) is responsible of the longitudinal relaxation of the magnetization towards its equilibrium value \(m_{e}(T)\).