# Investigation on the Effect of Femtosecond Laser Induced Spin Transfer Torque of GdFeCo Alloy
## 2 Method
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline exchange constant of Gd–Fe & \(J_{Gd-Fe}\) & \(-1.09\times 10^{-21}\) & J/link \\ exchange constant of Gd–Gd & \(J_{Gd}\) & \(1.26\times 10^{-21}\) & J/link \\ exchange constant of Fe–Fe & \(J_{Fe}\) & \(2.835\times 10^{-21}\) & J/link \\ anisotropy energy constant & \(k_{u}\) & \(8.072\times 10^{-24}\) & J/atom \\ spin moment of Gd & \(\mu_{Gd}\) & \(7.63\) & \(\mu_{\text{B}}\) \\ spin moment of Fe & \(\mu_{Fe}\) & \(1.92\) & \(\mu_{\text{B}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The values and units of critical physical parameters in atomistic models of different sizes. Figure 3: Atomistic models structure of Gd\({}_{25}\)Fe\({}_{75}\) amorphous alloys with different sizes. (**a**) Gd\({}_{25}\)Fe\({}_{75}\) amorphous cubic alloy with side length of 1 nm, in which the spin of Fe atom is black and the spin of Gd atom is gray; (**b**) Gd\({}_{25}\)Fe\({}_{75}\) amorphous cubic alloy with side length of 10 nm. and as the laser acts on the whole space, the spin magnetization will be influenced in the whole space scope. The width of laser pulse is 60 fs and the wavelength is 800 nm. The balance temperature is 300 K and the time step of integration is 1 fs. The expression of the two-temperature model is as follows:  
\[ \begin{array}{c}C_{e}(T_{e})\frac{\partial T_{e}}{\partial t}=\
abla[k_{e}(T_ {e})\
abla T_{e}]-G(T_{e}-T_{l})+S(r,t)\\ C_{l}(T_{l})\frac{\partial T_{l}}{\partial t}=G(T_{e}-T_{l})\end{array}  \tag{5}\]  
where \(C_{e}=\gamma_{e}T_{e}\) and \(C_{l}\) are the heat capacities of electrons and lattices respectively; \(\gamma_{e}\) is the electron heat capacity constant; \(T_{e}\) and \(T_{l}\) are the temperatures of electrons and lattices respectively; \(G\) is the electron-lattice coupling factor; \(k_{e}\) is the electron heat conduction coefficient; \(S(r,t)\) is the incident power density of the femtosecond laser light source, and its value is related to the spot radius and the irradiation duration. When the two-temperature model is used to study the AOS, the temperature of the electron is generally taken as the benchmark because the electron has a smaller heat capacity, and the temperature rises faster after being excited by the laser, and the peak value is also higher. The physical parameters of the atomic-scale LLG equation and two-temperature model are given in Table 2. Due to the difference in heat capacity values, the change rate of electrons and lattices temperature are very different; the temperature of lattices will lag much behind the temperature of electrons. Thus, when the electronic temperature exceeds the Curie temperature of the material, the material begins to demagnetize, while the lattice temperature slowly rises to just above room temperature to ensure that the material's structure will not be destroyed by the ultrafast laser. In order to simulate the pumping generation and attenuation of spin current in the actual situation, we fit the equation of current attenuation with incident laser pumping based on the previous experimental results [25; 26]. The equation is given as follows:  
\[ \begin{array}{c}J_{e}=AJ_{0}\left(1-e^{-\frac{L}{\tau_{0}}}\right)^{3}e^{- \frac{L}{\tau_{0}}}\end{array}  \tag{6}\]  
where \(J_{0}\) is the maximum injection current density; \(A\) is the amplitude amplification factor; \(\tau_{a}\) and \(\tau_{b}\) are the current pumping constant and current attenuation constant respectively.