# Investigation on the Effect of Femtosecond Laser Induced Spin Transfer Torque of GdFeCo Alloy
## 2 Method  
A Co-Cu-Co three-layer structure model was constructed by [PERSON] et al. [34] to describe the macro spin transfer torque effect. The term corresponding to the effect of spin transfer torque was added to the LLG equation to study the magnetization dynamics' influence of the spin current on the magnetic free layer in the model [35]. A three-layer structure is schematically shown in Figure 1. The first layer is a magnetically fixed layer with a magnetization intensity of \(\mathbf{p}\) and a fixed direction. The second one is a film composed of nonmagnetic conductor; the third one is a magnetically free layer, with magnetization intensity \(\mathbf{m}\) and freely altering direction. After the unpolarized current enters the fixed layer, the electron spin is polarized, forming a spin-polarized current with the same direction as \(\mathbf{p}\). The spin-polarized current from the fixed layer flows into the free layer, and then the spin-polarized electrons interact with the free layer media, causing the magnetization direction and magnitude of the free layer to change. The exploration of magnetization dynamics of ferromagnetic materials is mainly to study the interaction between different sublattice materials. Since Co element in GdFeCo alloy films mainly plays the role of adjusting Curie temperature and compensating temperature, it has little effect on other properties of materials, but it will greatly increase the complexity of the model and the amount of calculation. Therefore, in this study, Co and Fe were regarded as the same sublattice, which is a transition metal element. In order to reduce the computational complexity, the object of numerical simulation is Gd\({}_{25}\)Fe\({}_{75}\) alloy and it was assumed to be amorphous, in which the spins of Gd and Fe are randomly distributed in the periodic structure, The GdFe alloy atomic model also can reflect both the nature of magnetic interaction and the ferromagnetic properties of the material. In the atomistic model of GdFe alloy, rare earth elements and transition metal elements can be considered as the fixed layers and free layers in the three-layer structure respectively, while the non-magnetic conductor in the middle of the three-layer structure only plays the role of transporting the spin current. Therefore, it is not necessary to consider the role of the interlayer when considering the sublattice magnetization kinetics of GdFe alloys. In our study, the direction of spin polarization is related to the initial magnetization direction of the Gd sublattice magnetization. The whole process can be described in Figure 2.  
Figure 1: Schematic diagram of three-layer structure model. Ultrafast linearly polarized femtosecond laser acts on GdFeCo amorphous alloy thin films. Due to the temperature gradient effect, a certain order of magnitude of excited electrons are generated. The injection of electrons into the Gd sublattice results in a spin-polarized current. The spin transfer torque effect induced by spin-polarized current impacts on the spin of the Fe sublattice results in the spin reversal of the Fe sublattice first. The electron temperature then drops rapidly below Curie temperature, and the exchange interaction between the Fe and Gd causes the spin reversal of the Gd sublattice. To this end, a mathematical model describing the magnetic physical process is established. Our model for GdFe amorphous alloy, based on the extended Heisenberg spin Hamiltonian.