Goos-Hänchen-like shift related to spin and valley polarization in ferromagnetic silicene

We study the Goos-Hänchen-like shift of single silicene barrier under the external perpendicular electric field, off-resonant circularly polarized light and the exchange field modulation using the stationary-phase method. The results show that the Goos-Hänchen-like shift of silicene resulting from the external perpendicular electric field does not have the characteristics of spin or valley polarization, while that from off-resonant circularly polarized light or the exchange field is spin-polarized. More importantly, the combined effect of the external perpendicular electric field and the exchange field or off-resonant circularly polarized light can cause the Goos-Hänchen-like shift of the system to be spin and valley polarized. It is particularly worth noting that when the three modulations are considered at the same time, as the exchange field changes, the system will have a positive or negative Goos-Hänchen-like shift.