Anti-ferromagnetic states widely exist on graphene zigzag edges. Our previous work (Xie et al 2018 New J. Phys. 20 013035) shows there are also various spin density wave (SDW) states in the graphene nanoribbons (GNR). In this paper, we propose some excitation mechanism of these SDW by the absorbed magnetic atoms with the mean-field Hubbard model and the first-principles calculations. With the Floquet theory, we also find that by regulating the temperature or the light intensity, there are a lot of phase transitions for these SDW. The temperature or light can dramatically modify the inter-edge coupling or the spin stiffness of GNR. The artificial magnetization technique is employed to explore the establishment process of these SDW states. Some interesting intermedia phase transitions and the corresponding spin orders are discovered. This research may be helpful in the understandings and technique controls of magnetic orders in future nano magnetic devices.