Rashba spin splitting and perpendicular magnetic anisotropy of Gd-adsorbed zigzag graphene nanoribbon modulated by edge states under external electric fields

The one-dimensional (1D) Rashba effect has become much important due to its key role in basic science to realize exotic electronic phenomena, such as Majorana bound states. Similar to the 2D or 3D systems, the modulation of Rashba effect in 1D matrix is the kernel of spintronics for manipulating electron spin. Herein, by investigating the effects of transverse and vertical external electric field (EEF) on the Rashba spin splitting and magnetic anisotropy energy (MAE) of Gd-adsorbed zigzag graphene nanoribbons from first principles, we found that the Rashba spin splitting in such 1D system can be effectively regulated by the transverse EEF. Moreover, perpendicular magnetic anisotropy holds with either transverse or vertical EEF applied, despite obvious modulation of the MAE contributions in k-space as well as the Rashba spin splitting. It is found the modulation of Gd-5dx²-y², dxy by C-p_z orbitals of edge states is the key to manipulating the magnetic anisotropy, which even plays a decisive role on modifying the Rashba spin splitting in such 1D nanoribbon system. Our study introduces a new strategy to manipulate Rashba spin splitting by edge states and provides new insight into the magnetic anisotropy in 1D Rashba system.