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 quite important due to its key role in basic science to realize exotic electronic phenomena, such as Majorana bound states. Similar to the two-dimensional or three dimensional 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) in a type of highly flexible 1D system (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. The modulation mechanism is further analyzed from the orbital-decomposed band structures and spin density for Gd-zigzag graphene nanoribbons (ZGNRs) at different electric-field values. It is found the modulation of $\mathrm{Gd}\phantom{\rule{0.16em}{0ex}}5{d}_{{x}^{2}\ensuremath{-}{y}^{2}},{d}_{xy}$ by C ${p}_{z}$ orbitals of edge states is the key to manipulating the magnetic anisotropy, which even plays a decisive role in modifying the Rashba spin splitting in such 1D nanoribbon system. The MAE and 1D Rashba spin splitting are expected to be controlled through modifying the edge states in such systems via EEF or other means. Our study introduces a strategy to manipulate Rashba spin splitting by edge states and provides insight into the magnetic anisotropy in 1D Rashba system, which would revitalize further research in ZGNR-based systems within the spintronics and exotic electronic phenomena.