Transverse Rashba Effect and Unconventional Magnetocrystalline Anisotropy in Double-Gd-adsorbed Zigzag Graphene Nanoribbon

The transverse Rashba effect is proposed and investigated by the first-principle calculations based on density functional theory in a quasi-one-dimensional antiferromagnet with a strong perpendicular magnetocrystalline anisotropy, which is materialized by the Gd-adsorbed graphene nanoribbon with a centric symmetry. The Rashba effect in this system is associated with the local dipole field transverse to and in the plane of the nanoribbon. That dipole field is induced by the off-center adsorption of the Gd adatom above the hex-carbon ring near the nanoribbon edges. The transverse Rashba effect at the two Gd adatoms enhances each other in the antiferromagnetic (AFM) ground state and cancels each other in the ferromagnetic (FM) meta-stable state, because of the centrosymmetric atomic structure. The transverse Rashba parameter is 1.51 eV A. This system shows a strong perpendicular magnetocrystalline anisotropy (MCA), which is 1.4 meV per Gd atom in the AFM state or 2.2 meV per Gd atom in the FM state. The origin of the perpendicular MCA is analyzed in k-space by filtering out the contribution of the transverse Rashba effect from the band structures perturbed by the spin-orbit coupling interactions. The first-order perturbation of the orbit and spin angular momentum coupling is the major source of the MCA, which is associated with the one-dimensionality of the system. The transverse Rashba effect and the strong perpendicular magnetization hosted simultaneously by the proposed AFM Gd-adsorbed graphene nanoribbon lock the up- (or down-) spin quantization direction to the forward (or backward) movement. This finding offers a magnetic approach to a high coherency spin propagation in one-dimensionality, and open a new door to manipulating spin transportation in graphene-based spintronics.