  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.
