Unconventional magnetic anisotropy in one-dimensional Rashba system realized by adsorbing Gd atom on zigzag graphene nanoribbons.

The Rashba effect, a spin splitting in electronic band structures, attracts much attention for potential applications in spintronics with no requirement of an external magnetic field. Realizing a one-dimensional (1D) Rashba system is a big challenge due to the difficulties of growing high-quality heavy-metal nanowires or introducing strong spin-orbit coupling (SOC) and broken inversion symmetry in flexible materials. Here, based on first-principles calculations, we propose a pathway to realize the Rashba spin-split by adsorbing Gd atom on zigzag graphene nanoribbons (Gd-ZGNR) and further investigate the magnetic anisotropy energy (MAE). Perpendicular MAE and unconventional MAE contributions in k-space are found in the self-assembled Gd-ZGNR system, which presents a remarkable Rashba effect (the estimated strength is 1.89 eV Å) due to the strong SOC (∼65.6 meV) and the asymmetric adsorption sites at the nanoribbon edge. Moreover, first-order MAE is connected to the intrinsic Rashba effect beyond the traditional second-order MAE, which is confirmed based on the analysis of electronic structures perturbed with SOC in comparison with metastable Gd-ZGNR at the central symmetric adsorption site. The dependence on the ribbon width of the first-order MAE and the Rashba effect on Gd-ZGNRs are also examined. This work not only opens a new gate for designing the 1D Rashba system but also provides insight into the unconventional MAE due to the intrinsic Rashba effect, which would be of great significance for searching Majorana fermions and promoting potential applications in spintronics.