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The Rashba effect, a spin splitting in electronic band structure, attractsmuch attention for the potential applications in spintronics with norequirement of external magnetic field. Realizing one-dimensional (1D) Rashbasystem is a big challenge due to the difficulties of growing high-qualityheavy-metal nanowires or introducing strong spin-orbit coupling (SOC) andbroken inversion symmetry in flexible materials. Here, based onfirst-principles calculations, we propose a pathway to realize the Rashbaspin-split by adsorbing Gd atom on zigzag graphene nanoribbons (Gd-ZGNR) andfurther investigate the magnetic anisotropy energy (MAE). Perpendicular MAE andunconventional MAE contributions in k-space are found in the self-assembledGd-ZGNR system, which present a remarkable Rashba effect (the estimatedstrength is 1.89 eV {\AA}) attributed to strong SOC (~65.6 meV) and theasymmetric adsorption site at the nanoribbons edge. Moreover, first-order MAEis connected to the intrinsic Rashba effect beyond the traditional second-orderMAE, which is confirmed based on the analysis of electronic structuresperturbed with SOC in comparison with metastable Gd-ZGNR at central symmetricadsorption site. The dependence of first-order MAE as well as Rashba effect ofGd-ZGNRs on the ribbon width are also examined. This work offers newperspective to achieve 1D Rashba system and provides fundamental understandingon the magnetic anisotropy, which would be of great significance for searchingMajorana fermions and promoting the potential applications in spintronics.

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