Perpendicular magnetic anisotropy in one-dimensional Rashba system under external electric fields: First-principles study

External electric field (EEF) control of magnetization attracts much attention for potential applications in spintronics and is also a key challenge for designing quantum magnetic properties. Noticed, the role of EEF on magnetic properties of one-dimensional (1D) Rashba system has not been explored, even lacking in theoretical. In this work, we comprehensively studied the effect of EEF (parallel or vertical) on the magnetic properties of our previous predicted 1D Rashba system—Gd adsorbed zigzag graphene nanoribbons (Gd-ZGNRs) from first-principles study. Our calculations show that a moderate negative (positive) electric field stabilizes out-of-plane magnetization, where Gd-ZGNR performs perpendicular magnetic anisotropy (PMA) whether the direction of the electric field is vertical or parallel, and intrinsic Rashba effect always exist. It is confirmed that the Rashba spin splitting and PMA are interrelated in 1D Gd-ZGNR, in consistent with previous theoretical models. Furthermore, the (non)-perturbed band structures under EEFs are analyzed to explore the underlying physics of MAE based on our proposed methods combined with traditional second-order theory. Our results would provide a new insight into the mechanism of the magnetoelectric coupling at low-dimensional Rashba system.