Graphene supports long spin lifetimes and long diffusion lengths, making it promising for spintronics. However, rendering graphene magnetic remains a fundamental challenge. Among the different types of graphene, graphene with zig-zag edges and ripples are the most promising candidates, as zig-zag edges are predicted to host spin-polarized electronic states and ripples can induce spin–orbit coupling (SOC). We investigated the magnetoresistance (MR) of graphene grown on SiC/Si(001) wafers, in which inherent nanodomain boundaries (NBs) sandwich zig-zag structures between adjacent ripples of large curvature (Fig 1b). Localized states at the NBs result in an unprecedented positive in-plane MR (Fig 1c). Our work may offer an exciting way to add the spin degree of freedom to graphene.

   Figure 1d shows the calculated charge density distribution under various bias voltages. An obvious charge density accumulation occurs at the NB, and when the bias is increased to a value of 0.5 V, the charge density begins to spread across to the NB. The charge density is greater along the NB than in the pristine graphene, clearly demonstrating the 1D transport properties of the NBs at low bias voltages. Furthermore, the large curvature at the ripples of the graphene can result in SOC. To investigate the spin-dependent transport across the NBs with weak SOC, we calculated the spin density distribution under a bias voltage of 0.4 V in Fig. 1e. Clearly, only electrons with a particular spin can cross the NBs under a bias voltage of 0.4 V, indicating that NBs with ripples can work as spin filters and that the SOC at ripples causes spin-dependent energy splitting. Moreover, when an in-plane magnetic field is applied perpendicular to the NBs, fewer electrons can cross the NBs, implying a positive MR, which is consistent with the MR calculation. We also investigated the length variation in the NB, disorder within a single NB, and orientation of the magnetic field. The relative strengths of the spin filter and confinement effects are shown to be only marginally influenced, and the fundamental phenomenon is still observed.

   The NBs with ripples are shown to have the potential to work as a spin filter and can result in a positive MR at low temperature. Moreover, our work suggests that graphene with NBs has localized states and large spin-orbit interaction at the ripples. The confinement of electrons of a particular spin direction from 2D to 1D NBs by the Zeeman effect is responsible for the positive MR observed at high temperatures.