Spin-polarized nearly-free electron channels on the Ca$_{2}$N electrenes

Two-dimensional (2D) materials combined with the presence of surface nearly-free electrons (NFE) have been considered quite interesting platforms to be exploited for the development of 2D electronic devices. Further incorporation of foreign elements adds a new degree of freedom to engineer the electronic as well as the magnetic properties of 2D materials. Here we have performed an ab-initio study of Ca$_{2}$N, electrenes fully (i.e., both sides) adsorbed by hydrogen (H/Ca$_{2}$N/H) and fluorine (F/Ca$_{2}$N/F) atoms. The NFE states are suppressed in these systems, followed by the appearance of a net magnetic moment localized in the nitrogen atoms intercalated by the hydrogenated or fluorinated calcium layers. In the sequence, we have proposed lateral heterostructures combining the H/Ca$_{2}$N/H or F/Ca$_{2}$N/F regions with pristine Ca$_{2}$N, electrenes [(Ca$_{2}$N)(X/Ca$_{2}$N/X), with X=H or F]. We found that the magnetic moment of the hydrogenated or fluorinated regions promotes the emergence of spin-polarized NFE states confined along the pristine (Ca$_{2}$N) stripes. Further electronic transport calculations reveal that the (X/Ca$_{2}$N/X) regions act as spin-dependent scattering centers, spin-filters. We believe that these findings make an important contribution to the development of spintronic devices based on 2D electrides.