## 1 Introduction  
Graphene is an intrinsic zero-gap semiconductor, which can be chemically or structurally modified to satisfy specific needs of nanoelectronics and optoelectronics [1; 2; 3; 4; 5]. For instance, graphene nanoribbons (GNRs) result from a radical alteration of the graphene structure, where the reduction in dimensionality leads to a quasi-one-dimensional (1D) nanowire well suited for assembly into complex networksand nanocircuits with high-density functional units [6; 7; 8; 9; 10]. Compared to other options to build 1D carbon-based systems, such as carbon nanotubes, the planar nature of GNRs makes them particularly appealing, owing to the relative ease of their assembly into intricate geometries [11; 12; 13]. Theory predicts a broad set of singular properties [14; 15; 16], and advances in GNR fabrication have evolved at a fast pace. For instance, it is now feasible to grow narrow and pristine systems through pre-programmed and large-scale synthesis techniques [11; 17; 18; 19; 20; 21]. Even though the precise, controlled and scalable fabrication of carbon nanostructures with complex geometries remains a challenge from the experimental point of view, the developing bottom-up synthesis approaches of specific structures provide strong support to the eventual realization of this goal. Furthermore, depending on the details of their atomic structures, such as their widths and edge morphologies, GNRs' physical properties, including their electronic, transport, magnetic and thermal behaviors, can be fine-tuned for a desired response to external stimuli [14; 15; 16; 22]. Monohydrogenated zigzag-edged nanoribbons (zGNRs) possess nontrivial spin distributions, due to the high charge density instability at their edges in a non-polarized (paramagnetic (PM)) spin distribution. Instead of undergoing geometric (e.g., Peierls) distortions or electrical polarization processes, zGNRs mitigate this instability by adopting a ferromagnetic spin ordering along each edge [14; 16]. The ground state corresponds to an anti-ferromagnetic (AFM) edge-to-edge spin alignment [16], where the two A and B graphene sub-lattices display a net spin-up and -down population, respectively. While direct experimental evidence for the existence of these stable spin states at room temperature is still lacking [23; 24], published experimental data suggest the existence of such edge states, as scanning tunneling spectroscopy (STS) patterns measured in edged graphene samples can only be explained theoretically by considering spin polarization at the system edges [19; 25]. It follows that the conduction and valence bands in zGNRs are quasi-one-dimensional and correspond to localized states extending over the edges of the system. These states are essential to the physics of zGNRs, since they govern low-bias conduction processes. By definition, such edge Bloch states do not mix with states delocalized across the zGNR width. This attractive property turns out to become a potential curse for building up complex zGNR-based networks, since low-bias electrons will always flow along a given set of connected edges belonging to the same sub-lattice, effectively not penetrating deep into the network and, thereby, reducing drastically the number of useful operations that can be programmed into the network connections. In this paper, we describe the concept of a zGNR-based heterospin junction. While GNR hetero-junctions based on the assembly of different geometries (involving both aGNRs and zGNRs) [26] or on the connection of multiple terminals [27] have been considered before, here, we study a type of heterojunction made solely of zGNRs prepared in different spin distributions. The concept of a purely zGNR-based heterospin junction has been visited before, where it was shown that a mismatching mechanism, originating at the electrodes with opposite FM distributions, is responsible for the onset of magnetoresistance in such junctions [22].