Figure 3
From: Robust ferromagnetism in hydrogenated graphene mediated by spin-polarized pseudospin
Long-range magnetic interactions mediated by spin-polarized pseudospin. (a,b,c) Spin densities of the 864-atom graphene supercells containing two H adatoms on the same sublattice. The spin density of the expanded supercell is shown for the spin-up (yellow) and spin-down (blue) electrons at 0.0016 |e|/Å3. In (a), two localized spins in a supercell are in the FM state, while in (b), they are in the AFM state. The spin-density plot in (c) reveals the delocalized spin-polarized pseudospin (SPPS), which is present only for (a). The SPPS was extracted from the results in (a) and (b) in two steps; we first flipped the spin values for the “spin-down” triangles in (b) and calculated the difference between the spin density in (a) and the modified density of (b) to obtain the SPPS in (c). (d) Schematic showing the mechanism of the long-range FM interaction between two “A-vacancies”, which is mediated by the direct exchange interaction between the localized spins and the delocalized SPPS. (e) SPPS-mediated AFM interaction between two “vacancies” in opposite sublattices, which involves the superexchange interaction between the localized spins and the SPPS.
